Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/CMakeLists.txt b/Eigen/src/CMakeLists.txt
new file mode 100644
index 0000000..c326f37
--- /dev/null
+++ b/Eigen/src/CMakeLists.txt
@@ -0,0 +1,7 @@
+file(GLOB Eigen_src_subdirectories "*")
+escape_string_as_regex(ESCAPED_CMAKE_CURRENT_SOURCE_DIR "${CMAKE_CURRENT_SOURCE_DIR}")
+foreach(f ${Eigen_src_subdirectories})
+ if(NOT f MATCHES "\\.txt" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/[.].+" )
+ add_subdirectory(${f})
+ endif()
+endforeach()
diff --git a/Eigen/src/Cholesky/CMakeLists.txt b/Eigen/src/Cholesky/CMakeLists.txt
new file mode 100644
index 0000000..d01488b
--- /dev/null
+++ b/Eigen/src/Cholesky/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Cholesky_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Cholesky_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Cholesky COMPONENT Devel
+ )
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
new file mode 100644
index 0000000..e01ae82
--- /dev/null
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -0,0 +1,611 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LDLT_H
+#define EIGEN_LDLT_H
+
+namespace Eigen {
+
+namespace internal {
+ template<typename MatrixType, int UpLo> struct LDLT_Traits;
+
+ // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
+ enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
+}
+
+/** \ingroup Cholesky_Module
+ *
+ * \class LDLT
+ *
+ * \brief Robust Cholesky decomposition of a matrix with pivoting
+ *
+ * \param MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
+ * \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
+ * The other triangular part won't be read.
+ *
+ * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
+ * matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
+ * is lower triangular with a unit diagonal and D is a diagonal matrix.
+ *
+ * The decomposition uses pivoting to ensure stability, so that L will have
+ * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
+ * on D also stabilizes the computation.
+ *
+ * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
+ * decomposition to determine whether a system of equations has a solution.
+ *
+ * \sa MatrixBase::ldlt(), class LLT
+ */
+template<typename _MatrixType, int _UpLo> class LDLT
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options & ~RowMajorBit, // these are the options for the TmpMatrixType, we need a ColMajor matrix here!
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ UpLo = _UpLo
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> TmpMatrixType;
+
+ typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
+
+ typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LDLT::compute(const MatrixType&).
+ */
+ LDLT()
+ : m_matrix(),
+ m_transpositions(),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa LDLT()
+ */
+ LDLT(Index size)
+ : m_matrix(size, size),
+ m_transpositions(size),
+ m_temporary(size),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Constructor with decomposition
+ *
+ * This calculates the decomposition for the input \a matrix.
+ * \sa LDLT(Index size)
+ */
+ LDLT(const MatrixType& matrix)
+ : m_matrix(matrix.rows(), matrix.cols()),
+ m_transpositions(matrix.rows()),
+ m_temporary(matrix.rows()),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {
+ compute(matrix);
+ }
+
+ /** Clear any existing decomposition
+ * \sa rankUpdate(w,sigma)
+ */
+ void setZero()
+ {
+ m_isInitialized = false;
+ }
+
+ /** \returns a view of the upper triangular matrix U */
+ inline typename Traits::MatrixU matrixU() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return Traits::getU(m_matrix);
+ }
+
+ /** \returns a view of the lower triangular matrix L */
+ inline typename Traits::MatrixL matrixL() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return Traits::getL(m_matrix);
+ }
+
+ /** \returns the permutation matrix P as a transposition sequence.
+ */
+ inline const TranspositionType& transpositionsP() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_transpositions;
+ }
+
+ /** \returns the coefficients of the diagonal matrix D */
+ inline Diagonal<const MatrixType> vectorD() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_matrix.diagonal();
+ }
+
+ /** \returns true if the matrix is positive (semidefinite) */
+ inline bool isPositive() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
+ }
+
+ #ifdef EIGEN2_SUPPORT
+ inline bool isPositiveDefinite() const
+ {
+ return isPositive();
+ }
+ #endif
+
+ /** \returns true if the matrix is negative (semidefinite) */
+ inline bool isNegative(void) const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
+ }
+
+ /** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
+ *
+ * \note_about_checking_solutions
+ *
+ * More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
+ * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
+ * \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
+ * \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
+ * least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
+ * computes the least-square solution of \f$ A x = b \f$ is \f$ A \f$ is singular.
+ *
+ * \sa MatrixBase::ldlt()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<LDLT, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ eigen_assert(m_matrix.rows()==b.rows()
+ && "LDLT::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<LDLT, Rhs>(*this, b.derived());
+ }
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived, typename ResultType>
+ bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+ {
+ *result = this->solve(b);
+ return true;
+ }
+ #endif
+
+ template<typename Derived>
+ bool solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+ LDLT& compute(const MatrixType& matrix);
+
+ template <typename Derived>
+ LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
+
+ /** \returns the internal LDLT decomposition matrix
+ *
+ * TODO: document the storage layout
+ */
+ inline const MatrixType& matrixLDLT() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_matrix;
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return Success;
+ }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ /** \internal
+ * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
+ * The strict upper part is used during the decomposition, the strict lower
+ * part correspond to the coefficients of L (its diagonal is equal to 1 and
+ * is not stored), and the diagonal entries correspond to D.
+ */
+ MatrixType m_matrix;
+ TranspositionType m_transpositions;
+ TmpMatrixType m_temporary;
+ internal::SignMatrix m_sign;
+ bool m_isInitialized;
+};
+
+namespace internal {
+
+template<int UpLo> struct ldlt_inplace;
+
+template<> struct ldlt_inplace<Lower>
+{
+ template<typename MatrixType, typename TranspositionType, typename Workspace>
+ static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
+ {
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ eigen_assert(mat.rows()==mat.cols());
+ const Index size = mat.rows();
+
+ if (size <= 1)
+ {
+ transpositions.setIdentity();
+ if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef;
+ else if (numext::real(mat.coeff(0,0)) < 0) sign = NegativeSemiDef;
+ else sign = ZeroSign;
+ return true;
+ }
+
+ for (Index k = 0; k < size; ++k)
+ {
+ // Find largest diagonal element
+ Index index_of_biggest_in_corner;
+ mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
+ index_of_biggest_in_corner += k;
+
+ transpositions.coeffRef(k) = index_of_biggest_in_corner;
+ if(k != index_of_biggest_in_corner)
+ {
+ // apply the transposition while taking care to consider only
+ // the lower triangular part
+ Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
+ mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
+ mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
+ std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
+ for(int i=k+1;i<index_of_biggest_in_corner;++i)
+ {
+ Scalar tmp = mat.coeffRef(i,k);
+ mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
+ mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
+ }
+ if(NumTraits<Scalar>::IsComplex)
+ mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
+ }
+
+ // partition the matrix:
+ // A00 | - | -
+ // lu = A10 | A11 | -
+ // A20 | A21 | A22
+ Index rs = size - k - 1;
+ Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+ Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
+ Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
+
+ if(k>0)
+ {
+ temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
+ mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
+ if(rs>0)
+ A21.noalias() -= A20 * temp.head(k);
+ }
+
+ // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
+ // was smaller than the cutoff value. However, soince LDLT is not rank-revealing
+ // we should only make sure we do not introduce INF or NaN values.
+ // LAPACK also uses 0 as the cutoff value.
+ RealScalar realAkk = numext::real(mat.coeffRef(k,k));
+ if((rs>0) && (abs(realAkk) > RealScalar(0)))
+ A21 /= realAkk;
+
+ if (sign == PositiveSemiDef) {
+ if (realAkk < 0) sign = Indefinite;
+ } else if (sign == NegativeSemiDef) {
+ if (realAkk > 0) sign = Indefinite;
+ } else if (sign == ZeroSign) {
+ if (realAkk > 0) sign = PositiveSemiDef;
+ else if (realAkk < 0) sign = NegativeSemiDef;
+ }
+ }
+
+ return true;
+ }
+
+ // Reference for the algorithm: Davis and Hager, "Multiple Rank
+ // Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
+ // Trivial rearrangements of their computations (Timothy E. Holy)
+ // allow their algorithm to work for rank-1 updates even if the
+ // original matrix is not of full rank.
+ // Here only rank-1 updates are implemented, to reduce the
+ // requirement for intermediate storage and improve accuracy
+ template<typename MatrixType, typename WDerived>
+ static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ using numext::isfinite;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ const Index size = mat.rows();
+ eigen_assert(mat.cols() == size && w.size()==size);
+
+ RealScalar alpha = 1;
+
+ // Apply the update
+ for (Index j = 0; j < size; j++)
+ {
+ // Check for termination due to an original decomposition of low-rank
+ if (!(isfinite)(alpha))
+ break;
+
+ // Update the diagonal terms
+ RealScalar dj = numext::real(mat.coeff(j,j));
+ Scalar wj = w.coeff(j);
+ RealScalar swj2 = sigma*numext::abs2(wj);
+ RealScalar gamma = dj*alpha + swj2;
+
+ mat.coeffRef(j,j) += swj2/alpha;
+ alpha += swj2/dj;
+
+
+ // Update the terms of L
+ Index rs = size-j-1;
+ w.tail(rs) -= wj * mat.col(j).tail(rs);
+ if(gamma != 0)
+ mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
+ }
+ return true;
+ }
+
+ template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
+ static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ // Apply the permutation to the input w
+ tmp = transpositions * w;
+
+ return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
+ }
+};
+
+template<> struct ldlt_inplace<Upper>
+{
+ template<typename MatrixType, typename TranspositionType, typename Workspace>
+ static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
+ {
+ Transpose<MatrixType> matt(mat);
+ return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
+ }
+
+ template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
+ static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ Transpose<MatrixType> matt(mat);
+ return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
+ }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
+{
+ typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m; }
+ static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
+{
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
+ typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m.adjoint(); }
+ static inline MatrixU getU(const MatrixType& m) { return m; }
+};
+
+} // end namespace internal
+
+/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
+ */
+template<typename MatrixType, int _UpLo>
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
+{
+ check_template_parameters();
+
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+
+ m_matrix = a;
+
+ m_transpositions.resize(size);
+ m_isInitialized = false;
+ m_temporary.resize(size);
+ m_sign = internal::ZeroSign;
+
+ internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign);
+
+ m_isInitialized = true;
+ return *this;
+}
+
+/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
+ * \param w a vector to be incorporated into the decomposition.
+ * \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
+ * \sa setZero()
+ */
+template<typename MatrixType, int _UpLo>
+template<typename Derived>
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename NumTraits<typename MatrixType::Scalar>::Real& sigma)
+{
+ const Index size = w.rows();
+ if (m_isInitialized)
+ {
+ eigen_assert(m_matrix.rows()==size);
+ }
+ else
+ {
+ m_matrix.resize(size,size);
+ m_matrix.setZero();
+ m_transpositions.resize(size);
+ for (Index i = 0; i < size; i++)
+ m_transpositions.coeffRef(i) = i;
+ m_temporary.resize(size);
+ m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
+ m_isInitialized = true;
+ }
+
+ internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
+
+ return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int _UpLo, typename Rhs>
+struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
+ : solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs>
+{
+ typedef LDLT<_MatrixType,_UpLo> LDLTType;
+ EIGEN_MAKE_SOLVE_HELPERS(LDLTType,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ eigen_assert(rhs().rows() == dec().matrixLDLT().rows());
+ // dst = P b
+ dst = dec().transpositionsP() * rhs();
+
+ // dst = L^-1 (P b)
+ dec().matrixL().solveInPlace(dst);
+
+ // dst = D^-1 (L^-1 P b)
+ // more precisely, use pseudo-inverse of D (see bug 241)
+ using std::abs;
+ using std::max;
+ typedef typename LDLTType::MatrixType MatrixType;
+ typedef typename LDLTType::RealScalar RealScalar;
+ const typename Diagonal<const MatrixType>::RealReturnType vectorD(dec().vectorD());
+ // In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon
+ // as motivated by LAPACK's xGELSS:
+ // RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() *NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
+ // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
+ // diagonal element is not well justified and to numerical issues in some cases.
+ // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
+ RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest();
+
+ for (Index i = 0; i < vectorD.size(); ++i) {
+ if(abs(vectorD(i)) > tolerance)
+ dst.row(i) /= vectorD(i);
+ else
+ dst.row(i).setZero();
+ }
+
+ // dst = L^-T (D^-1 L^-1 P b)
+ dec().matrixU().solveInPlace(dst);
+
+ // dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b
+ dst = dec().transpositionsP().transpose() * dst;
+ }
+};
+}
+
+/** \internal use x = ldlt_object.solve(x);
+ *
+ * This is the \em in-place version of solve().
+ *
+ * \param bAndX represents both the right-hand side matrix b and result x.
+ *
+ * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+ *
+ * This version avoids a copy when the right hand side matrix b is not
+ * needed anymore.
+ *
+ * \sa LDLT::solve(), MatrixBase::ldlt()
+ */
+template<typename MatrixType,int _UpLo>
+template<typename Derived>
+bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ eigen_assert(m_matrix.rows() == bAndX.rows());
+
+ bAndX = this->solve(bAndX);
+
+ return true;
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^T L D L^* P.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int _UpLo>
+MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ const Index size = m_matrix.rows();
+ MatrixType res(size,size);
+
+ // P
+ res.setIdentity();
+ res = transpositionsP() * res;
+ // L^* P
+ res = matrixU() * res;
+ // D(L^*P)
+ res = vectorD().real().asDiagonal() * res;
+ // L(DL^*P)
+ res = matrixL() * res;
+ // P^T (LDL^*P)
+ res = transpositionsP().transpose() * res;
+
+ return res;
+}
+
+/** \cholesky_module
+ * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::ldlt() const
+{
+ return LDLT<PlainObject,UpLo>(m_matrix);
+}
+
+/** \cholesky_module
+ * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+ */
+template<typename Derived>
+inline const LDLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::ldlt() const
+{
+ return LDLT<PlainObject>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LDLT_H
diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
new file mode 100644
index 0000000..59723a6
--- /dev/null
+++ b/Eigen/src/Cholesky/LLT.h
@@ -0,0 +1,498 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LLT_H
+#define EIGEN_LLT_H
+
+namespace Eigen {
+
+namespace internal{
+template<typename MatrixType, int UpLo> struct LLT_Traits;
+}
+
+/** \ingroup Cholesky_Module
+ *
+ * \class LLT
+ *
+ * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
+ * \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
+ * The other triangular part won't be read.
+ *
+ * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
+ * matrix A such that A = LL^* = U^*U, where L is lower triangular.
+ *
+ * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
+ * for that purpose, we recommend the Cholesky decomposition without square root which is more stable
+ * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
+ * situations like generalised eigen problems with hermitian matrices.
+ *
+ * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
+ * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
+ * has a solution.
+ *
+ * Example: \include LLT_example.cpp
+ * Output: \verbinclude LLT_example.out
+ *
+ * \sa MatrixBase::llt(), class LDLT
+ */
+ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH)
+ * Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
+ * the strict lower part does not have to store correct values.
+ */
+template<typename _MatrixType, int _UpLo> class LLT
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ AlignmentMask = int(PacketSize)-1,
+ UpLo = _UpLo
+ };
+
+ typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LLT::compute(const MatrixType&).
+ */
+ LLT() : m_matrix(), m_isInitialized(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa LLT()
+ */
+ LLT(Index size) : m_matrix(size, size),
+ m_isInitialized(false) {}
+
+ LLT(const MatrixType& matrix)
+ : m_matrix(matrix.rows(), matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix);
+ }
+
+ /** \returns a view of the upper triangular matrix U */
+ inline typename Traits::MatrixU matrixU() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return Traits::getU(m_matrix);
+ }
+
+ /** \returns a view of the lower triangular matrix L */
+ inline typename Traits::MatrixL matrixL() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return Traits::getL(m_matrix);
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * Since this LLT class assumes anyway that the matrix A is invertible, the solution
+ * theoretically exists and is unique regardless of b.
+ *
+ * Example: \include LLT_solve.cpp
+ * Output: \verbinclude LLT_solve.out
+ *
+ * \sa solveInPlace(), MatrixBase::llt()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<LLT, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(m_matrix.rows()==b.rows()
+ && "LLT::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<LLT, Rhs>(*this, b.derived());
+ }
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived, typename ResultType>
+ bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+ {
+ *result = this->solve(b);
+ return true;
+ }
+
+ bool isPositiveDefinite() const { return true; }
+ #endif
+
+ template<typename Derived>
+ void solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+ LLT& compute(const MatrixType& matrix);
+
+ /** \returns the LLT decomposition matrix
+ *
+ * TODO: document the storage layout
+ */
+ inline const MatrixType& matrixLLT() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return m_matrix;
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return m_info;
+ }
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ template<typename VectorType>
+ LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ /** \internal
+ * Used to compute and store L
+ * The strict upper part is not used and even not initialized.
+ */
+ MatrixType m_matrix;
+ bool m_isInitialized;
+ ComputationInfo m_info;
+};
+
+namespace internal {
+
+template<typename Scalar, int UpLo> struct llt_inplace;
+
+template<typename MatrixType, typename VectorType>
+static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
+{
+ using std::sqrt;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::ColXpr ColXpr;
+ typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
+ typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
+ typedef Matrix<Scalar,Dynamic,1> TempVectorType;
+ typedef typename TempVectorType::SegmentReturnType TempVecSegment;
+
+ Index n = mat.cols();
+ eigen_assert(mat.rows()==n && vec.size()==n);
+
+ TempVectorType temp;
+
+ if(sigma>0)
+ {
+ // This version is based on Givens rotations.
+ // It is faster than the other one below, but only works for updates,
+ // i.e., for sigma > 0
+ temp = sqrt(sigma) * vec;
+
+ for(Index i=0; i<n; ++i)
+ {
+ JacobiRotation<Scalar> g;
+ g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
+
+ Index rs = n-i-1;
+ if(rs>0)
+ {
+ ColXprSegment x(mat.col(i).tail(rs));
+ TempVecSegment y(temp.tail(rs));
+ apply_rotation_in_the_plane(x, y, g);
+ }
+ }
+ }
+ else
+ {
+ temp = vec;
+ RealScalar beta = 1;
+ for(Index j=0; j<n; ++j)
+ {
+ RealScalar Ljj = numext::real(mat.coeff(j,j));
+ RealScalar dj = numext::abs2(Ljj);
+ Scalar wj = temp.coeff(j);
+ RealScalar swj2 = sigma*numext::abs2(wj);
+ RealScalar gamma = dj*beta + swj2;
+
+ RealScalar x = dj + swj2/beta;
+ if (x<=RealScalar(0))
+ return j;
+ RealScalar nLjj = sqrt(x);
+ mat.coeffRef(j,j) = nLjj;
+ beta += swj2/dj;
+
+ // Update the terms of L
+ Index rs = n-j-1;
+ if(rs)
+ {
+ temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
+ if(gamma != 0)
+ mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
+ }
+ }
+ }
+ return -1;
+}
+
+template<typename Scalar> struct llt_inplace<Scalar, Lower>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename MatrixType>
+ static typename MatrixType::Index unblocked(MatrixType& mat)
+ {
+ using std::sqrt;
+ typedef typename MatrixType::Index Index;
+
+ eigen_assert(mat.rows()==mat.cols());
+ const Index size = mat.rows();
+ for(Index k = 0; k < size; ++k)
+ {
+ Index rs = size-k-1; // remaining size
+
+ Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+ Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
+ Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
+
+ RealScalar x = numext::real(mat.coeff(k,k));
+ if (k>0) x -= A10.squaredNorm();
+ if (x<=RealScalar(0))
+ return k;
+ mat.coeffRef(k,k) = x = sqrt(x);
+ if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
+ if (rs>0) A21 *= RealScalar(1)/x;
+ }
+ return -1;
+ }
+
+ template<typename MatrixType>
+ static typename MatrixType::Index blocked(MatrixType& m)
+ {
+ typedef typename MatrixType::Index Index;
+ eigen_assert(m.rows()==m.cols());
+ Index size = m.rows();
+ if(size<32)
+ return unblocked(m);
+
+ Index blockSize = size/8;
+ blockSize = (blockSize/16)*16;
+ blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
+
+ for (Index k=0; k<size; k+=blockSize)
+ {
+ // partition the matrix:
+ // A00 | - | -
+ // lu = A10 | A11 | -
+ // A20 | A21 | A22
+ Index bs = (std::min)(blockSize, size-k);
+ Index rs = size - k - bs;
+ Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
+ Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
+ Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
+
+ Index ret;
+ if((ret=unblocked(A11))>=0) return k+ret;
+ if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
+ if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,-1); // bottleneck
+ }
+ return -1;
+ }
+
+ template<typename MatrixType, typename VectorType>
+ static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
+ {
+ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
+ }
+};
+
+template<typename Scalar> struct llt_inplace<Scalar, Upper>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ template<typename MatrixType>
+ static EIGEN_STRONG_INLINE typename MatrixType::Index unblocked(MatrixType& mat)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::unblocked(matt);
+ }
+ template<typename MatrixType>
+ static EIGEN_STRONG_INLINE typename MatrixType::Index blocked(MatrixType& mat)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::blocked(matt);
+ }
+ template<typename MatrixType, typename VectorType>
+ static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
+ }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
+{
+ typedef const TriangularView<const MatrixType, Lower> MatrixL;
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m; }
+ static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+ static bool inplace_decomposition(MatrixType& m)
+ { return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
+{
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
+ typedef const TriangularView<const MatrixType, Upper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m.adjoint(); }
+ static inline MatrixU getU(const MatrixType& m) { return m; }
+ static bool inplace_decomposition(MatrixType& m)
+ { return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
+};
+
+} // end namespace internal
+
+/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
+ *
+ * \returns a reference to *this
+ *
+ * Example: \include TutorialLinAlgComputeTwice.cpp
+ * Output: \verbinclude TutorialLinAlgComputeTwice.out
+ */
+template<typename MatrixType, int _UpLo>
+LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a)
+{
+ check_template_parameters();
+
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+ m_matrix.resize(size, size);
+ m_matrix = a;
+
+ m_isInitialized = true;
+ bool ok = Traits::inplace_decomposition(m_matrix);
+ m_info = ok ? Success : NumericalIssue;
+
+ return *this;
+}
+
+/** Performs a rank one update (or dowdate) of the current decomposition.
+ * If A = LL^* before the rank one update,
+ * then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
+ * of same dimension.
+ */
+template<typename _MatrixType, int _UpLo>
+template<typename VectorType>
+LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
+ eigen_assert(v.size()==m_matrix.cols());
+ eigen_assert(m_isInitialized);
+ if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
+ m_info = NumericalIssue;
+ else
+ m_info = Success;
+
+ return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int UpLo, typename Rhs>
+struct solve_retval<LLT<_MatrixType, UpLo>, Rhs>
+ : solve_retval_base<LLT<_MatrixType, UpLo>, Rhs>
+{
+ typedef LLT<_MatrixType,UpLo> LLTType;
+ EIGEN_MAKE_SOLVE_HELPERS(LLTType,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dst = rhs();
+ dec().solveInPlace(dst);
+ }
+};
+}
+
+/** \internal use x = llt_object.solve(x);
+ *
+ * This is the \em in-place version of solve().
+ *
+ * \param bAndX represents both the right-hand side matrix b and result x.
+ *
+ * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+ *
+ * This version avoids a copy when the right hand side matrix b is not
+ * needed anymore.
+ *
+ * \sa LLT::solve(), MatrixBase::llt()
+ */
+template<typename MatrixType, int _UpLo>
+template<typename Derived>
+void LLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(m_matrix.rows()==bAndX.rows());
+ matrixL().solveInPlace(bAndX);
+ matrixU().solveInPlace(bAndX);
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: L L^*.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int _UpLo>
+MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return matrixL() * matrixL().adjoint().toDenseMatrix();
+}
+
+/** \cholesky_module
+ * \returns the LLT decomposition of \c *this
+ */
+template<typename Derived>
+inline const LLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::llt() const
+{
+ return LLT<PlainObject>(derived());
+}
+
+/** \cholesky_module
+ * \returns the LLT decomposition of \c *this
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::llt() const
+{
+ return LLT<PlainObject,UpLo>(m_matrix);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LLT_H
diff --git a/Eigen/src/Cholesky/LLT_MKL.h b/Eigen/src/Cholesky/LLT_MKL.h
new file mode 100644
index 0000000..66675d7
--- /dev/null
+++ b/Eigen/src/Cholesky/LLT_MKL.h
@@ -0,0 +1,102 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * LLt decomposition based on LAPACKE_?potrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_LLT_MKL_H
+#define EIGEN_LLT_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+#include <iostream>
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar> struct mkl_llt;
+
+#define EIGEN_MKL_LLT(EIGTYPE, MKLTYPE, MKLPREFIX) \
+template<> struct mkl_llt<EIGTYPE> \
+{ \
+ template<typename MatrixType> \
+ static inline typename MatrixType::Index potrf(MatrixType& m, char uplo) \
+ { \
+ lapack_int matrix_order; \
+ lapack_int size, lda, info, StorageOrder; \
+ EIGTYPE* a; \
+ eigen_assert(m.rows()==m.cols()); \
+ /* Set up parameters for ?potrf */ \
+ size = m.rows(); \
+ StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \
+ matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
+ a = &(m.coeffRef(0,0)); \
+ lda = m.outerStride(); \
+\
+ info = LAPACKE_##MKLPREFIX##potrf( matrix_order, uplo, size, (MKLTYPE*)a, lda ); \
+ info = (info==0) ? -1 : info>0 ? info-1 : size; \
+ return info; \
+ } \
+}; \
+template<> struct llt_inplace<EIGTYPE, Lower> \
+{ \
+ template<typename MatrixType> \
+ static typename MatrixType::Index blocked(MatrixType& m) \
+ { \
+ return mkl_llt<EIGTYPE>::potrf(m, 'L'); \
+ } \
+ template<typename MatrixType, typename VectorType> \
+ static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
+ { return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \
+}; \
+template<> struct llt_inplace<EIGTYPE, Upper> \
+{ \
+ template<typename MatrixType> \
+ static typename MatrixType::Index blocked(MatrixType& m) \
+ { \
+ return mkl_llt<EIGTYPE>::potrf(m, 'U'); \
+ } \
+ template<typename MatrixType, typename VectorType> \
+ static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
+ { \
+ Transpose<MatrixType> matt(mat); \
+ return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \
+ } \
+};
+
+EIGEN_MKL_LLT(double, double, d)
+EIGEN_MKL_LLT(float, float, s)
+EIGEN_MKL_LLT(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_LLT(scomplex, MKL_Complex8, c)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_LLT_MKL_H
diff --git a/Eigen/src/CholmodSupport/CMakeLists.txt b/Eigen/src/CholmodSupport/CMakeLists.txt
new file mode 100644
index 0000000..814dfa6
--- /dev/null
+++ b/Eigen/src/CholmodSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_CholmodSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_CholmodSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/CholmodSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/CholmodSupport/CholmodSupport.h b/Eigen/src/CholmodSupport/CholmodSupport.h
new file mode 100644
index 0000000..c449960
--- /dev/null
+++ b/Eigen/src/CholmodSupport/CholmodSupport.h
@@ -0,0 +1,607 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CHOLMODSUPPORT_H
+#define EIGEN_CHOLMODSUPPORT_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar, typename CholmodType>
+void cholmod_configure_matrix(CholmodType& mat)
+{
+ if (internal::is_same<Scalar,float>::value)
+ {
+ mat.xtype = CHOLMOD_REAL;
+ mat.dtype = CHOLMOD_SINGLE;
+ }
+ else if (internal::is_same<Scalar,double>::value)
+ {
+ mat.xtype = CHOLMOD_REAL;
+ mat.dtype = CHOLMOD_DOUBLE;
+ }
+ else if (internal::is_same<Scalar,std::complex<float> >::value)
+ {
+ mat.xtype = CHOLMOD_COMPLEX;
+ mat.dtype = CHOLMOD_SINGLE;
+ }
+ else if (internal::is_same<Scalar,std::complex<double> >::value)
+ {
+ mat.xtype = CHOLMOD_COMPLEX;
+ mat.dtype = CHOLMOD_DOUBLE;
+ }
+ else
+ {
+ eigen_assert(false && "Scalar type not supported by CHOLMOD");
+ }
+}
+
+} // namespace internal
+
+/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
+ * Note that the data are shared.
+ */
+template<typename _Scalar, int _Options, typename _Index>
+cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
+{
+ cholmod_sparse res;
+ res.nzmax = mat.nonZeros();
+ res.nrow = mat.rows();;
+ res.ncol = mat.cols();
+ res.p = mat.outerIndexPtr();
+ res.i = mat.innerIndexPtr();
+ res.x = mat.valuePtr();
+ res.z = 0;
+ res.sorted = 1;
+ if(mat.isCompressed())
+ {
+ res.packed = 1;
+ res.nz = 0;
+ }
+ else
+ {
+ res.packed = 0;
+ res.nz = mat.innerNonZeroPtr();
+ }
+
+ res.dtype = 0;
+ res.stype = -1;
+
+ if (internal::is_same<_Index,int>::value)
+ {
+ res.itype = CHOLMOD_INT;
+ }
+ else if (internal::is_same<_Index,UF_long>::value)
+ {
+ res.itype = CHOLMOD_LONG;
+ }
+ else
+ {
+ eigen_assert(false && "Index type not supported yet");
+ }
+
+ // setup res.xtype
+ internal::cholmod_configure_matrix<_Scalar>(res);
+
+ res.stype = 0;
+
+ return res;
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
+{
+ cholmod_sparse res = viewAsCholmod(mat.const_cast_derived());
+ return res;
+}
+
+/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
+ * The data are not copied but shared. */
+template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
+cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
+{
+ cholmod_sparse res = viewAsCholmod(mat.matrix().const_cast_derived());
+
+ if(UpLo==Upper) res.stype = 1;
+ if(UpLo==Lower) res.stype = -1;
+
+ return res;
+}
+
+/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
+ * The data are not copied but shared. */
+template<typename Derived>
+cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
+{
+ EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ typedef typename Derived::Scalar Scalar;
+
+ cholmod_dense res;
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ res.nzmax = res.nrow * res.ncol;
+ res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
+ res.x = (void*)(mat.derived().data());
+ res.z = 0;
+
+ internal::cholmod_configure_matrix<Scalar>(res);
+
+ return res;
+}
+
+/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
+ * The data are not copied but shared. */
+template<typename Scalar, int Flags, typename Index>
+MappedSparseMatrix<Scalar,Flags,Index> viewAsEigen(cholmod_sparse& cm)
+{
+ return MappedSparseMatrix<Scalar,Flags,Index>
+ (cm.nrow, cm.ncol, static_cast<Index*>(cm.p)[cm.ncol],
+ static_cast<Index*>(cm.p), static_cast<Index*>(cm.i),static_cast<Scalar*>(cm.x) );
+}
+
+enum CholmodMode {
+ CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
+};
+
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodBase
+ * \brief The base class for the direct Cholesky factorization of Cholmod
+ * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
+ */
+template<typename _MatrixType, int _UpLo, typename Derived>
+class CholmodBase : internal::noncopyable
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum { UpLo = _UpLo };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef MatrixType CholMatrixType;
+ typedef typename MatrixType::Index Index;
+
+ public:
+
+ CholmodBase()
+ : m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
+ {
+ m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
+ cholmod_start(&m_cholmod);
+ }
+
+ CholmodBase(const MatrixType& matrix)
+ : m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
+ {
+ m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
+ cholmod_start(&m_cholmod);
+ compute(matrix);
+ }
+
+ ~CholmodBase()
+ {
+ if(m_cholmodFactor)
+ cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
+ cholmod_finish(&m_cholmod);
+ }
+
+ inline Index cols() const { return m_cholmodFactor->n; }
+ inline Index rows() const { return m_cholmodFactor->n; }
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ Derived& compute(const MatrixType& matrix)
+ {
+ analyzePattern(matrix);
+ factorize(matrix);
+ return derived();
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<CholmodBase, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<CholmodBase, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<CholmodBase, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<CholmodBase, Rhs>(*this, b.derived());
+ }
+
+ /** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ if(m_cholmodFactor)
+ {
+ cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
+ m_cholmodFactor = 0;
+ }
+ cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
+ m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);
+
+ this->m_isInitialized = true;
+ this->m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
+ cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod);
+
+ // If the factorization failed, minor is the column at which it did. On success minor == n.
+ this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
+ m_factorizationIsOk = true;
+ }
+
+ /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
+ * See the Cholmod user guide for details. */
+ cholmod_common& cholmod() { return m_cholmod; }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ const Index size = m_cholmodFactor->n;
+ EIGEN_UNUSED_VARIABLE(size);
+ eigen_assert(size==b.rows());
+
+ // note: cd stands for Cholmod Dense
+ Rhs& b_ref(b.const_cast_derived());
+ cholmod_dense b_cd = viewAsCholmod(b_ref);
+ cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
+ if(!x_cd)
+ {
+ this->m_info = NumericalIssue;
+ }
+ // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
+ dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
+ cholmod_free_dense(&x_cd, &m_cholmod);
+ }
+
+ /** \internal */
+ template<typename RhsScalar, int RhsOptions, typename RhsIndex, typename DestScalar, int DestOptions, typename DestIndex>
+ void _solve(const SparseMatrix<RhsScalar,RhsOptions,RhsIndex> &b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ const Index size = m_cholmodFactor->n;
+ EIGEN_UNUSED_VARIABLE(size);
+ eigen_assert(size==b.rows());
+
+ // note: cs stands for Cholmod Sparse
+ cholmod_sparse b_cs = viewAsCholmod(b);
+ cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);
+ if(!x_cs)
+ {
+ this->m_info = NumericalIssue;
+ }
+ // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
+ dest = viewAsEigen<DestScalar,DestOptions,DestIndex>(*x_cs);
+ cholmod_free_sparse(&x_cs, &m_cholmod);
+ }
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+
+ /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
+ *
+ * During the numerical factorization, an offset term is added to the diagonal coefficients:\n
+ * \c d_ii = \a offset + \c d_ii
+ *
+ * The default is \a offset=0.
+ *
+ * \returns a reference to \c *this.
+ */
+ Derived& setShift(const RealScalar& offset)
+ {
+ m_shiftOffset[0] = offset;
+ return derived();
+ }
+
+ template<typename Stream>
+ void dumpMemory(Stream& /*s*/)
+ {}
+
+ protected:
+ mutable cholmod_common m_cholmod;
+ cholmod_factor* m_cholmodFactor;
+ RealScalar m_shiftOffset[2];
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSimplicialLLT
+ * \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
+ * using the Cholmod library.
+ * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLLT
+ */
+template<typename _MatrixType, int _UpLo = Lower>
+class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
+{
+ typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef _MatrixType MatrixType;
+
+ CholmodSimplicialLLT() : Base() { init(); }
+
+ CholmodSimplicialLLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~CholmodSimplicialLLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 0;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ m_cholmod.final_ll = 1;
+ }
+};
+
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSimplicialLDLT
+ * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
+ * using the Cholmod library.
+ * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLDLT
+ */
+template<typename _MatrixType, int _UpLo = Lower>
+class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
+{
+ typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef _MatrixType MatrixType;
+
+ CholmodSimplicialLDLT() : Base() { init(); }
+
+ CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~CholmodSimplicialLDLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ }
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSupernodalLLT
+ * \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
+ * using the Cholmod library.
+ * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType, int _UpLo = Lower>
+class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
+{
+ typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef _MatrixType MatrixType;
+
+ CholmodSupernodalLLT() : Base() { init(); }
+
+ CholmodSupernodalLLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~CholmodSupernodalLLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
+ }
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodDecomposition
+ * \brief A general Cholesky factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
+ * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * This variant permits to change the underlying Cholesky method at runtime.
+ * On the other hand, it does not provide access to the result of the factorization.
+ * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType, int _UpLo = Lower>
+class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
+{
+ typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef _MatrixType MatrixType;
+
+ CholmodDecomposition() : Base() { init(); }
+
+ CholmodDecomposition(const MatrixType& matrix) : Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~CholmodDecomposition() {}
+
+ void setMode(CholmodMode mode)
+ {
+ switch(mode)
+ {
+ case CholmodAuto:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_AUTO;
+ break;
+ case CholmodSimplicialLLt:
+ m_cholmod.final_asis = 0;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ m_cholmod.final_ll = 1;
+ break;
+ case CholmodSupernodalLLt:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
+ break;
+ case CholmodLDLt:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ break;
+ default:
+ break;
+ }
+ }
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_AUTO;
+ }
+};
+
+namespace internal {
+
+template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
+struct solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
+ : solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
+{
+ typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
+struct sparse_solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
+ : sparse_solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
+{
+ typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CHOLMODSUPPORT_H
diff --git a/Eigen/src/Core/Array.h b/Eigen/src/Core/Array.h
new file mode 100644
index 0000000..0ab03ef
--- /dev/null
+++ b/Eigen/src/Core/Array.h
@@ -0,0 +1,308 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAY_H
+#define EIGEN_ARRAY_H
+
+namespace Eigen {
+
+/** \class Array
+ * \ingroup Core_Module
+ *
+ * \brief General-purpose arrays with easy API for coefficient-wise operations
+ *
+ * The %Array class is very similar to the Matrix class. It provides
+ * general-purpose one- and two-dimensional arrays. The difference between the
+ * %Array and the %Matrix class is primarily in the API: the API for the
+ * %Array class provides easy access to coefficient-wise operations, while the
+ * API for the %Matrix class provides easy access to linear-algebra
+ * operations.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
+ *
+ * \sa \ref TutorialArrayClass, \ref TopicClassHierarchy
+ */
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+ typedef ArrayXpr XprKind;
+ typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
+};
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+class Array
+ : public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+ public:
+
+ typedef PlainObjectBase<Array> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Array)
+
+ enum { Options = _Options };
+ typedef typename Base::PlainObject PlainObject;
+
+ protected:
+ template <typename Derived, typename OtherDerived, bool IsVector>
+ friend struct internal::conservative_resize_like_impl;
+
+ using Base::m_storage;
+
+ public:
+
+ using Base::base;
+ using Base::coeff;
+ using Base::coeffRef;
+
+ /**
+ * The usage of
+ * using Base::operator=;
+ * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
+ * the usage of 'using'. This should be done only for operator=.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
+ {
+ return Base::operator=(other);
+ }
+
+ /** Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Array& operator=(const ArrayBase<OtherDerived>& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_STRONG_INLINE Array& operator=(const Array& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** Default constructor.
+ *
+ * For fixed-size matrices, does nothing.
+ *
+ * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+ * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+ * a matrix to 0 is not supported.
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_STRONG_INLINE Array() : Base()
+ {
+ Base::_check_template_params();
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ // FIXME is it still needed ??
+ /** \internal */
+ Array(internal::constructor_without_unaligned_array_assert)
+ : Base(internal::constructor_without_unaligned_array_assert())
+ {
+ Base::_check_template_params();
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+#endif
+
+ /** Constructs a vector or row-vector with given dimension. \only_for_vectors
+ *
+ * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+ * it is redundant to pass the dimension here, so it makes more sense to use the default
+ * constructor Matrix() instead.
+ */
+ EIGEN_STRONG_INLINE explicit Array(Index dim)
+ : Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Array)
+ eigen_assert(dim >= 0);
+ eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename T0, typename T1>
+ EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1)
+ {
+ Base::_check_template_params();
+ this->template _init2<T0,T1>(val0, val1);
+ }
+ #else
+ /** constructs an uninitialized matrix with \a rows rows and \a cols columns.
+ *
+ * This is useful for dynamic-size matrices. For fixed-size matrices,
+ * it is redundant to pass these parameters, so one should use the default constructor
+ * Matrix() instead. */
+ Array(Index rows, Index cols);
+ /** constructs an initialized 2D vector with given coefficients */
+ Array(const Scalar& val0, const Scalar& val1);
+ #endif
+
+ /** constructs an initialized 3D vector with given coefficients */
+ EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
+ m_storage.data()[0] = val0;
+ m_storage.data()[1] = val1;
+ m_storage.data()[2] = val2;
+ }
+ /** constructs an initialized 4D vector with given coefficients */
+ EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
+ m_storage.data()[0] = val0;
+ m_storage.data()[1] = val1;
+ m_storage.data()[2] = val2;
+ m_storage.data()[3] = val3;
+ }
+
+ explicit Array(const Scalar *data);
+
+ /** Constructor copying the value of the expression \a other */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Array(const ArrayBase<OtherDerived>& other)
+ : Base(other.rows() * other.cols(), other.rows(), other.cols())
+ {
+ Base::_check_template_params();
+ Base::_set_noalias(other);
+ }
+ /** Copy constructor */
+ EIGEN_STRONG_INLINE Array(const Array& other)
+ : Base(other.rows() * other.cols(), other.rows(), other.cols())
+ {
+ Base::_check_template_params();
+ Base::_set_noalias(other);
+ }
+ /** Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Array(const ReturnByValue<OtherDerived>& other)
+ {
+ Base::_check_template_params();
+ Base::resize(other.rows(), other.cols());
+ other.evalTo(*this);
+ }
+
+ /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other)
+ : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+ {
+ Base::_check_template_params();
+ Base::_resize_to_match(other);
+ *this = other;
+ }
+
+ /** Override MatrixBase::swap() since for dynamic-sized matrices of same type it is enough to swap the
+ * data pointers.
+ */
+ template<typename OtherDerived>
+ void swap(ArrayBase<OtherDerived> const & other)
+ { this->_swap(other.derived()); }
+
+ inline Index innerStride() const { return 1; }
+ inline Index outerStride() const { return this->innerSize(); }
+
+ #ifdef EIGEN_ARRAY_PLUGIN
+ #include EIGEN_ARRAY_PLUGIN
+ #endif
+
+ private:
+
+ template<typename MatrixType, typename OtherDerived, bool SwapPointers>
+ friend struct internal::matrix_swap_impl;
+};
+
+/** \defgroup arraytypedefs Global array typedefs
+ * \ingroup Core_Module
+ *
+ * Eigen defines several typedef shortcuts for most common 1D and 2D array types.
+ *
+ * The general patterns are the following:
+ *
+ * \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+ * for complex double.
+ *
+ * For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
+ *
+ * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
+ * a fixed-size 1D array of 4 complex floats.
+ *
+ * \sa class Array
+ */
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix; \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, 1> Array##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix; \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_LARGE
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
+using Eigen::Matrix##SizeSuffix##TypeSuffix; \
+using Eigen::Vector##SizeSuffix##TypeSuffix; \
+using Eigen::RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
+
+#define EIGEN_USING_ARRAY_TYPEDEFS \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAY_H
diff --git a/Eigen/src/Core/ArrayBase.h b/Eigen/src/Core/ArrayBase.h
new file mode 100644
index 0000000..3885260
--- /dev/null
+++ b/Eigen/src/Core/ArrayBase.h
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAYBASE_H
+#define EIGEN_ARRAYBASE_H
+
+namespace Eigen {
+
+template<typename ExpressionType> class MatrixWrapper;
+
+/** \class ArrayBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all 1D and 2D array, and related expressions
+ *
+ * An array is similar to a dense vector or matrix. While matrices are mathematical
+ * objects with well defined linear algebra operators, an array is just a collection
+ * of scalar values arranged in a one or two dimensionnal fashion. As the main consequence,
+ * all operations applied to an array are performed coefficient wise. Furthermore,
+ * arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
+ * constructors allowing to easily write generic code working for both scalar values
+ * and arrays.
+ *
+ * This class is the base that is inherited by all array expression types.
+ *
+ * \tparam Derived is the derived type, e.g., an array or an expression type.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
+ *
+ * \sa class MatrixBase, \ref TopicClassHierarchy
+ */
+template<typename Derived> class ArrayBase
+ : public DenseBase<Derived>
+{
+ public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** The base class for a given storage type. */
+ typedef ArrayBase StorageBaseType;
+
+ typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
+
+ using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+ typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ typedef DenseBase<Derived> Base;
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+ using Base::CoeffReadCost;
+
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::operator=;
+ using Base::operator+=;
+ using Base::operator-=;
+ using Base::operator*=;
+ using Base::operator/=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
+ * exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
+ * reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either
+ * PlainObject or const PlainObject&.
+ */
+ typedef Array<typename internal::traits<Derived>::Scalar,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime,
+ AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime
+ > PlainObject;
+
+
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
+# include "../plugins/CommonCwiseUnaryOps.h"
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/ArrayCwiseUnaryOps.h"
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# include "../plugins/ArrayCwiseBinaryOps.h"
+# ifdef EIGEN_ARRAYBASE_PLUGIN
+# include EIGEN_ARRAYBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ Derived& operator=(const ArrayBase& other)
+ {
+ return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+ }
+
+ Derived& operator+=(const Scalar& scalar)
+ { return *this = derived() + scalar; }
+ Derived& operator-=(const Scalar& scalar)
+ { return *this = derived() - scalar; }
+
+ template<typename OtherDerived>
+ Derived& operator+=(const ArrayBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ Derived& operator-=(const ArrayBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ Derived& operator*=(const ArrayBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ Derived& operator/=(const ArrayBase<OtherDerived>& other);
+
+ public:
+ ArrayBase<Derived>& array() { return *this; }
+ const ArrayBase<Derived>& array() const { return *this; }
+
+ /** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array
+ * \sa MatrixBase::array() */
+ MatrixWrapper<Derived> matrix() { return derived(); }
+ const MatrixWrapper<const Derived> matrix() const { return derived(); }
+
+// template<typename Dest>
+// inline void evalTo(Dest& dst) const { dst = matrix(); }
+
+ protected:
+ ArrayBase() : Base() {}
+
+ private:
+ explicit ArrayBase(Index);
+ ArrayBase(Index,Index);
+ template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
+ protected:
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+};
+
+/** replaces \c *this by \c *this - \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
+{
+ SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
+{
+ SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+/** replaces \c *this by \c *this * \a other coefficient wise.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
+{
+ SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+/** replaces \c *this by \c *this / \a other coefficient wise.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
+{
+ SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAYBASE_H
diff --git a/Eigen/src/Core/ArrayWrapper.h b/Eigen/src/Core/ArrayWrapper.h
new file mode 100644
index 0000000..b4641e2
--- /dev/null
+++ b/Eigen/src/Core/ArrayWrapper.h
@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAYWRAPPER_H
+#define EIGEN_ARRAYWRAPPER_H
+
+namespace Eigen {
+
+/** \class ArrayWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a mathematical vector or matrix as an array object
+ *
+ * This class is the return type of MatrixBase::array(), and most of the time
+ * this is the only way it is use.
+ *
+ * \sa MatrixBase::array(), class MatrixWrapper
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ArrayWrapper<ExpressionType> >
+ : public traits<typename remove_all<typename ExpressionType::Nested>::type >
+{
+ typedef ArrayXpr XprKind;
+ // Let's remove NestByRefBit
+ enum {
+ Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+ Flags = Flags0 & ~NestByRefBit
+ };
+};
+}
+
+template<typename ExpressionType>
+class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
+{
+ public:
+ typedef ArrayBase<ArrayWrapper> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<ExpressionType>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
+
+ inline ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
+
+ inline Index rows() const { return m_expression.rows(); }
+ inline Index cols() const { return m_expression.cols(); }
+ inline Index outerStride() const { return m_expression.outerStride(); }
+ inline Index innerStride() const { return m_expression.innerStride(); }
+
+ inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
+ inline const Scalar* data() const { return m_expression.data(); }
+
+ inline CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ return m_expression.coeff(rowId, colId);
+ }
+
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ return m_expression.const_cast_derived().coeffRef(rowId, colId);
+ }
+
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_expression.const_cast_derived().coeffRef(rowId, colId);
+ }
+
+ inline CoeffReturnType coeff(Index index) const
+ {
+ return m_expression.coeff(index);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index rowId, Index colId) const
+ {
+ return m_expression.template packet<LoadMode>(rowId, colId);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(rowId, colId, val);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_expression.template packet<LoadMode>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(index, val);
+ }
+
+ template<typename Dest>
+ inline void evalTo(Dest& dst) const { dst = m_expression; }
+
+ const typename internal::remove_all<NestedExpressionType>::type&
+ nestedExpression() const
+ {
+ return m_expression;
+ }
+
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index) */
+ void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index,Index)*/
+ void resize(Index nbRows, Index nbCols) { m_expression.const_cast_derived().resize(nbRows,nbCols); }
+
+ protected:
+ NestedExpressionType m_expression;
+};
+
+/** \class MatrixWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of an array as a mathematical vector or matrix
+ *
+ * This class is the return type of ArrayBase::matrix(), and most of the time
+ * this is the only way it is use.
+ *
+ * \sa MatrixBase::matrix(), class ArrayWrapper
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<MatrixWrapper<ExpressionType> >
+ : public traits<typename remove_all<typename ExpressionType::Nested>::type >
+{
+ typedef MatrixXpr XprKind;
+ // Let's remove NestByRefBit
+ enum {
+ Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+ Flags = Flags0 & ~NestByRefBit
+ };
+};
+}
+
+template<typename ExpressionType>
+class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
+{
+ public:
+ typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<ExpressionType>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
+
+ inline MatrixWrapper(ExpressionType& a_matrix) : m_expression(a_matrix) {}
+
+ inline Index rows() const { return m_expression.rows(); }
+ inline Index cols() const { return m_expression.cols(); }
+ inline Index outerStride() const { return m_expression.outerStride(); }
+ inline Index innerStride() const { return m_expression.innerStride(); }
+
+ inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
+ inline const Scalar* data() const { return m_expression.data(); }
+
+ inline CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ return m_expression.coeff(rowId, colId);
+ }
+
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ return m_expression.const_cast_derived().coeffRef(rowId, colId);
+ }
+
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_expression.derived().coeffRef(rowId, colId);
+ }
+
+ inline CoeffReturnType coeff(Index index) const
+ {
+ return m_expression.coeff(index);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index rowId, Index colId) const
+ {
+ return m_expression.template packet<LoadMode>(rowId, colId);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(rowId, colId, val);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_expression.template packet<LoadMode>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(index, val);
+ }
+
+ const typename internal::remove_all<NestedExpressionType>::type&
+ nestedExpression() const
+ {
+ return m_expression;
+ }
+
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index) */
+ void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index,Index)*/
+ void resize(Index nbRows, Index nbCols) { m_expression.const_cast_derived().resize(nbRows,nbCols); }
+
+ protected:
+ NestedExpressionType m_expression;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAYWRAPPER_H
diff --git a/Eigen/src/Core/Assign.h b/Eigen/src/Core/Assign.h
new file mode 100644
index 0000000..bcfc261
--- /dev/null
+++ b/Eigen/src/Core/Assign.h
@@ -0,0 +1,590 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ASSIGN_H
+#define EIGEN_ASSIGN_H
+
+namespace Eigen {
+
+namespace internal {
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for traversal and unrolling *
+***************************************************************************/
+
+template <typename Derived, typename OtherDerived>
+struct assign_traits
+{
+public:
+ enum {
+ DstIsAligned = Derived::Flags & AlignedBit,
+ DstHasDirectAccess = Derived::Flags & DirectAccessBit,
+ SrcIsAligned = OtherDerived::Flags & AlignedBit,
+ JointAlignment = bool(DstIsAligned) && bool(SrcIsAligned) ? Aligned : Unaligned
+ };
+
+private:
+ enum {
+ InnerSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::SizeAtCompileTime)
+ : int(Derived::Flags)&RowMajorBit ? int(Derived::ColsAtCompileTime)
+ : int(Derived::RowsAtCompileTime),
+ InnerMaxSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::MaxSizeAtCompileTime)
+ : int(Derived::Flags)&RowMajorBit ? int(Derived::MaxColsAtCompileTime)
+ : int(Derived::MaxRowsAtCompileTime),
+ MaxSizeAtCompileTime = Derived::SizeAtCompileTime,
+ PacketSize = packet_traits<typename Derived::Scalar>::size
+ };
+
+ enum {
+ StorageOrdersAgree = (int(Derived::IsRowMajor) == int(OtherDerived::IsRowMajor)),
+ MightVectorize = StorageOrdersAgree
+ && (int(Derived::Flags) & int(OtherDerived::Flags) & ActualPacketAccessBit),
+ MayInnerVectorize = MightVectorize && int(InnerSize)!=Dynamic && int(InnerSize)%int(PacketSize)==0
+ && int(DstIsAligned) && int(SrcIsAligned),
+ MayLinearize = StorageOrdersAgree && (int(Derived::Flags) & int(OtherDerived::Flags) & LinearAccessBit),
+ MayLinearVectorize = MightVectorize && MayLinearize && DstHasDirectAccess
+ && (DstIsAligned || MaxSizeAtCompileTime == Dynamic),
+ /* If the destination isn't aligned, we have to do runtime checks and we don't unroll,
+ so it's only good for large enough sizes. */
+ MaySliceVectorize = MightVectorize && DstHasDirectAccess
+ && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=3*PacketSize)
+ /* slice vectorization can be slow, so we only want it if the slices are big, which is
+ indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block
+ in a fixed-size matrix */
+ };
+
+public:
+ enum {
+ Traversal = int(MayInnerVectorize) ? int(InnerVectorizedTraversal)
+ : int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
+ : int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
+ : int(MayLinearize) ? int(LinearTraversal)
+ : int(DefaultTraversal),
+ Vectorized = int(Traversal) == InnerVectorizedTraversal
+ || int(Traversal) == LinearVectorizedTraversal
+ || int(Traversal) == SliceVectorizedTraversal
+ };
+
+private:
+ enum {
+ UnrollingLimit = EIGEN_UNROLLING_LIMIT * (Vectorized ? int(PacketSize) : 1),
+ MayUnrollCompletely = int(Derived::SizeAtCompileTime) != Dynamic
+ && int(OtherDerived::CoeffReadCost) != Dynamic
+ && int(Derived::SizeAtCompileTime) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit),
+ MayUnrollInner = int(InnerSize) != Dynamic
+ && int(OtherDerived::CoeffReadCost) != Dynamic
+ && int(InnerSize) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit)
+ };
+
+public:
+ enum {
+ Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal))
+ ? (
+ int(MayUnrollCompletely) ? int(CompleteUnrolling)
+ : int(MayUnrollInner) ? int(InnerUnrolling)
+ : int(NoUnrolling)
+ )
+ : int(Traversal) == int(LinearVectorizedTraversal)
+ ? ( bool(MayUnrollCompletely) && bool(DstIsAligned) ? int(CompleteUnrolling) : int(NoUnrolling) )
+ : int(Traversal) == int(LinearTraversal)
+ ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) : int(NoUnrolling) )
+ : int(NoUnrolling)
+ };
+
+#ifdef EIGEN_DEBUG_ASSIGN
+ static void debug()
+ {
+ EIGEN_DEBUG_VAR(DstIsAligned)
+ EIGEN_DEBUG_VAR(SrcIsAligned)
+ EIGEN_DEBUG_VAR(JointAlignment)
+ EIGEN_DEBUG_VAR(InnerSize)
+ EIGEN_DEBUG_VAR(InnerMaxSize)
+ EIGEN_DEBUG_VAR(PacketSize)
+ EIGEN_DEBUG_VAR(StorageOrdersAgree)
+ EIGEN_DEBUG_VAR(MightVectorize)
+ EIGEN_DEBUG_VAR(MayLinearize)
+ EIGEN_DEBUG_VAR(MayInnerVectorize)
+ EIGEN_DEBUG_VAR(MayLinearVectorize)
+ EIGEN_DEBUG_VAR(MaySliceVectorize)
+ EIGEN_DEBUG_VAR(Traversal)
+ EIGEN_DEBUG_VAR(UnrollingLimit)
+ EIGEN_DEBUG_VAR(MayUnrollCompletely)
+ EIGEN_DEBUG_VAR(MayUnrollInner)
+ EIGEN_DEBUG_VAR(Unrolling)
+ }
+#endif
+};
+
+/***************************************************************************
+* Part 2 : meta-unrollers
+***************************************************************************/
+
+/************************
+*** Default traversal ***
+************************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_DefaultTraversal_CompleteUnrolling
+{
+ enum {
+ outer = Index / Derived1::InnerSizeAtCompileTime,
+ inner = Index % Derived1::InnerSizeAtCompileTime
+ };
+
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ dst.copyCoeffByOuterInner(outer, inner, src);
+ assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_DefaultTraversal_InnerUnrolling
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, typename Derived1::Index outer)
+ {
+ dst.copyCoeffByOuterInner(outer, Index, src);
+ assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src, outer);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, typename Derived1::Index) {}
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_LinearTraversal_CompleteUnrolling
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ dst.copyCoeff(Index, src);
+ assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_innervec_CompleteUnrolling
+{
+ enum {
+ outer = Index / Derived1::InnerSizeAtCompileTime,
+ inner = Index % Derived1::InnerSizeAtCompileTime,
+ JointAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+ };
+
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ dst.template copyPacketByOuterInner<Derived2, Aligned, JointAlignment>(outer, inner, src);
+ assign_innervec_CompleteUnrolling<Derived1, Derived2,
+ Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_innervec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_innervec_InnerUnrolling
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, typename Derived1::Index outer)
+ {
+ dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, Index, src);
+ assign_innervec_InnerUnrolling<Derived1, Derived2,
+ Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src, outer);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_innervec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, typename Derived1::Index) {}
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Derived1, typename Derived2,
+ int Traversal = assign_traits<Derived1, Derived2>::Traversal,
+ int Unrolling = assign_traits<Derived1, Derived2>::Unrolling,
+ int Version = Specialized>
+struct assign_impl;
+
+/************************
+*** Default traversal ***
+************************/
+
+template<typename Derived1, typename Derived2, int Unrolling, int Version>
+struct assign_impl<Derived1, Derived2, InvalidTraversal, Unrolling, Version>
+{
+ static inline void run(Derived1 &, const Derived2 &) { }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, NoUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index innerSize = dst.innerSize();
+ const Index outerSize = dst.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer)
+ for(Index inner = 0; inner < innerSize; ++inner)
+ dst.copyCoeffByOuterInner(outer, inner, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, CompleteUnrolling, Version>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+ ::run(dst, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, InnerUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index outerSize = dst.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer)
+ assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
+ ::run(dst, src, outer);
+ }
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, LinearTraversal, NoUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index size = dst.size();
+ for(Index i = 0; i < size; ++i)
+ dst.copyCoeff(i, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, LinearTraversal, CompleteUnrolling, Version>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+ ::run(dst, src);
+ }
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, NoUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index innerSize = dst.innerSize();
+ const Index outerSize = dst.outerSize();
+ const Index packetSize = packet_traits<typename Derived1::Scalar>::size;
+ for(Index outer = 0; outer < outerSize; ++outer)
+ for(Index inner = 0; inner < innerSize; inner+=packetSize)
+ dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, inner, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, CompleteUnrolling, Version>
+{
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+ ::run(dst, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, InnerUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index outerSize = dst.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer)
+ assign_innervec_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
+ ::run(dst, src, outer);
+ }
+};
+
+/***************************
+*** Linear vectorization ***
+***************************/
+
+template <bool IsAligned = false>
+struct unaligned_assign_impl
+{
+ template <typename Derived, typename OtherDerived>
+ static EIGEN_STRONG_INLINE void run(const Derived&, OtherDerived&, typename Derived::Index, typename Derived::Index) {}
+};
+
+template <>
+struct unaligned_assign_impl<false>
+{
+ // MSVC must not inline this functions. If it does, it fails to optimize the
+ // packet access path.
+#ifdef _MSC_VER
+ template <typename Derived, typename OtherDerived>
+ static EIGEN_DONT_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
+#else
+ template <typename Derived, typename OtherDerived>
+ static EIGEN_STRONG_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
+#endif
+ {
+ for (typename Derived::Index index = start; index < end; ++index)
+ dst.copyCoeff(index, src);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, NoUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ const Index size = dst.size();
+ typedef packet_traits<typename Derived1::Scalar> PacketTraits;
+ enum {
+ packetSize = PacketTraits::size,
+ dstAlignment = PacketTraits::AlignedOnScalar ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
+ srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+ };
+ const Index alignedStart = assign_traits<Derived1,Derived2>::DstIsAligned ? 0
+ : internal::first_aligned(&dst.coeffRef(0), size);
+ const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
+
+ unaligned_assign_impl<assign_traits<Derived1,Derived2>::DstIsAligned!=0>::run(src,dst,0,alignedStart);
+
+ for(Index index = alignedStart; index < alignedEnd; index += packetSize)
+ {
+ dst.template copyPacket<Derived2, dstAlignment, srcAlignment>(index, src);
+ }
+
+ unaligned_assign_impl<>::run(src,dst,alignedEnd,size);
+ }
+};
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, CompleteUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
+ {
+ enum { size = Derived1::SizeAtCompileTime,
+ packetSize = packet_traits<typename Derived1::Scalar>::size,
+ alignedSize = (size/packetSize)*packetSize };
+
+ assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, alignedSize>::run(dst, src);
+ assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, alignedSize, size>::run(dst, src);
+ }
+};
+
+/**************************
+*** Slice vectorization ***
+***************************/
+
+template<typename Derived1, typename Derived2, int Version>
+struct assign_impl<Derived1, Derived2, SliceVectorizedTraversal, NoUnrolling, Version>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ typedef typename Derived1::Scalar Scalar;
+ typedef packet_traits<Scalar> PacketTraits;
+ enum {
+ packetSize = PacketTraits::size,
+ alignable = PacketTraits::AlignedOnScalar,
+ dstIsAligned = assign_traits<Derived1,Derived2>::DstIsAligned,
+ dstAlignment = alignable ? Aligned : int(dstIsAligned),
+ srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+ };
+ const Scalar *dst_ptr = &dst.coeffRef(0,0);
+ if((!bool(dstIsAligned)) && (Index(dst_ptr) % sizeof(Scalar))>0)
+ {
+ // the pointer is not aligend-on scalar, so alignment is not possible
+ return assign_impl<Derived1,Derived2,DefaultTraversal,NoUnrolling>::run(dst, src);
+ }
+ const Index packetAlignedMask = packetSize - 1;
+ const Index innerSize = dst.innerSize();
+ const Index outerSize = dst.outerSize();
+ const Index alignedStep = alignable ? (packetSize - dst.outerStride() % packetSize) & packetAlignedMask : 0;
+ Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, innerSize);
+
+ for(Index outer = 0; outer < outerSize; ++outer)
+ {
+ const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);
+ // do the non-vectorizable part of the assignment
+ for(Index inner = 0; inner<alignedStart ; ++inner)
+ dst.copyCoeffByOuterInner(outer, inner, src);
+
+ // do the vectorizable part of the assignment
+ for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize)
+ dst.template copyPacketByOuterInner<Derived2, dstAlignment, Unaligned>(outer, inner, src);
+
+ // do the non-vectorizable part of the assignment
+ for(Index inner = alignedEnd; inner<innerSize ; ++inner)
+ dst.copyCoeffByOuterInner(outer, inner, src);
+
+ alignedStart = std::min<Index>((alignedStart+alignedStep)%packetSize, innerSize);
+ }
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Part 4 : implementation of DenseBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
+ ::lazyAssign(const DenseBase<OtherDerived>& other)
+{
+ enum{
+ SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
+ };
+
+ EIGEN_STATIC_ASSERT_LVALUE(Derived)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+#ifdef EIGEN_DEBUG_ASSIGN
+ internal::assign_traits<Derived, OtherDerived>::debug();
+#endif
+ eigen_assert(rows() == other.rows() && cols() == other.cols());
+ internal::assign_impl<Derived, OtherDerived, int(SameType) ? int(internal::assign_traits<Derived, OtherDerived>::Traversal)
+ : int(InvalidTraversal)>::run(derived(),other.derived());
+#ifndef EIGEN_NO_DEBUG
+ checkTransposeAliasing(other.derived());
+#endif
+ return derived();
+}
+
+namespace internal {
+
+template<typename Derived, typename OtherDerived,
+ bool EvalBeforeAssigning = (int(internal::traits<OtherDerived>::Flags) & EvalBeforeAssigningBit) != 0,
+ bool NeedToTranspose = ((int(Derived::RowsAtCompileTime) == 1 && int(OtherDerived::ColsAtCompileTime) == 1)
+ | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
+ // revert to || as soon as not needed anymore.
+ (int(Derived::ColsAtCompileTime) == 1 && int(OtherDerived::RowsAtCompileTime) == 1))
+ && int(Derived::SizeAtCompileTime) != 1>
+struct assign_selector;
+
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,false,false> {
+ static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
+ template<typename ActualDerived, typename ActualOtherDerived>
+ static EIGEN_STRONG_INLINE Derived& evalTo(ActualDerived& dst, const ActualOtherDerived& other) { other.evalTo(dst); return dst; }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,true,false> {
+ static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.eval()); }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,false,true> {
+ static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose()); }
+ template<typename ActualDerived, typename ActualOtherDerived>
+ static EIGEN_STRONG_INLINE Derived& evalTo(ActualDerived& dst, const ActualOtherDerived& other) { Transpose<ActualDerived> dstTrans(dst); other.evalTo(dstTrans); return dst; }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,true,true> {
+ static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose().eval()); }
+};
+
+} // end namespace internal
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+ return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
+{
+ return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
+{
+ return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+ return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
+{
+ return internal::assign_selector<Derived,OtherDerived,false>::evalTo(derived(), other.derived());
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+ return internal::assign_selector<Derived,OtherDerived,false>::evalTo(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ASSIGN_H
diff --git a/Eigen/src/Core/Assign_MKL.h b/Eigen/src/Core/Assign_MKL.h
new file mode 100644
index 0000000..7772951
--- /dev/null
+++ b/Eigen/src/Core/Assign_MKL.h
@@ -0,0 +1,224 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_ASSIGN_VML_H
+#define EIGEN_ASSIGN_VML_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Op> struct vml_call
+{ enum { IsSupported = 0 }; };
+
+template<typename Dst, typename Src, typename UnaryOp>
+class vml_assign_traits
+{
+ private:
+ enum {
+ DstHasDirectAccess = Dst::Flags & DirectAccessBit,
+ SrcHasDirectAccess = Src::Flags & DirectAccessBit,
+
+ StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),
+ InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
+ : int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime)
+ : int(Dst::RowsAtCompileTime),
+ InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
+ : int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
+ : int(Dst::MaxRowsAtCompileTime),
+ MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
+
+ MightEnableVml = vml_call<UnaryOp>::IsSupported && StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess
+ && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,
+ MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
+ VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
+ LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD,
+ MayEnableVml = MightEnableVml && LargeEnough,
+ MayLinearize = MayEnableVml && MightLinearize
+ };
+ public:
+ enum {
+ Traversal = MayLinearize ? LinearVectorizedTraversal
+ : MayEnableVml ? InnerVectorizedTraversal
+ : DefaultTraversal
+ };
+};
+
+template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling,
+ int VmlTraversal = vml_assign_traits<Derived1, Derived2, UnaryOp>::Traversal >
+struct vml_assign_impl
+ : assign_impl<Derived1, Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>
+{
+};
+
+template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling>
+struct vml_assign_impl<Derived1, Derived2, UnaryOp, Traversal, Unrolling, InnerVectorizedTraversal>
+{
+ typedef typename Derived1::Scalar Scalar;
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1& dst, const CwiseUnaryOp<UnaryOp, Derived2>& src)
+ {
+ // in case we want to (or have to) skip VML at runtime we can call:
+ // assign_impl<Derived1,Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>::run(dst,src);
+ const Index innerSize = dst.innerSize();
+ const Index outerSize = dst.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer) {
+ const Scalar *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) :
+ &(src.nestedExpression().coeffRef(0, outer));
+ Scalar *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));
+ vml_call<UnaryOp>::run(src.functor(), innerSize, src_ptr, dst_ptr );
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling>
+struct vml_assign_impl<Derived1, Derived2, UnaryOp, Traversal, Unrolling, LinearVectorizedTraversal>
+{
+ static inline void run(Derived1& dst, const CwiseUnaryOp<UnaryOp, Derived2>& src)
+ {
+ // in case we want to (or have to) skip VML at runtime we can call:
+ // assign_impl<Derived1,Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>::run(dst,src);
+ vml_call<UnaryOp>::run(src.functor(), dst.size(), src.nestedExpression().data(), dst.data() );
+ }
+};
+
+// Macroses
+
+#define EIGEN_MKL_VML_SPECIALIZE_ASSIGN(TRAVERSAL,UNROLLING) \
+ template<typename Derived1, typename Derived2, typename UnaryOp> \
+ struct assign_impl<Derived1, Eigen::CwiseUnaryOp<UnaryOp, Derived2>, TRAVERSAL, UNROLLING, Specialized> { \
+ static inline void run(Derived1 &dst, const Eigen::CwiseUnaryOp<UnaryOp, Derived2> &src) { \
+ vml_assign_impl<Derived1,Derived2,UnaryOp,TRAVERSAL,UNROLLING>::run(dst, src); \
+ } \
+ };
+
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,NoUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,CompleteUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,InnerUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearTraversal,NoUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearTraversal,CompleteUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,NoUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,CompleteUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,InnerUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearVectorizedTraversal,CompleteUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearVectorizedTraversal,NoUnrolling)
+EIGEN_MKL_VML_SPECIALIZE_ASSIGN(SliceVectorizedTraversal,NoUnrolling)
+
+
+#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
+#define EIGEN_MKL_VML_MODE VML_HA
+#else
+#define EIGEN_MKL_VML_MODE VML_LA
+#endif
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
+ template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
+ enum { IsSupported = 1 }; \
+ static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& /*func*/, \
+ int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
+ VMLOP(size, (const VMLTYPE*)src, (VMLTYPE*)dst); \
+ } \
+ };
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
+ template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
+ enum { IsSupported = 1 }; \
+ static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& /*func*/, \
+ int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
+ MKL_INT64 vmlMode = EIGEN_MKL_VML_MODE; \
+ VMLOP(size, (const VMLTYPE*)src, (VMLTYPE*)dst, vmlMode); \
+ } \
+ };
+
+#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
+ template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
+ enum { IsSupported = 1 }; \
+ static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& func, \
+ int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
+ EIGENTYPE exponent = func.m_exponent; \
+ MKL_INT64 vmlMode = EIGEN_MKL_VML_MODE; \
+ VMLOP(&size, (const VMLTYPE*)src, (const VMLTYPE*)&exponent, \
+ (VMLTYPE*)dst, &vmlMode); \
+ } \
+ };
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vs##VMLOP, float, float) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vd##VMLOP, double, double)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vc##VMLOP, scomplex, MKL_Complex8) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vz##VMLOP, dcomplex, MKL_Complex16)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX(EIGENOP, VMLOP)
+
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL_LA(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vms##VMLOP, float, float) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmd##VMLOP, double, double)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX_LA(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmc##VMLOP, scomplex, MKL_Complex8) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmz##VMLOP, dcomplex, MKL_Complex16)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL_LA(EIGENOP, VMLOP) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX_LA(EIGENOP, VMLOP)
+
+
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(sin, Sin)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(asin, Asin)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(cos, Cos)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(acos, Acos)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(tan, Tan)
+//EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(exp, Exp)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(log, Ln)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(sqrt, Sqrt)
+
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr)
+
+// The vm*powx functions are not avaibale in the windows version of MKL.
+#ifndef _WIN32
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmspowx_, float, float)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdpowx_, double, double)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcpowx_, scomplex, MKL_Complex8)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzpowx_, dcomplex, MKL_Complex16)
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ASSIGN_VML_H
diff --git a/Eigen/src/Core/BandMatrix.h b/Eigen/src/Core/BandMatrix.h
new file mode 100644
index 0000000..ffd7fe8
--- /dev/null
+++ b/Eigen/src/Core/BandMatrix.h
@@ -0,0 +1,334 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BANDMATRIX_H
+#define EIGEN_BANDMATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+class BandMatrixBase : public EigenBase<Derived>
+{
+ public:
+
+ enum {
+ Flags = internal::traits<Derived>::Flags,
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+ Supers = internal::traits<Derived>::Supers,
+ Subs = internal::traits<Derived>::Subs,
+ Options = internal::traits<Derived>::Options
+ };
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
+ typedef typename DenseMatrixType::Index Index;
+ typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
+ typedef EigenBase<Derived> Base;
+
+ protected:
+ enum {
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
+ ? 1 + Supers + Subs
+ : Dynamic,
+ SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
+ };
+
+ public:
+
+ using Base::derived;
+ using Base::rows;
+ using Base::cols;
+
+ /** \returns the number of super diagonals */
+ inline Index supers() const { return derived().supers(); }
+
+ /** \returns the number of sub diagonals */
+ inline Index subs() const { return derived().subs(); }
+
+ /** \returns an expression of the underlying coefficient matrix */
+ inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
+
+ /** \returns an expression of the underlying coefficient matrix */
+ inline CoefficientsType& coeffs() { return derived().coeffs(); }
+
+ /** \returns a vector expression of the \a i -th column,
+ * only the meaningful part is returned.
+ * \warning the internal storage must be column major. */
+ inline Block<CoefficientsType,Dynamic,1> col(Index i)
+ {
+ EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ Index start = 0;
+ Index len = coeffs().rows();
+ if (i<=supers())
+ {
+ start = supers()-i;
+ len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
+ }
+ else if (i>=rows()-subs())
+ len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
+ return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
+ }
+
+ /** \returns a vector expression of the main diagonal */
+ inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
+ { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+ /** \returns a vector expression of the main diagonal (const version) */
+ inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
+ { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+ template<int Index> struct DiagonalIntReturnType {
+ enum {
+ ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),
+ Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
+ ActualIndex = ReturnOpposite ? -Index : Index,
+ DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
+ ? Dynamic
+ : (ActualIndex<0
+ ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
+ : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
+ };
+ typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
+ typedef typename internal::conditional<Conjugate,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
+ BuildType>::type Type;
+ };
+
+ /** \returns a vector expression of the \a N -th sub or super diagonal */
+ template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
+ {
+ return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+ }
+
+ /** \returns a vector expression of the \a N -th sub or super diagonal */
+ template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
+ {
+ return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+ }
+
+ /** \returns a vector expression of the \a i -th sub or super diagonal */
+ inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
+ {
+ eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+ return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+ }
+
+ /** \returns a vector expression of the \a i -th sub or super diagonal */
+ inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
+ {
+ eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+ return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+ }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ dst.resize(rows(),cols());
+ dst.setZero();
+ dst.diagonal() = diagonal();
+ for (Index i=1; i<=supers();++i)
+ dst.diagonal(i) = diagonal(i);
+ for (Index i=1; i<=subs();++i)
+ dst.diagonal(-i) = diagonal(-i);
+ }
+
+ DenseMatrixType toDenseMatrix() const
+ {
+ DenseMatrixType res(rows(),cols());
+ evalTo(res);
+ return res;
+ }
+
+ protected:
+
+ inline Index diagonalLength(Index i) const
+ { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
+};
+
+/**
+ * \class BandMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a rectangular matrix with a banded storage
+ *
+ * \param _Scalar Numeric type, i.e. float, double, int
+ * \param Rows Number of rows, or \b Dynamic
+ * \param Cols Number of columns, or \b Dynamic
+ * \param Supers Number of super diagonal
+ * \param Subs Number of sub diagonal
+ * \param _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
+ * The former controls \ref TopicStorageOrders "storage order", and defaults to
+ * column-major. The latter controls whether the matrix represents a selfadjoint
+ * matrix in which case either Supers of Subs have to be null.
+ *
+ * \sa class TridiagonalMatrix
+ */
+
+template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
+struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+ typedef _Scalar Scalar;
+ typedef Dense StorageKind;
+ typedef DenseIndex Index;
+ enum {
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ RowsAtCompileTime = _Rows,
+ ColsAtCompileTime = _Cols,
+ MaxRowsAtCompileTime = _Rows,
+ MaxColsAtCompileTime = _Cols,
+ Flags = LvalueBit,
+ Supers = _Supers,
+ Subs = _Subs,
+ Options = _Options,
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+ };
+ typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;
+};
+
+template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
+class BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >
+{
+ public:
+
+ typedef typename internal::traits<BandMatrix>::Scalar Scalar;
+ typedef typename internal::traits<BandMatrix>::Index Index;
+ typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
+
+ inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
+ : m_coeffs(1+supers+subs,cols),
+ m_rows(rows), m_supers(supers), m_subs(subs)
+ {
+ }
+
+ /** \returns the number of columns */
+ inline Index rows() const { return m_rows.value(); }
+
+ /** \returns the number of rows */
+ inline Index cols() const { return m_coeffs.cols(); }
+
+ /** \returns the number of super diagonals */
+ inline Index supers() const { return m_supers.value(); }
+
+ /** \returns the number of sub diagonals */
+ inline Index subs() const { return m_subs.value(); }
+
+ inline const CoefficientsType& coeffs() const { return m_coeffs; }
+ inline CoefficientsType& coeffs() { return m_coeffs; }
+
+ protected:
+
+ CoefficientsType m_coeffs;
+ internal::variable_if_dynamic<Index, Rows> m_rows;
+ internal::variable_if_dynamic<Index, Supers> m_supers;
+ internal::variable_if_dynamic<Index, Subs> m_subs;
+};
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+class BandMatrixWrapper;
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+ typedef typename _CoefficientsType::Scalar Scalar;
+ typedef typename _CoefficientsType::StorageKind StorageKind;
+ typedef typename _CoefficientsType::Index Index;
+ enum {
+ CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
+ RowsAtCompileTime = _Rows,
+ ColsAtCompileTime = _Cols,
+ MaxRowsAtCompileTime = _Rows,
+ MaxColsAtCompileTime = _Cols,
+ Flags = LvalueBit,
+ Supers = _Supers,
+ Subs = _Subs,
+ Options = _Options,
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+ };
+ typedef _CoefficientsType CoefficientsType;
+};
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+ public:
+
+ typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
+ typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
+ typedef typename internal::traits<BandMatrixWrapper>::Index Index;
+
+ inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
+ : m_coeffs(coeffs),
+ m_rows(rows), m_supers(supers), m_subs(subs)
+ {
+ EIGEN_UNUSED_VARIABLE(cols);
+ //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
+ }
+
+ /** \returns the number of columns */
+ inline Index rows() const { return m_rows.value(); }
+
+ /** \returns the number of rows */
+ inline Index cols() const { return m_coeffs.cols(); }
+
+ /** \returns the number of super diagonals */
+ inline Index supers() const { return m_supers.value(); }
+
+ /** \returns the number of sub diagonals */
+ inline Index subs() const { return m_subs.value(); }
+
+ inline const CoefficientsType& coeffs() const { return m_coeffs; }
+
+ protected:
+
+ const CoefficientsType& m_coeffs;
+ internal::variable_if_dynamic<Index, _Rows> m_rows;
+ internal::variable_if_dynamic<Index, _Supers> m_supers;
+ internal::variable_if_dynamic<Index, _Subs> m_subs;
+};
+
+/**
+ * \class TridiagonalMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a tridiagonal matrix with a compact banded storage
+ *
+ * \param _Scalar Numeric type, i.e. float, double, int
+ * \param Size Number of rows and cols, or \b Dynamic
+ * \param _Options Can be 0 or \b SelfAdjoint
+ *
+ * \sa class BandMatrix
+ */
+template<typename Scalar, int Size, int Options>
+class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
+{
+ typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
+ typedef typename Base::Index Index;
+ public:
+ TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
+
+ inline typename Base::template DiagonalIntReturnType<1>::Type super()
+ { return Base::template diagonal<1>(); }
+ inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
+ { return Base::template diagonal<1>(); }
+ inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
+ { return Base::template diagonal<-1>(); }
+ inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
+ { return Base::template diagonal<-1>(); }
+ protected:
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BANDMATRIX_H
diff --git a/Eigen/src/Core/Block.h b/Eigen/src/Core/Block.h
new file mode 100644
index 0000000..8278944
--- /dev/null
+++ b/Eigen/src/Core/Block.h
@@ -0,0 +1,406 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLOCK_H
+#define EIGEN_BLOCK_H
+
+namespace Eigen {
+
+/** \class Block
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a fixed-size or dynamic-size block
+ *
+ * \param XprType the type of the expression in which we are taking a block
+ * \param BlockRows the number of rows of the block we are taking at compile time (optional)
+ * \param BlockCols the number of columns of the block we are taking at compile time (optional)
+ *
+ * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
+ * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
+ * most of the time this is the only way it is used.
+ *
+ * However, if you want to directly maniputate block expressions,
+ * for instance if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * Here is an example illustrating the dynamic case:
+ * \include class_Block.cpp
+ * Output: \verbinclude class_Block.out
+ *
+ * \note Even though this expression has dynamic size, in the case where \a XprType
+ * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+ * it does not cause a dynamic memory allocation.
+ *
+ * Here is an example illustrating the fixed-size case:
+ * \include class_FixedBlock.cpp
+ * Output: \verbinclude class_FixedBlock.out
+ *
+ * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
+ */
+
+namespace internal {
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>
+{
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename traits<XprType>::StorageKind StorageKind;
+ typedef typename traits<XprType>::XprKind XprKind;
+ typedef typename nested<XprType>::type XprTypeNested;
+ typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
+ enum{
+ MatrixRows = traits<XprType>::RowsAtCompileTime,
+ MatrixCols = traits<XprType>::ColsAtCompileTime,
+ RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
+ ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
+ MaxRowsAtCompileTime = BlockRows==0 ? 0
+ : RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
+ : int(traits<XprType>::MaxRowsAtCompileTime),
+ MaxColsAtCompileTime = BlockCols==0 ? 0
+ : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
+ : int(traits<XprType>::MaxColsAtCompileTime),
+ XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
+ IsDense = is_same<StorageKind,Dense>::value,
+ IsRowMajor = (IsDense&&MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+ : (IsDense&&MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+ : XprTypeIsRowMajor,
+ HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
+ InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+ InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
+ ? int(inner_stride_at_compile_time<XprType>::ret)
+ : int(outer_stride_at_compile_time<XprType>::ret),
+ OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
+ ? int(outer_stride_at_compile_time<XprType>::ret)
+ : int(inner_stride_at_compile_time<XprType>::ret),
+ MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits<Scalar>::size) == 0)
+ && (InnerStrideAtCompileTime == 1)
+ ? PacketAccessBit : 0,
+ MaskAlignedBit = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
+ FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 || (InnerPanel && (traits<XprType>::Flags&LinearAccessBit))) ? LinearAccessBit : 0,
+ FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
+ FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
+ Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) |
+ DirectAccessBit |
+ MaskPacketAccessBit |
+ MaskAlignedBit),
+ Flags = Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit
+ };
+};
+
+template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false,
+ bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class BlockImpl_dense;
+
+} // end namespace internal
+
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;
+
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block
+ : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>
+{
+ typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;
+ public:
+ //typedef typename Impl::Base Base;
+ typedef Impl Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+ /** Column or Row constructor
+ */
+ inline Block(XprType& xpr, Index i) : Impl(xpr,i)
+ {
+ eigen_assert( (i>=0) && (
+ ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
+ ||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
+ }
+
+ /** Fixed-size constructor
+ */
+ inline Block(XprType& xpr, Index a_startRow, Index a_startCol)
+ : Impl(xpr, a_startRow, a_startCol)
+ {
+ EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+ eigen_assert(a_startRow >= 0 && BlockRows >= 1 && a_startRow + BlockRows <= xpr.rows()
+ && a_startCol >= 0 && BlockCols >= 1 && a_startCol + BlockCols <= xpr.cols());
+ }
+
+ /** Dynamic-size constructor
+ */
+ inline Block(XprType& xpr,
+ Index a_startRow, Index a_startCol,
+ Index blockRows, Index blockCols)
+ : Impl(xpr, a_startRow, a_startCol, blockRows, blockCols)
+ {
+ eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+ && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+ eigen_assert(a_startRow >= 0 && blockRows >= 0 && a_startRow <= xpr.rows() - blockRows
+ && a_startCol >= 0 && blockCols >= 0 && a_startCol <= xpr.cols() - blockCols);
+ }
+};
+
+// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense
+// that must be specialized for direct and non-direct access...
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>
+ : public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel>
+{
+ typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;
+ typedef typename XprType::Index Index;
+ public:
+ typedef Impl Base;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+ inline BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {}
+ inline BlockImpl(XprType& xpr, Index a_startRow, Index a_startCol) : Impl(xpr, a_startRow, a_startCol) {}
+ inline BlockImpl(XprType& xpr, Index a_startRow, Index a_startCol, Index blockRows, Index blockCols)
+ : Impl(xpr, a_startRow, a_startCol, blockRows, blockCols) {}
+};
+
+namespace internal {
+
+/** \internal Internal implementation of dense Blocks in the general case. */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class BlockImpl_dense
+ : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type
+{
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+ public:
+
+ typedef typename internal::dense_xpr_base<BlockType>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
+
+ class InnerIterator;
+
+ /** Column or Row constructor
+ */
+ inline BlockImpl_dense(XprType& xpr, Index i)
+ : m_xpr(xpr),
+ // It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
+ // and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
+ // all other cases are invalid.
+ // The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
+ m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+ m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+ m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+ m_blockCols(BlockCols==1 ? 1 : xpr.cols())
+ {}
+
+ /** Fixed-size constructor
+ */
+ inline BlockImpl_dense(XprType& xpr, Index a_startRow, Index a_startCol)
+ : m_xpr(xpr), m_startRow(a_startRow), m_startCol(a_startCol),
+ m_blockRows(BlockRows), m_blockCols(BlockCols)
+ {}
+
+ /** Dynamic-size constructor
+ */
+ inline BlockImpl_dense(XprType& xpr,
+ Index a_startRow, Index a_startCol,
+ Index blockRows, Index blockCols)
+ : m_xpr(xpr), m_startRow(a_startRow), m_startCol(a_startCol),
+ m_blockRows(blockRows), m_blockCols(blockCols)
+ {}
+
+ inline Index rows() const { return m_blockRows.value(); }
+ inline Index cols() const { return m_blockCols.value(); }
+
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ return m_xpr.const_cast_derived()
+ .coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_xpr.derived()
+ .coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ return m_xpr.const_cast_derived()
+ .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_xpr.const_cast_derived()
+ .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const CoeffReturnType coeff(Index index) const
+ {
+ return m_xpr
+ .coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ template<int LoadMode>
+ inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ return m_xpr.template packet<Unaligned>
+ (rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ m_xpr.const_cast_derived().template writePacket<Unaligned>
+ (rowId + m_startRow.value(), colId + m_startCol.value(), val);
+ }
+
+ template<int LoadMode>
+ inline PacketScalar packet(Index index) const
+ {
+ return m_xpr.template packet<Unaligned>
+ (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ m_xpr.const_cast_derived().template writePacket<Unaligned>
+ (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \sa MapBase::data() */
+ inline const Scalar* data() const;
+ inline Index innerStride() const;
+ inline Index outerStride() const;
+ #endif
+
+ const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
+ {
+ return m_xpr;
+ }
+
+ Index startRow() const
+ {
+ return m_startRow.value();
+ }
+
+ Index startCol() const
+ {
+ return m_startCol.value();
+ }
+
+ protected:
+
+ const typename XprType::Nested m_xpr;
+ const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+ const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;
+};
+
+/** \internal Internal implementation of dense Blocks in the direct access case.*/
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
+ : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >
+{
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+ public:
+
+ typedef MapBase<BlockType> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
+
+ /** Column or Row constructor
+ */
+ inline BlockImpl_dense(XprType& xpr, Index i)
+ : Base(internal::const_cast_ptr(&xpr.coeffRef(
+ (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0,
+ (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)),
+ BlockRows==1 ? 1 : xpr.rows(),
+ BlockCols==1 ? 1 : xpr.cols()),
+ m_xpr(xpr)
+ {
+ init();
+ }
+
+ /** Fixed-size constructor
+ */
+ inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
+ : Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol))), m_xpr(xpr)
+ {
+ init();
+ }
+
+ /** Dynamic-size constructor
+ */
+ inline BlockImpl_dense(XprType& xpr,
+ Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+ : Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol)), blockRows, blockCols),
+ m_xpr(xpr)
+ {
+ init();
+ }
+
+ const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
+ {
+ return m_xpr;
+ }
+
+ /** \sa MapBase::innerStride() */
+ inline Index innerStride() const
+ {
+ return internal::traits<BlockType>::HasSameStorageOrderAsXprType
+ ? m_xpr.innerStride()
+ : m_xpr.outerStride();
+ }
+
+ /** \sa MapBase::outerStride() */
+ inline Index outerStride() const
+ {
+ return m_outerStride;
+ }
+
+ #ifndef __SUNPRO_CC
+ // FIXME sunstudio is not friendly with the above friend...
+ // META-FIXME there is no 'friend' keyword around here. Is this obsolete?
+ protected:
+ #endif
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal used by allowAligned() */
+ inline BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
+ : Base(data, blockRows, blockCols), m_xpr(xpr)
+ {
+ init();
+ }
+ #endif
+
+ protected:
+ void init()
+ {
+ m_outerStride = internal::traits<BlockType>::HasSameStorageOrderAsXprType
+ ? m_xpr.outerStride()
+ : m_xpr.innerStride();
+ }
+
+ typename XprType::Nested m_xpr;
+ Index m_outerStride;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLOCK_H
diff --git a/Eigen/src/Core/BooleanRedux.h b/Eigen/src/Core/BooleanRedux.h
new file mode 100644
index 0000000..be9f48a
--- /dev/null
+++ b/Eigen/src/Core/BooleanRedux.h
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ALLANDANY_H
+#define EIGEN_ALLANDANY_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived, int UnrollCount>
+struct all_unroller
+{
+ enum {
+ col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived::RowsAtCompileTime
+ };
+
+ static inline bool run(const Derived &mat)
+ {
+ return all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
+ }
+};
+
+template<typename Derived>
+struct all_unroller<Derived, 0>
+{
+ static inline bool run(const Derived &/*mat*/) { return true; }
+};
+
+template<typename Derived>
+struct all_unroller<Derived, Dynamic>
+{
+ static inline bool run(const Derived &) { return false; }
+};
+
+template<typename Derived, int UnrollCount>
+struct any_unroller
+{
+ enum {
+ col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived::RowsAtCompileTime
+ };
+
+ static inline bool run(const Derived &mat)
+ {
+ return any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
+ }
+};
+
+template<typename Derived>
+struct any_unroller<Derived, 0>
+{
+ static inline bool run(const Derived & /*mat*/) { return false; }
+};
+
+template<typename Derived>
+struct any_unroller<Derived, Dynamic>
+{
+ static inline bool run(const Derived &) { return false; }
+};
+
+} // end namespace internal
+
+/** \returns true if all coefficients are true
+ *
+ * Example: \include MatrixBase_all.cpp
+ * Output: \verbinclude MatrixBase_all.out
+ *
+ * \sa any(), Cwise::operator<()
+ */
+template<typename Derived>
+inline bool DenseBase<Derived>::all() const
+{
+ enum {
+ unroll = SizeAtCompileTime != Dynamic
+ && CoeffReadCost != Dynamic
+ && NumTraits<Scalar>::AddCost != Dynamic
+ && SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
+ };
+ if(unroll)
+ return internal::all_unroller<Derived, unroll ? int(SizeAtCompileTime) : Dynamic>::run(derived());
+ else
+ {
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if (!coeff(i, j)) return false;
+ return true;
+ }
+}
+
+/** \returns true if at least one coefficient is true
+ *
+ * \sa all()
+ */
+template<typename Derived>
+inline bool DenseBase<Derived>::any() const
+{
+ enum {
+ unroll = SizeAtCompileTime != Dynamic
+ && CoeffReadCost != Dynamic
+ && NumTraits<Scalar>::AddCost != Dynamic
+ && SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
+ };
+ if(unroll)
+ return internal::any_unroller<Derived, unroll ? int(SizeAtCompileTime) : Dynamic>::run(derived());
+ else
+ {
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if (coeff(i, j)) return true;
+ return false;
+ }
+}
+
+/** \returns the number of coefficients which evaluate to true
+ *
+ * \sa all(), any()
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::Index DenseBase<Derived>::count() const
+{
+ return derived().template cast<bool>().template cast<Index>().sum();
+}
+
+/** \returns true is \c *this contains at least one Not A Number (NaN).
+ *
+ * \sa allFinite()
+ */
+template<typename Derived>
+inline bool DenseBase<Derived>::hasNaN() const
+{
+ return !((derived().array()==derived().array()).all());
+}
+
+/** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values.
+ *
+ * \sa hasNaN()
+ */
+template<typename Derived>
+inline bool DenseBase<Derived>::allFinite() const
+{
+ return !((derived()-derived()).hasNaN());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ALLANDANY_H
diff --git a/Eigen/src/Core/CMakeLists.txt b/Eigen/src/Core/CMakeLists.txt
new file mode 100644
index 0000000..2346fc2
--- /dev/null
+++ b/Eigen/src/Core/CMakeLists.txt
@@ -0,0 +1,10 @@
+FILE(GLOB Eigen_Core_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core COMPONENT Devel
+ )
+
+ADD_SUBDIRECTORY(products)
+ADD_SUBDIRECTORY(util)
+ADD_SUBDIRECTORY(arch)
diff --git a/Eigen/src/Core/CommaInitializer.h b/Eigen/src/Core/CommaInitializer.h
new file mode 100644
index 0000000..a036d8c
--- /dev/null
+++ b/Eigen/src/Core/CommaInitializer.h
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMMAINITIALIZER_H
+#define EIGEN_COMMAINITIALIZER_H
+
+namespace Eigen {
+
+/** \class CommaInitializer
+ * \ingroup Core_Module
+ *
+ * \brief Helper class used by the comma initializer operator
+ *
+ * This class is internally used to implement the comma initializer feature. It is
+ * the return type of MatrixBase::operator<<, and most of the time this is the only
+ * way it is used.
+ *
+ * \sa \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
+ */
+template<typename XprType>
+struct CommaInitializer
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::Index Index;
+
+ inline CommaInitializer(XprType& xpr, const Scalar& s)
+ : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
+ {
+ m_xpr.coeffRef(0,0) = s;
+ }
+
+ template<typename OtherDerived>
+ inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
+ : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
+ {
+ m_xpr.block(0, 0, other.rows(), other.cols()) = other;
+ }
+
+ /* Copy/Move constructor which transfers ownership. This is crucial in
+ * absence of return value optimization to avoid assertions during destruction. */
+ // FIXME in C++11 mode this could be replaced by a proper RValue constructor
+ inline CommaInitializer(const CommaInitializer& o)
+ : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
+ // Mark original object as finished. In absence of R-value references we need to const_cast:
+ const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
+ const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();
+ const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;
+ }
+
+ /* inserts a scalar value in the target matrix */
+ CommaInitializer& operator,(const Scalar& s)
+ {
+ if (m_col==m_xpr.cols())
+ {
+ m_row+=m_currentBlockRows;
+ m_col = 0;
+ m_currentBlockRows = 1;
+ eigen_assert(m_row<m_xpr.rows()
+ && "Too many rows passed to comma initializer (operator<<)");
+ }
+ eigen_assert(m_col<m_xpr.cols()
+ && "Too many coefficients passed to comma initializer (operator<<)");
+ eigen_assert(m_currentBlockRows==1);
+ m_xpr.coeffRef(m_row, m_col++) = s;
+ return *this;
+ }
+
+ /* inserts a matrix expression in the target matrix */
+ template<typename OtherDerived>
+ CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
+ {
+ if(other.cols()==0 || other.rows()==0)
+ return *this;
+ if (m_col==m_xpr.cols())
+ {
+ m_row+=m_currentBlockRows;
+ m_col = 0;
+ m_currentBlockRows = other.rows();
+ eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
+ && "Too many rows passed to comma initializer (operator<<)");
+ }
+ eigen_assert(m_col<m_xpr.cols()
+ && "Too many coefficients passed to comma initializer (operator<<)");
+ eigen_assert(m_currentBlockRows==other.rows());
+ if (OtherDerived::SizeAtCompileTime != Dynamic)
+ m_xpr.template block<OtherDerived::RowsAtCompileTime != Dynamic ? OtherDerived::RowsAtCompileTime : 1,
+ OtherDerived::ColsAtCompileTime != Dynamic ? OtherDerived::ColsAtCompileTime : 1>
+ (m_row, m_col) = other;
+ else
+ m_xpr.block(m_row, m_col, other.rows(), other.cols()) = other;
+ m_col += other.cols();
+ return *this;
+ }
+
+ inline ~CommaInitializer()
+ {
+ eigen_assert((m_row+m_currentBlockRows) == m_xpr.rows()
+ && m_col == m_xpr.cols()
+ && "Too few coefficients passed to comma initializer (operator<<)");
+ }
+
+ /** \returns the built matrix once all its coefficients have been set.
+ * Calling finished is 100% optional. Its purpose is to write expressions
+ * like this:
+ * \code
+ * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
+ * \endcode
+ */
+ inline XprType& finished() { return m_xpr; }
+
+ XprType& m_xpr; // target expression
+ Index m_row; // current row id
+ Index m_col; // current col id
+ Index m_currentBlockRows; // current block height
+};
+
+/** \anchor MatrixBaseCommaInitRef
+ * Convenient operator to set the coefficients of a matrix.
+ *
+ * The coefficients must be provided in a row major order and exactly match
+ * the size of the matrix. Otherwise an assertion is raised.
+ *
+ * Example: \include MatrixBase_set.cpp
+ * Output: \verbinclude MatrixBase_set.out
+ *
+ * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
+ *
+ * \sa CommaInitializer::finished(), class CommaInitializer
+ */
+template<typename Derived>
+inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)
+{
+ return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
+}
+
+/** \sa operator<<(const Scalar&) */
+template<typename Derived>
+template<typename OtherDerived>
+inline CommaInitializer<Derived>
+DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
+{
+ return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMMAINITIALIZER_H
diff --git a/Eigen/src/Core/CoreIterators.h b/Eigen/src/Core/CoreIterators.h
new file mode 100644
index 0000000..6da4683
--- /dev/null
+++ b/Eigen/src/Core/CoreIterators.h
@@ -0,0 +1,61 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COREITERATORS_H
+#define EIGEN_COREITERATORS_H
+
+namespace Eigen {
+
+/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core
+ */
+
+/** \ingroup SparseCore_Module
+ * \class InnerIterator
+ * \brief An InnerIterator allows to loop over the element of a sparse (or dense) matrix or expression
+ *
+ * todo
+ */
+
+// generic version for dense matrix and expressions
+template<typename Derived> class DenseBase<Derived>::InnerIterator
+{
+ protected:
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Index Index;
+
+ enum { IsRowMajor = (Derived::Flags&RowMajorBit)==RowMajorBit };
+ public:
+ EIGEN_STRONG_INLINE InnerIterator(const Derived& expr, Index outer)
+ : m_expression(expr), m_inner(0), m_outer(outer), m_end(expr.innerSize())
+ {}
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ {
+ return (IsRowMajor) ? m_expression.coeff(m_outer, m_inner)
+ : m_expression.coeff(m_inner, m_outer);
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++() { m_inner++; return *this; }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_inner; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }
+
+ protected:
+ const Derived& m_expression;
+ Index m_inner;
+ const Index m_outer;
+ const Index m_end;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_COREITERATORS_H
diff --git a/Eigen/src/Core/CwiseBinaryOp.h b/Eigen/src/Core/CwiseBinaryOp.h
new file mode 100644
index 0000000..586f77a
--- /dev/null
+++ b/Eigen/src/Core/CwiseBinaryOp.h
@@ -0,0 +1,229 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_BINARY_OP_H
+#define EIGEN_CWISE_BINARY_OP_H
+
+namespace Eigen {
+
+/** \class CwiseBinaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
+ *
+ * \param BinaryOp template functor implementing the operator
+ * \param Lhs the type of the left-hand side
+ * \param Rhs the type of the right-hand side
+ *
+ * This class represents an expression where a coefficient-wise binary operator is applied to two expressions.
+ * It is the return type of binary operators, by which we mean only those binary operators where
+ * both the left-hand side and the right-hand side are Eigen expressions.
+ * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
+ *
+ * Most of the time, this is the only way that it is used, so you typically don't have to name
+ * CwiseBinaryOp types explicitly.
+ *
+ * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
+ */
+
+namespace internal {
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ // we must not inherit from traits<Lhs> since it has
+ // the potential to cause problems with MSVC
+ typedef typename remove_all<Lhs>::type Ancestor;
+ typedef typename traits<Ancestor>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
+ ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
+ };
+
+ // even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
+ // we still want to handle the case when the result type is different.
+ typedef typename result_of<
+ BinaryOp(
+ typename Lhs::Scalar,
+ typename Rhs::Scalar
+ )
+ >::type Scalar;
+ typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
+ typename traits<Rhs>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<Lhs>::Index,
+ typename traits<Rhs>::Index>::type Index;
+ typedef typename Lhs::Nested LhsNested;
+ typedef typename Rhs::Nested RhsNested;
+ typedef typename remove_reference<LhsNested>::type _LhsNested;
+ typedef typename remove_reference<RhsNested>::type _RhsNested;
+ enum {
+ LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+ RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+ LhsFlags = _LhsNested::Flags,
+ RhsFlags = _RhsNested::Flags,
+ SameType = is_same<typename _LhsNested::Scalar,typename _RhsNested::Scalar>::value,
+ StorageOrdersAgree = (int(Lhs::Flags)&RowMajorBit)==(int(Rhs::Flags)&RowMajorBit),
+ Flags0 = (int(LhsFlags) | int(RhsFlags)) & (
+ HereditaryBits
+ | (int(LhsFlags) & int(RhsFlags) &
+ ( AlignedBit
+ | (StorageOrdersAgree ? LinearAccessBit : 0)
+ | (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)
+ )
+ )
+ ),
+ Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
+ CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + functor_traits<BinaryOp>::Cost
+ };
+};
+} // end namespace internal
+
+// we require Lhs and Rhs to have the same scalar type. Currently there is no example of a binary functor
+// that would take two operands of different types. If there were such an example, then this check should be
+// moved to the BinaryOp functors, on a per-case basis. This would however require a change in the BinaryOp functors, as
+// currently they take only one typename Scalar template parameter.
+// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
+// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
+// add together a float matrix and a double matrix.
+#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
+ EIGEN_STATIC_ASSERT((internal::functor_is_product_like<BINOP>::ret \
+ ? int(internal::scalar_product_traits<LHS, RHS>::Defined) \
+ : int(internal::is_same<LHS, RHS>::value)), \
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
+class CwiseBinaryOpImpl;
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOp : internal::no_assignment_operator,
+ public CwiseBinaryOpImpl<
+ BinaryOp, Lhs, Rhs,
+ typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
+ typename internal::traits<Rhs>::StorageKind>::ret>
+{
+ public:
+
+ typedef typename CwiseBinaryOpImpl<
+ BinaryOp, Lhs, Rhs,
+ typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
+ typename internal::traits<Rhs>::StorageKind>::ret>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
+
+ typedef typename internal::nested<Lhs>::type LhsNested;
+ typedef typename internal::nested<Rhs>::type RhsNested;
+ typedef typename internal::remove_reference<LhsNested>::type _LhsNested;
+ typedef typename internal::remove_reference<RhsNested>::type _RhsNested;
+
+ EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp())
+ : m_lhs(aLhs), m_rhs(aRhs), m_functor(func)
+ {
+ EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);
+ // require the sizes to match
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
+ eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const {
+ // return the fixed size type if available to enable compile time optimizations
+ if (internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic)
+ return m_rhs.rows();
+ else
+ return m_lhs.rows();
+ }
+ EIGEN_STRONG_INLINE Index cols() const {
+ // return the fixed size type if available to enable compile time optimizations
+ if (internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic)
+ return m_rhs.cols();
+ else
+ return m_lhs.cols();
+ }
+
+ /** \returns the left hand side nested expression */
+ const _LhsNested& lhs() const { return m_lhs; }
+ /** \returns the right hand side nested expression */
+ const _RhsNested& rhs() const { return m_rhs; }
+ /** \returns the functor representing the binary operation */
+ const BinaryOp& functor() const { return m_functor; }
+
+ protected:
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+ const BinaryOp m_functor;
+};
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Dense>
+ : public internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
+{
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;
+ public:
+
+ typedef typename internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE( Derived )
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index rowId, Index colId) const
+ {
+ return derived().functor()(derived().lhs().coeff(rowId, colId),
+ derived().rhs().coeff(rowId, colId));
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const
+ {
+ return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(rowId, colId),
+ derived().rhs().template packet<LoadMode>(rowId, colId));
+ }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+ {
+ return derived().functor()(derived().lhs().coeff(index),
+ derived().rhs().coeff(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+ {
+ return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(index),
+ derived().rhs().template packet<LoadMode>(index));
+ }
+};
+
+/** replaces \c *this by \c *this - \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
+{
+ SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
+{
+ SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
+ tmp = other.derived();
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_BINARY_OP_H
diff --git a/Eigen/src/Core/CwiseNullaryOp.h b/Eigen/src/Core/CwiseNullaryOp.h
new file mode 100644
index 0000000..a93bab2
--- /dev/null
+++ b/Eigen/src/Core/CwiseNullaryOp.h
@@ -0,0 +1,864 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_NULLARY_OP_H
+#define EIGEN_CWISE_NULLARY_OP_H
+
+namespace Eigen {
+
+/** \class CwiseNullaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression of a matrix where all coefficients are defined by a functor
+ *
+ * \param NullaryOp template functor implementing the operator
+ * \param PlainObjectType the underlying plain matrix/array type
+ *
+ * This class represents an expression of a generic nullary operator.
+ * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
+ * and most of the time this is the only way it is used.
+ *
+ * However, if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
+ */
+
+namespace internal {
+template<typename NullaryOp, typename PlainObjectType>
+struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
+{
+ enum {
+ Flags = (traits<PlainObjectType>::Flags
+ & ( HereditaryBits
+ | (functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
+ | (functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
+ | (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
+ CoeffReadCost = functor_traits<NullaryOp>::Cost
+ };
+};
+}
+
+template<typename NullaryOp, typename PlainObjectType>
+class CwiseNullaryOp : internal::no_assignment_operator,
+ public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
+
+ CwiseNullaryOp(Index nbRows, Index nbCols, const NullaryOp& func = NullaryOp())
+ : m_rows(nbRows), m_cols(nbCols), m_functor(func)
+ {
+ eigen_assert(nbRows >= 0
+ && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == nbRows)
+ && nbCols >= 0
+ && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == nbCols));
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index rowId, Index colId) const
+ {
+ return m_functor(rowId, colId);
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const
+ {
+ return m_functor.packetOp(rowId, colId);
+ }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+ {
+ return m_functor(index);
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+ {
+ return m_functor.packetOp(index);
+ }
+
+ /** \returns the functor representing the nullary operation */
+ const NullaryOp& functor() const { return m_functor; }
+
+ protected:
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+ const NullaryOp m_functor;
+};
+
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
+{
+ return CwiseNullaryOp<CustomNullaryOp, Derived>(rows, cols, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, Derived>(1, size, func);
+ else return CwiseNullaryOp<CustomNullaryOp, Derived>(size, 1, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
+{
+ return CwiseNullaryOp<CustomNullaryOp, Derived>(RowsAtCompileTime, ColsAtCompileTime, func);
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * The parameters \a nbRows and \a nbCols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this DenseBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a nbRows and \a nbCols as arguments, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index nbRows, Index nbCols, const Scalar& value)
+{
+ return DenseBase<Derived>::NullaryExpr(nbRows, nbCols, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this DenseBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index size, const Scalar& value)
+{
+ return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(const Scalar& value)
+{
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
+}
+
+/**
+ * \brief Sets a linearly space vector.
+ *
+ * The function generates 'size' equally spaced values in the closed interval [low,high].
+ * This particular version of LinSpaced() uses sequential access, i.e. vector access is
+ * assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization
+ * and yields faster code than the random access version.
+ *
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_LinSpaced_seq.cpp
+ * Output: \verbinclude DenseBase_LinSpaced_seq.out
+ *
+ * \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,false>(low,high,size));
+}
+
+/**
+ * \copydoc DenseBase::LinSpaced(Sequential_t, Index, const Scalar&, const Scalar&)
+ * Special version for fixed size types which does not require the size parameter.
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,false>(low,high,Derived::SizeAtCompileTime));
+}
+
+/**
+ * \brief Sets a linearly space vector.
+ *
+ * The function generates 'size' equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_LinSpaced.cpp
+ * Output: \verbinclude DenseBase_LinSpaced.out
+ *
+ * \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,true>(low,high,size));
+}
+
+/**
+ * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
+ * Special version for fixed size types which does not require the size parameter.
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,true>(low,high,Derived::SizeAtCompileTime));
+}
+
+/** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
+template<typename Derived>
+bool DenseBase<Derived>::isApproxToConstant
+(const Scalar& val, const RealScalar& prec) const
+{
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if(!internal::isApprox(this->coeff(i, j), val, prec))
+ return false;
+ return true;
+}
+
+/** This is just an alias for isApproxToConstant().
+ *
+ * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+bool DenseBase<Derived>::isConstant
+(const Scalar& val, const RealScalar& prec) const
+{
+ return isApproxToConstant(val, prec);
+}
+
+/** Alias for setConstant(): sets all coefficients in this expression to \a val.
+ *
+ * \sa setConstant(), Constant(), class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
+{
+ setConstant(val);
+}
+
+/** Sets all coefficients in this expression to \a value.
+ *
+ * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
+{
+ return derived() = Constant(rows(), cols(), val);
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to the given \a value.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setConstant_int.cpp
+ * Output: \verbinclude Matrix_setConstant_int.out
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
+{
+ resize(size);
+ return setConstant(val);
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to the given \a value.
+ *
+ * \param nbRows the new number of rows
+ * \param nbCols the new number of columns
+ * \param val the value to which all coefficients are set
+ *
+ * Example: \include Matrix_setConstant_int_int.cpp
+ * Output: \verbinclude Matrix_setConstant_int_int.out
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index nbRows, Index nbCols, const Scalar& val)
+{
+ resize(nbRows, nbCols);
+ return setConstant(val);
+}
+
+/**
+ * \brief Sets a linearly space vector.
+ *
+ * The function generates 'size' equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_setLinSpaced.cpp
+ * Output: \verbinclude DenseBase_setLinSpaced.out
+ *
+ * \sa CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,false>(low,high,newSize));
+}
+
+/**
+ * \brief Sets a linearly space vector.
+ *
+ * The function fill *this with equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * \sa setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return setLinSpaced(size(), low, high);
+}
+
+// zero:
+
+/** \returns an expression of a zero matrix.
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_zero_int_int.cpp
+ * Output: \verbinclude MatrixBase_zero_int_int.out
+ *
+ * \sa Zero(), Zero(Index)
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index nbRows, Index nbCols)
+{
+ return Constant(nbRows, nbCols, Scalar(0));
+}
+
+/** \returns an expression of a zero vector.
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_zero_int.cpp
+ * Output: \verbinclude MatrixBase_zero_int.out
+ *
+ * \sa Zero(), Zero(Index,Index)
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index size)
+{
+ return Constant(size, Scalar(0));
+}
+
+/** \returns an expression of a fixed-size zero matrix or vector.
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_zero.cpp
+ * Output: \verbinclude MatrixBase_zero.out
+ *
+ * \sa Zero(Index), Zero(Index,Index)
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero()
+{
+ return Constant(Scalar(0));
+}
+
+/** \returns true if *this is approximately equal to the zero matrix,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isZero.cpp
+ * Output: \verbinclude MatrixBase_isZero.out
+ *
+ * \sa class CwiseNullaryOp, Zero()
+ */
+template<typename Derived>
+bool DenseBase<Derived>::isZero(const RealScalar& prec) const
+{
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<Scalar>(1), prec))
+ return false;
+ return true;
+}
+
+/** Sets all coefficients in this expression to zero.
+ *
+ * Example: \include MatrixBase_setZero.cpp
+ * Output: \verbinclude MatrixBase_setZero.out
+ *
+ * \sa class CwiseNullaryOp, Zero()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
+{
+ return setConstant(Scalar(0));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setZero_int.cpp
+ * Output: \verbinclude Matrix_setZero_int.out
+ *
+ * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index newSize)
+{
+ resize(newSize);
+ return setConstant(Scalar(0));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to zero.
+ *
+ * \param nbRows the new number of rows
+ * \param nbCols the new number of columns
+ *
+ * Example: \include Matrix_setZero_int_int.cpp
+ * Output: \verbinclude Matrix_setZero_int_int.out
+ *
+ * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index nbRows, Index nbCols)
+{
+ resize(nbRows, nbCols);
+ return setConstant(Scalar(0));
+}
+
+// ones:
+
+/** \returns an expression of a matrix where all coefficients equal one.
+ *
+ * The parameters \a nbRows and \a nbCols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_ones_int_int.cpp
+ * Output: \verbinclude MatrixBase_ones_int_int.out
+ *
+ * \sa Ones(), Ones(Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index nbRows, Index nbCols)
+{
+ return Constant(nbRows, nbCols, Scalar(1));
+}
+
+/** \returns an expression of a vector where all coefficients equal one.
+ *
+ * The parameter \a newSize is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Ones() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_ones_int.cpp
+ * Output: \verbinclude MatrixBase_ones_int.out
+ *
+ * \sa Ones(), Ones(Index,Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index newSize)
+{
+ return Constant(newSize, Scalar(1));
+}
+
+/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_ones.cpp
+ * Output: \verbinclude MatrixBase_ones.out
+ *
+ * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones()
+{
+ return Constant(Scalar(1));
+}
+
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+ * are equal to 1, within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isOnes.cpp
+ * Output: \verbinclude MatrixBase_isOnes.out
+ *
+ * \sa class CwiseNullaryOp, Ones()
+ */
+template<typename Derived>
+bool DenseBase<Derived>::isOnes
+(const RealScalar& prec) const
+{
+ return isApproxToConstant(Scalar(1), prec);
+}
+
+/** Sets all coefficients in this expression to one.
+ *
+ * Example: \include MatrixBase_setOnes.cpp
+ * Output: \verbinclude MatrixBase_setOnes.out
+ *
+ * \sa class CwiseNullaryOp, Ones()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
+{
+ return setConstant(Scalar(1));
+}
+
+/** Resizes to the given \a newSize, and sets all coefficients in this expression to one.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setOnes_int.cpp
+ * Output: \verbinclude Matrix_setOnes_int.out
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index newSize)
+{
+ resize(newSize);
+ return setConstant(Scalar(1));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to one.
+ *
+ * \param nbRows the new number of rows
+ * \param nbCols the new number of columns
+ *
+ * Example: \include Matrix_setOnes_int_int.cpp
+ * Output: \verbinclude Matrix_setOnes_int_int.out
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index nbRows, Index nbCols)
+{
+ resize(nbRows, nbCols);
+ return setConstant(Scalar(1));
+}
+
+// Identity:
+
+/** \returns an expression of the identity matrix (not necessarily square).
+ *
+ * The parameters \a nbRows and \a nbCols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_identity_int_int.cpp
+ * Output: \verbinclude MatrixBase_identity_int_int.out
+ *
+ * \sa Identity(), setIdentity(), isIdentity()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity(Index nbRows, Index nbCols)
+{
+ return DenseBase<Derived>::NullaryExpr(nbRows, nbCols, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns an expression of the identity matrix (not necessarily square).
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variant taking size arguments.
+ *
+ * Example: \include MatrixBase_identity.cpp
+ * Output: \verbinclude MatrixBase_identity.out
+ *
+ * \sa Identity(Index,Index), setIdentity(), isIdentity()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity()
+{
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns true if *this is approximately equal to the identity matrix
+ * (not necessarily square),
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isIdentity.cpp
+ * Output: \verbinclude MatrixBase_isIdentity.out
+ *
+ * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isIdentity
+(const RealScalar& prec) const
+{
+ for(Index j = 0; j < cols(); ++j)
+ {
+ for(Index i = 0; i < rows(); ++i)
+ {
+ if(i == j)
+ {
+ if(!internal::isApprox(this->coeff(i, j), static_cast<Scalar>(1), prec))
+ return false;
+ }
+ else
+ {
+ if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<RealScalar>(1), prec))
+ return false;
+ }
+ }
+ }
+ return true;
+}
+
+namespace internal {
+
+template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
+struct setIdentity_impl
+{
+ static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+ {
+ return m = Derived::Identity(m.rows(), m.cols());
+ }
+};
+
+template<typename Derived>
+struct setIdentity_impl<Derived, true>
+{
+ typedef typename Derived::Index Index;
+ static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+ {
+ m.setZero();
+ const Index size = (std::min)(m.rows(), m.cols());
+ for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
+ return m;
+ }
+};
+
+} // end namespace internal
+
+/** Writes the identity expression (not necessarily square) into *this.
+ *
+ * Example: \include MatrixBase_setIdentity.cpp
+ * Output: \verbinclude MatrixBase_setIdentity.out
+ *
+ * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
+{
+ return internal::setIdentity_impl<Derived>::run(derived());
+}
+
+/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
+ *
+ * \param nbRows the new number of rows
+ * \param nbCols the new number of columns
+ *
+ * Example: \include Matrix_setIdentity_int_int.cpp
+ * Output: \verbinclude Matrix_setIdentity_int_int.out
+ *
+ * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index nbRows, Index nbCols)
+{
+ derived().resize(nbRows, nbCols);
+ return setIdentity();
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i);
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+ *
+ * \only_for_vectors
+ *
+ * This variant is for fixed-size vector only.
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return BasisReturnType(SquareMatrixType::Identity(),i);
+}
+
+/** \returns an expression of the X axis unit vector (1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
+{ return Derived::Unit(0); }
+
+/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
+{ return Derived::Unit(1); }
+
+/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
+{ return Derived::Unit(2); }
+
+/** \returns an expression of the W axis unit vector (0,0,0,1)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
+{ return Derived::Unit(3); }
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_NULLARY_OP_H
diff --git a/Eigen/src/Core/CwiseUnaryOp.h b/Eigen/src/Core/CwiseUnaryOp.h
new file mode 100644
index 0000000..f2de749
--- /dev/null
+++ b/Eigen/src/Core/CwiseUnaryOp.h
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_UNARY_OP_H
+#define EIGEN_CWISE_UNARY_OP_H
+
+namespace Eigen {
+
+/** \class CwiseUnaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression where a coefficient-wise unary operator is applied to an expression
+ *
+ * \param UnaryOp template functor implementing the operator
+ * \param XprType the type of the expression to which we are applying the unary operator
+ *
+ * This class represents an expression where a unary operator is applied to an expression.
+ * It is the return type of all operations taking exactly 1 input expression, regardless of the
+ * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
+ * is considered unary, because only the right-hand side is an expression, and its
+ * return type is a specialization of CwiseUnaryOp.
+ *
+ * Most of the time, this is the only way that it is used, so you typically don't have to name
+ * CwiseUnaryOp types explicitly.
+ *
+ * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
+ */
+
+namespace internal {
+template<typename UnaryOp, typename XprType>
+struct traits<CwiseUnaryOp<UnaryOp, XprType> >
+ : traits<XprType>
+{
+ typedef typename result_of<
+ UnaryOp(typename XprType::Scalar)
+ >::type Scalar;
+ typedef typename XprType::Nested XprTypeNested;
+ typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
+ enum {
+ Flags = _XprTypeNested::Flags & (
+ HereditaryBits | LinearAccessBit | AlignedBit
+ | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
+ CoeffReadCost = _XprTypeNested::CoeffReadCost + functor_traits<UnaryOp>::Cost
+ };
+};
+}
+
+template<typename UnaryOp, typename XprType, typename StorageKind>
+class CwiseUnaryOpImpl;
+
+template<typename UnaryOp, typename XprType>
+class CwiseUnaryOp : internal::no_assignment_operator,
+ public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>
+{
+ public:
+
+ typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
+
+ inline CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+ : m_xpr(xpr), m_functor(func) {}
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_xpr.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_xpr.cols(); }
+
+ /** \returns the functor representing the unary operation */
+ const UnaryOp& functor() const { return m_functor; }
+
+ /** \returns the nested expression */
+ const typename internal::remove_all<typename XprType::Nested>::type&
+ nestedExpression() const { return m_xpr; }
+
+ /** \returns the nested expression */
+ typename internal::remove_all<typename XprType::Nested>::type&
+ nestedExpression() { return m_xpr.const_cast_derived(); }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const UnaryOp m_functor;
+};
+
+// This is the generic implementation for dense storage.
+// It can be used for any expression types implementing the dense concept.
+template<typename UnaryOp, typename XprType>
+class CwiseUnaryOpImpl<UnaryOp,XprType,Dense>
+ : public internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
+{
+ public:
+
+ typedef CwiseUnaryOp<UnaryOp, XprType> Derived;
+ typedef typename internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index rowId, Index colId) const
+ {
+ return derived().functor()(derived().nestedExpression().coeff(rowId, colId));
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const
+ {
+ return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(rowId, colId));
+ }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+ {
+ return derived().functor()(derived().nestedExpression().coeff(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+ {
+ return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(index));
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_UNARY_OP_H
diff --git a/Eigen/src/Core/CwiseUnaryView.h b/Eigen/src/Core/CwiseUnaryView.h
new file mode 100644
index 0000000..b2638d3
--- /dev/null
+++ b/Eigen/src/Core/CwiseUnaryView.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_UNARY_VIEW_H
+#define EIGEN_CWISE_UNARY_VIEW_H
+
+namespace Eigen {
+
+/** \class CwiseUnaryView
+ * \ingroup Core_Module
+ *
+ * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
+ *
+ * \param ViewOp template functor implementing the view
+ * \param MatrixType the type of the matrix we are applying the unary operator
+ *
+ * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
+ * It is the return type of real() and imag(), and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
+ */
+
+namespace internal {
+template<typename ViewOp, typename MatrixType>
+struct traits<CwiseUnaryView<ViewOp, MatrixType> >
+ : traits<MatrixType>
+{
+ typedef typename result_of<
+ ViewOp(typename traits<MatrixType>::Scalar)
+ >::type Scalar;
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ Flags = (traits<_MatrixTypeNested>::Flags & (HereditaryBits | LvalueBit | LinearAccessBit | DirectAccessBit)),
+ CoeffReadCost = traits<_MatrixTypeNested>::CoeffReadCost + functor_traits<ViewOp>::Cost,
+ MatrixTypeInnerStride = inner_stride_at_compile_time<MatrixType>::ret,
+ // need to cast the sizeof's from size_t to int explicitly, otherwise:
+ // "error: no integral type can represent all of the enumerator values
+ InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic
+ ? int(Dynamic)
+ : int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),
+ OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret == Dynamic
+ ? int(Dynamic)
+ : outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar))
+ };
+};
+}
+
+template<typename ViewOp, typename MatrixType, typename StorageKind>
+class CwiseUnaryViewImpl;
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
+{
+ public:
+
+ typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
+
+ inline CwiseUnaryView(const MatrixType& mat, const ViewOp& func = ViewOp())
+ : m_matrix(mat), m_functor(func) {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
+
+ /** \returns the functor representing unary operation */
+ const ViewOp& functor() const { return m_functor; }
+
+ /** \returns the nested expression */
+ const typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() const { return m_matrix; }
+
+ /** \returns the nested expression */
+ typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() { return m_matrix.const_cast_derived(); }
+
+ protected:
+ // FIXME changed from MatrixType::Nested because of a weird compilation error with sun CC
+ typename internal::nested<MatrixType>::type m_matrix;
+ ViewOp m_functor;
+};
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
+ : public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type
+{
+ public:
+
+ typedef CwiseUnaryView<ViewOp, MatrixType> Derived;
+ typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
+
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
+
+ inline Scalar* data() { return &coeffRef(0); }
+ inline const Scalar* data() const { return &coeff(0); }
+
+ inline Index innerStride() const
+ {
+ return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
+ }
+
+ inline Index outerStride() const
+ {
+ return derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
+ }
+
+ EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
+ {
+ return derived().functor()(derived().nestedExpression().coeff(row, col));
+ }
+
+ EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return derived().functor()(derived().nestedExpression().coeff(index));
+ }
+
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+ {
+ return derived().functor()(const_cast_derived().nestedExpression().coeffRef(row, col));
+ }
+
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ return derived().functor()(const_cast_derived().nestedExpression().coeffRef(index));
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_UNARY_VIEW_H
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
new file mode 100644
index 0000000..32f60d8
--- /dev/null
+++ b/Eigen/src/Core/DenseBase.h
@@ -0,0 +1,525 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSEBASE_H
+#define EIGEN_DENSEBASE_H
+
+namespace Eigen {
+
+namespace internal {
+
+// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
+// This dummy function simply aims at checking that at compile time.
+static inline void check_DenseIndex_is_signed() {
+ EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);
+}
+
+} // end namespace internal
+
+/** \class DenseBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all dense matrices, vectors, and arrays
+ *
+ * This class is the base that is inherited by all dense objects (matrix, vector, arrays,
+ * and related expression types). The common Eigen API for dense objects is contained in this class.
+ *
+ * \tparam Derived is the derived type, e.g., a matrix type or an expression.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived> class DenseBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ : public internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+ typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>
+#else
+ : public DenseCoeffsBase<Derived>
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+{
+ public:
+ using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+ typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
+
+ class InnerIterator;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+
+ /** \brief The type of indices
+ * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+ * \sa \ref TopicPreprocessorDirectives.
+ */
+ typedef typename internal::traits<Derived>::Index Index;
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ typedef DenseCoeffsBase<Derived> Base;
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::rowIndexByOuterInner;
+ using Base::colIndexByOuterInner;
+ using Base::coeff;
+ using Base::coeffByOuterInner;
+ using Base::packet;
+ using Base::packetByOuterInner;
+ using Base::writePacket;
+ using Base::writePacketByOuterInner;
+ using Base::coeffRef;
+ using Base::coeffRefByOuterInner;
+ using Base::copyCoeff;
+ using Base::copyCoeffByOuterInner;
+ using Base::copyPacket;
+ using Base::copyPacketByOuterInner;
+ using Base::operator();
+ using Base::operator[];
+ using Base::x;
+ using Base::y;
+ using Base::z;
+ using Base::w;
+ using Base::stride;
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ enum {
+
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ /**< The number of rows at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ /**< The number of columns at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+ SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ /**< This value is equal to the maximum possible number of rows that this expression
+ * might have. If this expression might have an arbitrarily high number of rows,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
+ */
+
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+ /**< This value is equal to the maximum possible number of columns that this expression
+ * might have. If this expression might have an arbitrarily high number of columns,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
+ */
+
+ MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime>::ret),
+ /**< This value is equal to the maximum possible number of coefficients that this expression
+ * might have. If this expression might have an arbitrarily high number of coefficients,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
+ */
+
+ IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
+ || internal::traits<Derived>::MaxColsAtCompileTime == 1,
+ /**< This is set to true if either the number of rows or the number of
+ * columns is known at compile-time to be equal to 1. Indeed, in that case,
+ * we are dealing with a column-vector (if there is only one column) or with
+ * a row-vector (if there is only one row). */
+
+ Flags = internal::traits<Derived>::Flags,
+ /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+ * constructed from this one. See the \ref flags "list of flags".
+ */
+
+ IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
+
+ InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
+ : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ /**< This is a rough measure of how expensive it is to read one coefficient from
+ * this expression.
+ */
+
+ InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
+ OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
+ };
+
+ enum { ThisConstantIsPrivateInPlainObjectBase };
+
+ /** \returns the number of nonzero coefficients which is in practice the number
+ * of stored coefficients. */
+ inline Index nonZeros() const { return size(); }
+ /** \returns true if either the number of rows or the number of columns is equal to 1.
+ * In other words, this function returns
+ * \code rows()==1 || cols()==1 \endcode
+ * \sa rows(), cols(), IsVectorAtCompileTime. */
+
+ /** \returns the outer size.
+ *
+ * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
+ * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
+ * column-major matrix, and the number of rows for a row-major matrix. */
+ Index outerSize() const
+ {
+ return IsVectorAtCompileTime ? 1
+ : int(IsRowMajor) ? this->rows() : this->cols();
+ }
+
+ /** \returns the inner size.
+ *
+ * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
+ * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
+ * column-major matrix, and the number of columns for a row-major matrix. */
+ Index innerSize() const
+ {
+ return IsVectorAtCompileTime ? this->size()
+ : int(IsRowMajor) ? this->cols() : this->rows();
+ }
+
+ /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+ * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+ * nothing else.
+ */
+ void resize(Index newSize)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(newSize);
+ eigen_assert(newSize == this->size()
+ && "DenseBase::resize() does not actually allow to resize.");
+ }
+ /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+ * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+ * nothing else.
+ */
+ void resize(Index nbRows, Index nbCols)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(nbRows);
+ EIGEN_ONLY_USED_FOR_DEBUG(nbCols);
+ eigen_assert(nbRows == this->rows() && nbCols == this->cols()
+ && "DenseBase::resize() does not actually allow to resize.");
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+ /** \internal Represents a vector with linearly spaced coefficients that allows sequential access only. */
+ typedef CwiseNullaryOp<internal::linspaced_op<Scalar,false>,Derived> SequentialLinSpacedReturnType;
+ /** \internal Represents a vector with linearly spaced coefficients that allows random access. */
+ typedef CwiseNullaryOp<internal::linspaced_op<Scalar,true>,Derived> RandomAccessLinSpacedReturnType;
+ /** \internal the return type of MatrixBase::eigenvalues() */
+ typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ /** Copies \a other into *this. \returns a reference to *this. */
+ template<typename OtherDerived>
+ Derived& operator=(const DenseBase<OtherDerived>& other);
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ Derived& operator=(const DenseBase& other);
+
+ template<typename OtherDerived>
+ Derived& operator=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ Derived& operator+=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ Derived& operator-=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ Derived& operator=(const ReturnByValue<OtherDerived>& func);
+
+ /** \internal Copies \a other into *this without evaluating other. \returns a reference to *this. */
+ template<typename OtherDerived>
+ Derived& lazyAssign(const DenseBase<OtherDerived>& other);
+
+ /** \internal Evaluates \a other into *this. \returns a reference to *this. */
+ template<typename OtherDerived>
+ Derived& lazyAssign(const ReturnByValue<OtherDerived>& other);
+
+ CommaInitializer<Derived> operator<< (const Scalar& s);
+
+ template<unsigned int Added,unsigned int Removed>
+ const Flagged<Derived, Added, Removed> flagged() const;
+
+ template<typename OtherDerived>
+ CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
+
+ Eigen::Transpose<Derived> transpose();
+ typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;
+ ConstTransposeReturnType transpose() const;
+ void transposeInPlace();
+#ifndef EIGEN_NO_DEBUG
+ protected:
+ template<typename OtherDerived>
+ void checkTransposeAliasing(const OtherDerived& other) const;
+ public:
+#endif
+
+
+ static const ConstantReturnType
+ Constant(Index rows, Index cols, const Scalar& value);
+ static const ConstantReturnType
+ Constant(Index size, const Scalar& value);
+ static const ConstantReturnType
+ Constant(const Scalar& value);
+
+ static const SequentialLinSpacedReturnType
+ LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
+ static const RandomAccessLinSpacedReturnType
+ LinSpaced(Index size, const Scalar& low, const Scalar& high);
+ static const SequentialLinSpacedReturnType
+ LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
+ static const RandomAccessLinSpacedReturnType
+ LinSpaced(const Scalar& low, const Scalar& high);
+
+ template<typename CustomNullaryOp>
+ static const CwiseNullaryOp<CustomNullaryOp, Derived>
+ NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
+ template<typename CustomNullaryOp>
+ static const CwiseNullaryOp<CustomNullaryOp, Derived>
+ NullaryExpr(Index size, const CustomNullaryOp& func);
+ template<typename CustomNullaryOp>
+ static const CwiseNullaryOp<CustomNullaryOp, Derived>
+ NullaryExpr(const CustomNullaryOp& func);
+
+ static const ConstantReturnType Zero(Index rows, Index cols);
+ static const ConstantReturnType Zero(Index size);
+ static const ConstantReturnType Zero();
+ static const ConstantReturnType Ones(Index rows, Index cols);
+ static const ConstantReturnType Ones(Index size);
+ static const ConstantReturnType Ones();
+
+ void fill(const Scalar& value);
+ Derived& setConstant(const Scalar& value);
+ Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
+ Derived& setLinSpaced(const Scalar& low, const Scalar& high);
+ Derived& setZero();
+ Derived& setOnes();
+ Derived& setRandom();
+
+ template<typename OtherDerived>
+ bool isApprox(const DenseBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isMuchSmallerThan(const RealScalar& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ template<typename OtherDerived>
+ bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ inline bool hasNaN() const;
+ inline bool allFinite() const;
+
+ inline Derived& operator*=(const Scalar& other);
+ inline Derived& operator/=(const Scalar& other);
+
+ typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;
+ /** \returns the matrix or vector obtained by evaluating this expression.
+ *
+ * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+ * a const reference, in order to avoid a useless copy.
+ */
+ EIGEN_STRONG_INLINE EvalReturnType eval() const
+ {
+ // Even though MSVC does not honor strong inlining when the return type
+ // is a dynamic matrix, we desperately need strong inlining for fixed
+ // size types on MSVC.
+ return typename internal::eval<Derived>::type(derived());
+ }
+
+ /** swaps *this with the expression \a other.
+ *
+ */
+ template<typename OtherDerived>
+ void swap(const DenseBase<OtherDerived>& other,
+ int = OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
+ {
+ SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
+ }
+
+ /** swaps *this with the matrix or array \a other.
+ *
+ */
+ template<typename OtherDerived>
+ void swap(PlainObjectBase<OtherDerived>& other)
+ {
+ SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
+ }
+
+
+ inline const NestByValue<Derived> nestByValue() const;
+ inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
+ inline ForceAlignedAccess<Derived> forceAlignedAccess();
+ template<bool Enable> inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;
+ template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
+
+ Scalar sum() const;
+ Scalar mean() const;
+ Scalar trace() const;
+
+ Scalar prod() const;
+
+ typename internal::traits<Derived>::Scalar minCoeff() const;
+ typename internal::traits<Derived>::Scalar maxCoeff() const;
+
+ template<typename IndexType>
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
+ template<typename IndexType>
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
+ template<typename IndexType>
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
+ template<typename IndexType>
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
+
+ template<typename BinaryOp>
+ typename internal::result_of<BinaryOp(typename internal::traits<Derived>::Scalar)>::type
+ redux(const BinaryOp& func) const;
+
+ template<typename Visitor>
+ void visit(Visitor& func) const;
+
+ inline const WithFormat<Derived> format(const IOFormat& fmt) const;
+
+ /** \returns the unique coefficient of a 1x1 expression */
+ CoeffReturnType value() const
+ {
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ return derived().coeff(0,0);
+ }
+
+ bool all(void) const;
+ bool any(void) const;
+ Index count() const;
+
+ typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
+ typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
+ typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
+ typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
+
+ ConstRowwiseReturnType rowwise() const;
+ RowwiseReturnType rowwise();
+ ConstColwiseReturnType colwise() const;
+ ColwiseReturnType colwise();
+
+ static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index rows, Index cols);
+ static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index size);
+ static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random();
+
+ template<typename ThenDerived,typename ElseDerived>
+ const Select<Derived,ThenDerived,ElseDerived>
+ select(const DenseBase<ThenDerived>& thenMatrix,
+ const DenseBase<ElseDerived>& elseMatrix) const;
+
+ template<typename ThenDerived>
+ inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
+ select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;
+
+ template<typename ElseDerived>
+ inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
+ select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
+
+ template<int p> RealScalar lpNorm() const;
+
+ template<int RowFactor, int ColFactor>
+ inline const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+
+ typedef Replicate<Derived,Dynamic,Dynamic> ReplicateReturnType;
+ inline const ReplicateReturnType replicate(Index rowFacor,Index colFactor) const;
+
+ typedef Reverse<Derived, BothDirections> ReverseReturnType;
+ typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
+ ReverseReturnType reverse();
+ ConstReverseReturnType reverse() const;
+ void reverseInPlace();
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
+# include "../plugins/BlockMethods.h"
+# ifdef EIGEN_DENSEBASE_PLUGIN
+# include EIGEN_DENSEBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+#ifdef EIGEN2_SUPPORT
+
+ Block<Derived> corner(CornerType type, Index cRows, Index cCols);
+ const Block<Derived> corner(CornerType type, Index cRows, Index cCols) const;
+ template<int CRows, int CCols>
+ Block<Derived, CRows, CCols> corner(CornerType type);
+ template<int CRows, int CCols>
+ const Block<Derived, CRows, CCols> corner(CornerType type) const;
+
+#endif // EIGEN2_SUPPORT
+
+
+ // disable the use of evalTo for dense objects with a nice compilation error
+ template<typename Dest> inline void evalTo(Dest& ) const
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
+ }
+
+ protected:
+ /** Default constructor. Do nothing. */
+ DenseBase()
+ {
+ /* Just checks for self-consistency of the flags.
+ * Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down
+ */
+#ifdef EIGEN_INTERNAL_DEBUGGING
+ EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
+ && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
+ INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
+#endif
+ }
+
+ private:
+ explicit DenseBase(int);
+ DenseBase(int,int);
+ template<typename OtherDerived> explicit DenseBase(const DenseBase<OtherDerived>&);
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSEBASE_H
diff --git a/Eigen/src/Core/DenseCoeffsBase.h b/Eigen/src/Core/DenseCoeffsBase.h
new file mode 100644
index 0000000..3c890f2
--- /dev/null
+++ b/Eigen/src/Core/DenseCoeffsBase.h
@@ -0,0 +1,754 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSECOEFFSBASE_H
+#define EIGEN_DENSECOEFFSBASE_H
+
+namespace Eigen {
+
+namespace internal {
+template<typename T> struct add_const_on_value_type_if_arithmetic
+{
+ typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
+};
+}
+
+/** \brief Base class providing read-only coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ * \tparam #ReadOnlyAccessors Constant indicating read-only access
+ *
+ * This class defines the \c operator() \c const function and friends, which can be used to read specific
+ * entries of a matrix or array.
+ *
+ * \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
+ * \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
+{
+ public:
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+
+ // Explanation for this CoeffReturnType typedef.
+ // - This is the return type of the coeff() method.
+ // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
+ // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
+ // - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
+ // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
+ // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
+ typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
+ const Scalar&,
+ typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type
+ >::type CoeffReturnType;
+
+ typedef typename internal::add_const_on_value_type_if_arithmetic<
+ typename internal::packet_traits<Scalar>::type
+ >::type PacketReturnType;
+
+ typedef EigenBase<Derived> Base;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
+ {
+ return int(Derived::RowsAtCompileTime) == 1 ? 0
+ : int(Derived::ColsAtCompileTime) == 1 ? inner
+ : int(Derived::Flags)&RowMajorBit ? outer
+ : inner;
+ }
+
+ EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
+ {
+ return int(Derived::ColsAtCompileTime) == 1 ? 0
+ : int(Derived::RowsAtCompileTime) == 1 ? inner
+ : int(Derived::Flags)&RowMajorBit ? inner
+ : outer;
+ }
+
+ /** Short version: don't use this function, use
+ * \link operator()(Index,Index) const \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator()(Index,Index) const \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator()(Index,Index) const \endlink.
+ *
+ * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
+ */
+ EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return derived().coeff(row, col);
+ }
+
+ EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
+ {
+ return coeff(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \returns the coefficient at given the given row and column.
+ *
+ * \sa operator()(Index,Index), operator[](Index)
+ */
+ EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
+ {
+ eigen_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return derived().coeff(row, col);
+ }
+
+ /** Short version: don't use this function, use
+ * \link operator[](Index) const \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator[](Index) const \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameter \a index is in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator[](Index) const \endlink.
+ *
+ * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
+ */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ coeff(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return derived().coeff(index);
+ }
+
+
+ /** \returns the coefficient at given index.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+ * z() const, w() const
+ */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ operator[](Index index) const
+ {
+ #ifndef EIGEN2_SUPPORT
+ EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+ THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+ #endif
+ eigen_assert(index >= 0 && index < size());
+ return derived().coeff(index);
+ }
+
+ /** \returns the coefficient at given index.
+ *
+ * This is synonymous to operator[](Index) const.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+ * z() const, w() const
+ */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ operator()(Index index) const
+ {
+ eigen_assert(index >= 0 && index < size());
+ return derived().coeff(index);
+ }
+
+ /** equivalent to operator[](0). */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ x() const { return (*this)[0]; }
+
+ /** equivalent to operator[](1). */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ y() const { return (*this)[1]; }
+
+ /** equivalent to operator[](2). */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ z() const { return (*this)[2]; }
+
+ /** equivalent to operator[](3). */
+
+ EIGEN_STRONG_INLINE CoeffReturnType
+ w() const { return (*this)[3]; }
+
+ /** \internal
+ * \returns the packet of coefficients starting at the given row and column. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return derived().template packet<LoadMode>(row,col);
+ }
+
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
+ {
+ return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \internal
+ * \returns the packet of coefficients starting at the given index. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit and the LinearAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return derived().template packet<LoadMode>(index);
+ }
+
+ protected:
+ // explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
+ // But some methods are only available in the DirectAccess case.
+ // So we add dummy methods here with these names, so that "using... " doesn't fail.
+ // It's not private so that the child class DenseBase can access them, and it's not public
+ // either since it's an implementation detail, so has to be protected.
+ void coeffRef();
+ void coeffRefByOuterInner();
+ void writePacket();
+ void writePacketByOuterInner();
+ void copyCoeff();
+ void copyCoeffByOuterInner();
+ void copyPacket();
+ void copyPacketByOuterInner();
+ void stride();
+ void innerStride();
+ void outerStride();
+ void rowStride();
+ void colStride();
+};
+
+/** \brief Base class providing read/write coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ * \tparam #WriteAccessors Constant indicating read/write access
+ *
+ * This class defines the non-const \c operator() function and friends, which can be used to write specific
+ * entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
+ * defines the const variant for reading specific entries.
+ *
+ * \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::coeff;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+ using Base::rowIndexByOuterInner;
+ using Base::colIndexByOuterInner;
+ using Base::operator[];
+ using Base::operator();
+ using Base::x;
+ using Base::y;
+ using Base::z;
+ using Base::w;
+
+ /** Short version: don't use this function, use
+ * \link operator()(Index,Index) \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator()(Index,Index) \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator()(Index,Index) \endlink.
+ *
+ * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
+ */
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return derived().coeffRef(row, col);
+ }
+
+ EIGEN_STRONG_INLINE Scalar&
+ coeffRefByOuterInner(Index outer, Index inner)
+ {
+ return coeffRef(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \returns a reference to the coefficient at given the given row and column.
+ *
+ * \sa operator[](Index)
+ */
+
+ EIGEN_STRONG_INLINE Scalar&
+ operator()(Index row, Index col)
+ {
+ eigen_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return derived().coeffRef(row, col);
+ }
+
+
+ /** Short version: don't use this function, use
+ * \link operator[](Index) \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator[](Index) \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator[](Index) \endlink.
+ *
+ * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
+ */
+
+ EIGEN_STRONG_INLINE Scalar&
+ coeffRef(Index index)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return derived().coeffRef(index);
+ }
+
+ /** \returns a reference to the coefficient at given index.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+ */
+
+ EIGEN_STRONG_INLINE Scalar&
+ operator[](Index index)
+ {
+ #ifndef EIGEN2_SUPPORT
+ EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+ THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+ #endif
+ eigen_assert(index >= 0 && index < size());
+ return derived().coeffRef(index);
+ }
+
+ /** \returns a reference to the coefficient at given index.
+ *
+ * This is synonymous to operator[](Index).
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+ */
+
+ EIGEN_STRONG_INLINE Scalar&
+ operator()(Index index)
+ {
+ eigen_assert(index >= 0 && index < size());
+ return derived().coeffRef(index);
+ }
+
+ /** equivalent to operator[](0). */
+
+ EIGEN_STRONG_INLINE Scalar&
+ x() { return (*this)[0]; }
+
+ /** equivalent to operator[](1). */
+
+ EIGEN_STRONG_INLINE Scalar&
+ y() { return (*this)[1]; }
+
+ /** equivalent to operator[](2). */
+
+ EIGEN_STRONG_INLINE Scalar&
+ z() { return (*this)[2]; }
+
+ /** equivalent to operator[](3). */
+
+ EIGEN_STRONG_INLINE Scalar&
+ w() { return (*this)[3]; }
+
+ /** \internal
+ * Stores the given packet of coefficients, at the given row and column of this expression. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket
+ (Index row, Index col, const typename internal::packet_traits<Scalar>::type& val)
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ derived().template writePacket<StoreMode>(row,col,val);
+ }
+
+
+ /** \internal */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacketByOuterInner
+ (Index outer, Index inner, const typename internal::packet_traits<Scalar>::type& val)
+ {
+ writePacket<StoreMode>(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner),
+ val);
+ }
+
+ /** \internal
+ * Stores the given packet of coefficients, at the given index in this expression. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit and the LinearAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket
+ (Index index, const typename internal::packet_traits<Scalar>::type& val)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ derived().template writePacket<StoreMode>(index,val);
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+ /** \internal Copies the coefficient at position (row,col) of other into *this.
+ *
+ * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+ * with usual assignments.
+ *
+ * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+ */
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ derived().coeffRef(row, col) = other.derived().coeff(row, col);
+ }
+
+ /** \internal Copies the coefficient at the given index of other into *this.
+ *
+ * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+ * with usual assignments.
+ *
+ * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+ */
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ derived().coeffRef(index) = other.derived().coeff(index);
+ }
+
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void copyCoeffByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
+ {
+ const Index row = rowIndexByOuterInner(outer,inner);
+ const Index col = colIndexByOuterInner(outer,inner);
+ // derived() is important here: copyCoeff() may be reimplemented in Derived!
+ derived().copyCoeff(row, col, other);
+ }
+
+ /** \internal Copies the packet at position (row,col) of other into *this.
+ *
+ * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+ * with usual assignments.
+ *
+ * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+ */
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ EIGEN_STRONG_INLINE void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ derived().template writePacket<StoreMode>(row, col,
+ other.derived().template packet<LoadMode>(row, col));
+ }
+
+ /** \internal Copies the packet at the given index of other into *this.
+ *
+ * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+ * with usual assignments.
+ *
+ * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+ */
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ EIGEN_STRONG_INLINE void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ derived().template writePacket<StoreMode>(index,
+ other.derived().template packet<LoadMode>(index));
+ }
+
+ /** \internal */
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ EIGEN_STRONG_INLINE void copyPacketByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
+ {
+ const Index row = rowIndexByOuterInner(outer,inner);
+ const Index col = colIndexByOuterInner(outer,inner);
+ // derived() is important here: copyCoeff() may be reimplemented in Derived!
+ derived().template copyPacket< OtherDerived, StoreMode, LoadMode>(row, col, other);
+ }
+#endif
+
+};
+
+/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ * \tparam #DirectAccessors Constant indicating direct access
+ *
+ * This class defines functions to work with strides which can be used to access entries directly. This class
+ * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
+ * \c operator() .
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+ *
+ * \sa outerStride(), rowStride(), colStride()
+ */
+ inline Index innerStride() const
+ {
+ return derived().innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+ * in a column-major matrix).
+ *
+ * \sa innerStride(), rowStride(), colStride()
+ */
+ inline Index outerStride() const
+ {
+ return derived().outerStride();
+ }
+
+ // FIXME shall we remove it ?
+ inline Index stride() const
+ {
+ return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive rows.
+ *
+ * \sa innerStride(), outerStride(), colStride()
+ */
+ inline Index rowStride() const
+ {
+ return Derived::IsRowMajor ? outerStride() : innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive columns.
+ *
+ * \sa innerStride(), outerStride(), rowStride()
+ */
+ inline Index colStride() const
+ {
+ return Derived::IsRowMajor ? innerStride() : outerStride();
+ }
+};
+
+/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ * \tparam #DirectWriteAccessors Constant indicating direct access
+ *
+ * This class defines functions to work with strides which can be used to access entries directly. This class
+ * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
+ * \c operator().
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectWriteAccessors>
+ : public DenseCoeffsBase<Derived, WriteAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+ *
+ * \sa outerStride(), rowStride(), colStride()
+ */
+ inline Index innerStride() const
+ {
+ return derived().innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+ * in a column-major matrix).
+ *
+ * \sa innerStride(), rowStride(), colStride()
+ */
+ inline Index outerStride() const
+ {
+ return derived().outerStride();
+ }
+
+ // FIXME shall we remove it ?
+ inline Index stride() const
+ {
+ return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive rows.
+ *
+ * \sa innerStride(), outerStride(), colStride()
+ */
+ inline Index rowStride() const
+ {
+ return Derived::IsRowMajor ? outerStride() : innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive columns.
+ *
+ * \sa innerStride(), outerStride(), rowStride()
+ */
+ inline Index colStride() const
+ {
+ return Derived::IsRowMajor ? innerStride() : outerStride();
+ }
+};
+
+namespace internal {
+
+template<typename Derived, bool JustReturnZero>
+struct first_aligned_impl
+{
+ static inline typename Derived::Index run(const Derived&)
+ { return 0; }
+};
+
+template<typename Derived>
+struct first_aligned_impl<Derived, false>
+{
+ static inline typename Derived::Index run(const Derived& m)
+ {
+ return internal::first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
+ }
+};
+
+/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
+ *
+ * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
+ * documentation.
+ */
+template<typename Derived>
+static inline typename Derived::Index first_aligned(const Derived& m)
+{
+ return first_aligned_impl
+ <Derived, (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
+ ::run(m);
+}
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct inner_stride_at_compile_time
+{
+ enum { ret = traits<Derived>::InnerStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct inner_stride_at_compile_time<Derived, false>
+{
+ enum { ret = 0 };
+};
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct outer_stride_at_compile_time
+{
+ enum { ret = traits<Derived>::OuterStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct outer_stride_at_compile_time<Derived, false>
+{
+ enum { ret = 0 };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSECOEFFSBASE_H
diff --git a/Eigen/src/Core/DenseStorage.h b/Eigen/src/Core/DenseStorage.h
new file mode 100644
index 0000000..a72738e
--- /dev/null
+++ b/Eigen/src/Core/DenseStorage.h
@@ -0,0 +1,339 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXSTORAGE_H
+#define EIGEN_MATRIXSTORAGE_H
+
+#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
+#else
+ #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+#endif
+
+namespace Eigen {
+
+namespace internal {
+
+struct constructor_without_unaligned_array_assert {};
+
+template<typename T, int Size> void check_static_allocation_size()
+{
+ // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit
+ #if EIGEN_STACK_ALLOCATION_LIMIT
+ EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+ #endif
+}
+
+/** \internal
+ * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
+ * to 16 bytes boundary if the total size is a multiple of 16 bytes.
+ */
+template <typename T, int Size, int MatrixOrArrayOptions,
+ int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0
+ : (((Size*sizeof(T))%16)==0) ? 16
+ : 0 >
+struct plain_array
+{
+ T array[Size];
+
+ plain_array()
+ {
+ check_static_allocation_size<T,Size>();
+ }
+
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)
+#elif EIGEN_GNUC_AT_LEAST(4,7)
+ // GCC 4.7 is too aggressive in its optimizations and remove the alignement test based on the fact the array is declared to be aligned.
+ // See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900
+ // Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined:
+ template<typename PtrType>
+ EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; }
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
+ eigen_assert((reinterpret_cast<size_t>(eigen_unaligned_array_assert_workaround_gcc47(array)) & sizemask) == 0 \
+ && "this assertion is explained here: " \
+ "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
+ " **** READ THIS WEB PAGE !!! ****");
+#else
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
+ eigen_assert((reinterpret_cast<size_t>(array) & sizemask) == 0 \
+ && "this assertion is explained here: " \
+ "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
+ " **** READ THIS WEB PAGE !!! ****");
+#endif
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 16>
+{
+ EIGEN_USER_ALIGN16 T array[Size];
+
+ plain_array()
+ {
+ EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(0xf);
+ check_static_allocation_size<T,Size>();
+ }
+
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+template <typename T, int MatrixOrArrayOptions, int Alignment>
+struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
+{
+ EIGEN_USER_ALIGN16 T array[1];
+ plain_array() {}
+ plain_array(constructor_without_unaligned_array_assert) {}
+};
+
+} // end namespace internal
+
+/** \internal
+ *
+ * \class DenseStorage
+ * \ingroup Core_Module
+ *
+ * \brief Stores the data of a matrix
+ *
+ * This class stores the data of fixed-size, dynamic-size or mixed matrices
+ * in a way as compact as possible.
+ *
+ * \sa Matrix
+ */
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage;
+
+// purely fixed-size matrix
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage
+{
+ internal::plain_array<T,Size,_Options> m_data;
+ public:
+ inline DenseStorage() {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()) {}
+ inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+ inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }
+ static inline DenseIndex rows(void) {return _Rows;}
+ static inline DenseIndex cols(void) {return _Cols;}
+ inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+ inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+ inline const T *data() const { return m_data.array; }
+ inline T *data() { return m_data.array; }
+};
+
+// null matrix
+template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
+{
+ public:
+ inline DenseStorage() {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert) {}
+ inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+ inline void swap(DenseStorage& ) {}
+ static inline DenseIndex rows(void) {return _Rows;}
+ static inline DenseIndex cols(void) {return _Cols;}
+ inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+ inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+ inline const T *data() const { return 0; }
+ inline T *data() { return 0; }
+};
+
+// more specializations for null matrices; these are necessary to resolve ambiguities
+template<typename T, int _Options> class DenseStorage<T, 0, Dynamic, Dynamic, _Options>
+: public DenseStorage<T, 0, 0, 0, _Options> { };
+
+template<typename T, int _Rows, int _Options> class DenseStorage<T, 0, _Rows, Dynamic, _Options>
+: public DenseStorage<T, 0, 0, 0, _Options> { };
+
+template<typename T, int _Cols, int _Options> class DenseStorage<T, 0, Dynamic, _Cols, _Options>
+: public DenseStorage<T, 0, 0, 0, _Options> { };
+
+// dynamic-size matrix with fixed-size storage
+template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic, Dynamic, _Options>
+{
+ internal::plain_array<T,Size,_Options> m_data;
+ DenseIndex m_rows;
+ DenseIndex m_cols;
+ public:
+ inline DenseStorage() : m_rows(0), m_cols(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
+ inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) : m_rows(nbRows), m_cols(nbCols) {}
+ inline void swap(DenseStorage& other)
+ { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+ inline DenseIndex rows() const {return m_rows;}
+ inline DenseIndex cols() const {return m_cols;}
+ inline void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
+ inline void resize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
+ inline const T *data() const { return m_data.array; }
+ inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed width
+template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Size, Dynamic, _Cols, _Options>
+{
+ internal::plain_array<T,Size,_Options> m_data;
+ DenseIndex m_rows;
+ public:
+ inline DenseStorage() : m_rows(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
+ inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex) : m_rows(nbRows) {}
+ inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+ inline DenseIndex rows(void) const {return m_rows;}
+ inline DenseIndex cols(void) const {return _Cols;}
+ inline void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+ inline void resize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+ inline const T *data() const { return m_data.array; }
+ inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed height
+template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Size, _Rows, Dynamic, _Options>
+{
+ internal::plain_array<T,Size,_Options> m_data;
+ DenseIndex m_cols;
+ public:
+ inline DenseStorage() : m_cols(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
+ inline DenseStorage(DenseIndex, DenseIndex, DenseIndex nbCols) : m_cols(nbCols) {}
+ inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+ inline DenseIndex rows(void) const {return _Rows;}
+ inline DenseIndex cols(void) const {return m_cols;}
+ inline void conservativeResize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+ inline void resize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+ inline const T *data() const { return m_data.array; }
+ inline T *data() { return m_data.array; }
+};
+
+// purely dynamic matrix.
+template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynamic, _Options>
+{
+ T *m_data;
+ DenseIndex m_rows;
+ DenseIndex m_cols;
+ public:
+ inline DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(0), m_rows(0), m_cols(0) {}
+ inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
+ : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows), m_cols(nbCols)
+ { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+ inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
+ inline void swap(DenseStorage& other)
+ { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+ inline DenseIndex rows(void) const {return m_rows;}
+ inline DenseIndex cols(void) const {return m_cols;}
+ inline void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);
+ m_rows = nbRows;
+ m_cols = nbCols;
+ }
+ void resize(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
+ {
+ if(size != m_rows*m_cols)
+ {
+ internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols);
+ if (size)
+ m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+ }
+ m_rows = nbRows;
+ m_cols = nbCols;
+ }
+ inline const T *data() const { return m_data; }
+ inline T *data() { return m_data; }
+};
+
+// matrix with dynamic width and fixed height (so that matrix has dynamic size).
+template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Rows, Dynamic, _Options>
+{
+ T *m_data;
+ DenseIndex m_cols;
+ public:
+ inline DenseStorage() : m_data(0), m_cols(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
+ inline DenseStorage(DenseIndex size, DenseIndex, DenseIndex nbCols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(nbCols)
+ { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+ inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
+ inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+ static inline DenseIndex rows(void) {return _Rows;}
+ inline DenseIndex cols(void) const {return m_cols;}
+ inline void conservativeResize(DenseIndex size, DenseIndex, DenseIndex nbCols)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);
+ m_cols = nbCols;
+ }
+ EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex, DenseIndex nbCols)
+ {
+ if(size != _Rows*m_cols)
+ {
+ internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols);
+ if (size)
+ m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+ }
+ m_cols = nbCols;
+ }
+ inline const T *data() const { return m_data; }
+ inline T *data() { return m_data; }
+};
+
+// matrix with dynamic height and fixed width (so that matrix has dynamic size).
+template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dynamic, _Cols, _Options>
+{
+ T *m_data;
+ DenseIndex m_rows;
+ public:
+ inline DenseStorage() : m_data(0), m_rows(0) {}
+ inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
+ inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows)
+ { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+ inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
+ inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+ inline DenseIndex rows(void) const {return m_rows;}
+ static inline DenseIndex cols(void) {return _Cols;}
+ inline void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);
+ m_rows = nbRows;
+ }
+ EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex nbRows, DenseIndex)
+ {
+ if(size != m_rows*_Cols)
+ {
+ internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows);
+ if (size)
+ m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+ }
+ m_rows = nbRows;
+ }
+ inline const T *data() const { return m_data; }
+ inline T *data() { return m_data; }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_H
diff --git a/Eigen/src/Core/Diagonal.h b/Eigen/src/Core/Diagonal.h
new file mode 100644
index 0000000..68cf6d4
--- /dev/null
+++ b/Eigen/src/Core/Diagonal.h
@@ -0,0 +1,237 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONAL_H
+#define EIGEN_DIAGONAL_H
+
+namespace Eigen {
+
+/** \class Diagonal
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
+ *
+ * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
+ * \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
+ * A positive value means a superdiagonal, a negative value means a subdiagonal.
+ * You can also use Dynamic so the index can be set at runtime.
+ *
+ * The matrix is not required to be square.
+ *
+ * This class represents an expression of the main diagonal, or any sub/super diagonal
+ * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
+ * time this is the only way it is used.
+ *
+ * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
+ */
+
+namespace internal {
+template<typename MatrixType, int DiagIndex>
+struct traits<Diagonal<MatrixType,DiagIndex> >
+ : traits<MatrixType>
+{
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+ typedef typename MatrixType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
+ : (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
+ MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
+ ColsAtCompileTime = 1,
+ MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
+ : DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
+ MatrixType::MaxColsAtCompileTime)
+ : (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
+ MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
+ MaxColsAtCompileTime = 1,
+ MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags = (unsigned int)_MatrixTypeNested::Flags & (HereditaryBits | LinearAccessBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit,
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost,
+ MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
+ InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
+ OuterStrideAtCompileTime = 0
+ };
+};
+}
+
+template<typename MatrixType, int _DiagIndex> class Diagonal
+ : public internal::dense_xpr_base< Diagonal<MatrixType,_DiagIndex> >::type
+{
+ public:
+
+ enum { DiagIndex = _DiagIndex };
+ typedef typename internal::dense_xpr_base<Diagonal>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
+
+ inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index) {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
+
+ inline Index rows() const
+ { return m_index.value()<0 ? (std::min<Index>)(m_matrix.cols(),m_matrix.rows()+m_index.value()) : (std::min<Index>)(m_matrix.rows(),m_matrix.cols()-m_index.value()); }
+
+ inline Index cols() const { return 1; }
+
+ inline Index innerStride() const
+ {
+ return m_matrix.outerStride() + 1;
+ }
+
+ inline Index outerStride() const
+ {
+ return 0;
+ }
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<MatrixType>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
+ inline const Scalar* data() const { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
+
+ inline Scalar& coeffRef(Index row, Index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+ }
+
+ inline const Scalar& coeffRef(Index row, Index) const
+ {
+ return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+ }
+
+ inline CoeffReturnType coeff(Index row, Index) const
+ {
+ return m_matrix.coeff(row+rowOffset(), row+colOffset());
+ }
+
+ inline Scalar& coeffRef(Index idx)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return m_matrix.const_cast_derived().coeffRef(idx+rowOffset(), idx+colOffset());
+ }
+
+ inline const Scalar& coeffRef(Index idx) const
+ {
+ return m_matrix.const_cast_derived().coeffRef(idx+rowOffset(), idx+colOffset());
+ }
+
+ inline CoeffReturnType coeff(Index idx) const
+ {
+ return m_matrix.coeff(idx+rowOffset(), idx+colOffset());
+ }
+
+ const typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ int index() const
+ {
+ return m_index.value();
+ }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+ const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
+
+ private:
+ // some compilers may fail to optimize std::max etc in case of compile-time constants...
+ EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
+ EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
+ EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
+ // triger a compile time error is someone try to call packet
+ template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
+ template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
+};
+
+/** \returns an expression of the main diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * Example: \include MatrixBase_diagonal.cpp
+ * Output: \verbinclude MatrixBase_diagonal.out
+ *
+ * \sa class Diagonal */
+template<typename Derived>
+inline typename MatrixBase<Derived>::DiagonalReturnType
+MatrixBase<Derived>::diagonal()
+{
+ return derived();
+}
+
+/** This is the const version of diagonal(). */
+template<typename Derived>
+inline typename MatrixBase<Derived>::ConstDiagonalReturnType
+MatrixBase<Derived>::diagonal() const
+{
+ return ConstDiagonalReturnType(derived());
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+ * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+ *
+ * Example: \include MatrixBase_diagonal_int.cpp
+ * Output: \verbinclude MatrixBase_diagonal_int.out
+ *
+ * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+inline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType
+MatrixBase<Derived>::diagonal(Index index)
+{
+ return DiagonalDynamicIndexReturnType(derived(), index);
+}
+
+/** This is the const version of diagonal(Index). */
+template<typename Derived>
+inline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType
+MatrixBase<Derived>::diagonal(Index index) const
+{
+ return ConstDiagonalDynamicIndexReturnType(derived(), index);
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+ * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+ *
+ * Example: \include MatrixBase_diagonal_template_int.cpp
+ * Output: \verbinclude MatrixBase_diagonal_template_int.out
+ *
+ * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+template<int Index>
+inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index>::Type
+MatrixBase<Derived>::diagonal()
+{
+ return derived();
+}
+
+/** This is the const version of diagonal<int>(). */
+template<typename Derived>
+template<int Index>
+inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index>::Type
+MatrixBase<Derived>::diagonal() const
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONAL_H
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
new file mode 100644
index 0000000..e6c220f
--- /dev/null
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -0,0 +1,313 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONALMATRIX_H
+#define EIGEN_DIAGONALMATRIX_H
+
+namespace Eigen {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename Derived>
+class DiagonalBase : public EigenBase<Derived>
+{
+ public:
+ typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
+ typedef typename DiagonalVectorType::Scalar Scalar;
+ typedef typename DiagonalVectorType::RealScalar RealScalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+
+ enum {
+ RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ IsVectorAtCompileTime = 0,
+ Flags = 0
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
+ typedef DenseMatrixType DenseType;
+ typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
+
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ DenseMatrixType toDenseMatrix() const { return derived(); }
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived> &other) const;
+ template<typename DenseDerived>
+ void addTo(MatrixBase<DenseDerived> &other) const
+ { other.diagonal() += diagonal(); }
+ template<typename DenseDerived>
+ void subTo(MatrixBase<DenseDerived> &other) const
+ { other.diagonal() -= diagonal(); }
+
+ inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
+ inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
+
+ inline Index rows() const { return diagonal().size(); }
+ inline Index cols() const { return diagonal().size(); }
+
+ /** \returns the diagonal matrix product of \c *this by the matrix \a matrix.
+ */
+ template<typename MatrixDerived>
+ const DiagonalProduct<MatrixDerived, Derived, OnTheLeft>
+ operator*(const MatrixBase<MatrixDerived> &matrix) const
+ {
+ return DiagonalProduct<MatrixDerived, Derived, OnTheLeft>(matrix.derived(), derived());
+ }
+
+ inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> >
+ inverse() const
+ {
+ return diagonal().cwiseInverse();
+ }
+
+ inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
+ operator*(const Scalar& scalar) const
+ {
+ return diagonal() * scalar;
+ }
+ friend inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
+ operator*(const Scalar& scalar, const DiagonalBase& other)
+ {
+ return other.diagonal() * scalar;
+ }
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived>
+ bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+ {
+ return diagonal().isApprox(other.diagonal(), precision);
+ }
+ template<typename OtherDerived>
+ bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+ {
+ return toDenseMatrix().isApprox(other, precision);
+ }
+ #endif
+};
+
+template<typename Derived>
+template<typename DenseDerived>
+void DiagonalBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
+{
+ other.setZero();
+ other.diagonal() = diagonal();
+}
+#endif
+
+/** \class DiagonalMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a diagonal matrix with its storage
+ *
+ * \param _Scalar the type of coefficients
+ * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
+ * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
+ * to SizeAtCompileTime. Most of the time, you do not need to specify it.
+ *
+ * \sa class DiagonalWrapper
+ */
+
+namespace internal {
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
+ : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
+ typedef Dense StorageKind;
+ typedef DenseIndex Index;
+ enum {
+ Flags = LvalueBit
+ };
+};
+}
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+class DiagonalMatrix
+ : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
+ typedef const DiagonalMatrix& Nested;
+ typedef _Scalar Scalar;
+ typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
+ typedef typename internal::traits<DiagonalMatrix>::Index Index;
+ #endif
+
+ protected:
+
+ DiagonalVectorType m_diagonal;
+
+ public:
+
+ /** const version of diagonal(). */
+ inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
+ /** \returns a reference to the stored vector of diagonal coefficients. */
+ inline DiagonalVectorType& diagonal() { return m_diagonal; }
+
+ /** Default constructor without initialization */
+ inline DiagonalMatrix() {}
+
+ /** Constructs a diagonal matrix with given dimension */
+ inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
+
+ /** 2D constructor. */
+ inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
+
+ /** 3D constructor. */
+ inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
+ inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
+ #endif
+
+ /** generic constructor from expression of the diagonal coefficients */
+ template<typename OtherDerived>
+ explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
+ {}
+
+ /** Copy operator. */
+ template<typename OtherDerived>
+ DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
+ {
+ m_diagonal = other.diagonal();
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ DiagonalMatrix& operator=(const DiagonalMatrix& other)
+ {
+ m_diagonal = other.diagonal();
+ return *this;
+ }
+ #endif
+
+ /** Resizes to given size. */
+ inline void resize(Index size) { m_diagonal.resize(size); }
+ /** Sets all coefficients to zero. */
+ inline void setZero() { m_diagonal.setZero(); }
+ /** Resizes and sets all coefficients to zero. */
+ inline void setZero(Index size) { m_diagonal.setZero(size); }
+ /** Sets this matrix to be the identity matrix of the current size. */
+ inline void setIdentity() { m_diagonal.setOnes(); }
+ /** Sets this matrix to be the identity matrix of the given size. */
+ inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
+};
+
+/** \class DiagonalWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a diagonal matrix
+ *
+ * \param _DiagonalVectorType the type of the vector of diagonal coefficients
+ *
+ * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
+ * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
+ */
+
+namespace internal {
+template<typename _DiagonalVectorType>
+struct traits<DiagonalWrapper<_DiagonalVectorType> >
+{
+ typedef _DiagonalVectorType DiagonalVectorType;
+ typedef typename DiagonalVectorType::Scalar Scalar;
+ typedef typename DiagonalVectorType::Index Index;
+ typedef typename DiagonalVectorType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ MaxColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ Flags = traits<DiagonalVectorType>::Flags & LvalueBit
+ };
+};
+}
+
+template<typename _DiagonalVectorType>
+class DiagonalWrapper
+ : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef _DiagonalVectorType DiagonalVectorType;
+ typedef DiagonalWrapper Nested;
+ #endif
+
+ /** Constructor from expression of diagonal coefficients to wrap. */
+ inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
+
+ /** \returns a const reference to the wrapped expression of diagonal coefficients. */
+ const DiagonalVectorType& diagonal() const { return m_diagonal; }
+
+ protected:
+ typename DiagonalVectorType::Nested m_diagonal;
+};
+
+/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
+ *
+ * \only_for_vectors
+ *
+ * Example: \include MatrixBase_asDiagonal.cpp
+ * Output: \verbinclude MatrixBase_asDiagonal.out
+ *
+ * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
+ **/
+template<typename Derived>
+inline const DiagonalWrapper<const Derived>
+MatrixBase<Derived>::asDiagonal() const
+{
+ return derived();
+}
+
+/** \returns true if *this is approximately equal to a diagonal matrix,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isDiagonal.cpp
+ * Output: \verbinclude MatrixBase_isDiagonal.out
+ *
+ * \sa asDiagonal()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
+{
+ using std::abs;
+ if(cols() != rows()) return false;
+ RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ {
+ RealScalar absOnDiagonal = abs(coeff(j,j));
+ if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
+ }
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < j; ++i)
+ {
+ if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+ if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+ }
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONALMATRIX_H
diff --git a/Eigen/src/Core/DiagonalProduct.h b/Eigen/src/Core/DiagonalProduct.h
new file mode 100644
index 0000000..00f8f29
--- /dev/null
+++ b/Eigen/src/Core/DiagonalProduct.h
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONALPRODUCT_H
+#define EIGEN_DIAGONALPRODUCT_H
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType, typename DiagonalType, int ProductOrder>
+struct traits<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
+ : traits<MatrixType>
+{
+ typedef typename scalar_product_traits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+
+ _StorageOrder = MatrixType::Flags & RowMajorBit ? RowMajor : ColMajor,
+ _ScalarAccessOnDiag = !((int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheLeft)
+ ||(int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheRight)),
+ _SameTypes = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,
+ // FIXME currently we need same types, but in the future the next rule should be the one
+ //_Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagonalType::DiagonalVectorType::Flags)&PacketAccessBit))),
+ _Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && _SameTypes && (_ScalarAccessOnDiag || (bool(int(DiagonalType::DiagonalVectorType::Flags)&PacketAccessBit))),
+ _LinearAccessMask = (RowsAtCompileTime==1 || ColsAtCompileTime==1) ? LinearAccessBit : 0,
+
+ Flags = ((HereditaryBits|_LinearAccessMask|AlignedBit) & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0),//(int(MatrixType::Flags)&int(DiagonalType::DiagonalVectorType::Flags)&AlignedBit),
+ CoeffReadCost = NumTraits<Scalar>::MulCost + MatrixType::CoeffReadCost + DiagonalType::DiagonalVectorType::CoeffReadCost
+ };
+};
+}
+
+template<typename MatrixType, typename DiagonalType, int ProductOrder>
+class DiagonalProduct : internal::no_assignment_operator,
+ public MatrixBase<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
+{
+ public:
+
+ typedef MatrixBase<DiagonalProduct> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(DiagonalProduct)
+
+ inline DiagonalProduct(const MatrixType& matrix, const DiagonalType& diagonal)
+ : m_matrix(matrix), m_diagonal(diagonal)
+ {
+ eigen_assert(diagonal.diagonal().size() == (ProductOrder == OnTheLeft ? matrix.rows() : matrix.cols()));
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+ {
+ return m_diagonal.diagonal().coeff(ProductOrder == OnTheLeft ? row : col) * m_matrix.coeff(row, col);
+ }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const
+ {
+ enum {
+ StorageOrder = int(MatrixType::Flags) & RowMajorBit ? RowMajor : ColMajor
+ };
+ return coeff(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+ {
+ enum {
+ StorageOrder = Flags & RowMajorBit ? RowMajor : ColMajor
+ };
+ const Index indexInDiagonalVector = ProductOrder == OnTheLeft ? row : col;
+ return packet_impl<LoadMode>(row,col,indexInDiagonalVector,typename internal::conditional<
+ ((int(StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
+ ||(int(StorageOrder) == ColMajor && int(ProductOrder) == OnTheRight)), internal::true_type, internal::false_type>::type());
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index idx) const
+ {
+ enum {
+ StorageOrder = int(MatrixType::Flags) & RowMajorBit ? RowMajor : ColMajor
+ };
+ return packet<LoadMode>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+ }
+
+ protected:
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::true_type) const
+ {
+ return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
+ internal::pset1<PacketScalar>(m_diagonal.diagonal().coeff(id)));
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::false_type) const
+ {
+ enum {
+ InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
+ DiagonalVectorPacketLoadMode = (LoadMode == Aligned && (((InnerSize%16) == 0) || (int(DiagonalType::DiagonalVectorType::Flags)&AlignedBit)==AlignedBit) ? Aligned : Unaligned)
+ };
+ return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
+ m_diagonal.diagonal().template packet<DiagonalVectorPacketLoadMode>(id));
+ }
+
+ typename MatrixType::Nested m_matrix;
+ typename DiagonalType::Nested m_diagonal;
+};
+
+/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
+ */
+template<typename Derived>
+template<typename DiagonalDerived>
+inline const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
+MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &a_diagonal) const
+{
+ return DiagonalProduct<Derived, DiagonalDerived, OnTheRight>(derived(), a_diagonal.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONALPRODUCT_H
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
new file mode 100644
index 0000000..9d7651f
--- /dev/null
+++ b/Eigen/src/Core/Dot.h
@@ -0,0 +1,263 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DOT_H
+#define EIGEN_DOT_H
+
+namespace Eigen {
+
+namespace internal {
+
+// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
+// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
+// looking at the static assertions. Thus this is a trick to get better compile errors.
+template<typename T, typename U,
+// the NeedToTranspose condition here is taken straight from Assign.h
+ bool NeedToTranspose = T::IsVectorAtCompileTime
+ && U::IsVectorAtCompileTime
+ && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
+ | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
+ // revert to || as soon as not needed anymore.
+ (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
+>
+struct dot_nocheck
+{
+ typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+ static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+ {
+ return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+ }
+};
+
+template<typename T, typename U>
+struct dot_nocheck<T, U, true>
+{
+ typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+ static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+ {
+ return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+ }
+};
+
+} // end namespace internal
+
+/** \returns the dot product of *this with other.
+ *
+ * \only_for_vectors
+ *
+ * \note If the scalar type is complex numbers, then this function returns the hermitian
+ * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
+ * second variable.
+ *
+ * \sa squaredNorm(), norm()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
+ EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
+
+ eigen_assert(size() == other.size());
+
+ return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
+}
+
+#ifdef EIGEN2_SUPPORT
+/** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable
+ * (conjugating the second variable). Of course this only makes a difference in the complex case.
+ *
+ * This method is only available in EIGEN2_SUPPORT mode.
+ *
+ * \only_for_vectors
+ *
+ * \sa dot()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(size() == other.size());
+
+ return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
+}
+#endif
+
+
+//---------- implementation of L2 norm and related functions ----------
+
+/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm.
+ * In both cases, it consists in the sum of the square of all the matrix entries.
+ * For vectors, this is also equals to the dot product of \c *this with itself.
+ *
+ * \sa dot(), norm()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
+{
+ return numext::real((*this).cwiseAbs2().sum());
+}
+
+/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
+ * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
+ * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
+ *
+ * \sa dot(), squaredNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
+{
+ using std::sqrt;
+ return sqrt(squaredNorm());
+}
+
+/** \returns an expression of the quotient of *this by its own norm.
+ *
+ * \only_for_vectors
+ *
+ * \sa norm(), normalize()
+ */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::normalized() const
+{
+ typedef typename internal::nested<Derived>::type Nested;
+ typedef typename internal::remove_reference<Nested>::type _Nested;
+ _Nested n(derived());
+ return n / n.norm();
+}
+
+/** Normalizes the vector, i.e. divides it by its own norm.
+ *
+ * \only_for_vectors
+ *
+ * \sa norm(), normalized()
+ */
+template<typename Derived>
+inline void MatrixBase<Derived>::normalize()
+{
+ *this /= norm();
+}
+
+//---------- implementation of other norms ----------
+
+namespace internal {
+
+template<typename Derived, int p>
+struct lpNorm_selector
+{
+ typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
+ static inline RealScalar run(const MatrixBase<Derived>& m)
+ {
+ using std::pow;
+ return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 1>
+{
+ static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+ {
+ return m.cwiseAbs().sum();
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 2>
+{
+ static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+ {
+ return m.norm();
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, Infinity>
+{
+ static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+ {
+ return m.cwiseAbs().maxCoeff();
+ }
+};
+
+} // end namespace internal
+
+/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
+ * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
+ * norm, that is the maximum of the absolute values of the coefficients of *this.
+ *
+ * \sa norm()
+ */
+template<typename Derived>
+template<int p>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::lpNorm() const
+{
+ return internal::lpNorm_selector<Derived, p>::run(*this);
+}
+
+//---------- implementation of isOrthogonal / isUnitary ----------
+
+/** \returns true if *this is approximately orthogonal to \a other,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isOrthogonal.cpp
+ * Output: \verbinclude MatrixBase_isOrthogonal.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isOrthogonal
+(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
+{
+ typename internal::nested<Derived,2>::type nested(derived());
+ typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
+ return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
+}
+
+/** \returns true if *this is approximately an unitary matrix,
+ * within the precision given by \a prec. In the case where the \a Scalar
+ * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
+ *
+ * \note This can be used to check whether a family of vectors forms an orthonormal basis.
+ * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
+ * orthonormal basis.
+ *
+ * Example: \include MatrixBase_isUnitary.cpp
+ * Output: \verbinclude MatrixBase_isUnitary.out
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
+{
+ typename Derived::Nested nested(derived());
+ for(Index i = 0; i < cols(); ++i)
+ {
+ if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
+ return false;
+ for(Index j = 0; j < i; ++j)
+ if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
+ return false;
+ }
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DOT_H
diff --git a/Eigen/src/Core/EigenBase.h b/Eigen/src/Core/EigenBase.h
new file mode 100644
index 0000000..fadb458
--- /dev/null
+++ b/Eigen/src/Core/EigenBase.h
@@ -0,0 +1,131 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EIGENBASE_H
+#define EIGEN_EIGENBASE_H
+
+namespace Eigen {
+
+/** Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
+ *
+ * In other words, an EigenBase object is an object that can be copied into a MatrixBase.
+ *
+ * Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
+ *
+ * Notice that this class is trivial, it is only used to disambiguate overloaded functions.
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived> struct EigenBase
+{
+// typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+
+ /** \returns a reference to the derived object */
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ /** \returns a const reference to the derived object */
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ inline Derived& const_cast_derived() const
+ { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
+ inline const Derived& const_derived() const
+ { return *static_cast<const Derived*>(this); }
+
+ /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+ inline Index rows() const { return derived().rows(); }
+ /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+ inline Index cols() const { return derived().cols(); }
+ /** \returns the number of coefficients, which is rows()*cols().
+ * \sa rows(), cols(), SizeAtCompileTime. */
+ inline Index size() const { return rows() * cols(); }
+
+ /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ { derived().evalTo(dst); }
+
+ /** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
+ template<typename Dest> inline void addTo(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ typename Dest::PlainObject res(rows(),cols());
+ evalTo(res);
+ dst += res;
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
+ template<typename Dest> inline void subTo(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ typename Dest::PlainObject res(rows(),cols());
+ evalTo(res);
+ dst -= res;
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
+ template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ dst = dst * this->derived();
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
+ template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ dst = this->derived() * dst;
+ }
+
+};
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \brief Copies the generic expression \a other into *this.
+ *
+ * \details The expression must provide a (templated) evalTo(Derived& dst) const
+ * function which does the actual job. In practice, this allows any user to write
+ * its own special matrix without having to modify MatrixBase
+ *
+ * \returns a reference to *this.
+ */
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
+{
+ other.derived().evalTo(derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
+{
+ other.derived().addTo(derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
+{
+ other.derived().subTo(derived());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EIGENBASE_H
diff --git a/Eigen/src/Core/Flagged.h b/Eigen/src/Core/Flagged.h
new file mode 100644
index 0000000..1f2955f
--- /dev/null
+++ b/Eigen/src/Core/Flagged.h
@@ -0,0 +1,140 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FLAGGED_H
+#define EIGEN_FLAGGED_H
+
+namespace Eigen {
+
+/** \class Flagged
+ * \ingroup Core_Module
+ *
+ * \brief Expression with modified flags
+ *
+ * \param ExpressionType the type of the object of which we are modifying the flags
+ * \param Added the flags added to the expression
+ * \param Removed the flags removed from the expression (has priority over Added).
+ *
+ * This class represents an expression whose flags have been modified.
+ * It is the return type of MatrixBase::flagged()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::flagged()
+ */
+
+namespace internal {
+template<typename ExpressionType, unsigned int Added, unsigned int Removed>
+struct traits<Flagged<ExpressionType, Added, Removed> > : traits<ExpressionType>
+{
+ enum { Flags = (ExpressionType::Flags | Added) & ~Removed };
+};
+}
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged
+ : public MatrixBase<Flagged<ExpressionType, Added, Removed> >
+{
+ public:
+
+ typedef MatrixBase<Flagged> Base;
+
+ EIGEN_DENSE_PUBLIC_INTERFACE(Flagged)
+ typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+ ExpressionType, const ExpressionType&>::type ExpressionTypeNested;
+ typedef typename ExpressionType::InnerIterator InnerIterator;
+
+ inline Flagged(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index outerStride() const { return m_matrix.outerStride(); }
+ inline Index innerStride() const { return m_matrix.innerStride(); }
+
+ inline CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(row, col);
+ }
+
+ inline CoeffReturnType coeff(Index index) const
+ {
+ return m_matrix.coeff(index);
+ }
+
+ inline const Scalar& coeffRef(Index row, Index col) const
+ {
+ return m_matrix.const_cast_derived().coeffRef(row, col);
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_matrix.const_cast_derived().coeffRef(index);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_matrix.const_cast_derived().coeffRef(row, col);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_matrix.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index row, Index col) const
+ {
+ return m_matrix.template packet<LoadMode>(row, col);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& x)
+ {
+ m_matrix.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_matrix.template packet<LoadMode>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ m_matrix.const_cast_derived().template writePacket<LoadMode>(index, x);
+ }
+
+ const ExpressionType& _expression() const { return m_matrix; }
+
+ template<typename OtherDerived>
+ typename ExpressionType::PlainObject solveTriangular(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived>
+ void solveTriangularInPlace(const MatrixBase<OtherDerived>& other) const;
+
+ protected:
+ ExpressionTypeNested m_matrix;
+};
+
+/** \returns an expression of *this with added and removed flags
+ *
+ * This is mostly for internal use.
+ *
+ * \sa class Flagged
+ */
+template<typename Derived>
+template<unsigned int Added,unsigned int Removed>
+inline const Flagged<Derived, Added, Removed>
+DenseBase<Derived>::flagged() const
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FLAGGED_H
diff --git a/Eigen/src/Core/ForceAlignedAccess.h b/Eigen/src/Core/ForceAlignedAccess.h
new file mode 100644
index 0000000..807c7a2
--- /dev/null
+++ b/Eigen/src/Core/ForceAlignedAccess.h
@@ -0,0 +1,146 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FORCEALIGNEDACCESS_H
+#define EIGEN_FORCEALIGNEDACCESS_H
+
+namespace Eigen {
+
+/** \class ForceAlignedAccess
+ * \ingroup Core_Module
+ *
+ * \brief Enforce aligned packet loads and stores regardless of what is requested
+ *
+ * \param ExpressionType the type of the object of which we are forcing aligned packet access
+ *
+ * This class is the return type of MatrixBase::forceAlignedAccess()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::forceAlignedAccess()
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
+{};
+}
+
+template<typename ExpressionType> class ForceAlignedAccess
+ : public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
+
+ inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
+
+ inline Index rows() const { return m_expression.rows(); }
+ inline Index cols() const { return m_expression.cols(); }
+ inline Index outerStride() const { return m_expression.outerStride(); }
+ inline Index innerStride() const { return m_expression.innerStride(); }
+
+ inline const CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_expression.coeff(row, col);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_expression.const_cast_derived().coeffRef(row, col);
+ }
+
+ inline const CoeffReturnType coeff(Index index) const
+ {
+ return m_expression.coeff(index);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index row, Index col) const
+ {
+ return m_expression.template packet<Aligned>(row, col);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_expression.template packet<Aligned>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
+ }
+
+ operator const ExpressionType&() const { return m_expression; }
+
+ protected:
+ const ExpressionType& m_expression;
+
+ private:
+ ForceAlignedAccess& operator=(const ForceAlignedAccess&);
+};
+
+/** \returns an expression of *this with forced aligned access
+ * \sa forceAlignedAccessIf(),class ForceAlignedAccess
+ */
+template<typename Derived>
+inline const ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess() const
+{
+ return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access
+ * \sa forceAlignedAccessIf(), class ForceAlignedAccess
+ */
+template<typename Derived>
+inline ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess()
+{
+ return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+ * \sa forceAlignedAccess(), class ForceAlignedAccess
+ */
+template<typename Derived>
+template<bool Enable>
+inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type
+MatrixBase<Derived>::forceAlignedAccessIf() const
+{
+ return derived();
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+ * \sa forceAlignedAccess(), class ForceAlignedAccess
+ */
+template<typename Derived>
+template<bool Enable>
+inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type
+MatrixBase<Derived>::forceAlignedAccessIf()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FORCEALIGNEDACCESS_H
diff --git a/Eigen/src/Core/Functors.h b/Eigen/src/Core/Functors.h
new file mode 100644
index 0000000..5f14c65
--- /dev/null
+++ b/Eigen/src/Core/Functors.h
@@ -0,0 +1,1026 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FUNCTORS_H
+#define EIGEN_FUNCTORS_H
+
+namespace Eigen {
+
+namespace internal {
+
+// associative functors:
+
+/** \internal
+ * \brief Template functor to compute the sum of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, MatrixBase::sum()
+ */
+template<typename Scalar> struct scalar_sum_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::padd(a,b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+ { return internal::predux(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sum_op<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasAdd
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the product of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
+ */
+template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
+ enum {
+ // TODO vectorize mixed product
+ Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
+ };
+ typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
+ EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmul(a,b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
+ { return internal::predux_mul(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
+ PacketAccess = scalar_product_op<LhsScalar,RhsScalar>::Vectorizable
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the conjugate product of two scalars
+ *
+ * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
+ */
+template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
+
+ enum {
+ Conj = NumTraits<LhsScalar>::IsComplex
+ };
+
+ typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
+ EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
+ { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
+
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = NumTraits<LhsScalar>::MulCost,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the min of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
+ */
+template<typename Scalar> struct scalar_min_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::min; return (min)(a, b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmin(a,b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+ { return internal::predux_min(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_min_op<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasMin
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the max of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
+ */
+template<typename Scalar> struct scalar_max_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::max; return (max)(a, b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmax(a,b); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+ { return internal::predux_max(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_max_op<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasMax
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the hypot of two scalars
+ *
+ * \sa MatrixBase::stableNorm(), class Redux
+ */
+template<typename Scalar> struct scalar_hypot_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
+// typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
+ {
+ using std::max;
+ using std::min;
+ using std::sqrt;
+ Scalar p = (max)(_x, _y);
+ Scalar q = (min)(_x, _y);
+ Scalar qp = q/p;
+ return p * sqrt(Scalar(1) + qp*qp);
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_hypot_op<Scalar> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
+};
+
+/** \internal
+ * \brief Template functor to compute the pow of two scalars
+ */
+template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
+ inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return numext::pow(a, b); }
+};
+template<typename Scalar, typename OtherScalar>
+struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
+};
+
+// other binary functors:
+
+/** \internal
+ * \brief Template functor to compute the difference of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator-
+ */
+template<typename Scalar> struct scalar_difference_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::psub(a,b); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_difference_op<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasSub
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the quotient of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator/()
+ */
+template<typename LhsScalar,typename RhsScalar> struct scalar_quotient_op {
+ enum {
+ // TODO vectorize mixed product
+ Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv
+ };
+ typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
+ EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pdiv(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost), // rough estimate!
+ PacketAccess = scalar_quotient_op<LhsScalar,RhsScalar>::Vectorizable
+ };
+};
+
+
+
+/** \internal
+ * \brief Template functor to compute the and of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator&&
+ */
+struct scalar_boolean_and_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)
+ EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
+};
+template<> struct functor_traits<scalar_boolean_and_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the or of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator||
+ */
+struct scalar_boolean_or_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)
+ EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
+};
+template<> struct functor_traits<scalar_boolean_or_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functors for comparison of two scalars
+ * \todo Implement packet-comparisons
+ */
+template<typename Scalar, ComparisonName cmp> struct scalar_cmp_op;
+
+template<typename Scalar, ComparisonName cmp>
+struct functor_traits<scalar_cmp_op<Scalar, cmp> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = false
+ };
+};
+
+template<ComparisonName Cmp, typename Scalar>
+struct result_of<scalar_cmp_op<Scalar, Cmp>(Scalar,Scalar)> {
+ typedef bool type;
+};
+
+
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_EQ> {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a==b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LT> {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LE> {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<=b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_UNORD> {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return !(a<=b || b<=a);}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_NEQ> {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a!=b;}
+};
+
+// unary functors:
+
+/** \internal
+ * \brief Template functor to compute the opposite of a scalar
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::operator-
+ */
+template<typename Scalar> struct scalar_opposite_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pnegate(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_opposite_op<Scalar> >
+{ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasNegate };
+};
+
+/** \internal
+ * \brief Template functor to compute the absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs
+ */
+template<typename Scalar> struct scalar_abs_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { using std::abs; return abs(a); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pabs(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasAbs
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the squared absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs2
+ */
+template<typename Scalar> struct scalar_abs2_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs2_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
+
+/** \internal
+ * \brief Template functor to compute the conjugate of a complex value
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::conjugate()
+ */
+template<typename Scalar> struct scalar_conjugate_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using numext::conj; return conj(a); }
+ template<typename Packet>
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_conjugate_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
+ PacketAccess = packet_traits<Scalar>::HasConj
+ };
+};
+
+/** \internal
+ * \brief Template functor to cast a scalar to another type
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::cast()
+ */
+template<typename Scalar, typename NewType>
+struct scalar_cast_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
+ typedef NewType result_type;
+ EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
+};
+template<typename Scalar, typename NewType>
+struct functor_traits<scalar_cast_op<Scalar,NewType> >
+{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the real part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template<typename Scalar>
+struct scalar_real_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the imaginary part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template<typename Scalar>
+struct scalar_imag_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the real part of a complex as a reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template<typename Scalar>
+struct scalar_real_ref_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the imaginary part of a complex as a reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template<typename Scalar>
+struct scalar_imag_ref_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ *
+ * \brief Template functor to compute the exponential of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::exp()
+ */
+template<typename Scalar> struct scalar_exp_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::exp; return exp(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_exp_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasExp }; };
+
+/** \internal
+ *
+ * \brief Template functor to compute the logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::log()
+ */
+template<typename Scalar> struct scalar_log_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::log; return log(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_log_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
+
+/** \internal
+ * \brief Template functor to multiply a scalar by a fixed other one
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::operator*, MatrixBase::operator/
+ */
+/* NOTE why doing the pset1() in packetOp *is* an optimization ?
+ * indeed it seems better to declare m_other as a Packet and do the pset1() once
+ * in the constructor. However, in practice:
+ * - GCC does not like m_other as a Packet and generate a load every time it needs it
+ * - on the other hand GCC is able to moves the pset1() outside the loop :)
+ * - simpler code ;)
+ * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
+ */
+template<typename Scalar>
+struct scalar_multiple_op {
+ typedef typename packet_traits<Scalar>::type Packet;
+ // FIXME default copy constructors seems bugged with std::complex<>
+ EIGEN_STRONG_INLINE scalar_multiple_op(const scalar_multiple_op& other) : m_other(other.m_other) { }
+ EIGEN_STRONG_INLINE scalar_multiple_op(const Scalar& other) : m_other(other) { }
+ EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a, pset1<Packet>(m_other)); }
+ typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_multiple_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+template<typename Scalar1, typename Scalar2>
+struct scalar_multiple2_op {
+ typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
+ EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
+ EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
+ EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
+ typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
+};
+template<typename Scalar1,typename Scalar2>
+struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
+{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to divide a scalar by a fixed other one
+ *
+ * This functor is used to implement the quotient of a matrix by
+ * a scalar where the scalar type is not necessarily a floating point type.
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::operator/
+ */
+template<typename Scalar>
+struct scalar_quotient1_op {
+ typedef typename packet_traits<Scalar>::type Packet;
+ // FIXME default copy constructors seems bugged with std::complex<>
+ EIGEN_STRONG_INLINE scalar_quotient1_op(const scalar_quotient1_op& other) : m_other(other.m_other) { }
+ EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) : m_other(other) {}
+ EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
+ EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pdiv(a, pset1<Packet>(m_other)); }
+ typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_quotient1_op<Scalar> >
+{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
+
+// nullary functors
+
+template<typename Scalar>
+struct scalar_constant_op {
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
+ EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index, Index = 0) const { return m_other; }
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Packet packetOp(Index, Index = 0) const { return internal::pset1<Packet>(m_other); }
+ const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_constant_op<Scalar> >
+// FIXME replace this packet test by a safe one
+{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
+
+template<typename Scalar> struct scalar_identity_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const { return row==col ? Scalar(1) : Scalar(0); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_identity_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
+
+template <typename Scalar, bool RandomAccess> struct linspaced_op_impl;
+
+// linear access for packet ops:
+// 1) initialization
+// base = [low, ..., low] + ([step, ..., step] * [-size, ..., 0])
+// 2) each step (where size is 1 for coeff access or PacketSize for packet access)
+// base += [size*step, ..., size*step]
+//
+// TODO: Perhaps it's better to initialize lazily (so not in the constructor but in packetOp)
+// in order to avoid the padd() in operator() ?
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,false>
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+
+ linspaced_op_impl(const Scalar& low, const Scalar& step) :
+ m_low(low), m_step(step),
+ m_packetStep(pset1<Packet>(packet_traits<Scalar>::size*step)),
+ m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(step),plset<Scalar>(-packet_traits<Scalar>::size)))) {}
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index i) const
+ {
+ m_base = padd(m_base, pset1<Packet>(m_step));
+ return m_low+Scalar(i)*m_step;
+ }
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Packet packetOp(Index) const { return m_base = padd(m_base,m_packetStep); }
+
+ const Scalar m_low;
+ const Scalar m_step;
+ const Packet m_packetStep;
+ mutable Packet m_base;
+};
+
+// random access for packet ops:
+// 1) each step
+// [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,true>
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+
+ linspaced_op_impl(const Scalar& low, const Scalar& step) :
+ m_low(low), m_step(step),
+ m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Scalar>(0)) {}
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Packet packetOp(Index i) const
+ { return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(Scalar(i)),m_interPacket))); }
+
+ const Scalar m_low;
+ const Scalar m_step;
+ const Packet m_lowPacket;
+ const Packet m_stepPacket;
+ const Packet m_interPacket;
+};
+
+// ----- Linspace functor ----------------------------------------------------------------
+
+// Forward declaration (we default to random access which does not really give
+// us a speed gain when using packet access but it allows to use the functor in
+// nested expressions).
+template <typename Scalar, bool RandomAccess = true> struct linspaced_op;
+template <typename Scalar, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,RandomAccess> >
+{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
+template <typename Scalar, bool RandomAccess> struct linspaced_op
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ linspaced_op(const Scalar& low, const Scalar& high, DenseIndex num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1))) {}
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
+
+ // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
+ // there row==0 and col is used for the actual iteration.
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const
+ {
+ eigen_assert(col==0 || row==0);
+ return impl(col + row);
+ }
+
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Packet packetOp(Index i) const { return impl.packetOp(i); }
+
+ // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
+ // there row==0 and col is used for the actual iteration.
+ template<typename Index>
+ EIGEN_STRONG_INLINE const Packet packetOp(Index row, Index col) const
+ {
+ eigen_assert(col==0 || row==0);
+ return impl.packetOp(col + row);
+ }
+
+ // This proxy object handles the actual required temporaries, the different
+ // implementations (random vs. sequential access) as well as the
+ // correct piping to size 2/4 packet operations.
+ const linspaced_op_impl<Scalar,RandomAccess> impl;
+};
+
+// all functors allow linear access, except scalar_identity_op. So we fix here a quick meta
+// to indicate whether a functor allows linear access, just always answering 'yes' except for
+// scalar_identity_op.
+// FIXME move this to functor_traits adding a functor_default
+template<typename Functor> struct functor_has_linear_access { enum { ret = 1 }; };
+template<typename Scalar> struct functor_has_linear_access<scalar_identity_op<Scalar> > { enum { ret = 0 }; };
+
+// In Eigen, any binary op (Product, CwiseBinaryOp) require the Lhs and Rhs to have the same scalar type, except for multiplication
+// where the mixing of different types is handled by scalar_product_traits
+// In particular, real * complex<real> is allowed.
+// FIXME move this to functor_traits adding a functor_default
+template<typename Functor> struct functor_is_product_like { enum { ret = 0 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_quotient_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+
+
+/** \internal
+ * \brief Template functor to add a scalar to a fixed other one
+ * \sa class CwiseUnaryOp, Array::operator+
+ */
+/* If you wonder why doing the pset1() in packetOp() is an optimization check scalar_multiple_op */
+template<typename Scalar>
+struct scalar_add_op {
+ typedef typename packet_traits<Scalar>::type Packet;
+ // FIXME default copy constructors seems bugged with std::complex<>
+ inline scalar_add_op(const scalar_add_op& other) : m_other(other.m_other) { }
+ inline scalar_add_op(const Scalar& other) : m_other(other) { }
+ inline Scalar operator() (const Scalar& a) const { return a + m_other; }
+ inline const Packet packetOp(const Packet& a) const
+ { return internal::padd(a, pset1<Packet>(m_other)); }
+ const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_add_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
+
+/** \internal
+ * \brief Template functor to compute the square root of a scalar
+ * \sa class CwiseUnaryOp, Cwise::sqrt()
+ */
+template<typename Scalar> struct scalar_sqrt_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::sqrt; return sqrt(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sqrt_op<Scalar> >
+{ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasSqrt
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::cos()
+ */
+template<typename Scalar> struct scalar_cos_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
+ inline Scalar operator() (const Scalar& a) const { using std::cos; return cos(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cos_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasCos
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::sin()
+ */
+template<typename Scalar> struct scalar_sin_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::sin; return sin(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sin_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasSin
+ };
+};
+
+
+/** \internal
+ * \brief Template functor to compute the tan of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::tan()
+ */
+template<typename Scalar> struct scalar_tan_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::tan; return tan(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_tan_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasTan
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the arc cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::acos()
+ */
+template<typename Scalar> struct scalar_acos_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::acos; return acos(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_acos_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasACos
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the arc sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::asin()
+ */
+template<typename Scalar> struct scalar_asin_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
+ inline const Scalar operator() (const Scalar& a) const { using std::asin; return asin(a); }
+ typedef typename packet_traits<Scalar>::type Packet;
+ inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_asin_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasASin
+ };
+};
+
+/** \internal
+ * \brief Template functor to raise a scalar to a power
+ * \sa class CwiseUnaryOp, Cwise::pow
+ */
+template<typename Scalar>
+struct scalar_pow_op {
+ // FIXME default copy constructors seems bugged with std::complex<>
+ inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
+ inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
+ inline Scalar operator() (const Scalar& a) const { return numext::pow(a, m_exponent); }
+ const Scalar m_exponent;
+};
+template<typename Scalar>
+struct functor_traits<scalar_pow_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to compute the quotient between a scalar and array entries.
+ * \sa class CwiseUnaryOp, Cwise::inverse()
+ */
+template<typename Scalar>
+struct scalar_inverse_mult_op {
+ scalar_inverse_mult_op(const Scalar& other) : m_other(other) {}
+ inline Scalar operator() (const Scalar& a) const { return m_other / a; }
+ template<typename Packet>
+ inline const Packet packetOp(const Packet& a) const
+ { return internal::pdiv(pset1<Packet>(m_other),a); }
+ Scalar m_other;
+};
+
+/** \internal
+ * \brief Template functor to compute the inverse of a scalar
+ * \sa class CwiseUnaryOp, Cwise::inverse()
+ */
+template<typename Scalar>
+struct scalar_inverse_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)
+ inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
+ template<typename Packet>
+ inline const Packet packetOp(const Packet& a) const
+ { return internal::pdiv(pset1<Packet>(Scalar(1)),a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_inverse_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
+
+/** \internal
+ * \brief Template functor to compute the square of a scalar
+ * \sa class CwiseUnaryOp, Cwise::square()
+ */
+template<typename Scalar>
+struct scalar_square_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
+ inline Scalar operator() (const Scalar& a) const { return a*a; }
+ template<typename Packet>
+ inline const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_square_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+/** \internal
+ * \brief Template functor to compute the cube of a scalar
+ * \sa class CwiseUnaryOp, Cwise::cube()
+ */
+template<typename Scalar>
+struct scalar_cube_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
+ inline Scalar operator() (const Scalar& a) const { return a*a*a; }
+ template<typename Packet>
+ inline const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,pmul(a,a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cube_op<Scalar> >
+{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+// default functor traits for STL functors:
+
+template<typename T>
+struct functor_traits<std::multiplies<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::divides<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::plus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::minus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::negate<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_or<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_and<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_not<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::not_equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binder2nd<T> >
+{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binder1st<T> >
+{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::unary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+
+#ifdef EIGEN_STDEXT_SUPPORT
+
+template<typename T0,typename T1>
+struct functor_traits<std::project1st<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::project2nd<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select2nd<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select1st<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::unary_compose<T0,T1> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };
+
+template<typename T0,typename T1,typename T2>
+struct functor_traits<std::binary_compose<T0,T1,T2> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };
+
+#endif // EIGEN_STDEXT_SUPPORT
+
+// allow to add new functors and specializations of functor_traits from outside Eigen.
+// this macro is really needed because functor_traits must be specialized after it is declared but before it is used...
+#ifdef EIGEN_FUNCTORS_PLUGIN
+#include EIGEN_FUNCTORS_PLUGIN
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_FUNCTORS_H
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
new file mode 100644
index 0000000..fe63bd2
--- /dev/null
+++ b/Eigen/src/Core/Fuzzy.h
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FUZZY_H
+#define EIGEN_FUZZY_H
+
+namespace Eigen {
+
+namespace internal
+{
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isApprox_selector
+{
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
+ {
+ using std::min;
+ typename internal::nested<Derived,2>::type nested(x);
+ typename internal::nested<OtherDerived,2>::type otherNested(y);
+ return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isApprox_selector<Derived, OtherDerived, true>
+{
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == y.matrix();
+ }
+};
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_object_selector
+{
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
+ {
+ return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
+{
+ static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+ }
+};
+
+template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_scalar_selector
+{
+ static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
+ {
+ return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
+ }
+};
+
+template<typename Derived>
+struct isMuchSmallerThan_scalar_selector<Derived, true>
+{
+ static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+ }
+};
+
+} // end namespace internal
+
+
+/** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
+ * are considered to be approximately equal within precision \f$ p \f$ if
+ * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
+ * L2 norm).
+ *
+ * \note Because of the multiplicativeness of this comparison, one can't use this function
+ * to check whether \c *this is approximately equal to the zero matrix or vector.
+ * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
+ * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
+ * RealScalar&, RealScalar) instead.
+ *
+ * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
+ */
+template<typename Derived>
+template<typename OtherDerived>
+bool DenseBase<Derived>::isApprox(
+ const DenseBase<OtherDerived>& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than \a other,
+ * within the precision determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+ * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
+ * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
+ *
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
+ * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
+ * of a reference matrix of same dimensions.
+ *
+ * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
+ */
+template<typename Derived>
+bool DenseBase<Derived>::isMuchSmallerThan(
+ const typename NumTraits<Scalar>::Real& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
+ * within the precision determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+ * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
+ * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm.
+ *
+ * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
+ */
+template<typename Derived>
+template<typename OtherDerived>
+bool DenseBase<Derived>::isMuchSmallerThan(
+ const DenseBase<OtherDerived>& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FUZZY_H
diff --git a/Eigen/src/Core/GeneralProduct.h b/Eigen/src/Core/GeneralProduct.h
new file mode 100644
index 0000000..9e805a8
--- /dev/null
+++ b/Eigen/src/Core/GeneralProduct.h
@@ -0,0 +1,635 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_PRODUCT_H
+#define EIGEN_GENERAL_PRODUCT_H
+
+namespace Eigen {
+
+/** \class GeneralProduct
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the product of two general matrices or vectors
+ *
+ * \param LhsNested the type used to store the left-hand side
+ * \param RhsNested the type used to store the right-hand side
+ * \param ProductMode the type of the product
+ *
+ * This class represents an expression of the product of two general matrices.
+ * We call a general matrix, a dense matrix with full storage. For instance,
+ * This excludes triangular, selfadjoint, and sparse matrices.
+ * It is the return type of the operator* between general matrices. Its template
+ * arguments are determined automatically by ProductReturnType. Therefore,
+ * GeneralProduct should never be used direclty. To determine the result type of a
+ * function which involves a matrix product, use ProductReturnType::Type.
+ *
+ * \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+ */
+template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
+class GeneralProduct;
+
+enum {
+ Large = 2,
+ Small = 3
+};
+
+namespace internal {
+
+template<int Rows, int Cols, int Depth> struct product_type_selector;
+
+template<int Size, int MaxSize> struct product_size_category
+{
+ enum { is_large = MaxSize == Dynamic ||
+ Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
+ value = is_large ? Large
+ : Size == 1 ? 1
+ : Small
+ };
+};
+
+template<typename Lhs, typename Rhs> struct product_type
+{
+ typedef typename remove_all<Lhs>::type _Lhs;
+ typedef typename remove_all<Rhs>::type _Rhs;
+ enum {
+ MaxRows = _Lhs::MaxRowsAtCompileTime,
+ Rows = _Lhs::RowsAtCompileTime,
+ MaxCols = _Rhs::MaxColsAtCompileTime,
+ Cols = _Rhs::ColsAtCompileTime,
+ MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
+ _Rhs::MaxRowsAtCompileTime),
+ Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
+ _Rhs::RowsAtCompileTime),
+ LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+ };
+
+ // the splitting into different lines of code here, introducing the _select enums and the typedef below,
+ // is to work around an internal compiler error with gcc 4.1 and 4.2.
+private:
+ enum {
+ rows_select = product_size_category<Rows,MaxRows>::value,
+ cols_select = product_size_category<Cols,MaxCols>::value,
+ depth_select = product_size_category<Depth,MaxDepth>::value
+ };
+ typedef product_type_selector<rows_select, cols_select, depth_select> selector;
+
+public:
+ enum {
+ value = selector::ret
+ };
+#ifdef EIGEN_DEBUG_PRODUCT
+ static void debug()
+ {
+ EIGEN_DEBUG_VAR(Rows);
+ EIGEN_DEBUG_VAR(Cols);
+ EIGEN_DEBUG_VAR(Depth);
+ EIGEN_DEBUG_VAR(rows_select);
+ EIGEN_DEBUG_VAR(cols_select);
+ EIGEN_DEBUG_VAR(depth_select);
+ EIGEN_DEBUG_VAR(value);
+ }
+#endif
+};
+
+
+/* The following allows to select the kind of product at compile time
+ * based on the three dimensions of the product.
+ * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
+// FIXME I'm not sure the current mapping is the ideal one.
+template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
+template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
+template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
+template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
+template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
+template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Small,Small> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Small,Large,Small> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
+
+} // end namespace internal
+
+/** \class ProductReturnType
+ * \ingroup Core_Module
+ *
+ * \brief Helper class to get the correct and optimized returned type of operator*
+ *
+ * \param Lhs the type of the left-hand side
+ * \param Rhs the type of the right-hand side
+ * \param ProductMode the type of the product (determined automatically by internal::product_mode)
+ *
+ * This class defines the typename Type representing the optimized product expression
+ * between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
+ * is the recommended way to define the result type of a function returning an expression
+ * which involve a matrix product. The class Product should never be
+ * used directly.
+ *
+ * \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+ */
+template<typename Lhs, typename Rhs, int ProductType>
+struct ProductReturnType
+{
+ // TODO use the nested type to reduce instanciations ????
+// typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+// typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+
+ typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
+};
+
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
+{
+ typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
+ typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
+ typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
+};
+
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
+{
+ typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
+ typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
+ typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
+};
+
+// this is a workaround for sun CC
+template<typename Lhs, typename Rhs>
+struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
+{};
+
+/***********************************************************************
+* Implementation of Inner Vector Vector Product
+***********************************************************************/
+
+// FIXME : maybe the "inner product" could return a Scalar
+// instead of a 1x1 matrix ??
+// Pro: more natural for the user
+// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
+// product ends up to a row-vector times col-vector product... To tackle this use
+// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
+
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
+ : traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
+{};
+
+}
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, InnerProduct>
+ : internal::no_assignment_operator,
+ public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
+{
+ typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
+ public:
+ GeneralProduct(const Lhs& lhs, const Rhs& rhs)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
+ }
+
+ /** Convertion to scalar */
+ operator const typename Base::Scalar() const {
+ return Base::coeff(0,0);
+ }
+};
+
+/***********************************************************************
+* Implementation of Outer Vector Vector Product
+***********************************************************************/
+
+namespace internal {
+
+// Column major
+template<typename ProductType, typename Dest, typename Func>
+EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const false_type&)
+{
+ typedef typename Dest::Index Index;
+ // FIXME make sure lhs is sequentially stored
+ // FIXME not very good if rhs is real and lhs complex while alpha is real too
+ const Index cols = dest.cols();
+ for (Index j=0; j<cols; ++j)
+ func(dest.col(j), prod.rhs().coeff(0,j) * prod.lhs());
+}
+
+// Row major
+template<typename ProductType, typename Dest, typename Func>
+EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const true_type&) {
+ typedef typename Dest::Index Index;
+ // FIXME make sure rhs is sequentially stored
+ // FIXME not very good if lhs is real and rhs complex while alpha is real too
+ const Index rows = dest.rows();
+ for (Index i=0; i<rows; ++i)
+ func(dest.row(i), prod.lhs().coeff(i,0) * prod.rhs());
+}
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
+{};
+
+}
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, OuterProduct>
+ : public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
+{
+ template<typename T> struct IsRowMajor : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
+
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+ GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ }
+
+ struct set { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() = src; } };
+ struct add { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
+ struct sub { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
+ struct adds {
+ Scalar m_scale;
+ adds(const Scalar& s) : m_scale(s) {}
+ template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const {
+ dst.const_cast_derived() += m_scale * src;
+ }
+ };
+
+ template<typename Dest>
+ inline void evalTo(Dest& dest) const {
+ internal::outer_product_selector_run(*this, dest, set(), IsRowMajor<Dest>());
+ }
+
+ template<typename Dest>
+ inline void addTo(Dest& dest) const {
+ internal::outer_product_selector_run(*this, dest, add(), IsRowMajor<Dest>());
+ }
+
+ template<typename Dest>
+ inline void subTo(Dest& dest) const {
+ internal::outer_product_selector_run(*this, dest, sub(), IsRowMajor<Dest>());
+ }
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ internal::outer_product_selector_run(*this, dest, adds(alpha), IsRowMajor<Dest>());
+ }
+};
+
+/***********************************************************************
+* Implementation of General Matrix Vector Product
+***********************************************************************/
+
+/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
+ * 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
+ * 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
+ * 3 - all other cases are handled using a simple loop along the outer-storage direction.
+ * Therefore we need a lower level meta selector.
+ * Furthermore, if the matrix is the rhs, then the product has to be transposed.
+ */
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
+{};
+
+template<int Side, int StorageOrder, bool BlasCompatible>
+struct gemv_selector;
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, GemvProduct>
+ : public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+
+ GeneralProduct(const Lhs& a_lhs, const Rhs& a_rhs) : Base(a_lhs,a_rhs)
+ {
+// EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
+// YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ }
+
+ enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
+ typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
+ internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
+ bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
+ }
+};
+
+namespace internal {
+
+// The vector is on the left => transposition
+template<int StorageOrder, bool BlasCompatible>
+struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
+{
+ template<typename ProductType, typename Dest>
+ static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
+ {
+ Transpose<Dest> destT(dest);
+ enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
+ gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
+ ::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
+ (prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
+ }
+};
+
+template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
+{
+ EIGEN_STRONG_INLINE Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
+};
+
+template<typename Scalar,int Size>
+struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
+{
+ EIGEN_STRONG_INLINE Scalar* data() { return 0; }
+};
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
+{
+ #if EIGEN_ALIGN_STATICALLY
+ internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
+ EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
+ #else
+ // Some architectures cannot align on the stack,
+ // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
+ enum {
+ ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
+ PacketSize = internal::packet_traits<Scalar>::size
+ };
+ internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
+ EIGEN_STRONG_INLINE Scalar* data() {
+ return ForceAlignment
+ ? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
+ : m_data.array;
+ }
+ #endif
+};
+
+template<> struct gemv_selector<OnTheRight,ColMajor,true>
+{
+ template<typename ProductType, typename Dest>
+ static inline void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
+ {
+ typedef typename ProductType::Index Index;
+ typedef typename ProductType::LhsScalar LhsScalar;
+ typedef typename ProductType::RhsScalar RhsScalar;
+ typedef typename ProductType::Scalar ResScalar;
+ typedef typename ProductType::RealScalar RealScalar;
+ typedef typename ProductType::ActualLhsType ActualLhsType;
+ typedef typename ProductType::ActualRhsType ActualRhsType;
+ typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+ typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+ typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
+
+ ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
+ ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+ * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
+ ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
+ MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
+ };
+
+ gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+
+ bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
+ bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
+
+ RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ evalToDest ? dest.data() : static_dest.data());
+
+ if(!evalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ int size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ if(!alphaIsCompatible)
+ {
+ MappedDest(actualDestPtr, dest.size()).setZero();
+ compatibleAlpha = RhsScalar(1);
+ }
+ else
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ general_matrix_vector_product
+ <Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
+ actualLhs.rows(), actualLhs.cols(),
+ actualLhs.data(), actualLhs.outerStride(),
+ actualRhs.data(), actualRhs.innerStride(),
+ actualDestPtr, 1,
+ compatibleAlpha);
+
+ if (!evalToDest)
+ {
+ if(!alphaIsCompatible)
+ dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
+ else
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+ }
+};
+
+template<> struct gemv_selector<OnTheRight,RowMajor,true>
+{
+ template<typename ProductType, typename Dest>
+ static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
+ {
+ typedef typename ProductType::LhsScalar LhsScalar;
+ typedef typename ProductType::RhsScalar RhsScalar;
+ typedef typename ProductType::Scalar ResScalar;
+ typedef typename ProductType::Index Index;
+ typedef typename ProductType::ActualLhsType ActualLhsType;
+ typedef typename ProductType::ActualRhsType ActualRhsType;
+ typedef typename ProductType::_ActualRhsType _ActualRhsType;
+ typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+ typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+
+ typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+ typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+ * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
+ };
+
+ gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
+ DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
+
+ if(!DirectlyUseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ int size = actualRhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+ }
+
+ general_matrix_vector_product
+ <Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
+ actualLhs.rows(), actualLhs.cols(),
+ actualLhs.data(), actualLhs.outerStride(),
+ actualRhsPtr, 1,
+ dest.data(), dest.innerStride(),
+ actualAlpha);
+ }
+};
+
+template<> struct gemv_selector<OnTheRight,ColMajor,false>
+{
+ template<typename ProductType, typename Dest>
+ static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
+ {
+ typedef typename Dest::Index Index;
+ // TODO makes sure dest is sequentially stored in memory, otherwise use a temp
+ const Index size = prod.rhs().rows();
+ for(Index k=0; k<size; ++k)
+ dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
+ }
+};
+
+template<> struct gemv_selector<OnTheRight,RowMajor,false>
+{
+ template<typename ProductType, typename Dest>
+ static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
+ {
+ typedef typename Dest::Index Index;
+ // TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
+ const Index rows = prod.rows();
+ for(Index i=0; i<rows; ++i)
+ dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \returns the matrix product of \c *this and \a other.
+ *
+ * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
+ *
+ * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline const typename ProductReturnType<Derived, OtherDerived>::Type
+MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+ // A note regarding the function declaration: In MSVC, this function will sometimes
+ // not be inlined since DenseStorage is an unwindable object for dynamic
+ // matrices and product types are holding a member to store the result.
+ // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
+ enum {
+ ProductIsValid = Derived::ColsAtCompileTime==Dynamic
+ || OtherDerived::RowsAtCompileTime==Dynamic
+ || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+ AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwiseProduct(v2)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+#ifdef EIGEN_DEBUG_PRODUCT
+ internal::product_type<Derived,OtherDerived>::debug();
+#endif
+ return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
+ *
+ * The returned product will behave like any other expressions: the coefficients of the product will be
+ * computed once at a time as requested. This might be useful in some extremely rare cases when only
+ * a small and no coherent fraction of the result's coefficients have to be computed.
+ *
+ * \warning This version of the matrix product can be much much slower. So use it only if you know
+ * what you are doing and that you measured a true speed improvement.
+ *
+ * \sa operator*(const MatrixBase&)
+ */
+template<typename Derived>
+template<typename OtherDerived>
+const typename LazyProductReturnType<Derived,OtherDerived>::Type
+MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
+{
+ enum {
+ ProductIsValid = Derived::ColsAtCompileTime==Dynamic
+ || OtherDerived::RowsAtCompileTime==Dynamic
+ || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+ AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwiseProduct(v2)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+
+ return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PRODUCT_H
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
new file mode 100644
index 0000000..5f783eb
--- /dev/null
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -0,0 +1,350 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERIC_PACKET_MATH_H
+#define EIGEN_GENERIC_PACKET_MATH_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \file GenericPacketMath.h
+ *
+ * Default implementation for types not supported by the vectorization.
+ * In practice these functions are provided to make easier the writing
+ * of generic vectorized code.
+ */
+
+#ifndef EIGEN_DEBUG_ALIGNED_LOAD
+#define EIGEN_DEBUG_ALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
+#define EIGEN_DEBUG_UNALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_ALIGNED_STORE
+#define EIGEN_DEBUG_ALIGNED_STORE
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_STORE
+#define EIGEN_DEBUG_UNALIGNED_STORE
+#endif
+
+struct default_packet_traits
+{
+ enum {
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 1,
+
+ HasDiv = 0,
+ HasSqrt = 0,
+ HasExp = 0,
+ HasLog = 0,
+ HasPow = 0,
+
+ HasSin = 0,
+ HasCos = 0,
+ HasTan = 0,
+ HasASin = 0,
+ HasACos = 0,
+ HasATan = 0
+ };
+};
+
+template<typename T> struct packet_traits : default_packet_traits
+{
+ typedef T type;
+ enum {
+ Vectorizable = 0,
+ size = 1,
+ AlignedOnScalar = 0
+ };
+ enum {
+ HasAdd = 0,
+ HasSub = 0,
+ HasMul = 0,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0
+ };
+};
+
+/** \internal \returns a + b (coeff-wise) */
+template<typename Packet> inline Packet
+padd(const Packet& a,
+ const Packet& b) { return a+b; }
+
+/** \internal \returns a - b (coeff-wise) */
+template<typename Packet> inline Packet
+psub(const Packet& a,
+ const Packet& b) { return a-b; }
+
+/** \internal \returns -a (coeff-wise) */
+template<typename Packet> inline Packet
+pnegate(const Packet& a) { return -a; }
+
+/** \internal \returns conj(a) (coeff-wise) */
+template<typename Packet> inline Packet
+pconj(const Packet& a) { return numext::conj(a); }
+
+/** \internal \returns a * b (coeff-wise) */
+template<typename Packet> inline Packet
+pmul(const Packet& a,
+ const Packet& b) { return a*b; }
+
+/** \internal \returns a / b (coeff-wise) */
+template<typename Packet> inline Packet
+pdiv(const Packet& a,
+ const Packet& b) { return a/b; }
+
+/** \internal \returns the min of \a a and \a b (coeff-wise) */
+template<typename Packet> inline Packet
+pmin(const Packet& a,
+ const Packet& b) { using std::min; return (min)(a, b); }
+
+/** \internal \returns the max of \a a and \a b (coeff-wise) */
+template<typename Packet> inline Packet
+pmax(const Packet& a,
+ const Packet& b) { using std::max; return (max)(a, b); }
+
+/** \internal \returns the absolute value of \a a */
+template<typename Packet> inline Packet
+pabs(const Packet& a) { using std::abs; return abs(a); }
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> inline Packet
+pand(const Packet& a, const Packet& b) { return a & b; }
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> inline Packet
+por(const Packet& a, const Packet& b) { return a | b; }
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> inline Packet
+pxor(const Packet& a, const Packet& b) { return a ^ b; }
+
+/** \internal \returns the bitwise andnot of \a a and \a b */
+template<typename Packet> inline Packet
+pandnot(const Packet& a, const Packet& b) { return a & (!b); }
+
+/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
+template<typename Packet> inline Packet
+pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet version of \a *from, (un-aligned load) */
+template<typename Packet> inline Packet
+ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with elements of \a *from duplicated.
+ * For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and
+ * duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]}
+ * Currently, this function is only used for scalar * complex products.
+ */
+template<typename Packet> inline Packet
+ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
+template<typename Packet> inline Packet
+pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
+
+/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
+template<typename Scalar> inline typename packet_traits<Scalar>::type
+plset(const Scalar& a) { return a; }
+
+/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal tries to do cache prefetching of \a addr */
+template<typename Scalar> inline void prefetch(const Scalar* addr)
+{
+#if !defined(_MSC_VER)
+__builtin_prefetch(addr);
+#endif
+}
+
+/** \internal \returns the first element of a packet */
+template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
+{ return a; }
+
+/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
+template<typename Packet> inline Packet
+preduxp(const Packet* vecs) { return vecs[0]; }
+
+/** \internal \returns the sum of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
+{ return a; }
+
+/** \internal \returns the product of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
+{ return a; }
+
+/** \internal \returns the min of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
+{ return a; }
+
+/** \internal \returns the max of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
+{ return a; }
+
+/** \internal \returns the reversed elements of \a a*/
+template<typename Packet> inline Packet preverse(const Packet& a)
+{ return a; }
+
+
+/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
+template<typename Packet> inline Packet pcplxflip(const Packet& a)
+{
+ // FIXME: uncomment the following in case we drop the internal imag and real functions.
+// using std::imag;
+// using std::real;
+ return Packet(imag(a),real(a));
+}
+
+/**************************
+* Special math functions
+***************************/
+
+/** \internal \returns the sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin(const Packet& a) { using std::sin; return sin(a); }
+
+/** \internal \returns the cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos(const Packet& a) { using std::cos; return cos(a); }
+
+/** \internal \returns the tan of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ptan(const Packet& a) { using std::tan; return tan(a); }
+
+/** \internal \returns the arc sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin(const Packet& a) { using std::asin; return asin(a); }
+
+/** \internal \returns the arc cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos(const Packet& a) { using std::acos; return acos(a); }
+
+/** \internal \returns the exp of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp(const Packet& a) { using std::exp; return exp(a); }
+
+/** \internal \returns the log of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog(const Packet& a) { using std::log; return log(a); }
+
+/** \internal \returns the square-root of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
+
+/***************************************************************************
+* The following functions might not have to be overwritten for vectorized types
+***************************************************************************/
+
+/** \internal copy a packet with constant coeficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
+// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
+template<typename Packet>
+inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
+{
+ pstore(to, pset1<Packet>(a));
+}
+
+/** \internal \returns a * b + c (coeff-wise) */
+template<typename Packet> inline Packet
+pmadd(const Packet& a,
+ const Packet& b,
+ const Packet& c)
+{ return padd(pmul(a, b),c); }
+
+/** \internal \returns a packet version of \a *from.
+ * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
+template<typename Packet, int LoadMode>
+inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
+{
+ if(LoadMode == Aligned)
+ return pload<Packet>(from);
+ else
+ return ploadu<Packet>(from);
+}
+
+/** \internal copy the packet \a from to \a *to.
+ * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet, int LoadMode>
+inline void pstoret(Scalar* to, const Packet& from)
+{
+ if(LoadMode == Aligned)
+ pstore(to, from);
+ else
+ pstoreu(to, from);
+}
+
+/** \internal default implementation of palign() allowing partial specialization */
+template<int Offset,typename PacketType>
+struct palign_impl
+{
+ // by default data are aligned, so there is nothing to be done :)
+ static inline void run(PacketType&, const PacketType&) {}
+};
+
+/** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
+ * of \a first and \a Offset first elements of \a second.
+ *
+ * This function is currently only used to optimize matrix-vector products on unligned matrices.
+ * It takes 2 packets that represent a contiguous memory array, and returns a packet starting
+ * at the position \a Offset. For instance, for packets of 4 elements, we have:
+ * Input:
+ * - first = {f0,f1,f2,f3}
+ * - second = {s0,s1,s2,s3}
+ * Output:
+ * - if Offset==0 then {f0,f1,f2,f3}
+ * - if Offset==1 then {f1,f2,f3,s0}
+ * - if Offset==2 then {f2,f3,s0,s1}
+ * - if Offset==3 then {f3,s0,s1,s3}
+ */
+template<int Offset,typename PacketType>
+inline void palign(PacketType& first, const PacketType& second)
+{
+ palign_impl<Offset,PacketType>::run(first,second);
+}
+
+/***************************************************************************
+* Fast complex products (GCC generates a function call which is very slow)
+***************************************************************************/
+
+template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
+{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
+{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERIC_PACKET_MATH_H
+
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
new file mode 100644
index 0000000..2acf977
--- /dev/null
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -0,0 +1,92 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GLOBAL_FUNCTIONS_H
+#define EIGEN_GLOBAL_FUNCTIONS_H
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR) \
+ template<typename Derived> \
+ inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
+ NAME(const Eigen::ArrayBase<Derived>& x) { \
+ return x.derived(); \
+ }
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
+ \
+ template<typename Derived> \
+ struct NAME##_retval<ArrayBase<Derived> > \
+ { \
+ typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
+ }; \
+ template<typename Derived> \
+ struct NAME##_impl<ArrayBase<Derived> > \
+ { \
+ static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
+ { \
+ return x.derived(); \
+ } \
+ };
+
+
+namespace Eigen
+{
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op)
+
+ template<typename Derived>
+ inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
+ pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
+ return x.derived().pow(exponent);
+ }
+
+ template<typename Derived>
+ inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const Derived, const Derived>
+ pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<Derived>& exponents)
+ {
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const Derived, const Derived>(
+ x.derived(),
+ exponents.derived()
+ );
+ }
+
+ /**
+ * \brief Component-wise division of a scalar by array elements.
+ **/
+ template <typename Derived>
+ inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
+ operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
+ {
+ return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
+ a.derived(),
+ Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>(s)
+ );
+ }
+
+ namespace internal
+ {
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
+ }
+}
+
+// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
+
+#endif // EIGEN_GLOBAL_FUNCTIONS_H
diff --git a/Eigen/src/Core/IO.h b/Eigen/src/Core/IO.h
new file mode 100644
index 0000000..8d4bc59
--- /dev/null
+++ b/Eigen/src/Core/IO.h
@@ -0,0 +1,250 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_IO_H
+#define EIGEN_IO_H
+
+namespace Eigen {
+
+enum { DontAlignCols = 1 };
+enum { StreamPrecision = -1,
+ FullPrecision = -2 };
+
+namespace internal {
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);
+}
+
+/** \class IOFormat
+ * \ingroup Core_Module
+ *
+ * \brief Stores a set of parameters controlling the way matrices are printed
+ *
+ * List of available parameters:
+ * - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
+ * The default is the special value \c StreamPrecision which means to use the
+ * stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
+ * \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
+ * type.
+ * - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which
+ * allows to disable the alignment of columns, resulting in faster code.
+ * - \b coeffSeparator string printed between two coefficients of the same row
+ * - \b rowSeparator string printed between two rows
+ * - \b rowPrefix string printed at the beginning of each row
+ * - \b rowSuffix string printed at the end of each row
+ * - \b matPrefix string printed at the beginning of the matrix
+ * - \b matSuffix string printed at the end of the matrix
+ *
+ * Example: \include IOFormat.cpp
+ * Output: \verbinclude IOFormat.out
+ *
+ * \sa DenseBase::format(), class WithFormat
+ */
+struct IOFormat
+{
+ /** Default contructor, see class IOFormat for the meaning of the parameters */
+ IOFormat(int _precision = StreamPrecision, int _flags = 0,
+ const std::string& _coeffSeparator = " ",
+ const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
+ const std::string& _matPrefix="", const std::string& _matSuffix="")
+ : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
+ rowSpacer(""), coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
+ {
+ int i = int(matSuffix.length())-1;
+ while (i>=0 && matSuffix[i]!='\n')
+ {
+ rowSpacer += ' ';
+ i--;
+ }
+ }
+ std::string matPrefix, matSuffix;
+ std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
+ std::string coeffSeparator;
+ int precision;
+ int flags;
+};
+
+/** \class WithFormat
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing matrix output with given format
+ *
+ * \param ExpressionType the type of the object on which IO stream operations are performed
+ *
+ * This class represents an expression with stream operators controlled by a given IOFormat.
+ * It is the return type of DenseBase::format()
+ * and most of the time this is the only way it is used.
+ *
+ * See class IOFormat for some examples.
+ *
+ * \sa DenseBase::format(), class IOFormat
+ */
+template<typename ExpressionType>
+class WithFormat
+{
+ public:
+
+ WithFormat(const ExpressionType& matrix, const IOFormat& format)
+ : m_matrix(matrix), m_format(format)
+ {}
+
+ friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
+ {
+ return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
+ }
+
+ protected:
+ const typename ExpressionType::Nested m_matrix;
+ IOFormat m_format;
+};
+
+/** \returns a WithFormat proxy object allowing to print a matrix the with given
+ * format \a fmt.
+ *
+ * See class IOFormat for some examples.
+ *
+ * \sa class IOFormat, class WithFormat
+ */
+template<typename Derived>
+inline const WithFormat<Derived>
+DenseBase<Derived>::format(const IOFormat& fmt) const
+{
+ return WithFormat<Derived>(derived(), fmt);
+}
+
+namespace internal {
+
+template<typename Scalar, bool IsInteger>
+struct significant_decimals_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline int run()
+ {
+ using std::ceil;
+ using std::log;
+ return cast<RealScalar,int>(ceil(-log(NumTraits<RealScalar>::epsilon())/log(RealScalar(10))));
+ }
+};
+
+template<typename Scalar>
+struct significant_decimals_default_impl<Scalar, true>
+{
+ static inline int run()
+ {
+ return 0;
+ }
+};
+
+template<typename Scalar>
+struct significant_decimals_impl
+ : significant_decimals_default_impl<Scalar, NumTraits<Scalar>::IsInteger>
+{};
+
+/** \internal
+ * print the matrix \a _m to the output stream \a s using the output format \a fmt */
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
+{
+ if(_m.size() == 0)
+ {
+ s << fmt.matPrefix << fmt.matSuffix;
+ return s;
+ }
+
+ typename Derived::Nested m = _m;
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Index Index;
+
+ Index width = 0;
+
+ std::streamsize explicit_precision;
+ if(fmt.precision == StreamPrecision)
+ {
+ explicit_precision = 0;
+ }
+ else if(fmt.precision == FullPrecision)
+ {
+ if (NumTraits<Scalar>::IsInteger)
+ {
+ explicit_precision = 0;
+ }
+ else
+ {
+ explicit_precision = significant_decimals_impl<Scalar>::run();
+ }
+ }
+ else
+ {
+ explicit_precision = fmt.precision;
+ }
+
+ std::streamsize old_precision = 0;
+ if(explicit_precision) old_precision = s.precision(explicit_precision);
+
+ bool align_cols = !(fmt.flags & DontAlignCols);
+ if(align_cols)
+ {
+ // compute the largest width
+ for(Index j = 0; j < m.cols(); ++j)
+ for(Index i = 0; i < m.rows(); ++i)
+ {
+ std::stringstream sstr;
+ sstr.copyfmt(s);
+ sstr << m.coeff(i,j);
+ width = std::max<Index>(width, Index(sstr.str().length()));
+ }
+ }
+ s << fmt.matPrefix;
+ for(Index i = 0; i < m.rows(); ++i)
+ {
+ if (i)
+ s << fmt.rowSpacer;
+ s << fmt.rowPrefix;
+ if(width) s.width(width);
+ s << m.coeff(i, 0);
+ for(Index j = 1; j < m.cols(); ++j)
+ {
+ s << fmt.coeffSeparator;
+ if (width) s.width(width);
+ s << m.coeff(i, j);
+ }
+ s << fmt.rowSuffix;
+ if( i < m.rows() - 1)
+ s << fmt.rowSeparator;
+ }
+ s << fmt.matSuffix;
+ if(explicit_precision) s.precision(old_precision);
+ return s;
+}
+
+} // end namespace internal
+
+/** \relates DenseBase
+ *
+ * Outputs the matrix, to the given stream.
+ *
+ * If you wish to print the matrix with a format different than the default, use DenseBase::format().
+ *
+ * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
+ * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
+ *
+ * \sa DenseBase::format()
+ */
+template<typename Derived>
+std::ostream & operator <<
+(std::ostream & s,
+ const DenseBase<Derived> & m)
+{
+ return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_IO_H
diff --git a/Eigen/src/Core/Map.h b/Eigen/src/Core/Map.h
new file mode 100644
index 0000000..f804c89
--- /dev/null
+++ b/Eigen/src/Core/Map.h
@@ -0,0 +1,192 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MAP_H
+#define EIGEN_MAP_H
+
+namespace Eigen {
+
+/** \class Map
+ * \ingroup Core_Module
+ *
+ * \brief A matrix or vector expression mapping an existing array of data.
+ *
+ * \tparam PlainObjectType the equivalent matrix type of the mapped data
+ * \tparam MapOptions specifies whether the pointer is \c #Aligned, or \c #Unaligned.
+ * The default is \c #Unaligned.
+ * \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
+ * of an ordinary, contiguous array. This can be overridden by specifying strides.
+ * The type passed here must be a specialization of the Stride template, see examples below.
+ *
+ * This class represents a matrix or vector expression mapping an existing array of data.
+ * It can be used to let Eigen interface without any overhead with non-Eigen data structures,
+ * such as plain C arrays or structures from other libraries. By default, it assumes that the
+ * data is laid out contiguously in memory. You can however override this by explicitly specifying
+ * inner and outer strides.
+ *
+ * Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
+ * \include Map_simple.cpp
+ * Output: \verbinclude Map_simple.out
+ *
+ * If you need to map non-contiguous arrays, you can do so by specifying strides:
+ *
+ * Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
+ * increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
+ * fixed value.
+ * \include Map_inner_stride.cpp
+ * Output: \verbinclude Map_inner_stride.out
+ *
+ * Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
+ * as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
+ * Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
+ * a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
+ * is \c Dynamic
+ * \include Map_outer_stride.cpp
+ * Output: \verbinclude Map_outer_stride.out
+ *
+ * For more details and for an example of specifying both an inner and an outer stride, see class Stride.
+ *
+ * \b Tip: to change the array of data mapped by a Map object, you can use the C++
+ * placement new syntax:
+ *
+ * Example: \include Map_placement_new.cpp
+ * Output: \verbinclude Map_placement_new.out
+ *
+ * This class is the return type of PlainObjectBase::Map() but can also be used directly.
+ *
+ * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+ */
+
+namespace internal {
+template<typename PlainObjectType, int MapOptions, typename StrideType>
+struct traits<Map<PlainObjectType, MapOptions, StrideType> >
+ : public traits<PlainObjectType>
+{
+ typedef traits<PlainObjectType> TraitsBase;
+ typedef typename PlainObjectType::Index Index;
+ typedef typename PlainObjectType::Scalar Scalar;
+ enum {
+ InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+ ? int(PlainObjectType::InnerStrideAtCompileTime)
+ : int(StrideType::InnerStrideAtCompileTime),
+ OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+ ? int(PlainObjectType::OuterStrideAtCompileTime)
+ : int(StrideType::OuterStrideAtCompileTime),
+ HasNoInnerStride = InnerStrideAtCompileTime == 1,
+ HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,
+ HasNoStride = HasNoInnerStride && HasNoOuterStride,
+ IsAligned = bool(EIGEN_ALIGN) && ((int(MapOptions)&Aligned)==Aligned),
+ IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic,
+ KeepsPacketAccess = bool(HasNoInnerStride)
+ && ( bool(IsDynamicSize)
+ || HasNoOuterStride
+ || ( OuterStrideAtCompileTime!=Dynamic
+ && ((static_cast<int>(sizeof(Scalar))*OuterStrideAtCompileTime)%16)==0 ) ),
+ Flags0 = TraitsBase::Flags & (~NestByRefBit),
+ Flags1 = IsAligned ? (int(Flags0) | AlignedBit) : (int(Flags0) & ~AlignedBit),
+ Flags2 = (bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime))
+ ? int(Flags1) : int(Flags1 & ~LinearAccessBit),
+ Flags3 = is_lvalue<PlainObjectType>::value ? int(Flags2) : (int(Flags2) & ~LvalueBit),
+ Flags = KeepsPacketAccess ? int(Flags3) : (int(Flags3) & ~PacketAccessBit)
+ };
+private:
+ enum { Options }; // Expressions don't have Options
+};
+}
+
+template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
+ : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
+{
+ public:
+
+ typedef MapBase<Map> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Map)
+
+ typedef typename Base::PointerType PointerType;
+#if EIGEN2_SUPPORT_STAGE <= STAGE30_FULL_EIGEN3_API
+ typedef const Scalar* PointerArgType;
+ inline PointerType cast_to_pointer_type(PointerArgType ptr) { return const_cast<PointerType>(ptr); }
+#else
+ typedef PointerType PointerArgType;
+ inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
+#endif
+
+ inline Index innerStride() const
+ {
+ return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
+ }
+
+ inline Index outerStride() const
+ {
+ return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+ : IsVectorAtCompileTime ? this->size()
+ : int(Flags)&RowMajorBit ? this->cols()
+ : this->rows();
+ }
+
+ /** Constructor in the fixed-size case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param a_stride optional Stride object, passing the strides.
+ */
+ inline Map(PointerArgType dataPtr, const StrideType& a_stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr)), m_stride(a_stride)
+ {
+ PlainObjectType::Base::_check_template_params();
+ }
+
+ /** Constructor in the dynamic-size vector case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param a_size the size of the vector expression
+ * \param a_stride optional Stride object, passing the strides.
+ */
+ inline Map(PointerArgType dataPtr, Index a_size, const StrideType& a_stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr), a_size), m_stride(a_stride)
+ {
+ PlainObjectType::Base::_check_template_params();
+ }
+
+ /** Constructor in the dynamic-size matrix case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param nbRows the number of rows of the matrix expression
+ * \param nbCols the number of columns of the matrix expression
+ * \param a_stride optional Stride object, passing the strides.
+ */
+ inline Map(PointerArgType dataPtr, Index nbRows, Index nbCols, const StrideType& a_stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr), nbRows, nbCols), m_stride(a_stride)
+ {
+ PlainObjectType::Base::_check_template_params();
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+
+ protected:
+ StrideType m_stride;
+};
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+inline Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
+ ::Array(const Scalar *data)
+{
+ this->_set_noalias(Eigen::Map<const Array>(data));
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+inline Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
+ ::Matrix(const Scalar *data)
+{
+ this->_set_noalias(Eigen::Map<const Matrix>(data));
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MAP_H
diff --git a/Eigen/src/Core/MapBase.h b/Eigen/src/Core/MapBase.h
new file mode 100644
index 0000000..92e1141
--- /dev/null
+++ b/Eigen/src/Core/MapBase.h
@@ -0,0 +1,247 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MAPBASE_H
+#define EIGEN_MAPBASE_H
+
+#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
+ EIGEN_STATIC_ASSERT((int(internal::traits<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
+ YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
+
+namespace Eigen {
+
+/** \class MapBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for Map and Block expression with direct access
+ *
+ * \sa class Map, class Block
+ */
+template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
+ : public internal::dense_xpr_base<Derived>::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Derived>::type Base;
+ enum {
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ SizeAtCompileTime = Base::SizeAtCompileTime
+ };
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::conditional<
+ bool(internal::is_lvalue<Derived>::value),
+ Scalar *,
+ const Scalar *>::type
+ PointerType;
+
+ using Base::derived;
+// using Base::RowsAtCompileTime;
+// using Base::ColsAtCompileTime;
+// using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+ using Base::IsRowMajor;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::eval;
+
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+
+ // bug 217 - compile error on ICC 11.1
+ using Base::operator=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ inline Index rows() const { return m_rows.value(); }
+ inline Index cols() const { return m_cols.value(); }
+
+ /** Returns a pointer to the first coefficient of the matrix or vector.
+ *
+ * \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
+ *
+ * \sa innerStride(), outerStride()
+ */
+ inline const Scalar* data() const { return m_data; }
+
+ inline const Scalar& coeff(Index rowId, Index colId) const
+ {
+ return m_data[colId * colStride() + rowId * rowStride()];
+ }
+
+ inline const Scalar& coeff(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return m_data[index * innerStride()];
+ }
+
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return this->m_data[colId * colStride() + rowId * rowStride()];
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return this->m_data[index * innerStride()];
+ }
+
+ template<int LoadMode>
+ inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>
+ (m_data + (colId * colStride() + rowId * rowStride()));
+ }
+
+ template<int LoadMode>
+ inline PacketScalar packet(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
+ }
+
+ inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+ {
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ checkSanity();
+ }
+
+ inline MapBase(PointerType dataPtr, Index vecSize)
+ : m_data(dataPtr),
+ m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),
+ m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime))
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ eigen_assert(vecSize >= 0);
+ eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
+ checkSanity();
+ }
+
+ inline MapBase(PointerType dataPtr, Index nbRows, Index nbCols)
+ : m_data(dataPtr), m_rows(nbRows), m_cols(nbCols)
+ {
+ eigen_assert( (dataPtr == 0)
+ || ( nbRows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == nbRows)
+ && nbCols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == nbCols)));
+ checkSanity();
+ }
+
+ protected:
+
+ void checkSanity() const
+ {
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(internal::traits<Derived>::Flags&PacketAccessBit,
+ internal::inner_stride_at_compile_time<Derived>::ret==1),
+ PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);
+ eigen_assert(EIGEN_IMPLIES(internal::traits<Derived>::Flags&AlignedBit, (size_t(m_data) % 16) == 0)
+ && "input pointer is not aligned on a 16 byte boundary");
+ }
+
+ PointerType m_data;
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+};
+
+template<typename Derived> class MapBase<Derived, WriteAccessors>
+ : public MapBase<Derived, ReadOnlyAccessors>
+{
+ typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
+ public:
+
+ typedef MapBase<Derived, ReadOnlyAccessors> Base;
+
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::PacketScalar PacketScalar;
+ typedef typename Base::Index Index;
+ typedef typename Base::PointerType PointerType;
+
+ using Base::derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<Derived>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ inline const Scalar* data() const { return this->m_data; }
+ inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
+
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
+ {
+ return this->m_data[col * colStride() + row * rowStride()];
+ }
+
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return this->m_data[index * innerStride()];
+ }
+
+ template<int StoreMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (this->m_data + (col * colStride() + row * rowStride()), val);
+ }
+
+ template<int StoreMode>
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (this->m_data + index * innerStride(), val);
+ }
+
+ explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}
+ inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}
+ inline MapBase(PointerType dataPtr, Index nbRows, Index nbCols) : Base(dataPtr, nbRows, nbCols) {}
+
+ Derived& operator=(const MapBase& other)
+ {
+ ReadOnlyMapBase::Base::operator=(other);
+ return derived();
+ }
+
+ // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
+ // see bugs 821 and 920.
+ using ReadOnlyMapBase::Base::operator=;
+};
+
+#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS
+
+} // end namespace Eigen
+
+#endif // EIGEN_MAPBASE_H
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
new file mode 100644
index 0000000..2bfc5eb
--- /dev/null
+++ b/Eigen/src/Core/MathFunctions.h
@@ -0,0 +1,768 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATHFUNCTIONS_H
+#define EIGEN_MATHFUNCTIONS_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \struct global_math_functions_filtering_base
+ *
+ * What it does:
+ * Defines a typedef 'type' as follows:
+ * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
+ * global_math_functions_filtering_base<T>::type is a typedef for it.
+ * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
+ *
+ * How it's used:
+ * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
+ * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
+ * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
+ * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
+ * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
+ *
+ * How it's implemented:
+ * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
+ * the typename dummy by an integer template parameter, it doesn't work anymore!
+ */
+
+template<typename T, typename dummy = void>
+struct global_math_functions_filtering_base
+{
+ typedef T type;
+};
+
+template<typename T> struct always_void { typedef void type; };
+
+template<typename T>
+struct global_math_functions_filtering_base
+ <T,
+ typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
+ >
+{
+ typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
+};
+
+#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
+#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
+
+/****************************************************************************
+* Implementation of real *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct real_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x)
+ {
+ return x;
+ }
+};
+
+template<typename Scalar>
+struct real_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x)
+ {
+ using std::real;
+ return real(x);
+ }
+};
+
+template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
+
+template<typename Scalar>
+struct real_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+
+/****************************************************************************
+* Implementation of imag *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct imag_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar&)
+ {
+ return RealScalar(0);
+ }
+};
+
+template<typename Scalar>
+struct imag_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x)
+ {
+ using std::imag;
+ return imag(x);
+ }
+};
+
+template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
+
+template<typename Scalar>
+struct imag_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of real_ref *
+****************************************************************************/
+
+template<typename Scalar>
+struct real_ref_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar& run(Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[0];
+ }
+ static inline const RealScalar& run(const Scalar& x)
+ {
+ return reinterpret_cast<const RealScalar*>(&x)[0];
+ }
+};
+
+template<typename Scalar>
+struct real_ref_retval
+{
+ typedef typename NumTraits<Scalar>::Real & type;
+};
+
+/****************************************************************************
+* Implementation of imag_ref *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct imag_ref_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar& run(Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[1];
+ }
+ static inline const RealScalar& run(const Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[1];
+ }
+};
+
+template<typename Scalar>
+struct imag_ref_default_impl<Scalar, false>
+{
+ static inline Scalar run(Scalar&)
+ {
+ return Scalar(0);
+ }
+ static inline const Scalar run(const Scalar&)
+ {
+ return Scalar(0);
+ }
+};
+
+template<typename Scalar>
+struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+struct imag_ref_retval
+{
+ typedef typename NumTraits<Scalar>::Real & type;
+};
+
+/****************************************************************************
+* Implementation of conj *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct conj_impl
+{
+ static inline Scalar run(const Scalar& x)
+ {
+ return x;
+ }
+};
+
+template<typename Scalar>
+struct conj_impl<Scalar,true>
+{
+ static inline Scalar run(const Scalar& x)
+ {
+ using std::conj;
+ return conj(x);
+ }
+};
+
+template<typename Scalar>
+struct conj_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of abs2 *
+****************************************************************************/
+
+template<typename Scalar>
+struct abs2_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x)
+ {
+ return x*x;
+ }
+};
+
+template<typename RealScalar>
+struct abs2_impl<std::complex<RealScalar> >
+{
+ static inline RealScalar run(const std::complex<RealScalar>& x)
+ {
+ return real(x)*real(x) + imag(x)*imag(x);
+ }
+};
+
+template<typename Scalar>
+struct abs2_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of norm1 *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct norm1_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x)
+ {
+ using std::abs;
+ return abs(real(x)) + abs(imag(x));
+ }
+};
+
+template<typename Scalar>
+struct norm1_default_impl<Scalar, false>
+{
+ static inline Scalar run(const Scalar& x)
+ {
+ using std::abs;
+ return abs(x);
+ }
+};
+
+template<typename Scalar>
+struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+struct norm1_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of hypot *
+****************************************************************************/
+
+template<typename Scalar>
+struct hypot_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline RealScalar run(const Scalar& x, const Scalar& y)
+ {
+ using std::max;
+ using std::min;
+ using std::abs;
+ using std::sqrt;
+ RealScalar _x = abs(x);
+ RealScalar _y = abs(y);
+ RealScalar p = (max)(_x, _y);
+ if(p==RealScalar(0)) return 0;
+ RealScalar q = (min)(_x, _y);
+ RealScalar qp = q/p;
+ return p * sqrt(RealScalar(1) + qp*qp);
+ }
+};
+
+template<typename Scalar>
+struct hypot_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of cast *
+****************************************************************************/
+
+template<typename OldType, typename NewType>
+struct cast_impl
+{
+ static inline NewType run(const OldType& x)
+ {
+ return static_cast<NewType>(x);
+ }
+};
+
+// here, for once, we're plainly returning NewType: we don't want cast to do weird things.
+
+template<typename OldType, typename NewType>
+inline NewType cast(const OldType& x)
+{
+ return cast_impl<OldType, NewType>::run(x);
+}
+
+/****************************************************************************
+* Implementation of atanh2 *
+****************************************************************************/
+
+template<typename Scalar, bool IsInteger>
+struct atanh2_default_impl
+{
+ typedef Scalar retval;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ using std::abs;
+ using std::log;
+ using std::sqrt;
+ Scalar z = x / y;
+ if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))
+ return RealScalar(0.5) * log((y + x) / (y - x));
+ else
+ return z + z*z*z / RealScalar(3);
+ }
+};
+
+template<typename Scalar>
+struct atanh2_default_impl<Scalar, true>
+{
+ static inline Scalar run(const Scalar&, const Scalar&)
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+ return Scalar(0);
+ }
+};
+
+template<typename Scalar>
+struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct atanh2_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of pow *
+****************************************************************************/
+
+template<typename Scalar, bool IsInteger>
+struct pow_default_impl
+{
+ typedef Scalar retval;
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ using std::pow;
+ return pow(x, y);
+ }
+};
+
+template<typename Scalar>
+struct pow_default_impl<Scalar, true>
+{
+ static inline Scalar run(Scalar x, Scalar y)
+ {
+ Scalar res(1);
+ eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
+ if(y & 1) res *= x;
+ y >>= 1;
+ while(y)
+ {
+ x *= x;
+ if(y&1) res *= x;
+ y >>= 1;
+ }
+ return res;
+ }
+};
+
+template<typename Scalar>
+struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct pow_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of random *
+****************************************************************************/
+
+template<typename Scalar,
+ bool IsComplex,
+ bool IsInteger>
+struct random_default_impl {};
+
+template<typename Scalar>
+struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct random_retval
+{
+ typedef Scalar type;
+};
+
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, false>
+{
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
+ }
+ static inline Scalar run()
+ {
+ return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
+ }
+};
+
+enum {
+ floor_log2_terminate,
+ floor_log2_move_up,
+ floor_log2_move_down,
+ floor_log2_bogus
+};
+
+template<unsigned int n, int lower, int upper> struct floor_log2_selector
+{
+ enum { middle = (lower + upper) / 2,
+ value = (upper <= lower + 1) ? int(floor_log2_terminate)
+ : (n < (1 << middle)) ? int(floor_log2_move_down)
+ : (n==0) ? int(floor_log2_bogus)
+ : int(floor_log2_move_up)
+ };
+};
+
+template<unsigned int n,
+ int lower = 0,
+ int upper = sizeof(unsigned int) * CHAR_BIT - 1,
+ int selector = floor_log2_selector<n, lower, upper>::value>
+struct floor_log2 {};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_move_down>
+{
+ enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_move_up>
+{
+ enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_terminate>
+{
+ enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_bogus>
+{
+ // no value, error at compile time
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, true>
+{
+ typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));
+ }
+
+ static inline Scalar run()
+ {
+#ifdef EIGEN_MAKING_DOCS
+ return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
+#else
+ enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,
+ scalar_bits = sizeof(Scalar) * CHAR_BIT,
+ shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
+ offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
+ };
+ return Scalar((std::rand() >> shift) - offset);
+#endif
+ }
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, true, false>
+{
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ return Scalar(random(real(x), real(y)),
+ random(imag(x), imag(y)));
+ }
+ static inline Scalar run()
+ {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ return Scalar(random<RealScalar>(), random<RealScalar>());
+ }
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
+{
+ return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
+}
+
+} // end namespace internal
+
+/****************************************************************************
+* Generic math function *
+****************************************************************************/
+
+namespace numext {
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
+{
+ return internal::real_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
+{
+ return internal::imag_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
+}
+
+// std::isfinite is non standard, so let's define our own version,
+// even though it is not very efficient.
+template<typename T> bool (isfinite)(const T& x)
+{
+ return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
+}
+
+} // end namespace numext
+
+namespace internal {
+
+/****************************************************************************
+* Implementation of fuzzy comparisons *
+****************************************************************************/
+
+template<typename Scalar,
+ bool IsComplex,
+ bool IsInteger>
+struct scalar_fuzzy_default_impl {};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, false>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar>
+ static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+ {
+ using std::abs;
+ return abs(x) <= abs(y) * prec;
+ }
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ using std::min;
+ using std::abs;
+ return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
+ }
+ static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ return x <= y || isApprox(x, y, prec);
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar>
+ static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
+ {
+ return x == Scalar(0);
+ }
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
+ {
+ return x == y;
+ }
+ static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
+ {
+ return x <= y;
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, true, false>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar>
+ static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+ {
+ return numext::abs2(x) <= numext::abs2(y) * prec * prec;
+ }
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ using std::min;
+ return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar, typename OtherScalar>
+inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool isApprox(const Scalar& x, const Scalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
+}
+
+/******************************************
+*** The special case of the bool type ***
+******************************************/
+
+template<> struct random_impl<bool>
+{
+ static inline bool run()
+ {
+ return random<int>(0,1)==0 ? false : true;
+ }
+};
+
+template<> struct scalar_fuzzy_impl<bool>
+{
+ typedef bool RealScalar;
+
+ template<typename OtherScalar>
+ static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
+ {
+ return !x;
+ }
+
+ static inline bool isApprox(bool x, bool y, bool)
+ {
+ return x == y;
+ }
+
+ static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
+ {
+ return (!x) || y;
+ }
+
+};
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATHFUNCTIONS_H
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
new file mode 100644
index 0000000..d7d0b5b
--- /dev/null
+++ b/Eigen/src/Core/Matrix.h
@@ -0,0 +1,405 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_H
+#define EIGEN_MATRIX_H
+
+namespace Eigen {
+
+/** \class Matrix
+ * \ingroup Core_Module
+ *
+ * \brief The matrix class, also used for vectors and row-vectors
+ *
+ * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
+ * Vectors are matrices with one column, and row-vectors are matrices with one row.
+ *
+ * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
+ *
+ * The first three template parameters are required:
+ * \tparam _Scalar \anchor matrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.
+ * User defined sclar types are supported as well (see \ref user_defined_scalars "here").
+ * \tparam _Rows Number of rows, or \b Dynamic
+ * \tparam _Cols Number of columns, or \b Dynamic
+ *
+ * The remaining template parameters are optional -- in most cases you don't have to worry about them.
+ * \tparam _Options \anchor matrix_tparam_options A combination of either \b #RowMajor or \b #ColMajor, and of either
+ * \b #AutoAlign or \b #DontAlign.
+ * The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
+ * for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
+ * \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
+ * \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
+ *
+ * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
+ *
+ * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
+ * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
+ * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
+ *
+ * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
+ * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
+ *
+ * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
+ * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
+ *
+ * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
+ *
+ * You can access elements of vectors and matrices using normal subscripting:
+ *
+ * \code
+ * Eigen::VectorXd v(10);
+ * v[0] = 0.1;
+ * v[1] = 0.2;
+ * v(0) = 0.3;
+ * v(1) = 0.4;
+ *
+ * Eigen::MatrixXi m(10, 10);
+ * m(0, 1) = 1;
+ * m(0, 2) = 2;
+ * m(0, 3) = 3;
+ * \endcode
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
+ *
+ * <i><b>Some notes:</b></i>
+ *
+ * <dl>
+ * <dt><b>\anchor dense Dense versus sparse:</b></dt>
+ * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
+ *
+ * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
+ * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
+ *
+ * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
+ * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
+ * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
+ * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
+ *
+ * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
+ * variables, and the array of coefficients is allocated dynamically on the heap.
+ *
+ * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
+ * If you want this behavior, see the Sparse module.</dd>
+ *
+ * <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
+ * <dd>In most cases, one just leaves these parameters to the default values.
+ * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
+ * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
+ * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
+ * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
+ * </dl>
+ *
+ * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
+ * \ref TopicStorageOrders
+ */
+
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+ typedef _Scalar Scalar;
+ typedef Dense StorageKind;
+ typedef DenseIndex Index;
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = _Rows,
+ ColsAtCompileTime = _Cols,
+ MaxRowsAtCompileTime = _MaxRows,
+ MaxColsAtCompileTime = _MaxCols,
+ Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ Options = _Options,
+ InnerStrideAtCompileTime = 1,
+ OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime
+ };
+};
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+class Matrix
+ : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+ public:
+
+ /** \brief Base class typedef.
+ * \sa PlainObjectBase
+ */
+ typedef PlainObjectBase<Matrix> Base;
+
+ enum { Options = _Options };
+
+ EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
+
+ typedef typename Base::PlainObject PlainObject;
+
+ using Base::base;
+ using Base::coeffRef;
+
+ /**
+ * \brief Assigns matrices to each other.
+ *
+ * \note This is a special case of the templated operator=. Its purpose is
+ * to prevent a default operator= from hiding the templated operator=.
+ *
+ * \callgraph
+ */
+ EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** \internal
+ * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
+ {
+ return Base::_set(other);
+ }
+
+ /* Here, doxygen failed to copy the brief information when using \copydoc */
+
+ /**
+ * \brief Copies the generic expression \a other into *this.
+ * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
+ {
+ return Base::operator=(other);
+ }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
+ {
+ return Base::operator=(func);
+ }
+
+ /** \brief Default constructor.
+ *
+ * For fixed-size matrices, does nothing.
+ *
+ * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+ * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+ * a matrix to 0 is not supported.
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_STRONG_INLINE Matrix() : Base()
+ {
+ Base::_check_template_params();
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ // FIXME is it still needed
+ Matrix(internal::constructor_without_unaligned_array_assert)
+ : Base(internal::constructor_without_unaligned_array_assert())
+ { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
+
+ /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
+ *
+ * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+ * it is redundant to pass the dimension here, so it makes more sense to use the default
+ * constructor Matrix() instead.
+ */
+ EIGEN_STRONG_INLINE explicit Matrix(Index dim)
+ : Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
+ eigen_assert(dim >= 0);
+ eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename T0, typename T1>
+ EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
+ {
+ Base::_check_template_params();
+ Base::template _init2<T0,T1>(x, y);
+ }
+ #else
+ /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
+ *
+ * This is useful for dynamic-size matrices. For fixed-size matrices,
+ * it is redundant to pass these parameters, so one should use the default constructor
+ * Matrix() instead. */
+ Matrix(Index rows, Index cols);
+ /** \brief Constructs an initialized 2D vector with given coefficients */
+ Matrix(const Scalar& x, const Scalar& y);
+ #endif
+
+ /** \brief Constructs an initialized 3D vector with given coefficients */
+ EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
+ m_storage.data()[0] = x;
+ m_storage.data()[1] = y;
+ m_storage.data()[2] = z;
+ }
+ /** \brief Constructs an initialized 4D vector with given coefficients */
+ EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
+ {
+ Base::_check_template_params();
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
+ m_storage.data()[0] = x;
+ m_storage.data()[1] = y;
+ m_storage.data()[2] = z;
+ m_storage.data()[3] = w;
+ }
+
+ explicit Matrix(const Scalar *data);
+
+ /** \brief Constructor copying the value of the expression \a other */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
+ : Base(other.rows() * other.cols(), other.rows(), other.cols())
+ {
+ // This test resides here, to bring the error messages closer to the user. Normally, these checks
+ // are performed deeply within the library, thus causing long and scary error traces.
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ Base::_check_template_params();
+ Base::_set_noalias(other);
+ }
+ /** \brief Copy constructor */
+ EIGEN_STRONG_INLINE Matrix(const Matrix& other)
+ : Base(other.rows() * other.cols(), other.rows(), other.cols())
+ {
+ Base::_check_template_params();
+ Base::_set_noalias(other);
+ }
+ /** \brief Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived>& other)
+ {
+ Base::_check_template_params();
+ Base::resize(other.rows(), other.cols());
+ other.evalTo(*this);
+ }
+
+ /** \brief Copy constructor for generic expressions.
+ * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
+ : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+ {
+ Base::_check_template_params();
+ Base::_resize_to_match(other);
+ // FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
+ // go for pure _set() implementations, right?
+ *this = other;
+ }
+
+ /** \internal
+ * \brief Override MatrixBase::swap() since for dynamic-sized matrices
+ * of same type it is enough to swap the data pointers.
+ */
+ template<typename OtherDerived>
+ void swap(MatrixBase<OtherDerived> const & other)
+ { this->_swap(other.derived()); }
+
+ inline Index innerStride() const { return 1; }
+ inline Index outerStride() const { return this->innerSize(); }
+
+ /////////// Geometry module ///////////
+
+ template<typename OtherDerived>
+ explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+ template<typename OtherDerived>
+ Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived>
+ explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+ template<typename OtherDerived>
+ Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+ #endif
+
+ // allow to extend Matrix outside Eigen
+ #ifdef EIGEN_MATRIX_PLUGIN
+ #include EIGEN_MATRIX_PLUGIN
+ #endif
+
+ protected:
+ template <typename Derived, typename OtherDerived, bool IsVector>
+ friend struct internal::conservative_resize_like_impl;
+
+ using Base::m_storage;
+};
+
+/** \defgroup matrixtypedefs Global matrix typedefs
+ *
+ * \ingroup Core_Module
+ *
+ * Eigen defines several typedef shortcuts for most common matrix and vector types.
+ *
+ * The general patterns are the following:
+ *
+ * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+ * for complex double.
+ *
+ * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
+ *
+ * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
+ * a fixed-size vector of 4 complex floats.
+ *
+ * \sa class Matrix
+ */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup matrixtypedefs */ \
+typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
+/** \ingroup matrixtypedefs */ \
+typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+#undef EIGEN_MAKE_FIXED_TYPEDEFS
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_H
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
new file mode 100644
index 0000000..b67a7c1
--- /dev/null
+++ b/Eigen/src/Core/MatrixBase.h
@@ -0,0 +1,554 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXBASE_H
+#define EIGEN_MATRIXBASE_H
+
+namespace Eigen {
+
+/** \class MatrixBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all dense matrices, vectors, and expressions
+ *
+ * This class is the base that is inherited by all matrix, vector, and related expression
+ * types. Most of the Eigen API is contained in this class, and its base classes. Other important
+ * classes for the Eigen API are Matrix, and VectorwiseOp.
+ *
+ * Note that some methods are defined in other modules such as the \ref LU_Module LU module
+ * for all functions related to matrix inversions.
+ *
+ * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
+ *
+ * When writing a function taking Eigen objects as argument, if you want your function
+ * to take as argument any matrix, vector, or expression, just let it take a
+ * MatrixBase argument. As an example, here is a function printFirstRow which, given
+ * a matrix, vector, or expression \a x, prints the first row of \a x.
+ *
+ * \code
+ template<typename Derived>
+ void printFirstRow(const Eigen::MatrixBase<Derived>& x)
+ {
+ cout << x.row(0) << endl;
+ }
+ * \endcode
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived> class MatrixBase
+ : public DenseBase<Derived>
+{
+ public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef MatrixBase StorageBaseType;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ typedef DenseBase<Derived> Base;
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+ using Base::CoeffReadCost;
+
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::eval;
+ using Base::operator+=;
+ using Base::operator-=;
+ using Base::operator*=;
+ using Base::operator/=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+ typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
+ typedef typename Base::RowXpr RowXpr;
+ typedef typename Base::ColXpr ColXpr;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** type of the equivalent square matrix */
+ typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
+ EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ /** \returns the size of the main diagonal, which is min(rows(),cols()).
+ * \sa rows(), cols(), SizeAtCompileTime. */
+ inline Index diagonalSize() const { return (std::min)(rows(),cols()); }
+
+ /** \brief The plain matrix type corresponding to this expression.
+ *
+ * This is not necessarily exactly the return type of eval(). In the case of plain matrices,
+ * the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
+ * that the return type of eval() is either PlainObject or const PlainObject&.
+ */
+ typedef Matrix<typename internal::traits<Derived>::Scalar,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime,
+ AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime
+ > PlainObject;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+ /** \internal the return type of MatrixBase::adjoint() */
+ typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
+ ConstTransposeReturnType
+ >::type AdjointReturnType;
+ /** \internal Return type of eigenvalues() */
+ typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
+ /** \internal the return type of identity */
+ typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,Derived> IdentityReturnType;
+ /** \internal the return type of unit vectors */
+ typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
+# include "../plugins/CommonCwiseUnaryOps.h"
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# ifdef EIGEN_MATRIXBASE_PLUGIN
+# include EIGEN_MATRIXBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ Derived& operator=(const MatrixBase& other);
+
+ // We cannot inherit here via Base::operator= since it is causing
+ // trouble with MSVC.
+
+ template <typename OtherDerived>
+ Derived& operator=(const DenseBase<OtherDerived>& other);
+
+ template <typename OtherDerived>
+ Derived& operator=(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ Derived& operator=(const ReturnByValue<OtherDerived>& other);
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
+
+ template<typename MatrixPower, typename Lhs, typename Rhs>
+ Derived& lazyAssign(const MatrixPowerProduct<MatrixPower, Lhs,Rhs>& other);
+
+ template<typename OtherDerived>
+ Derived& operator+=(const MatrixBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ Derived& operator-=(const MatrixBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ const typename ProductReturnType<Derived,OtherDerived>::Type
+ operator*(const MatrixBase<OtherDerived> &other) const;
+
+ template<typename OtherDerived>
+ const typename LazyProductReturnType<Derived,OtherDerived>::Type
+ lazyProduct(const MatrixBase<OtherDerived> &other) const;
+
+ template<typename OtherDerived>
+ Derived& operator*=(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ void applyOnTheLeft(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ void applyOnTheRight(const EigenBase<OtherDerived>& other);
+
+ template<typename DiagonalDerived>
+ const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
+ operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
+
+ template<typename OtherDerived>
+ typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+ dot(const MatrixBase<OtherDerived>& other) const;
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived>
+ Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
+ #endif
+
+ RealScalar squaredNorm() const;
+ RealScalar norm() const;
+ RealScalar stableNorm() const;
+ RealScalar blueNorm() const;
+ RealScalar hypotNorm() const;
+ const PlainObject normalized() const;
+ void normalize();
+
+ const AdjointReturnType adjoint() const;
+ void adjointInPlace();
+
+ typedef Diagonal<Derived> DiagonalReturnType;
+ DiagonalReturnType diagonal();
+ typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
+ ConstDiagonalReturnType diagonal() const;
+
+ template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
+ template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
+
+ template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
+ template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
+
+ typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
+ typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
+
+ DiagonalDynamicIndexReturnType diagonal(Index index);
+ ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
+
+ #ifdef EIGEN2_SUPPORT
+ template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
+ template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
+
+ // huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
+ // of an integer constant. Solution: overload the part() method template wrt template parameters list.
+ template<template<typename T, int N> class U>
+ const DiagonalWrapper<ConstDiagonalReturnType> part() const
+ { return diagonal().asDiagonal(); }
+ #endif // EIGEN2_SUPPORT
+
+ template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
+ template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
+
+ template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
+ template<unsigned int Mode> typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
+
+ template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
+ template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
+
+ template<unsigned int UpLo> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
+ template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
+
+ const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
+ const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
+ static const IdentityReturnType Identity();
+ static const IdentityReturnType Identity(Index rows, Index cols);
+ static const BasisReturnType Unit(Index size, Index i);
+ static const BasisReturnType Unit(Index i);
+ static const BasisReturnType UnitX();
+ static const BasisReturnType UnitY();
+ static const BasisReturnType UnitZ();
+ static const BasisReturnType UnitW();
+
+ const DiagonalWrapper<const Derived> asDiagonal() const;
+ const PermutationWrapper<const Derived> asPermutation() const;
+
+ Derived& setIdentity();
+ Derived& setIdentity(Index rows, Index cols);
+
+ bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ template<typename OtherDerived>
+ bool isOrthogonal(const MatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator!= */
+ template<typename OtherDerived>
+ inline bool operator==(const MatrixBase<OtherDerived>& other) const
+ { return cwiseEqual(other).all(); }
+
+ /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator== */
+ template<typename OtherDerived>
+ inline bool operator!=(const MatrixBase<OtherDerived>& other) const
+ { return cwiseNotEqual(other).any(); }
+
+ NoAlias<Derived,Eigen::MatrixBase > noalias();
+
+ inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
+ inline ForceAlignedAccess<Derived> forceAlignedAccess();
+ template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
+ template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
+
+ Scalar trace() const;
+
+/////////// Array module ///////////
+
+ template<int p> RealScalar lpNorm() const;
+
+ MatrixBase<Derived>& matrix() { return *this; }
+ const MatrixBase<Derived>& matrix() const { return *this; }
+
+ /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
+ * \sa ArrayBase::matrix() */
+ ArrayWrapper<Derived> array() { return derived(); }
+ const ArrayWrapper<const Derived> array() const { return derived(); }
+
+/////////// LU module ///////////
+
+ const FullPivLU<PlainObject> fullPivLu() const;
+ const PartialPivLU<PlainObject> partialPivLu() const;
+
+ #if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+ const LU<PlainObject> lu() const;
+ #endif
+
+ #ifdef EIGEN2_SUPPORT
+ const LU<PlainObject> eigen2_lu() const;
+ #endif
+
+ #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+ const PartialPivLU<PlainObject> lu() const;
+ #endif
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename ResultType>
+ void computeInverse(MatrixBase<ResultType> *result) const {
+ *result = this->inverse();
+ }
+ #endif
+
+ const internal::inverse_impl<Derived> inverse() const;
+ template<typename ResultType>
+ void computeInverseAndDetWithCheck(
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+ ) const;
+ template<typename ResultType>
+ void computeInverseWithCheck(
+ ResultType& inverse,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+ ) const;
+ Scalar determinant() const;
+
+/////////// Cholesky module ///////////
+
+ const LLT<PlainObject> llt() const;
+ const LDLT<PlainObject> ldlt() const;
+
+/////////// QR module ///////////
+
+ const HouseholderQR<PlainObject> householderQr() const;
+ const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
+ const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
+
+ #ifdef EIGEN2_SUPPORT
+ const QR<PlainObject> qr() const;
+ #endif
+
+ EigenvaluesReturnType eigenvalues() const;
+ RealScalar operatorNorm() const;
+
+/////////// SVD module ///////////
+
+ JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
+
+ #ifdef EIGEN2_SUPPORT
+ SVD<PlainObject> svd() const;
+ #endif
+
+/////////// Geometry module ///////////
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /// \internal helper struct to form the return type of the cross product
+ template<typename OtherDerived> struct cross_product_return_type {
+ typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
+ typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
+ };
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+ template<typename OtherDerived>
+ typename cross_product_return_type<OtherDerived>::type
+ cross(const MatrixBase<OtherDerived>& other) const;
+ template<typename OtherDerived>
+ PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
+ PlainObject unitOrthogonal(void) const;
+ Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
+
+ #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+ ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
+ // put this as separate enum value to work around possible GCC 4.3 bug (?)
+ enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
+ typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
+ HomogeneousReturnType homogeneous() const;
+ #endif
+
+ enum {
+ SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
+ };
+ typedef Block<const Derived,
+ internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
+ internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
+ typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
+ const ConstStartMinusOne > HNormalizedReturnType;
+
+ const HNormalizedReturnType hnormalized() const;
+
+////////// Householder module ///////////
+
+ void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
+ template<typename EssentialPart>
+ void makeHouseholder(EssentialPart& essential,
+ Scalar& tau, RealScalar& beta) const;
+ template<typename EssentialPart>
+ void applyHouseholderOnTheLeft(const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace);
+ template<typename EssentialPart>
+ void applyHouseholderOnTheRight(const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace);
+
+///////// Jacobi module /////////
+
+ template<typename OtherScalar>
+ void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+ template<typename OtherScalar>
+ void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+
+///////// MatrixFunctions module /////////
+
+ typedef typename internal::stem_function<Scalar>::type StemFunction;
+ const MatrixExponentialReturnValue<Derived> exp() const;
+ const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
+ const MatrixFunctionReturnValue<Derived> cosh() const;
+ const MatrixFunctionReturnValue<Derived> sinh() const;
+ const MatrixFunctionReturnValue<Derived> cos() const;
+ const MatrixFunctionReturnValue<Derived> sin() const;
+ const MatrixSquareRootReturnValue<Derived> sqrt() const;
+ const MatrixLogarithmReturnValue<Derived> log() const;
+ const MatrixPowerReturnValue<Derived> pow(const RealScalar& p) const;
+
+#ifdef EIGEN2_SUPPORT
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+ EvalBeforeAssigningBit>& other);
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+ EvalBeforeAssigningBit>& other);
+
+ /** \deprecated because .lazy() is deprecated
+ * Overloaded for cache friendly product evaluation */
+ template<typename OtherDerived>
+ Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
+ { return lazyAssign(other._expression()); }
+
+ template<unsigned int Added>
+ const Flagged<Derived, Added, 0> marked() const;
+ const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
+
+ inline const Cwise<Derived> cwise() const;
+ inline Cwise<Derived> cwise();
+
+ VectorBlock<Derived> start(Index size);
+ const VectorBlock<const Derived> start(Index size) const;
+ VectorBlock<Derived> end(Index size);
+ const VectorBlock<const Derived> end(Index size) const;
+ template<int Size> VectorBlock<Derived,Size> start();
+ template<int Size> const VectorBlock<const Derived,Size> start() const;
+ template<int Size> VectorBlock<Derived,Size> end();
+ template<int Size> const VectorBlock<const Derived,Size> end() const;
+
+ Minor<Derived> minor(Index row, Index col);
+ const Minor<Derived> minor(Index row, Index col) const;
+#endif
+
+ protected:
+ MatrixBase() : Base() {}
+
+ private:
+ explicit MatrixBase(int);
+ MatrixBase(int,int);
+ template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
+ protected:
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+};
+
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** replaces \c *this by \c *this * \a other.
+ *
+ * \returns a reference to \c *this
+ *
+ * Example: \include MatrixBase_applyOnTheRight.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheRight.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived&
+MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheRight(derived());
+ return derived();
+}
+
+/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
+ *
+ * Example: \include MatrixBase_applyOnTheRight.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheRight.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheRight(derived());
+}
+
+/** replaces \c *this by \a other * \c *this.
+ *
+ * Example: \include MatrixBase_applyOnTheLeft.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheLeft.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheLeft(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIXBASE_H
diff --git a/Eigen/src/Core/NestByValue.h b/Eigen/src/Core/NestByValue.h
new file mode 100644
index 0000000..a893b17
--- /dev/null
+++ b/Eigen/src/Core/NestByValue.h
@@ -0,0 +1,111 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NESTBYVALUE_H
+#define EIGEN_NESTBYVALUE_H
+
+namespace Eigen {
+
+/** \class NestByValue
+ * \ingroup Core_Module
+ *
+ * \brief Expression which must be nested by value
+ *
+ * \param ExpressionType the type of the object of which we are requiring nesting-by-value
+ *
+ * This class is the return type of MatrixBase::nestByValue()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::nestByValue()
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
+{};
+}
+
+template<typename ExpressionType> class NestByValue
+ : public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<NestByValue>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
+
+ inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
+
+ inline Index rows() const { return m_expression.rows(); }
+ inline Index cols() const { return m_expression.cols(); }
+ inline Index outerStride() const { return m_expression.outerStride(); }
+ inline Index innerStride() const { return m_expression.innerStride(); }
+
+ inline const CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_expression.coeff(row, col);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_expression.const_cast_derived().coeffRef(row, col);
+ }
+
+ inline const CoeffReturnType coeff(Index index) const
+ {
+ return m_expression.coeff(index);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index row, Index col) const
+ {
+ return m_expression.template packet<LoadMode>(row, col);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_expression.template packet<LoadMode>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
+ }
+
+ operator const ExpressionType&() const { return m_expression; }
+
+ protected:
+ const ExpressionType m_expression;
+};
+
+/** \returns an expression of the temporary version of *this.
+ */
+template<typename Derived>
+inline const NestByValue<Derived>
+DenseBase<Derived>::nestByValue() const
+{
+ return NestByValue<Derived>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_NESTBYVALUE_H
diff --git a/Eigen/src/Core/NoAlias.h b/Eigen/src/Core/NoAlias.h
new file mode 100644
index 0000000..768bfb1
--- /dev/null
+++ b/Eigen/src/Core/NoAlias.h
@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NOALIAS_H
+#define EIGEN_NOALIAS_H
+
+namespace Eigen {
+
+/** \class NoAlias
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing an operator = assuming no aliasing
+ *
+ * \param ExpressionType the type of the object on which to do the lazy assignment
+ *
+ * This class represents an expression with special assignment operators
+ * assuming no aliasing between the target expression and the source expression.
+ * More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
+ * It is the return type of MatrixBase::noalias()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::noalias()
+ */
+template<typename ExpressionType, template <typename> class StorageBase>
+class NoAlias
+{
+ typedef typename ExpressionType::Scalar Scalar;
+ public:
+ NoAlias(ExpressionType& expression) : m_expression(expression) {}
+
+ /** Behaves like MatrixBase::lazyAssign(other)
+ * \sa MatrixBase::lazyAssign() */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
+ { return internal::assign_selector<ExpressionType,OtherDerived,false>::run(m_expression,other.derived()); }
+
+ /** \sa MatrixBase::operator+= */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
+ {
+ typedef SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
+ SelfAdder tmp(m_expression);
+ typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
+ typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
+ internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
+ return m_expression;
+ }
+
+ /** \sa MatrixBase::operator-= */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
+ {
+ typedef SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
+ SelfAdder tmp(m_expression);
+ typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
+ typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
+ internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
+ return m_expression;
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE ExpressionType& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+ { other.derived().addTo(m_expression); return m_expression; }
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE ExpressionType& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+ { other.derived().subTo(m_expression); return m_expression; }
+
+ template<typename Lhs, typename Rhs, int NestingFlags>
+ EIGEN_STRONG_INLINE ExpressionType& operator+=(const CoeffBasedProduct<Lhs,Rhs,NestingFlags>& other)
+ { return m_expression.derived() += CoeffBasedProduct<Lhs,Rhs,NestByRefBit>(other.lhs(), other.rhs()); }
+
+ template<typename Lhs, typename Rhs, int NestingFlags>
+ EIGEN_STRONG_INLINE ExpressionType& operator-=(const CoeffBasedProduct<Lhs,Rhs,NestingFlags>& other)
+ { return m_expression.derived() -= CoeffBasedProduct<Lhs,Rhs,NestByRefBit>(other.lhs(), other.rhs()); }
+
+ template<typename OtherDerived>
+ ExpressionType& operator=(const ReturnByValue<OtherDerived>& func)
+ { return m_expression = func; }
+#endif
+
+ ExpressionType& expression() const
+ {
+ return m_expression;
+ }
+
+ protected:
+ ExpressionType& m_expression;
+};
+
+/** \returns a pseudo expression of \c *this with an operator= assuming
+ * no aliasing between \c *this and the source expression.
+ *
+ * More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
+ * Currently, even though several expressions may alias, only product
+ * expressions have this flag. Therefore, noalias() is only usefull when
+ * the source expression contains a matrix product.
+ *
+ * Here are some examples where noalias is usefull:
+ * \code
+ * D.noalias() = A * B;
+ * D.noalias() += A.transpose() * B;
+ * D.noalias() -= 2 * A * B.adjoint();
+ * \endcode
+ *
+ * On the other hand the following example will lead to a \b wrong result:
+ * \code
+ * A.noalias() = A * B;
+ * \endcode
+ * because the result matrix A is also an operand of the matrix product. Therefore,
+ * there is no alternative than evaluating A * B in a temporary, that is the default
+ * behavior when you write:
+ * \code
+ * A = A * B;
+ * \endcode
+ *
+ * \sa class NoAlias
+ */
+template<typename Derived>
+NoAlias<Derived,MatrixBase> MatrixBase<Derived>::noalias()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_NOALIAS_H
diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
new file mode 100644
index 0000000..bac9e50
--- /dev/null
+++ b/Eigen/src/Core/NumTraits.h
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NUMTRAITS_H
+#define EIGEN_NUMTRAITS_H
+
+namespace Eigen {
+
+/** \class NumTraits
+ * \ingroup Core_Module
+ *
+ * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
+ *
+ * \param T the numeric type at hand
+ *
+ * This class stores enums, typedefs and static methods giving information about a numeric type.
+ *
+ * The provided data consists of:
+ * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
+ * then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
+ * is a typedef to \a U.
+ * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
+ * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
+ * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
+ * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
+ * only intended as a helper for code that needs to explicitly promote types.
+ * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
+ * this means, just use \a T here.
+ * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
+ * type, and to 0 otherwise.
+ * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
+ * and to \c 0 otherwise.
+ * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
+ * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
+ * Stay vague here. No need to do architecture-specific stuff.
+ * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
+ * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
+ * be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
+ * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T.
+ * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
+ * value by the fuzzy comparison operators.
+ * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
+ */
+
+template<typename T> struct GenericNumTraits
+{
+ enum {
+ IsInteger = std::numeric_limits<T>::is_integer,
+ IsSigned = std::numeric_limits<T>::is_signed,
+ IsComplex = 0,
+ RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
+ ReadCost = 1,
+ AddCost = 1,
+ MulCost = 1
+ };
+
+ typedef T Real;
+ typedef typename internal::conditional<
+ IsInteger,
+ typename internal::conditional<sizeof(T)<=2, float, double>::type,
+ T
+ >::type NonInteger;
+ typedef T Nested;
+
+ static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); }
+ static inline Real dummy_precision()
+ {
+ // make sure to override this for floating-point types
+ return Real(0);
+ }
+ static inline T highest() { return (std::numeric_limits<T>::max)(); }
+ static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); }
+
+#ifdef EIGEN2_SUPPORT
+ enum {
+ HasFloatingPoint = !IsInteger
+ };
+ typedef NonInteger FloatingPoint;
+#endif
+};
+
+template<typename T> struct NumTraits : GenericNumTraits<T>
+{};
+
+template<> struct NumTraits<float>
+ : GenericNumTraits<float>
+{
+ static inline float dummy_precision() { return 1e-5f; }
+};
+
+template<> struct NumTraits<double> : GenericNumTraits<double>
+{
+ static inline double dummy_precision() { return 1e-12; }
+};
+
+template<> struct NumTraits<long double>
+ : GenericNumTraits<long double>
+{
+ static inline long double dummy_precision() { return 1e-15l; }
+};
+
+template<typename _Real> struct NumTraits<std::complex<_Real> >
+ : GenericNumTraits<std::complex<_Real> >
+{
+ typedef _Real Real;
+ enum {
+ IsComplex = 1,
+ RequireInitialization = NumTraits<_Real>::RequireInitialization,
+ ReadCost = 2 * NumTraits<_Real>::ReadCost,
+ AddCost = 2 * NumTraits<Real>::AddCost,
+ MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
+ };
+
+ static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
+ static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
+{
+ typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
+ typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
+ typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
+ typedef ArrayType & Nested;
+
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ IsInteger = NumTraits<Scalar>::IsInteger,
+ IsSigned = NumTraits<Scalar>::IsSigned,
+ RequireInitialization = 1,
+ ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
+ AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
+ MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
+ };
+
+ static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
+ static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_NUMTRAITS_H
diff --git a/Eigen/src/Core/PermutationMatrix.h b/Eigen/src/Core/PermutationMatrix.h
new file mode 100644
index 0000000..85ffae2
--- /dev/null
+++ b/Eigen/src/Core/PermutationMatrix.h
@@ -0,0 +1,721 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PERMUTATIONMATRIX_H
+#define EIGEN_PERMUTATIONMATRIX_H
+
+namespace Eigen {
+
+template<int RowCol,typename IndicesType,typename MatrixType, typename StorageKind> class PermutedImpl;
+
+/** \class PermutationBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for permutations
+ *
+ * \param Derived the derived class
+ *
+ * This class is the base class for all expressions representing a permutation matrix,
+ * internally stored as a vector of integers.
+ * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
+ * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
+ * \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
+ * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
+ * \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
+ *
+ * Permutation matrices are square and invertible.
+ *
+ * Notice that in addition to the member functions and operators listed here, there also are non-member
+ * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
+ * on either side.
+ *
+ * \sa class PermutationMatrix, class PermutationWrapper
+ */
+
+namespace internal {
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
+struct permut_matrix_product_retval;
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
+struct permut_sparsematrix_product_retval;
+enum PermPermProduct_t {PermPermProduct};
+
+} // end namespace internal
+
+template<typename Derived>
+class PermutationBase : public EigenBase<Derived>
+{
+ typedef internal::traits<Derived> Traits;
+ typedef EigenBase<Derived> Base;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ enum {
+ Flags = Traits::Flags,
+ CoeffReadCost = Traits::CoeffReadCost,
+ RowsAtCompileTime = Traits::RowsAtCompileTime,
+ ColsAtCompileTime = Traits::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
+ };
+ typedef typename Traits::Scalar Scalar;
+ typedef typename Traits::Index Index;
+ typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
+ DenseMatrixType;
+ typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,Index>
+ PlainPermutationType;
+ using Base::derived;
+ #endif
+
+ /** Copies the other permutation into *this */
+ template<typename OtherDerived>
+ Derived& operator=(const PermutationBase<OtherDerived>& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename OtherDerived>
+ Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
+ {
+ setIdentity(tr.size());
+ for(Index k=size()-1; k>=0; --k)
+ applyTranspositionOnTheRight(k,tr.coeff(k));
+ return derived();
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Derived& operator=(const PermutationBase& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+ #endif
+
+ /** \returns the number of rows */
+ inline Index rows() const { return Index(indices().size()); }
+
+ /** \returns the number of columns */
+ inline Index cols() const { return Index(indices().size()); }
+
+ /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
+ inline Index size() const { return Index(indices().size()); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& other) const
+ {
+ other.setZero();
+ for (int i=0; i<rows();++i)
+ other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
+ }
+ #endif
+
+ /** \returns a Matrix object initialized from this permutation matrix. Notice that it
+ * is inefficient to return this Matrix object by value. For efficiency, favor using
+ * the Matrix constructor taking EigenBase objects.
+ */
+ DenseMatrixType toDenseMatrix() const
+ {
+ return derived();
+ }
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return derived().indices(); }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return derived().indices(); }
+
+ /** Resizes to given size.
+ */
+ inline void resize(Index newSize)
+ {
+ indices().resize(newSize);
+ }
+
+ /** Sets *this to be the identity permutation matrix */
+ void setIdentity()
+ {
+ for(Index i = 0; i < size(); ++i)
+ indices().coeffRef(i) = i;
+ }
+
+ /** Sets *this to be the identity permutation matrix of given size.
+ */
+ void setIdentity(Index newSize)
+ {
+ resize(newSize);
+ setIdentity();
+ }
+
+ /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
+ *
+ * \returns a reference to *this.
+ *
+ * \warning This is much slower than applyTranspositionOnTheRight(int,int):
+ * this has linear complexity and requires a lot of branching.
+ *
+ * \sa applyTranspositionOnTheRight(int,int)
+ */
+ Derived& applyTranspositionOnTheLeft(Index i, Index j)
+ {
+ eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+ for(Index k = 0; k < size(); ++k)
+ {
+ if(indices().coeff(k) == i) indices().coeffRef(k) = j;
+ else if(indices().coeff(k) == j) indices().coeffRef(k) = i;
+ }
+ return derived();
+ }
+
+ /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
+ *
+ * \returns a reference to *this.
+ *
+ * This is a fast operation, it only consists in swapping two indices.
+ *
+ * \sa applyTranspositionOnTheLeft(int,int)
+ */
+ Derived& applyTranspositionOnTheRight(Index i, Index j)
+ {
+ eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+ std::swap(indices().coeffRef(i), indices().coeffRef(j));
+ return derived();
+ }
+
+ /** \returns the inverse permutation matrix.
+ *
+ * \note \note_try_to_help_rvo
+ */
+ inline Transpose<PermutationBase> inverse() const
+ { return derived(); }
+ /** \returns the tranpose permutation matrix.
+ *
+ * \note \note_try_to_help_rvo
+ */
+ inline Transpose<PermutationBase> transpose() const
+ { return derived(); }
+
+ /**** multiplication helpers to hopefully get RVO ****/
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ protected:
+ template<typename OtherDerived>
+ void assignTranspose(const PermutationBase<OtherDerived>& other)
+ {
+ for (int i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
+ }
+ template<typename Lhs,typename Rhs>
+ void assignProduct(const Lhs& lhs, const Rhs& rhs)
+ {
+ eigen_assert(lhs.cols() == rhs.rows());
+ for (int i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
+ }
+#endif
+
+ public:
+
+ /** \returns the product permutation matrix.
+ *
+ * \note \note_try_to_help_rvo
+ */
+ template<typename Other>
+ inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
+ { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
+
+ /** \returns the product of a permutation with another inverse permutation.
+ *
+ * \note \note_try_to_help_rvo
+ */
+ template<typename Other>
+ inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other) const
+ { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
+
+ /** \returns the product of an inverse permutation with another permutation.
+ *
+ * \note \note_try_to_help_rvo
+ */
+ template<typename Other> friend
+ inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
+ { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
+
+ /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.
+ *
+ * This function is O(\c n) procedure allocating a buffer of \c n booleans.
+ */
+ Index determinant() const
+ {
+ Index res = 1;
+ Index n = size();
+ Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
+ mask.fill(false);
+ Index r = 0;
+ while(r < n)
+ {
+ // search for the next seed
+ while(r<n && mask[r]) r++;
+ if(r>=n)
+ break;
+ // we got one, let's follow it until we are back to the seed
+ Index k0 = r++;
+ mask.coeffRef(k0) = true;
+ for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
+ {
+ mask.coeffRef(k) = true;
+ res = -res;
+ }
+ }
+ return res;
+ }
+
+ protected:
+
+};
+
+/** \class PermutationMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Permutation matrix
+ *
+ * \param SizeAtCompileTime the number of rows/cols, or Dynamic
+ * \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+ * \param IndexType the interger type of the indices
+ *
+ * This class represents a permutation matrix, internally stored as a vector of integers.
+ *
+ * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
+ */
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
+ : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef IndexType Index;
+ typedef Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
+{
+ typedef PermutationBase<PermutationMatrix> Base;
+ typedef internal::traits<PermutationMatrix> Traits;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ #endif
+
+ inline PermutationMatrix()
+ {}
+
+ /** Constructs an uninitialized permutation matrix of given size.
+ */
+ inline PermutationMatrix(int size) : m_indices(size)
+ {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
+ : m_indices(other.indices()) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** Standard copy constructor. Defined only to prevent a default copy constructor
+ * from hiding the other templated constructor */
+ inline PermutationMatrix(const PermutationMatrix& other) : m_indices(other.indices()) {}
+ #endif
+
+ /** Generic constructor from expression of the indices. The indices
+ * array has the meaning that the permutations sends each integer i to indices[i].
+ *
+ * \warning It is your responsibility to check that the indices array that you passes actually
+ * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
+ * array's size.
+ */
+ template<typename Other>
+ explicit inline PermutationMatrix(const MatrixBase<Other>& a_indices) : m_indices(a_indices)
+ {}
+
+ /** Convert the Transpositions \a tr to a permutation matrix */
+ template<typename Other>
+ explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
+ : m_indices(tr.size())
+ {
+ *this = tr;
+ }
+
+ /** Copies the other permutation into *this */
+ template<typename Other>
+ PermutationMatrix& operator=(const PermutationBase<Other>& other)
+ {
+ m_indices = other.indices();
+ return *this;
+ }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename Other>
+ PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
+ {
+ return Base::operator=(tr.derived());
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ PermutationMatrix& operator=(const PermutationMatrix& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return m_indices; }
+
+
+ /**** multiplication helpers to hopefully get RVO ****/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Other>
+ PermutationMatrix(const Transpose<PermutationBase<Other> >& other)
+ : m_indices(other.nestedPermutation().size())
+ {
+ for (int i=0; i<m_indices.size();++i) m_indices.coeffRef(other.nestedPermutation().indices().coeff(i)) = i;
+ }
+ template<typename Lhs,typename Rhs>
+ PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
+ : m_indices(lhs.indices().size())
+ {
+ Base::assignProduct(lhs,rhs);
+ }
+#endif
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
+ : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef IndexType Index;
+ typedef Map<const Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess>
+ : public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
+{
+ typedef PermutationBase<Map> Base;
+ typedef internal::traits<Map> Traits;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar Index;
+ #endif
+
+ inline Map(const Index* indicesPtr)
+ : m_indices(indicesPtr)
+ {}
+
+ inline Map(const Index* indicesPtr, Index size)
+ : m_indices(indicesPtr,size)
+ {}
+
+ /** Copies the other permutation into *this */
+ template<typename Other>
+ Map& operator=(const PermutationBase<Other>& other)
+ { return Base::operator=(other.derived()); }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename Other>
+ Map& operator=(const TranspositionsBase<Other>& tr)
+ { return Base::operator=(tr.derived()); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Map& operator=(const Map& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+/** \class PermutationWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Class to view a vector of integers as a permutation matrix
+ *
+ * \param _IndicesType the type of the vector of integer (can be any compatible expression)
+ *
+ * This class allows to view any vector expression of integers as a permutation matrix.
+ *
+ * \sa class PermutationBase, class PermutationMatrix
+ */
+
+struct PermutationStorage {};
+
+template<typename _IndicesType> class TranspositionsWrapper;
+namespace internal {
+template<typename _IndicesType>
+struct traits<PermutationWrapper<_IndicesType> >
+{
+ typedef PermutationStorage StorageKind;
+ typedef typename _IndicesType::Scalar Scalar;
+ typedef typename _IndicesType::Scalar Index;
+ typedef _IndicesType IndicesType;
+ enum {
+ RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
+ ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = IndicesType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = IndicesType::MaxColsAtCompileTime,
+ Flags = 0,
+ CoeffReadCost = _IndicesType::CoeffReadCost
+ };
+};
+}
+
+template<typename _IndicesType>
+class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
+{
+ typedef PermutationBase<PermutationWrapper> Base;
+ typedef internal::traits<PermutationWrapper> Traits;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ #endif
+
+ inline PermutationWrapper(const IndicesType& a_indices)
+ : m_indices(a_indices)
+ {}
+
+ /** const version of indices(). */
+ const typename internal::remove_all<typename IndicesType::Nested>::type&
+ indices() const { return m_indices; }
+
+ protected:
+
+ typename IndicesType::Nested m_indices;
+};
+
+/** \returns the matrix with the permutation applied to the columns.
+ */
+template<typename Derived, typename PermutationDerived>
+inline const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight>
+operator*(const MatrixBase<Derived>& matrix,
+ const PermutationBase<PermutationDerived> &permutation)
+{
+ return internal::permut_matrix_product_retval
+ <PermutationDerived, Derived, OnTheRight>
+ (permutation.derived(), matrix.derived());
+}
+
+/** \returns the matrix with the permutation applied to the rows.
+ */
+template<typename Derived, typename PermutationDerived>
+inline const internal::permut_matrix_product_retval
+ <PermutationDerived, Derived, OnTheLeft>
+operator*(const PermutationBase<PermutationDerived> &permutation,
+ const MatrixBase<Derived>& matrix)
+{
+ return internal::permut_matrix_product_retval
+ <PermutationDerived, Derived, OnTheLeft>
+ (permutation.derived(), matrix.derived());
+}
+
+namespace internal {
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct traits<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct permut_matrix_product_retval
+ : public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+ typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+ typedef typename MatrixType::Index Index;
+
+ permut_matrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
+ : m_permutation(perm), m_matrix(matrix)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ const Index n = Side==OnTheLeft ? rows() : cols();
+ // FIXME we need an is_same for expression that is not sensitive to constness. For instance
+ // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.
+ if( is_same<MatrixTypeNestedCleaned,Dest>::value
+ && blas_traits<MatrixTypeNestedCleaned>::HasUsableDirectAccess
+ && blas_traits<Dest>::HasUsableDirectAccess
+ && extract_data(dst) == extract_data(m_matrix))
+ {
+ // apply the permutation inplace
+ Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(m_permutation.size());
+ mask.fill(false);
+ Index r = 0;
+ while(r < m_permutation.size())
+ {
+ // search for the next seed
+ while(r<m_permutation.size() && mask[r]) r++;
+ if(r>=m_permutation.size())
+ break;
+ // we got one, let's follow it until we are back to the seed
+ Index k0 = r++;
+ Index kPrev = k0;
+ mask.coeffRef(k0) = true;
+ for(Index k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
+ {
+ Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
+ .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
+ (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
+
+ mask.coeffRef(k) = true;
+ kPrev = k;
+ }
+ }
+ }
+ else
+ {
+ for(int i = 0; i < n; ++i)
+ {
+ Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
+ (dst, ((Side==OnTheLeft) ^ Transposed) ? m_permutation.indices().coeff(i) : i)
+
+ =
+
+ Block<const MatrixTypeNestedCleaned,Side==OnTheLeft ? 1 : MatrixType::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixType::ColsAtCompileTime>
+ (m_matrix, ((Side==OnTheRight) ^ Transposed) ? m_permutation.indices().coeff(i) : i);
+ }
+ }
+ }
+
+ protected:
+ const PermutationType& m_permutation;
+ typename MatrixType::Nested m_matrix;
+};
+
+/* Template partial specialization for transposed/inverse permutations */
+
+template<typename Derived>
+struct traits<Transpose<PermutationBase<Derived> > >
+ : traits<Derived>
+{};
+
+} // end namespace internal
+
+template<typename Derived>
+class Transpose<PermutationBase<Derived> >
+ : public EigenBase<Transpose<PermutationBase<Derived> > >
+{
+ typedef Derived PermutationType;
+ typedef typename PermutationType::IndicesType IndicesType;
+ typedef typename PermutationType::PlainPermutationType PlainPermutationType;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef internal::traits<PermutationType> Traits;
+ typedef typename Derived::DenseMatrixType DenseMatrixType;
+ enum {
+ Flags = Traits::Flags,
+ CoeffReadCost = Traits::CoeffReadCost,
+ RowsAtCompileTime = Traits::RowsAtCompileTime,
+ ColsAtCompileTime = Traits::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
+ };
+ typedef typename Traits::Scalar Scalar;
+ #endif
+
+ Transpose(const PermutationType& p) : m_permutation(p) {}
+
+ inline int rows() const { return m_permutation.rows(); }
+ inline int cols() const { return m_permutation.cols(); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& other) const
+ {
+ other.setZero();
+ for (int i=0; i<rows();++i)
+ other.coeffRef(i, m_permutation.indices().coeff(i)) = typename DenseDerived::Scalar(1);
+ }
+ #endif
+
+ /** \return the equivalent permutation matrix */
+ PlainPermutationType eval() const { return *this; }
+
+ DenseMatrixType toDenseMatrix() const { return *this; }
+
+ /** \returns the matrix with the inverse permutation applied to the columns.
+ */
+ template<typename OtherDerived> friend
+ inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>
+ operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trPerm)
+ {
+ return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>(trPerm.m_permutation, matrix.derived());
+ }
+
+ /** \returns the matrix with the inverse permutation applied to the rows.
+ */
+ template<typename OtherDerived>
+ inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>
+ operator*(const MatrixBase<OtherDerived>& matrix) const
+ {
+ return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>(m_permutation, matrix.derived());
+ }
+
+ const PermutationType& nestedPermutation() const { return m_permutation; }
+
+ protected:
+ const PermutationType& m_permutation;
+};
+
+template<typename Derived>
+const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PERMUTATIONMATRIX_H
diff --git a/Eigen/src/Core/PlainObjectBase.h b/Eigen/src/Core/PlainObjectBase.h
new file mode 100644
index 0000000..8a3e454
--- /dev/null
+++ b/Eigen/src/Core/PlainObjectBase.h
@@ -0,0 +1,792 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSESTORAGEBASE_H
+#define EIGEN_DENSESTORAGEBASE_H
+
+#if defined(EIGEN_INITIALIZE_MATRICES_BY_ZERO)
+# define EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=Scalar(0);
+#elif defined(EIGEN_INITIALIZE_MATRICES_BY_NAN)
+# define EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=std::numeric_limits<Scalar>::quiet_NaN();
+#else
+# undef EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+#endif
+
+namespace Eigen {
+
+namespace internal {
+
+template<int MaxSizeAtCompileTime> struct check_rows_cols_for_overflow {
+ template<typename Index>
+ static EIGEN_ALWAYS_INLINE void run(Index, Index)
+ {
+ }
+};
+
+template<> struct check_rows_cols_for_overflow<Dynamic> {
+ template<typename Index>
+ static EIGEN_ALWAYS_INLINE void run(Index rows, Index cols)
+ {
+ // http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242
+ // we assume Index is signed
+ Index max_index = (size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed
+ bool error = (rows == 0 || cols == 0) ? false
+ : (rows > max_index / cols);
+ if (error)
+ throw_std_bad_alloc();
+ }
+};
+
+template <typename Derived,
+ typename OtherDerived = Derived,
+ bool IsVector = bool(Derived::IsVectorAtCompileTime) && bool(OtherDerived::IsVectorAtCompileTime)>
+struct conservative_resize_like_impl;
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;
+
+} // end namespace internal
+
+/** \class PlainObjectBase
+ * \brief %Dense storage base class for matrices and arrays.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_PLAINOBJECTBASE_PLUGIN.
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+namespace internal {
+
+// this is a warkaround to doxygen not being able to understand the inheritence logic
+// when it is hidden by the dense_xpr_base helper struct.
+template<typename Derived> struct dense_xpr_base_dispatcher_for_doxygen;// : public MatrixBase<Derived> {};
+/** This class is just a workaround for Doxygen and it does not not actually exist. */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct dense_xpr_base_dispatcher_for_doxygen<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+ : public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > {};
+/** This class is just a workaround for Doxygen and it does not not actually exist. */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct dense_xpr_base_dispatcher_for_doxygen<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+ : public ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > {};
+
+} // namespace internal
+
+template<typename Derived>
+class PlainObjectBase : public internal::dense_xpr_base_dispatcher_for_doxygen<Derived>
+#else
+template<typename Derived>
+class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
+#endif
+{
+ public:
+ enum { Options = internal::traits<Derived>::Options };
+ typedef typename internal::dense_xpr_base<Derived>::type Base;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Derived DenseType;
+
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+
+ template<typename PlainObjectType, int MapOptions, typename StrideType> friend class Eigen::Map;
+ friend class Eigen::Map<Derived, Unaligned>;
+ typedef Eigen::Map<Derived, Unaligned> MapType;
+ friend class Eigen::Map<const Derived, Unaligned>;
+ typedef const Eigen::Map<const Derived, Unaligned> ConstMapType;
+ friend class Eigen::Map<Derived, Aligned>;
+ typedef Eigen::Map<Derived, Aligned> AlignedMapType;
+ friend class Eigen::Map<const Derived, Aligned>;
+ typedef const Eigen::Map<const Derived, Aligned> ConstAlignedMapType;
+ template<typename StrideType> struct StridedMapType { typedef Eigen::Map<Derived, Unaligned, StrideType> type; };
+ template<typename StrideType> struct StridedConstMapType { typedef Eigen::Map<const Derived, Unaligned, StrideType> type; };
+ template<typename StrideType> struct StridedAlignedMapType { typedef Eigen::Map<Derived, Aligned, StrideType> type; };
+ template<typename StrideType> struct StridedConstAlignedMapType { typedef Eigen::Map<const Derived, Aligned, StrideType> type; };
+
+ protected:
+ DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;
+
+ public:
+ enum { NeedsToAlign = SizeAtCompileTime != Dynamic && (internal::traits<Derived>::Flags & AlignedBit) != 0 };
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+
+ Base& base() { return *static_cast<Base*>(this); }
+ const Base& base() const { return *static_cast<const Base*>(this); }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_storage.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_storage.cols(); }
+
+ EIGEN_STRONG_INLINE const Scalar& coeff(Index rowId, Index colId) const
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
+ {
+ return m_storage.data()[index];
+ }
+
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index rowId, Index colId)
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ return m_storage.data()[index];
+ }
+
+ EIGEN_STRONG_INLINE const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const
+ {
+ return m_storage.data()[index];
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>
+ (m_storage.data() + (Flags & RowMajorBit
+ ? colId + rowId * m_storage.cols()
+ : rowId + colId * m_storage.rows()));
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>(m_storage.data() + index);
+ }
+
+ /** \internal */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (m_storage.data() + (Flags & RowMajorBit
+ ? colId + rowId * m_storage.cols()
+ : rowId + colId * m_storage.rows()), val);
+ }
+
+ /** \internal */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, val);
+ }
+
+ /** \returns a const pointer to the data array of this matrix */
+ EIGEN_STRONG_INLINE const Scalar *data() const
+ { return m_storage.data(); }
+
+ /** \returns a pointer to the data array of this matrix */
+ EIGEN_STRONG_INLINE Scalar *data()
+ { return m_storage.data(); }
+
+ /** Resizes \c *this to a \a rows x \a cols matrix.
+ *
+ * This method is intended for dynamic-size matrices, although it is legal to call it on any
+ * matrix as long as fixed dimensions are left unchanged. If you only want to change the number
+ * of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).
+ *
+ * If the current number of coefficients of \c *this exactly matches the
+ * product \a rows * \a cols, then no memory allocation is performed and
+ * the current values are left unchanged. In all other cases, including
+ * shrinking, the data is reallocated and all previous values are lost.
+ *
+ * Example: \include Matrix_resize_int_int.cpp
+ * Output: \verbinclude Matrix_resize_int_int.out
+ *
+ * \sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)
+ */
+ EIGEN_STRONG_INLINE void resize(Index nbRows, Index nbCols)
+ {
+ eigen_assert( EIGEN_IMPLIES(RowsAtCompileTime!=Dynamic,nbRows==RowsAtCompileTime)
+ && EIGEN_IMPLIES(ColsAtCompileTime!=Dynamic,nbCols==ColsAtCompileTime)
+ && EIGEN_IMPLIES(RowsAtCompileTime==Dynamic && MaxRowsAtCompileTime!=Dynamic,nbRows<=MaxRowsAtCompileTime)
+ && EIGEN_IMPLIES(ColsAtCompileTime==Dynamic && MaxColsAtCompileTime!=Dynamic,nbCols<=MaxColsAtCompileTime)
+ && nbRows>=0 && nbCols>=0 && "Invalid sizes when resizing a matrix or array.");
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(nbRows, nbCols);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ Index size = nbRows*nbCols;
+ bool size_changed = size != this->size();
+ m_storage.resize(size, nbRows, nbCols);
+ if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ #else
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(nbRows, nbCols);
+ m_storage.resize(nbRows*nbCols, nbRows, nbCols);
+ #endif
+ }
+
+ /** Resizes \c *this to a vector of length \a size
+ *
+ * \only_for_vectors. This method does not work for
+ * partially dynamic matrices when the static dimension is anything other
+ * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+ *
+ * Example: \include Matrix_resize_int.cpp
+ * Output: \verbinclude Matrix_resize_int.out
+ *
+ * \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)
+ */
+ inline void resize(Index size)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)
+ eigen_assert(((SizeAtCompileTime == Dynamic && (MaxSizeAtCompileTime==Dynamic || size<=MaxSizeAtCompileTime)) || SizeAtCompileTime == size) && size>=0);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ bool size_changed = size != this->size();
+ #endif
+ if(RowsAtCompileTime == 1)
+ m_storage.resize(size, 1, size);
+ else
+ m_storage.resize(size, size, 1);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ #endif
+ }
+
+ /** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \c NoChange
+ * as in the example below.
+ *
+ * Example: \include Matrix_resize_NoChange_int.cpp
+ * Output: \verbinclude Matrix_resize_NoChange_int.out
+ *
+ * \sa resize(Index,Index)
+ */
+ inline void resize(NoChange_t, Index nbCols)
+ {
+ resize(rows(), nbCols);
+ }
+
+ /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \c NoChange
+ * as in the example below.
+ *
+ * Example: \include Matrix_resize_int_NoChange.cpp
+ * Output: \verbinclude Matrix_resize_int_NoChange.out
+ *
+ * \sa resize(Index,Index)
+ */
+ inline void resize(Index nbRows, NoChange_t)
+ {
+ resize(nbRows, cols());
+ }
+
+ /** Resizes \c *this to have the same dimensions as \a other.
+ * Takes care of doing all the checking that's needed.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void resizeLike(const EigenBase<OtherDerived>& _other)
+ {
+ const OtherDerived& other = _other.derived();
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(other.rows(), other.cols());
+ const Index othersize = other.rows()*other.cols();
+ if(RowsAtCompileTime == 1)
+ {
+ eigen_assert(other.rows() == 1 || other.cols() == 1);
+ resize(1, othersize);
+ }
+ else if(ColsAtCompileTime == 1)
+ {
+ eigen_assert(other.rows() == 1 || other.cols() == 1);
+ resize(othersize, 1);
+ }
+ else resize(other.rows(), other.cols());
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * The method is intended for matrices of dynamic size. If you only want to change the number
+ * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+ * conservativeResize(Index, NoChange_t).
+ *
+ * Matrices are resized relative to the top-left element. In case values need to be
+ * appended to the matrix they will be uninitialized.
+ */
+ EIGEN_STRONG_INLINE void conservativeResize(Index nbRows, Index nbCols)
+ {
+ internal::conservative_resize_like_impl<Derived>::run(*this, nbRows, nbCols);
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+ * the number of columns unchanged.
+ *
+ * In case the matrix is growing, new rows will be uninitialized.
+ */
+ EIGEN_STRONG_INLINE void conservativeResize(Index nbRows, NoChange_t)
+ {
+ // Note: see the comment in conservativeResize(Index,Index)
+ conservativeResize(nbRows, cols());
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+ * the number of rows unchanged.
+ *
+ * In case the matrix is growing, new columns will be uninitialized.
+ */
+ EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index nbCols)
+ {
+ // Note: see the comment in conservativeResize(Index,Index)
+ conservativeResize(rows(), nbCols);
+ }
+
+ /** Resizes the vector to \a size while retaining old values.
+ *
+ * \only_for_vectors. This method does not work for
+ * partially dynamic matrices when the static dimension is anything other
+ * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+ *
+ * When values are appended, they will be uninitialized.
+ */
+ EIGEN_STRONG_INLINE void conservativeResize(Index size)
+ {
+ internal::conservative_resize_like_impl<Derived>::run(*this, size);
+ }
+
+ /** Resizes the matrix to \a rows x \a cols of \c other, while leaving old values untouched.
+ *
+ * The method is intended for matrices of dynamic size. If you only want to change the number
+ * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+ * conservativeResize(Index, NoChange_t).
+ *
+ * Matrices are resized relative to the top-left element. In case values need to be
+ * appended to the matrix they will copied from \c other.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase<OtherDerived>& other)
+ {
+ internal::conservative_resize_like_impl<Derived,OtherDerived>::run(*this, other);
+ }
+
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other)
+ {
+ return _set(other);
+ }
+
+ /** \sa MatrixBase::lazyAssign() */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase<OtherDerived>& other)
+ {
+ _resize_to_match(other);
+ return Base::lazyAssign(other.derived());
+ }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue<OtherDerived>& func)
+ {
+ resize(func.rows(), func.cols());
+ return Base::operator=(func);
+ }
+
+ EIGEN_STRONG_INLINE PlainObjectBase() : m_storage()
+ {
+// _check_template_params();
+// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ // FIXME is it still needed ?
+ /** \internal */
+ PlainObjectBase(internal::constructor_without_unaligned_array_assert)
+ : m_storage(internal::constructor_without_unaligned_array_assert())
+ {
+// _check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+#endif
+
+ EIGEN_STRONG_INLINE PlainObjectBase(Index a_size, Index nbRows, Index nbCols)
+ : m_storage(a_size, nbRows, nbCols)
+ {
+// _check_template_params();
+// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ /** \copydoc MatrixBase::operator=(const EigenBase<OtherDerived>&)
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived> &other)
+ {
+ _resize_to_match(other);
+ Base::operator=(other.derived());
+ return this->derived();
+ }
+
+ /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase<OtherDerived> &other)
+ : m_storage(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+ {
+ _check_template_params();
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(other.derived().rows(), other.derived().cols());
+ Base::operator=(other.derived());
+ }
+
+ /** \name Map
+ * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
+ * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
+ * \a data pointers.
+ *
+ * \see class Map
+ */
+ //@{
+ static inline ConstMapType Map(const Scalar* data)
+ { return ConstMapType(data); }
+ static inline MapType Map(Scalar* data)
+ { return MapType(data); }
+ static inline ConstMapType Map(const Scalar* data, Index size)
+ { return ConstMapType(data, size); }
+ static inline MapType Map(Scalar* data, Index size)
+ { return MapType(data, size); }
+ static inline ConstMapType Map(const Scalar* data, Index rows, Index cols)
+ { return ConstMapType(data, rows, cols); }
+ static inline MapType Map(Scalar* data, Index rows, Index cols)
+ { return MapType(data, rows, cols); }
+
+ static inline ConstAlignedMapType MapAligned(const Scalar* data)
+ { return ConstAlignedMapType(data); }
+ static inline AlignedMapType MapAligned(Scalar* data)
+ { return AlignedMapType(data); }
+ static inline ConstAlignedMapType MapAligned(const Scalar* data, Index size)
+ { return ConstAlignedMapType(data, size); }
+ static inline AlignedMapType MapAligned(Scalar* data, Index size)
+ { return AlignedMapType(data, size); }
+ static inline ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
+ { return ConstAlignedMapType(data, rows, cols); }
+ static inline AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)
+ { return AlignedMapType(data, rows, cols); }
+
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ //@}
+
+ using Base::setConstant;
+ Derived& setConstant(Index size, const Scalar& value);
+ Derived& setConstant(Index rows, Index cols, const Scalar& value);
+
+ using Base::setZero;
+ Derived& setZero(Index size);
+ Derived& setZero(Index rows, Index cols);
+
+ using Base::setOnes;
+ Derived& setOnes(Index size);
+ Derived& setOnes(Index rows, Index cols);
+
+ using Base::setRandom;
+ Derived& setRandom(Index size);
+ Derived& setRandom(Index rows, Index cols);
+
+ #ifdef EIGEN_PLAINOBJECTBASE_PLUGIN
+ #include EIGEN_PLAINOBJECTBASE_PLUGIN
+ #endif
+
+ protected:
+ /** \internal Resizes *this in preparation for assigning \a other to it.
+ * Takes care of doing all the checking that's needed.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase<OtherDerived>& other)
+ {
+ #ifdef EIGEN_NO_AUTOMATIC_RESIZING
+ eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())
+ : (rows() == other.rows() && cols() == other.cols())))
+ && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
+ EIGEN_ONLY_USED_FOR_DEBUG(other);
+ if(this->size()==0)
+ resizeLike(other);
+ #else
+ resizeLike(other);
+ #endif
+ }
+
+ /**
+ * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ *
+ * \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
+ *
+ * \internal
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Derived& _set(const DenseBase<OtherDerived>& other)
+ {
+ _set_selector(other.derived(), typename internal::conditional<static_cast<bool>(int(OtherDerived::Flags) & EvalBeforeAssigningBit), internal::true_type, internal::false_type>::type());
+ return this->derived();
+ }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::true_type&) { _set_noalias(other.eval()); }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::false_type&) { _set_noalias(other); }
+
+ /** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
+ * is the case when creating a new matrix) so one can enforce lazy evaluation.
+ *
+ * \sa operator=(const MatrixBase<OtherDerived>&), _set()
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase<OtherDerived>& other)
+ {
+ // I don't think we need this resize call since the lazyAssign will anyways resize
+ // and lazyAssign will be called by the assign selector.
+ //_resize_to_match(other);
+ // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
+ // it wouldn't allow to copy a row-vector into a column-vector.
+ return internal::assign_selector<Derived,OtherDerived,false>::run(this->derived(), other.derived());
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_STRONG_INLINE void _init2(Index nbRows, Index nbCols, typename internal::enable_if<Base::SizeAtCompileTime!=2,T0>::type* = 0)
+ {
+ EIGEN_STATIC_ASSERT(bool(NumTraits<T0>::IsInteger) &&
+ bool(NumTraits<T1>::IsInteger),
+ FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)
+ resize(nbRows,nbCols);
+ }
+ template<typename T0, typename T1>
+ EIGEN_STRONG_INLINE void _init2(const Scalar& val0, const Scalar& val1, typename internal::enable_if<Base::SizeAtCompileTime==2,T0>::type* = 0)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)
+ m_storage.data()[0] = val0;
+ m_storage.data()[1] = val1;
+ }
+
+ template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+ friend struct internal::matrix_swap_impl;
+
+ /** \internal generic implementation of swap for dense storage since for dynamic-sized matrices of same type it is enough to swap the
+ * data pointers.
+ */
+ template<typename OtherDerived>
+ void _swap(DenseBase<OtherDerived> const & other)
+ {
+ enum { SwapPointers = internal::is_same<Derived, OtherDerived>::value && Base::SizeAtCompileTime==Dynamic };
+ internal::matrix_swap_impl<Derived, OtherDerived, bool(SwapPointers)>::run(this->derived(), other.const_cast_derived());
+ }
+
+ public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ static EIGEN_STRONG_INLINE void _check_template_params()
+ {
+ EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (Options&RowMajor)==RowMajor)
+ && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (Options&RowMajor)==0)
+ && ((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0))
+ && ((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0))
+ && ((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0))
+ && ((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0))
+ && (MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic)
+ && (MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic)
+ && (Options & (DontAlign|RowMajor)) == Options),
+ INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ }
+#endif
+
+private:
+ enum { ThisConstantIsPrivateInPlainObjectBase };
+};
+
+namespace internal {
+
+template <typename Derived, typename OtherDerived, bool IsVector>
+struct conservative_resize_like_impl
+{
+ typedef typename Derived::Index Index;
+ static void run(DenseBase<Derived>& _this, Index rows, Index cols)
+ {
+ if (_this.rows() == rows && _this.cols() == cols) return;
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+
+ if ( ( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows
+ (!Derived::IsRowMajor && _this.rows() == rows) ) // column-major and we change only the number of columns
+ {
+ internal::check_rows_cols_for_overflow<Derived::MaxSizeAtCompileTime>::run(rows, cols);
+ _this.derived().m_storage.conservativeResize(rows*cols,rows,cols);
+ }
+ else
+ {
+ // The storage order does not allow us to use reallocation.
+ typename Derived::PlainObject tmp(rows,cols);
+ const Index common_rows = (std::min)(rows, _this.rows());
+ const Index common_cols = (std::min)(cols, _this.cols());
+ tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+ _this.derived().swap(tmp);
+ }
+ }
+
+ static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+ {
+ if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+ // Note: Here is space for improvement. Basically, for conservativeResize(Index,Index),
+ // neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the
+ // dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or
+ // conservativeResize(NoChange_t, Index cols). For these methods new static asserts like
+ // EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good.
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived)
+
+ if ( ( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows
+ (!Derived::IsRowMajor && _this.rows() == other.rows()) ) // column-major and we change only the number of columns
+ {
+ const Index new_rows = other.rows() - _this.rows();
+ const Index new_cols = other.cols() - _this.cols();
+ _this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols());
+ if (new_rows>0)
+ _this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows);
+ else if (new_cols>0)
+ _this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols);
+ }
+ else
+ {
+ // The storage order does not allow us to use reallocation.
+ typename Derived::PlainObject tmp(other);
+ const Index common_rows = (std::min)(tmp.rows(), _this.rows());
+ const Index common_cols = (std::min)(tmp.cols(), _this.cols());
+ tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+ _this.derived().swap(tmp);
+ }
+ }
+};
+
+// Here, the specialization for vectors inherits from the general matrix case
+// to allow calling .conservativeResize(rows,cols) on vectors.
+template <typename Derived, typename OtherDerived>
+struct conservative_resize_like_impl<Derived,OtherDerived,true>
+ : conservative_resize_like_impl<Derived,OtherDerived,false>
+{
+ using conservative_resize_like_impl<Derived,OtherDerived,false>::run;
+
+ typedef typename Derived::Index Index;
+ static void run(DenseBase<Derived>& _this, Index size)
+ {
+ const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size;
+ const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1;
+ _this.derived().m_storage.conservativeResize(size,new_rows,new_cols);
+ }
+
+ static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+ {
+ if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+ const Index num_new_elements = other.size() - _this.size();
+
+ const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows();
+ const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1;
+ _this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols);
+
+ if (num_new_elements > 0)
+ _this.tail(num_new_elements) = other.tail(num_new_elements);
+ }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+struct matrix_swap_impl
+{
+ static inline void run(MatrixTypeA& a, MatrixTypeB& b)
+ {
+ a.base().swap(b);
+ }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB>
+struct matrix_swap_impl<MatrixTypeA, MatrixTypeB, true>
+{
+ static inline void run(MatrixTypeA& a, MatrixTypeB& b)
+ {
+ static_cast<typename MatrixTypeA::Base&>(a).m_storage.swap(static_cast<typename MatrixTypeB::Base&>(b).m_storage);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSESTORAGEBASE_H
diff --git a/Eigen/src/Core/ProductBase.h b/Eigen/src/Core/ProductBase.h
new file mode 100644
index 0000000..cf74470
--- /dev/null
+++ b/Eigen/src/Core/ProductBase.h
@@ -0,0 +1,290 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PRODUCTBASE_H
+#define EIGEN_PRODUCTBASE_H
+
+namespace Eigen {
+
+/** \class ProductBase
+ * \ingroup Core_Module
+ *
+ */
+
+namespace internal {
+template<typename Derived, typename _Lhs, typename _Rhs>
+struct traits<ProductBase<Derived,_Lhs,_Rhs> >
+{
+ typedef MatrixXpr XprKind;
+ typedef typename remove_all<_Lhs>::type Lhs;
+ typedef typename remove_all<_Rhs>::type Rhs;
+ typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+ typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
+ typename traits<Rhs>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<Lhs>::Index,
+ typename traits<Rhs>::Index>::type Index;
+ enum {
+ RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
+ ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
+ Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
+ | EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
+ // Note that EvalBeforeNestingBit and NestByRefBit
+ // are not used in practice because nested is overloaded for products
+ CoeffReadCost = 0 // FIXME why is it needed ?
+ };
+};
+}
+
+#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived) \
+ typedef ProductBase<Derived, Lhs, Rhs > Base; \
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+ typedef typename Base::LhsNested LhsNested; \
+ typedef typename Base::_LhsNested _LhsNested; \
+ typedef typename Base::LhsBlasTraits LhsBlasTraits; \
+ typedef typename Base::ActualLhsType ActualLhsType; \
+ typedef typename Base::_ActualLhsType _ActualLhsType; \
+ typedef typename Base::RhsNested RhsNested; \
+ typedef typename Base::_RhsNested _RhsNested; \
+ typedef typename Base::RhsBlasTraits RhsBlasTraits; \
+ typedef typename Base::ActualRhsType ActualRhsType; \
+ typedef typename Base::_ActualRhsType _ActualRhsType; \
+ using Base::m_lhs; \
+ using Base::m_rhs;
+
+template<typename Derived, typename Lhs, typename Rhs>
+class ProductBase : public MatrixBase<Derived>
+{
+ public:
+ typedef MatrixBase<Derived> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ProductBase)
+
+ typedef typename Lhs::Nested LhsNested;
+ typedef typename internal::remove_all<LhsNested>::type _LhsNested;
+ typedef internal::blas_traits<_LhsNested> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef typename internal::remove_all<ActualLhsType>::type _ActualLhsType;
+ typedef typename internal::traits<Lhs>::Scalar LhsScalar;
+
+ typedef typename Rhs::Nested RhsNested;
+ typedef typename internal::remove_all<RhsNested>::type _RhsNested;
+ typedef internal::blas_traits<_RhsNested> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef typename internal::remove_all<ActualRhsType>::type _ActualRhsType;
+ typedef typename internal::traits<Rhs>::Scalar RhsScalar;
+
+ // Diagonal of a product: no need to evaluate the arguments because they are going to be evaluated only once
+ typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType;
+
+ public:
+
+#ifndef EIGEN_NO_MALLOC
+ typedef typename Base::PlainObject BasePlainObject;
+ typedef Matrix<Scalar,RowsAtCompileTime==1?1:Dynamic,ColsAtCompileTime==1?1:Dynamic,BasePlainObject::Options> DynPlainObject;
+ typedef typename internal::conditional<(BasePlainObject::SizeAtCompileTime==Dynamic) || (BasePlainObject::SizeAtCompileTime*int(sizeof(Scalar)) < int(EIGEN_STACK_ALLOCATION_LIMIT)),
+ BasePlainObject, DynPlainObject>::type PlainObject;
+#else
+ typedef typename Base::PlainObject PlainObject;
+#endif
+
+ ProductBase(const Lhs& a_lhs, const Rhs& a_rhs)
+ : m_lhs(a_lhs), m_rhs(a_rhs)
+ {
+ eigen_assert(a_lhs.cols() == a_rhs.rows()
+ && "invalid matrix product"
+ && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
+ }
+
+ inline Index rows() const { return m_lhs.rows(); }
+ inline Index cols() const { return m_rhs.cols(); }
+
+ template<typename Dest>
+ inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst,Scalar(1)); }
+
+ template<typename Dest>
+ inline void addTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(1)); }
+
+ template<typename Dest>
+ inline void subTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(-1)); }
+
+ template<typename Dest>
+ inline void scaleAndAddTo(Dest& dst, const Scalar& alpha) const { derived().scaleAndAddTo(dst,alpha); }
+
+ const _LhsNested& lhs() const { return m_lhs; }
+ const _RhsNested& rhs() const { return m_rhs; }
+
+ // Implicit conversion to the nested type (trigger the evaluation of the product)
+ operator const PlainObject& () const
+ {
+ m_result.resize(m_lhs.rows(), m_rhs.cols());
+ derived().evalTo(m_result);
+ return m_result;
+ }
+
+ const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal() const
+ { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
+
+ template<int Index>
+ const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal() const
+ { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
+
+ const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal(Index index) const
+ { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs).diagonal(index); }
+
+ // restrict coeff accessors to 1x1 expressions. No need to care about mutators here since this isnt a Lvalue expression
+ typename Base::CoeffReturnType coeff(Index row, Index col) const
+ {
+#ifdef EIGEN2_SUPPORT
+ return lhs().row(row).cwiseProduct(rhs().col(col).transpose()).sum();
+#else
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ Matrix<Scalar,1,1> result = *this;
+ return result.coeff(row,col);
+#endif
+ }
+
+ typename Base::CoeffReturnType coeff(Index i) const
+ {
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ Matrix<Scalar,1,1> result = *this;
+ return result.coeff(i);
+ }
+
+ const Scalar& coeffRef(Index row, Index col) const
+ {
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ return derived().coeffRef(row,col);
+ }
+
+ const Scalar& coeffRef(Index i) const
+ {
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ return derived().coeffRef(i);
+ }
+
+ protected:
+
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+
+ mutable PlainObject m_result;
+};
+
+// here we need to overload the nested rule for products
+// such that the nested type is a const reference to a plain matrix
+namespace internal {
+template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
+struct nested<GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
+{
+ typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
+};
+template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
+struct nested<const GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
+{
+ typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
+};
+}
+
+template<typename NestedProduct>
+class ScaledProduct;
+
+// Note that these two operator* functions are not defined as member
+// functions of ProductBase, because, otherwise we would have to
+// define all overloads defined in MatrixBase. Furthermore, Using
+// "using Base::operator*" would not work with MSVC.
+//
+// Also note that here we accept any compatible scalar types
+template<typename Derived,typename Lhs,typename Rhs>
+const ScaledProduct<Derived>
+operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::Scalar& x)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+template<typename Derived,typename Lhs,typename Rhs>
+typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
+ const ScaledProduct<Derived> >::type
+operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::RealScalar& x)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+
+template<typename Derived,typename Lhs,typename Rhs>
+const ScaledProduct<Derived>
+operator*(const typename Derived::Scalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+template<typename Derived,typename Lhs,typename Rhs>
+typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
+ const ScaledProduct<Derived> >::type
+operator*(const typename Derived::RealScalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+namespace internal {
+template<typename NestedProduct>
+struct traits<ScaledProduct<NestedProduct> >
+ : traits<ProductBase<ScaledProduct<NestedProduct>,
+ typename NestedProduct::_LhsNested,
+ typename NestedProduct::_RhsNested> >
+{
+ typedef typename traits<NestedProduct>::StorageKind StorageKind;
+};
+}
+
+template<typename NestedProduct>
+class ScaledProduct
+ : public ProductBase<ScaledProduct<NestedProduct>,
+ typename NestedProduct::_LhsNested,
+ typename NestedProduct::_RhsNested>
+{
+ public:
+ typedef ProductBase<ScaledProduct<NestedProduct>,
+ typename NestedProduct::_LhsNested,
+ typename NestedProduct::_RhsNested> Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::PlainObject PlainObject;
+// EIGEN_PRODUCT_PUBLIC_INTERFACE(ScaledProduct)
+
+ ScaledProduct(const NestedProduct& prod, const Scalar& x)
+ : Base(prod.lhs(),prod.rhs()), m_prod(prod), m_alpha(x) {}
+
+ template<typename Dest>
+ inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst, Scalar(1)); }
+
+ template<typename Dest>
+ inline void addTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(1)); }
+
+ template<typename Dest>
+ inline void subTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(-1)); }
+
+ template<typename Dest>
+ inline void scaleAndAddTo(Dest& dst, const Scalar& a_alpha) const { m_prod.derived().scaleAndAddTo(dst,a_alpha * m_alpha); }
+
+ const Scalar& alpha() const { return m_alpha; }
+
+ protected:
+ const NestedProduct& m_prod;
+ Scalar m_alpha;
+};
+
+/** \internal
+ * Overloaded to perform an efficient C = (A*B).lazy() */
+template<typename Derived>
+template<typename ProductDerived, typename Lhs, typename Rhs>
+Derived& MatrixBase<Derived>::lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+{
+ other.derived().evalTo(derived());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PRODUCTBASE_H
diff --git a/Eigen/src/Core/Random.h b/Eigen/src/Core/Random.h
new file mode 100644
index 0000000..480fea4
--- /dev/null
+++ b/Eigen/src/Core/Random.h
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RANDOM_H
+#define EIGEN_RANDOM_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar> struct scalar_random_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_random_op)
+ template<typename Index>
+ inline const Scalar operator() (Index, Index = 0) const { return random<Scalar>(); }
+};
+
+template<typename Scalar>
+struct functor_traits<scalar_random_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };
+
+} // end namespace internal
+
+/** \returns a random matrix expression
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Random() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_random_int_int.cpp
+ * Output: \verbinclude MatrixBase_random_int_int.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * \sa MatrixBase::setRandom(), MatrixBase::Random(Index), MatrixBase::Random()
+ */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random(Index rows, Index cols)
+{
+ return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a random vector expression
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Random() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_random_int.cpp
+ * Output: \verbinclude MatrixBase_random_int.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary vector whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random()
+ */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random(Index size)
+{
+ return NullaryExpr(size, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a fixed-size random matrix or vector expression
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_random.cpp
+ * Output: \verbinclude MatrixBase_random.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random(Index)
+ */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random()
+{
+ return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
+}
+
+/** Sets all coefficients in this expression to random values.
+ *
+ * Example: \include MatrixBase_setRandom.cpp
+ * Output: \verbinclude MatrixBase_setRandom.out
+ *
+ * \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
+ */
+template<typename Derived>
+inline Derived& DenseBase<Derived>::setRandom()
+{
+ return *this = Random(rows(), cols());
+}
+
+/** Resizes to the given \a newSize, and sets all coefficients in this expression to random values.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setRandom_int.cpp
+ * Output: \verbinclude Matrix_setRandom_int.out
+ *
+ * \sa MatrixBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, MatrixBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index newSize)
+{
+ resize(newSize);
+ return setRandom();
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to random values.
+ *
+ * \param nbRows the new number of rows
+ * \param nbCols the new number of columns
+ *
+ * Example: \include Matrix_setRandom_int_int.cpp
+ * Output: \verbinclude Matrix_setRandom_int_int.out
+ *
+ * \sa MatrixBase::setRandom(), setRandom(Index), class CwiseNullaryOp, MatrixBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index nbRows, Index nbCols)
+{
+ resize(nbRows, nbCols);
+ return setRandom();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_RANDOM_H
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
new file mode 100644
index 0000000..50548fa
--- /dev/null
+++ b/Eigen/src/Core/Redux.h
@@ -0,0 +1,408 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REDUX_H
+#define EIGEN_REDUX_H
+
+namespace Eigen {
+
+namespace internal {
+
+// TODO
+// * implement other kind of vectorization
+// * factorize code
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Func, typename Derived>
+struct redux_traits
+{
+public:
+ enum {
+ PacketSize = packet_traits<typename Derived::Scalar>::size,
+ InnerMaxSize = int(Derived::IsRowMajor)
+ ? Derived::MaxColsAtCompileTime
+ : Derived::MaxRowsAtCompileTime
+ };
+
+ enum {
+ MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
+ && (functor_traits<Func>::PacketAccess),
+ MayLinearVectorize = MightVectorize && (int(Derived::Flags)&LinearAccessBit),
+ MaySliceVectorize = MightVectorize && int(InnerMaxSize)>=3*PacketSize
+ };
+
+public:
+ enum {
+ Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
+ : int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
+ : int(DefaultTraversal)
+ };
+
+public:
+ enum {
+ Cost = ( Derived::SizeAtCompileTime == Dynamic
+ || Derived::CoeffReadCost == Dynamic
+ || (Derived::SizeAtCompileTime!=1 && functor_traits<Func>::Cost == Dynamic)
+ ) ? Dynamic
+ : Derived::SizeAtCompileTime * Derived::CoeffReadCost
+ + (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
+ UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
+ };
+
+public:
+ enum {
+ Unrolling = Cost != Dynamic && Cost <= UnrollingLimit
+ ? CompleteUnrolling
+ : NoUnrolling
+ };
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Func, typename Derived, int Start, int Length>
+struct redux_novec_unroller
+{
+ enum {
+ HalfLength = Length/2
+ };
+
+ typedef typename Derived::Scalar Scalar;
+
+ static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
+ {
+ return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+ redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
+ }
+};
+
+template<typename Func, typename Derived, int Start>
+struct redux_novec_unroller<Func, Derived, Start, 1>
+{
+ enum {
+ outer = Start / Derived::InnerSizeAtCompileTime,
+ inner = Start % Derived::InnerSizeAtCompileTime
+ };
+
+ typedef typename Derived::Scalar Scalar;
+
+ static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&)
+ {
+ return mat.coeffByOuterInner(outer, inner);
+ }
+};
+
+// This is actually dead code and will never be called. It is required
+// to prevent false warnings regarding failed inlining though
+// for 0 length run() will never be called at all.
+template<typename Func, typename Derived, int Start>
+struct redux_novec_unroller<Func, Derived, Start, 0>
+{
+ typedef typename Derived::Scalar Scalar;
+ static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); }
+};
+
+/*** vectorization ***/
+
+template<typename Func, typename Derived, int Start, int Length>
+struct redux_vec_unroller
+{
+ enum {
+ PacketSize = packet_traits<typename Derived::Scalar>::size,
+ HalfLength = Length/2
+ };
+
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+
+ static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func)
+ {
+ return func.packetOp(
+ redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+ redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
+ }
+};
+
+template<typename Func, typename Derived, int Start>
+struct redux_vec_unroller<Func, Derived, Start, 1>
+{
+ enum {
+ index = Start * packet_traits<typename Derived::Scalar>::size,
+ outer = index / int(Derived::InnerSizeAtCompileTime),
+ inner = index % int(Derived::InnerSizeAtCompileTime),
+ alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
+ };
+
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+
+ static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&)
+ {
+ return mat.template packetByOuterInner<alignment>(outer, inner);
+ }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Func, typename Derived,
+ int Traversal = redux_traits<Func, Derived>::Traversal,
+ int Unrolling = redux_traits<Func, Derived>::Unrolling
+>
+struct redux_impl;
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Index Index;
+ static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
+ {
+ eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+ Scalar res;
+ res = mat.coeffByOuterInner(0, 0);
+ for(Index i = 1; i < mat.innerSize(); ++i)
+ res = func(res, mat.coeffByOuterInner(0, i));
+ for(Index i = 1; i < mat.outerSize(); ++i)
+ for(Index j = 0; j < mat.innerSize(); ++j)
+ res = func(res, mat.coeffByOuterInner(i, j));
+ return res;
+ }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
+ : public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
+{};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+ typedef typename Derived::Index Index;
+
+ static Scalar run(const Derived& mat, const Func& func)
+ {
+ const Index size = mat.size();
+ eigen_assert(size && "you are using an empty matrix");
+ const Index packetSize = packet_traits<Scalar>::size;
+ const Index alignedStart = internal::first_aligned(mat);
+ enum {
+ alignment = bool(Derived::Flags & DirectAccessBit) || bool(Derived::Flags & AlignedBit)
+ ? Aligned : Unaligned
+ };
+ const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
+ const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
+ const Index alignedEnd2 = alignedStart + alignedSize2;
+ const Index alignedEnd = alignedStart + alignedSize;
+ Scalar res;
+ if(alignedSize)
+ {
+ PacketScalar packet_res0 = mat.template packet<alignment>(alignedStart);
+ if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
+ {
+ PacketScalar packet_res1 = mat.template packet<alignment>(alignedStart+packetSize);
+ for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
+ {
+ packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(index));
+ packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment>(index+packetSize));
+ }
+
+ packet_res0 = func.packetOp(packet_res0,packet_res1);
+ if(alignedEnd>alignedEnd2)
+ packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(alignedEnd2));
+ }
+ res = func.predux(packet_res0);
+
+ for(Index index = 0; index < alignedStart; ++index)
+ res = func(res,mat.coeff(index));
+
+ for(Index index = alignedEnd; index < size; ++index)
+ res = func(res,mat.coeff(index));
+ }
+ else // too small to vectorize anything.
+ // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+ {
+ res = mat.coeff(0);
+ for(Index index = 1; index < size; ++index)
+ res = func(res,mat.coeff(index));
+ }
+
+ return res;
+ }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, SliceVectorizedTraversal, NoUnrolling>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+ typedef typename Derived::Index Index;
+
+ static Scalar run(const Derived& mat, const Func& func)
+ {
+ eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+ const Index innerSize = mat.innerSize();
+ const Index outerSize = mat.outerSize();
+ enum {
+ packetSize = packet_traits<Scalar>::size
+ };
+ const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
+ Scalar res;
+ if(packetedInnerSize)
+ {
+ PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
+ for(Index j=0; j<outerSize; ++j)
+ for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
+ packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned>(j,i));
+
+ res = func.predux(packet_res);
+ for(Index j=0; j<outerSize; ++j)
+ for(Index i=packetedInnerSize; i<innerSize; ++i)
+ res = func(res, mat.coeffByOuterInner(j,i));
+ }
+ else // too small to vectorize anything.
+ // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+ {
+ res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
+ }
+
+ return res;
+ }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+ enum {
+ PacketSize = packet_traits<Scalar>::size,
+ Size = Derived::SizeAtCompileTime,
+ VectorizedSize = (Size / PacketSize) * PacketSize
+ };
+ static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
+ {
+ eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+ Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
+ if (VectorizedSize != Size)
+ res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
+ return res;
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Part 4 : public API
+***************************************************************************/
+
+
+/** \returns the result of a full redux operation on the whole matrix or vector using \a func
+ *
+ * The template parameter \a BinaryOp is the type of the functor \a func which must be
+ * an associative operator. Both current STL and TR1 functor styles are handled.
+ *
+ * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
+ */
+template<typename Derived>
+template<typename Func>
+EIGEN_STRONG_INLINE typename internal::result_of<Func(typename internal::traits<Derived>::Scalar)>::type
+DenseBase<Derived>::redux(const Func& func) const
+{
+ typedef typename internal::remove_all<typename Derived::Nested>::type ThisNested;
+ return internal::redux_impl<Func, ThisNested>
+ ::run(derived(), func);
+}
+
+/** \returns the minimum of all coefficients of \c *this.
+ * \warning the result is undefined if \c *this contains NaN.
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff() const
+{
+ return this->redux(Eigen::internal::scalar_min_op<Scalar>());
+}
+
+/** \returns the maximum of all coefficients of \c *this.
+ * \warning the result is undefined if \c *this contains NaN.
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff() const
+{
+ return this->redux(Eigen::internal::scalar_max_op<Scalar>());
+}
+
+/** \returns the sum of all coefficients of *this
+ *
+ * \sa trace(), prod(), mean()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::sum() const
+{
+ if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+ return Scalar(0);
+ return this->redux(Eigen::internal::scalar_sum_op<Scalar>());
+}
+
+/** \returns the mean of all coefficients of *this
+*
+* \sa trace(), prod(), sum()
+*/
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::mean() const
+{
+ return Scalar(this->redux(Eigen::internal::scalar_sum_op<Scalar>())) / Scalar(this->size());
+}
+
+/** \returns the product of all coefficients of *this
+ *
+ * Example: \include MatrixBase_prod.cpp
+ * Output: \verbinclude MatrixBase_prod.out
+ *
+ * \sa sum(), mean(), trace()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::prod() const
+{
+ if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+ return Scalar(1);
+ return this->redux(Eigen::internal::scalar_product_op<Scalar>());
+}
+
+/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
+ *
+ * \c *this can be any matrix, not necessarily square.
+ *
+ * \sa diagonal(), sum()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+MatrixBase<Derived>::trace() const
+{
+ return derived().diagonal().sum();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REDUX_H
diff --git a/Eigen/src/Core/Ref.h b/Eigen/src/Core/Ref.h
new file mode 100644
index 0000000..f53674c
--- /dev/null
+++ b/Eigen/src/Core/Ref.h
@@ -0,0 +1,269 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REF_H
+#define EIGEN_REF_H
+
+namespace Eigen {
+
+template<typename Derived> class RefBase;
+template<typename PlainObjectType, int Options = 0,
+ typename StrideType = typename internal::conditional<PlainObjectType::IsVectorAtCompileTime,InnerStride<1>,OuterStride<> >::type > class Ref;
+
+/** \class Ref
+ * \ingroup Core_Module
+ *
+ * \brief A matrix or vector expression mapping an existing expressions
+ *
+ * \tparam PlainObjectType the equivalent matrix type of the mapped data
+ * \tparam Options specifies whether the pointer is \c #Aligned, or \c #Unaligned.
+ * The default is \c #Unaligned.
+ * \tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1),
+ * but accept a variable outer stride (leading dimension).
+ * This can be overridden by specifying strides.
+ * The type passed here must be a specialization of the Stride template, see examples below.
+ *
+ * This class permits to write non template functions taking Eigen's object as parameters while limiting the number of copies.
+ * A Ref<> object can represent either a const expression or a l-value:
+ * \code
+ * // in-out argument:
+ * void foo1(Ref<VectorXf> x);
+ *
+ * // read-only const argument:
+ * void foo2(const Ref<const VectorXf>& x);
+ * \endcode
+ *
+ * In the in-out case, the input argument must satisfies the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered.
+ * By default, a Ref<VectorXf> can reference any dense vector expression of float having a contiguous memory layout.
+ * Likewise, a Ref<MatrixXf> can reference any column major dense matrix expression of float whose column's elements are contiguously stored with
+ * the possibility to have a constant space inbetween each column, i.e.: the inner stride mmust be equal to 1, but the outer-stride (or leading dimension),
+ * can be greater than the number of rows.
+ *
+ * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function.
+ * Here are some examples:
+ * \code
+ * MatrixXf A;
+ * VectorXf a;
+ * foo1(a.head()); // OK
+ * foo1(A.col()); // OK
+ * foo1(A.row()); // compilation error because here innerstride!=1
+ * foo2(A.row()); // The row is copied into a contiguous temporary
+ * foo2(2*a); // The expression is evaluated into a temporary
+ * foo2(A.col().segment(2,4)); // No temporary
+ * \endcode
+ *
+ * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameter.
+ * Here is an example accepting an innerstride!=1:
+ * \code
+ * // in-out argument:
+ * void foo3(Ref<VectorXf,0,InnerStride<> > x);
+ * foo3(A.row()); // OK
+ * \endcode
+ * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involved more
+ * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overloads internally calling a
+ * template function, e.g.:
+ * \code
+ * // in the .h:
+ * void foo(const Ref<MatrixXf>& A);
+ * void foo(const Ref<MatrixXf,0,Stride<> >& A);
+ *
+ * // in the .cpp:
+ * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
+ * ... // crazy code goes here
+ * }
+ * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
+ * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
+ * \endcode
+ *
+ *
+ * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+ */
+
+namespace internal {
+
+template<typename _PlainObjectType, int _Options, typename _StrideType>
+struct traits<Ref<_PlainObjectType, _Options, _StrideType> >
+ : public traits<Map<_PlainObjectType, _Options, _StrideType> >
+{
+ typedef _PlainObjectType PlainObjectType;
+ typedef _StrideType StrideType;
+ enum {
+ Options = _Options,
+ Flags = traits<Map<_PlainObjectType, _Options, _StrideType> >::Flags | NestByRefBit
+ };
+
+ template<typename Derived> struct match {
+ enum {
+ HasDirectAccess = internal::has_direct_access<Derived>::ret,
+ StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),
+ InnerStrideMatch = int(StrideType::InnerStrideAtCompileTime)==int(Dynamic)
+ || int(StrideType::InnerStrideAtCompileTime)==int(Derived::InnerStrideAtCompileTime)
+ || (int(StrideType::InnerStrideAtCompileTime)==0 && int(Derived::InnerStrideAtCompileTime)==1),
+ OuterStrideMatch = Derived::IsVectorAtCompileTime
+ || int(StrideType::OuterStrideAtCompileTime)==int(Dynamic) || int(StrideType::OuterStrideAtCompileTime)==int(Derived::OuterStrideAtCompileTime),
+ AlignmentMatch = (_Options!=Aligned) || ((PlainObjectType::Flags&AlignedBit)==0) || ((traits<Derived>::Flags&AlignedBit)==AlignedBit),
+ ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,
+ MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch && ScalarTypeMatch
+ };
+ typedef typename internal::conditional<MatchAtCompileTime,internal::true_type,internal::false_type>::type type;
+ };
+
+};
+
+template<typename Derived>
+struct traits<RefBase<Derived> > : public traits<Derived> {};
+
+}
+
+template<typename Derived> class RefBase
+ : public MapBase<Derived>
+{
+ typedef typename internal::traits<Derived>::PlainObjectType PlainObjectType;
+ typedef typename internal::traits<Derived>::StrideType StrideType;
+
+public:
+
+ typedef MapBase<Derived> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)
+
+ inline Index innerStride() const
+ {
+ return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
+ }
+
+ inline Index outerStride() const
+ {
+ return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+ : IsVectorAtCompileTime ? this->size()
+ : int(Flags)&RowMajorBit ? this->cols()
+ : this->rows();
+ }
+
+ RefBase()
+ : Base(0,RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime),
+ // Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values:
+ m_stride(StrideType::OuterStrideAtCompileTime==Dynamic?0:StrideType::OuterStrideAtCompileTime,
+ StrideType::InnerStrideAtCompileTime==Dynamic?0:StrideType::InnerStrideAtCompileTime)
+ {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase)
+
+protected:
+
+ typedef Stride<StrideType::OuterStrideAtCompileTime,StrideType::InnerStrideAtCompileTime> StrideBase;
+
+ template<typename Expression>
+ void construct(Expression& expr)
+ {
+ if(PlainObjectType::RowsAtCompileTime==1)
+ {
+ eigen_assert(expr.rows()==1 || expr.cols()==1);
+ ::new (static_cast<Base*>(this)) Base(expr.data(), 1, expr.size());
+ }
+ else if(PlainObjectType::ColsAtCompileTime==1)
+ {
+ eigen_assert(expr.rows()==1 || expr.cols()==1);
+ ::new (static_cast<Base*>(this)) Base(expr.data(), expr.size(), 1);
+ }
+ else
+ ::new (static_cast<Base*>(this)) Base(expr.data(), expr.rows(), expr.cols());
+
+ if(Expression::IsVectorAtCompileTime && (!PlainObjectType::IsVectorAtCompileTime) && ((Expression::Flags&RowMajorBit)!=(PlainObjectType::Flags&RowMajorBit)))
+ ::new (&m_stride) StrideBase(expr.innerStride(), StrideType::InnerStrideAtCompileTime==0?0:1);
+ else
+ ::new (&m_stride) StrideBase(StrideType::OuterStrideAtCompileTime==0?0:expr.outerStride(),
+ StrideType::InnerStrideAtCompileTime==0?0:expr.innerStride());
+ }
+
+ StrideBase m_stride;
+};
+
+
+template<typename PlainObjectType, int Options, typename StrideType> class Ref
+ : public RefBase<Ref<PlainObjectType, Options, StrideType> >
+{
+ private:
+ typedef internal::traits<Ref> Traits;
+ template<typename Derived>
+ inline Ref(const PlainObjectBase<Derived>& expr,
+ typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0);
+ public:
+
+ typedef RefBase<Ref> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
+
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Derived>
+ inline Ref(PlainObjectBase<Derived>& expr,
+ typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
+ {
+ EIGEN_STATIC_ASSERT(static_cast<bool>(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ Base::construct(expr.derived());
+ }
+ template<typename Derived>
+ inline Ref(const DenseBase<Derived>& expr,
+ typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
+ #else
+ template<typename Derived>
+ inline Ref(DenseBase<Derived>& expr)
+ #endif
+ {
+ EIGEN_STATIC_ASSERT(static_cast<bool>(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ EIGEN_STATIC_ASSERT(static_cast<bool>(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ enum { THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY = Derived::ThisConstantIsPrivateInPlainObjectBase};
+ Base::construct(expr.const_cast_derived());
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref)
+
+};
+
+// this is the const ref version
+template<typename TPlainObjectType, int Options, typename StrideType> class Ref<const TPlainObjectType, Options, StrideType>
+ : public RefBase<Ref<const TPlainObjectType, Options, StrideType> >
+{
+ typedef internal::traits<Ref> Traits;
+ public:
+
+ typedef RefBase<Ref> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
+
+ template<typename Derived>
+ inline Ref(const DenseBase<Derived>& expr,
+ typename internal::enable_if<bool(Traits::template match<Derived>::ScalarTypeMatch),Derived>::type* = 0)
+ {
+// std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch << "," << match_helper<Derived>::InnerStrideMatch << "\n";
+// std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n";
+// std::cout << int(StrideType::InnerStrideAtCompileTime) << " - " << int(Derived::InnerStrideAtCompileTime) << "\n";
+ construct(expr.derived(), typename Traits::template match<Derived>::type());
+ }
+
+ protected:
+
+ template<typename Expression>
+ void construct(const Expression& expr,internal::true_type)
+ {
+ Base::construct(expr);
+ }
+
+ template<typename Expression>
+ void construct(const Expression& expr, internal::false_type)
+ {
+ m_object.lazyAssign(expr);
+ Base::construct(m_object);
+ }
+
+ protected:
+ TPlainObjectType m_object;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_REF_H
diff --git a/Eigen/src/Core/Replicate.h b/Eigen/src/Core/Replicate.h
new file mode 100644
index 0000000..ac4537c
--- /dev/null
+++ b/Eigen/src/Core/Replicate.h
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REPLICATE_H
+#define EIGEN_REPLICATE_H
+
+namespace Eigen {
+
+/**
+ * \class Replicate
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the multiple replication of a matrix or vector
+ *
+ * \param MatrixType the type of the object we are replicating
+ *
+ * This class represents an expression of the multiple replication of a matrix or vector.
+ * It is the return type of DenseBase::replicate() and most of the time
+ * this is the only way it is used.
+ *
+ * \sa DenseBase::replicate()
+ */
+
+namespace internal {
+template<typename MatrixType,int RowFactor,int ColFactor>
+struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
+ : traits<MatrixType>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ enum {
+ Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor
+ };
+ typedef typename nested<MatrixType,Factor>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic
+ ? Dynamic
+ : RowFactor * MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic
+ ? Dynamic
+ : ColFactor * MatrixType::ColsAtCompileTime,
+ //FIXME we don't propagate the max sizes !!!
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1
+ : MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0
+ : (MatrixType::Flags & RowMajorBit) ? 1 : 0,
+ Flags = (_MatrixTypeNested::Flags & HereditaryBits & ~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0),
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+ };
+};
+}
+
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
+ : public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type
+{
+ typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<Replicate>::_MatrixTypeNested _MatrixTypeNested;
+ public:
+
+ typedef typename internal::dense_xpr_base<Replicate>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)
+
+ template<typename OriginalMatrixType>
+ inline explicit Replicate(const OriginalMatrixType& a_matrix)
+ : m_matrix(a_matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
+ THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+ eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);
+ }
+
+ template<typename OriginalMatrixType>
+ inline Replicate(const OriginalMatrixType& a_matrix, Index rowFactor, Index colFactor)
+ : m_matrix(a_matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
+ THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+ }
+
+ inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
+ inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
+
+ inline Scalar coeff(Index rowId, Index colId) const
+ {
+ // try to avoid using modulo; this is a pure optimization strategy
+ const Index actual_row = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
+ : RowFactor==1 ? rowId
+ : rowId%m_matrix.rows();
+ const Index actual_col = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
+ : ColFactor==1 ? colId
+ : colId%m_matrix.cols();
+
+ return m_matrix.coeff(actual_row, actual_col);
+ }
+ template<int LoadMode>
+ inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ const Index actual_row = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
+ : RowFactor==1 ? rowId
+ : rowId%m_matrix.rows();
+ const Index actual_col = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
+ : ColFactor==1 ? colId
+ : colId%m_matrix.cols();
+
+ return m_matrix.template packet<LoadMode>(actual_row, actual_col);
+ }
+
+ const _MatrixTypeNested& nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;
+ const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;
+};
+
+/**
+ * \return an expression of the replication of \c *this
+ *
+ * Example: \include MatrixBase_replicate.cpp
+ * Output: \verbinclude MatrixBase_replicate.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
+ */
+template<typename Derived>
+template<int RowFactor, int ColFactor>
+const Replicate<Derived,RowFactor,ColFactor>
+DenseBase<Derived>::replicate() const
+{
+ return Replicate<Derived,RowFactor,ColFactor>(derived());
+}
+
+/**
+ * \return an expression of the replication of \c *this
+ *
+ * Example: \include MatrixBase_replicate_int_int.cpp
+ * Output: \verbinclude MatrixBase_replicate_int_int.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
+ */
+template<typename Derived>
+const typename DenseBase<Derived>::ReplicateReturnType
+DenseBase<Derived>::replicate(Index rowFactor,Index colFactor) const
+{
+ return Replicate<Derived,Dynamic,Dynamic>(derived(),rowFactor,colFactor);
+}
+
+/**
+ * \return an expression of the replication of each column (or row) of \c *this
+ *
+ * Example: \include DirectionWise_replicate_int.cpp
+ * Output: \verbinclude DirectionWise_replicate_int.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate
+ */
+template<typename ExpressionType, int Direction>
+const typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+VectorwiseOp<ExpressionType,Direction>::replicate(Index factor) const
+{
+ return typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+ (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REPLICATE_H
diff --git a/Eigen/src/Core/ReturnByValue.h b/Eigen/src/Core/ReturnByValue.h
new file mode 100644
index 0000000..f635598
--- /dev/null
+++ b/Eigen/src/Core/ReturnByValue.h
@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RETURNBYVALUE_H
+#define EIGEN_RETURNBYVALUE_H
+
+namespace Eigen {
+
+/** \class ReturnByValue
+ * \ingroup Core_Module
+ *
+ */
+
+namespace internal {
+
+template<typename Derived>
+struct traits<ReturnByValue<Derived> >
+ : public traits<typename traits<Derived>::ReturnType>
+{
+ enum {
+ // We're disabling the DirectAccess because e.g. the constructor of
+ // the Block-with-DirectAccess expression requires to have a coeffRef method.
+ // Also, we don't want to have to implement the stride stuff.
+ Flags = (traits<typename traits<Derived>::ReturnType>::Flags
+ | EvalBeforeNestingBit) & ~DirectAccessBit
+ };
+};
+
+/* The ReturnByValue object doesn't even have a coeff() method.
+ * So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix.
+ * So internal::nested always gives the plain return matrix type.
+ *
+ * FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ??
+ */
+template<typename Derived,int n,typename PlainObject>
+struct nested<ReturnByValue<Derived>, n, PlainObject>
+{
+ typedef typename traits<Derived>::ReturnType type;
+};
+
+} // end namespace internal
+
+template<typename Derived> class ReturnByValue
+ : internal::no_assignment_operator, public internal::dense_xpr_base< ReturnByValue<Derived> >::type
+{
+ public:
+ typedef typename internal::traits<Derived>::ReturnType ReturnType;
+
+ typedef typename internal::dense_xpr_base<ReturnByValue>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue)
+
+ template<typename Dest>
+ inline void evalTo(Dest& dst) const
+ { static_cast<const Derived*>(this)->evalTo(dst); }
+ inline Index rows() const { return static_cast<const Derived*>(this)->rows(); }
+ inline Index cols() const { return static_cast<const Derived*>(this)->cols(); }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT
+ class Unusable{
+ Unusable(const Unusable&) {}
+ Unusable& operator=(const Unusable&) {return *this;}
+ };
+ const Unusable& coeff(Index) const { return *reinterpret_cast<const Unusable*>(this); }
+ const Unusable& coeff(Index,Index) const { return *reinterpret_cast<const Unusable*>(this); }
+ Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }
+ Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }
+ template<int LoadMode> Unusable& packet(Index) const;
+ template<int LoadMode> Unusable& packet(Index, Index) const;
+#endif
+};
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+ other.evalTo(derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::lazyAssign(const ReturnByValue<OtherDerived>& other)
+{
+ other.evalTo(derived());
+ return derived();
+}
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_RETURNBYVALUE_H
diff --git a/Eigen/src/Core/Reverse.h b/Eigen/src/Core/Reverse.h
new file mode 100644
index 0000000..e30ae3d
--- /dev/null
+++ b/Eigen/src/Core/Reverse.h
@@ -0,0 +1,224 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REVERSE_H
+#define EIGEN_REVERSE_H
+
+namespace Eigen {
+
+/** \class Reverse
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the reverse of a vector or matrix
+ *
+ * \param MatrixType the type of the object of which we are taking the reverse
+ *
+ * This class represents an expression of the reverse of a vector.
+ * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::reverse(), VectorwiseOp::reverse()
+ */
+
+namespace internal {
+
+template<typename MatrixType, int Direction>
+struct traits<Reverse<MatrixType, Direction> >
+ : traits<MatrixType>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+
+ // let's enable LinearAccess only with vectorization because of the product overhead
+ LinearAccess = ( (Direction==BothDirections) && (int(_MatrixTypeNested::Flags)&PacketAccessBit) )
+ ? LinearAccessBit : 0,
+
+ Flags = int(_MatrixTypeNested::Flags) & (HereditaryBits | LvalueBit | PacketAccessBit | LinearAccess),
+
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+ };
+};
+
+template<typename PacketScalar, bool ReversePacket> struct reverse_packet_cond
+{
+ static inline PacketScalar run(const PacketScalar& x) { return preverse(x); }
+};
+
+template<typename PacketScalar> struct reverse_packet_cond<PacketScalar,false>
+{
+ static inline PacketScalar run(const PacketScalar& x) { return x; }
+};
+
+} // end namespace internal
+
+template<typename MatrixType, int Direction> class Reverse
+ : public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Reverse>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Reverse)
+ using Base::IsRowMajor;
+
+ // next line is necessary because otherwise const version of operator()
+ // is hidden by non-const version defined in this file
+ using Base::operator();
+
+ protected:
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ IsColMajor = !IsRowMajor,
+ ReverseRow = (Direction == Vertical) || (Direction == BothDirections),
+ ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
+ OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
+ OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1,
+ ReversePacket = (Direction == BothDirections)
+ || ((Direction == Vertical) && IsColMajor)
+ || ((Direction == Horizontal) && IsRowMajor)
+ };
+ typedef internal::reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;
+ public:
+
+ inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ inline Index innerStride() const
+ {
+ return -m_matrix.innerStride();
+ }
+
+ inline Scalar& operator()(Index row, Index col)
+ {
+ eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+ return coeffRef(row, col);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_matrix.const_cast_derived().coeffRef(ReverseRow ? m_matrix.rows() - row - 1 : row,
+ ReverseCol ? m_matrix.cols() - col - 1 : col);
+ }
+
+ inline CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(ReverseRow ? m_matrix.rows() - row - 1 : row,
+ ReverseCol ? m_matrix.cols() - col - 1 : col);
+ }
+
+ inline CoeffReturnType coeff(Index index) const
+ {
+ return m_matrix.coeff(m_matrix.size() - index - 1);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_matrix.const_cast_derived().coeffRef(m_matrix.size() - index - 1);
+ }
+
+ inline Scalar& operator()(Index index)
+ {
+ eigen_assert(index >= 0 && index < m_matrix.size());
+ return coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index row, Index col) const
+ {
+ return reverse_packet::run(m_matrix.template packet<LoadMode>(
+ ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+ ReverseCol ? m_matrix.cols() - col - OffsetCol : col));
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& x)
+ {
+ m_matrix.const_cast_derived().template writePacket<LoadMode>(
+ ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+ ReverseCol ? m_matrix.cols() - col - OffsetCol : col,
+ reverse_packet::run(x));
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return internal::preverse(m_matrix.template packet<LoadMode>( m_matrix.size() - index - PacketSize ));
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ m_matrix.const_cast_derived().template writePacket<LoadMode>(m_matrix.size() - index - PacketSize, internal::preverse(x));
+ }
+
+ const typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+/** \returns an expression of the reverse of *this.
+ *
+ * Example: \include MatrixBase_reverse.cpp
+ * Output: \verbinclude MatrixBase_reverse.out
+ *
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::ReverseReturnType
+DenseBase<Derived>::reverse()
+{
+ return derived();
+}
+
+/** This is the const version of reverse(). */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstReverseReturnType
+DenseBase<Derived>::reverse() const
+{
+ return derived();
+}
+
+/** This is the "in place" version of reverse: it reverses \c *this.
+ *
+ * In most cases it is probably better to simply use the reversed expression
+ * of a matrix. However, when reversing the matrix data itself is really needed,
+ * then this "in-place" version is probably the right choice because it provides
+ * the following additional features:
+ * - less error prone: doing the same operation with .reverse() requires special care:
+ * \code m = m.reverse().eval(); \endcode
+ * - this API allows to avoid creating a temporary (the current implementation creates a temporary, but that could be avoided using swap)
+ * - it allows future optimizations (cache friendliness, etc.)
+ *
+ * \sa reverse() */
+template<typename Derived>
+inline void DenseBase<Derived>::reverseInPlace()
+{
+ derived() = derived().reverse().eval();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REVERSE_H
diff --git a/Eigen/src/Core/Select.h b/Eigen/src/Core/Select.h
new file mode 100644
index 0000000..87993bb
--- /dev/null
+++ b/Eigen/src/Core/Select.h
@@ -0,0 +1,162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELECT_H
+#define EIGEN_SELECT_H
+
+namespace Eigen {
+
+/** \class Select
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
+ *
+ * \param ConditionMatrixType the type of the \em condition expression which must be a boolean matrix
+ * \param ThenMatrixType the type of the \em then expression
+ * \param ElseMatrixType the type of the \em else expression
+ *
+ * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+ * It is the return type of DenseBase::select() and most of the time this is the only way it is used.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
+ */
+
+namespace internal {
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+ : traits<ThenMatrixType>
+{
+ typedef typename traits<ThenMatrixType>::Scalar Scalar;
+ typedef Dense StorageKind;
+ typedef typename traits<ThenMatrixType>::XprKind XprKind;
+ typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
+ typedef typename ThenMatrixType::Nested ThenMatrixNested;
+ typedef typename ElseMatrixType::Nested ElseMatrixNested;
+ enum {
+ RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
+ Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & HereditaryBits,
+ CoeffReadCost = traits<typename remove_all<ConditionMatrixNested>::type>::CoeffReadCost
+ + EIGEN_SIZE_MAX(traits<typename remove_all<ThenMatrixNested>::type>::CoeffReadCost,
+ traits<typename remove_all<ElseMatrixNested>::type>::CoeffReadCost)
+ };
+};
+}
+
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+class Select : internal::no_assignment_operator,
+ public internal::dense_xpr_base< Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Select>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Select)
+
+ Select(const ConditionMatrixType& a_conditionMatrix,
+ const ThenMatrixType& a_thenMatrix,
+ const ElseMatrixType& a_elseMatrix)
+ : m_condition(a_conditionMatrix), m_then(a_thenMatrix), m_else(a_elseMatrix)
+ {
+ eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
+ eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
+ }
+
+ Index rows() const { return m_condition.rows(); }
+ Index cols() const { return m_condition.cols(); }
+
+ const Scalar coeff(Index i, Index j) const
+ {
+ if (m_condition.coeff(i,j))
+ return m_then.coeff(i,j);
+ else
+ return m_else.coeff(i,j);
+ }
+
+ const Scalar coeff(Index i) const
+ {
+ if (m_condition.coeff(i))
+ return m_then.coeff(i);
+ else
+ return m_else.coeff(i);
+ }
+
+ const ConditionMatrixType& conditionMatrix() const
+ {
+ return m_condition;
+ }
+
+ const ThenMatrixType& thenMatrix() const
+ {
+ return m_then;
+ }
+
+ const ElseMatrixType& elseMatrix() const
+ {
+ return m_else;
+ }
+
+ protected:
+ typename ConditionMatrixType::Nested m_condition;
+ typename ThenMatrixType::Nested m_then;
+ typename ElseMatrixType::Nested m_else;
+};
+
+
+/** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
+ * if \c *this(i,j), and \a elseMatrix(i,j) otherwise.
+ *
+ * Example: \include MatrixBase_select.cpp
+ * Output: \verbinclude MatrixBase_select.out
+ *
+ * \sa class Select
+ */
+template<typename Derived>
+template<typename ThenDerived,typename ElseDerived>
+inline const Select<Derived,ThenDerived,ElseDerived>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+ const DenseBase<ElseDerived>& elseMatrix) const
+{
+ return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+ * the \em else expression being a scalar value.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ */
+template<typename Derived>
+template<typename ThenDerived>
+inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+ const typename ThenDerived::Scalar& elseScalar) const
+{
+ return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
+ derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+ * the \em then expression being a scalar value.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ */
+template<typename Derived>
+template<typename ElseDerived>
+inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
+DenseBase<Derived>::select(const typename ElseDerived::Scalar& thenScalar,
+ const DenseBase<ElseDerived>& elseMatrix) const
+{
+ return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
+ derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELECT_H
diff --git a/Eigen/src/Core/SelfAdjointView.h b/Eigen/src/Core/SelfAdjointView.h
new file mode 100644
index 0000000..6fa7cd1
--- /dev/null
+++ b/Eigen/src/Core/SelfAdjointView.h
@@ -0,0 +1,314 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTMATRIX_H
+#define EIGEN_SELFADJOINTMATRIX_H
+
+namespace Eigen {
+
+/** \class SelfAdjointView
+ * \ingroup Core_Module
+ *
+ *
+ * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
+ *
+ * \param MatrixType the type of the dense matrix storing the coefficients
+ * \param TriangularPart can be either \c #Lower or \c #Upper
+ *
+ * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
+ * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa class TriangularBase, MatrixBase::selfadjointView()
+ */
+
+namespace internal {
+template<typename MatrixType, unsigned int UpLo>
+struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
+{
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+ typedef MatrixType ExpressionType;
+ typedef typename MatrixType::PlainObject DenseMatrixType;
+ enum {
+ Mode = UpLo | SelfAdjoint,
+ Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits)
+ & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)), // FIXME these flags should be preserved
+ CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
+ };
+};
+}
+
+template <typename Lhs, int LhsMode, bool LhsIsVector,
+ typename Rhs, int RhsMode, bool RhsIsVector>
+struct SelfadjointProductMatrix;
+
+// FIXME could also be called SelfAdjointWrapper to be consistent with DiagonalWrapper ??
+template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
+ : public TriangularBase<SelfAdjointView<MatrixType, UpLo> >
+{
+ public:
+
+ typedef TriangularBase<SelfAdjointView> Base;
+ typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
+
+ /** \brief The type of coefficients in this matrix */
+ typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
+
+ typedef typename MatrixType::Index Index;
+
+ enum {
+ Mode = internal::traits<SelfAdjointView>::Mode
+ };
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index outerStride() const { return m_matrix.outerStride(); }
+ inline Index innerStride() const { return m_matrix.innerStride(); }
+
+ /** \sa MatrixBase::coeff()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ inline Scalar coeff(Index row, Index col) const
+ {
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.coeff(row, col);
+ }
+
+ /** \sa MatrixBase::coeffRef()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.const_cast_derived().coeffRef(row, col);
+ }
+
+ /** \internal */
+ const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
+
+ const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+ MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
+
+ /** Efficient self-adjoint matrix times vector/matrix product */
+ template<typename OtherDerived>
+ SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return SelfadjointProductMatrix
+ <MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
+ (m_matrix, rhs.derived());
+ }
+
+ /** Efficient vector/matrix times self-adjoint matrix product */
+ template<typename OtherDerived> friend
+ SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
+ operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
+ {
+ return SelfadjointProductMatrix
+ <OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
+ (lhs.derived(),rhs.m_matrix);
+ }
+
+ /** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
+ * \returns a reference to \c *this
+ *
+ * The vectors \a u and \c v \b must be column vectors, however they can be
+ * a adjoint expression without any overhead. Only the meaningful triangular
+ * part of the matrix is updated, the rest is left unchanged.
+ *
+ * \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
+ */
+ template<typename DerivedU, typename DerivedV>
+ SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha = Scalar(1));
+
+ /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
+ *
+ * \returns a reference to \c *this
+ *
+ * Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
+ * call this function with u.adjoint().
+ *
+ * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
+ */
+ template<typename DerivedU>
+ SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
+
+/////////// Cholesky module ///////////
+
+ const LLT<PlainObject, UpLo> llt() const;
+ const LDLT<PlainObject, UpLo> ldlt() const;
+
+/////////// Eigenvalue module ///////////
+
+ /** Real part of #Scalar */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ /** Return type of eigenvalues() */
+ typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+ EigenvaluesReturnType eigenvalues() const;
+ RealScalar operatorNorm() const;
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived>
+ SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other)
+ {
+ enum {
+ OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
+ };
+ m_matrix.const_cast_derived().template triangularView<UpLo>() = other;
+ m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.adjoint();
+ return *this;
+ }
+ template<typename OtherMatrixType, unsigned int OtherMode>
+ SelfAdjointView& operator=(const TriangularView<OtherMatrixType, OtherMode>& other)
+ {
+ enum {
+ OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
+ };
+ m_matrix.const_cast_derived().template triangularView<UpLo>() = other.toDenseMatrix();
+ m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.toDenseMatrix().adjoint();
+ return *this;
+ }
+ #endif
+
+ protected:
+ MatrixTypeNested m_matrix;
+};
+
+
+// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
+// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
+// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
+// {
+// return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
+// }
+
+// selfadjoint to dense matrix
+
+namespace internal {
+
+template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount, ClearOpposite>
+{
+ enum {
+ col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+ };
+
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
+
+ if(row == col)
+ dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
+ else if(row < col)
+ dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, 0, ClearOpposite>
+{
+ static inline void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount, ClearOpposite>
+{
+ enum {
+ col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+ };
+
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
+
+ if(row == col)
+ dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
+ else if(row > col)
+ dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, 0, ClearOpposite>
+{
+ static inline void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ for(Index i = 0; i < j; ++i)
+ {
+ dst.copyCoeff(i, j, src);
+ dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
+ }
+ dst.copyCoeff(j, j, src);
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dynamic, ClearOpposite>
+{
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ typedef typename Derived1::Index Index;
+ for(Index i = 0; i < dst.rows(); ++i)
+ {
+ for(Index j = 0; j < i; ++j)
+ {
+ dst.copyCoeff(i, j, src);
+ dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
+ }
+ dst.copyCoeff(i, i, src);
+ }
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView() const
+{
+ return derived();
+}
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTMATRIX_H
diff --git a/Eigen/src/Core/SelfCwiseBinaryOp.h b/Eigen/src/Core/SelfCwiseBinaryOp.h
new file mode 100644
index 0000000..22f3047
--- /dev/null
+++ b/Eigen/src/Core/SelfCwiseBinaryOp.h
@@ -0,0 +1,197 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFCWISEBINARYOP_H
+#define EIGEN_SELFCWISEBINARYOP_H
+
+namespace Eigen {
+
+/** \class SelfCwiseBinaryOp
+ * \ingroup Core_Module
+ *
+ * \internal
+ *
+ * \brief Internal helper class for optimizing operators like +=, -=
+ *
+ * This is a pseudo expression class re-implementing the copyCoeff/copyPacket
+ * method to directly performs a +=/-= operations in an optimal way. In particular,
+ * this allows to make sure that the input/output data are loaded only once using
+ * aligned packet loads.
+ *
+ * \sa class SwapWrapper for a similar trick.
+ */
+
+namespace internal {
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct traits<SelfCwiseBinaryOp<BinaryOp,Lhs,Rhs> >
+ : traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >
+{
+ enum {
+ // Note that it is still a good idea to preserve the DirectAccessBit
+ // so that assign can correctly align the data.
+ Flags = traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >::Flags | (Lhs::Flags&DirectAccessBit) | (Lhs::Flags&LvalueBit),
+ OuterStrideAtCompileTime = Lhs::OuterStrideAtCompileTime,
+ InnerStrideAtCompileTime = Lhs::InnerStrideAtCompileTime
+ };
+};
+}
+
+template<typename BinaryOp, typename Lhs, typename Rhs> class SelfCwiseBinaryOp
+ : public internal::dense_xpr_base< SelfCwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<SelfCwiseBinaryOp>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(SelfCwiseBinaryOp)
+
+ typedef typename internal::packet_traits<Scalar>::type Packet;
+
+ inline SelfCwiseBinaryOp(Lhs& xpr, const BinaryOp& func = BinaryOp()) : m_matrix(xpr), m_functor(func) {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index outerStride() const { return m_matrix.outerStride(); }
+ inline Index innerStride() const { return m_matrix.innerStride(); }
+ inline const Scalar* data() const { return m_matrix.data(); }
+
+ // note that this function is needed by assign to correctly align loads/stores
+ // TODO make Assign use .data()
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(Lhs)
+ return m_matrix.const_cast_derived().coeffRef(row, col);
+ }
+ inline const Scalar& coeffRef(Index row, Index col) const
+ {
+ return m_matrix.coeffRef(row, col);
+ }
+
+ // note that this function is needed by assign to correctly align loads/stores
+ // TODO make Assign use .data()
+ inline Scalar& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(Lhs)
+ return m_matrix.const_cast_derived().coeffRef(index);
+ }
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_matrix.const_cast_derived().coeffRef(index);
+ }
+
+ template<typename OtherDerived>
+ void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ Scalar& tmp = m_matrix.coeffRef(row,col);
+ tmp = m_functor(tmp, _other.coeff(row,col));
+ }
+
+ template<typename OtherDerived>
+ void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(index >= 0 && index < m_matrix.size());
+ Scalar& tmp = m_matrix.coeffRef(index);
+ tmp = m_functor(tmp, _other.coeff(index));
+ }
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ m_matrix.template writePacket<StoreMode>(row, col,
+ m_functor.packetOp(m_matrix.template packet<StoreMode>(row, col),_other.template packet<LoadMode>(row, col)) );
+ }
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(index >= 0 && index < m_matrix.size());
+ m_matrix.template writePacket<StoreMode>(index,
+ m_functor.packetOp(m_matrix.template packet<StoreMode>(index),_other.template packet<LoadMode>(index)) );
+ }
+
+ // reimplement lazyAssign to handle complex *= real
+ // see CwiseBinaryOp ctor for details
+ template<typename RhsDerived>
+ EIGEN_STRONG_INLINE SelfCwiseBinaryOp& lazyAssign(const DenseBase<RhsDerived>& rhs)
+ {
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs,RhsDerived)
+ EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename RhsDerived::Scalar);
+
+ #ifdef EIGEN_DEBUG_ASSIGN
+ internal::assign_traits<SelfCwiseBinaryOp, RhsDerived>::debug();
+ #endif
+ eigen_assert(rows() == rhs.rows() && cols() == rhs.cols());
+ internal::assign_impl<SelfCwiseBinaryOp, RhsDerived>::run(*this,rhs.derived());
+ #ifndef EIGEN_NO_DEBUG
+ this->checkTransposeAliasing(rhs.derived());
+ #endif
+ return *this;
+ }
+
+ // overloaded to honor evaluation of special matrices
+ // maybe another solution would be to not use SelfCwiseBinaryOp
+ // at first...
+ SelfCwiseBinaryOp& operator=(const Rhs& _rhs)
+ {
+ typename internal::nested<Rhs>::type rhs(_rhs);
+ return Base::operator=(rhs);
+ }
+
+ Lhs& expression() const
+ {
+ return m_matrix;
+ }
+
+ const BinaryOp& functor() const
+ {
+ return m_functor;
+ }
+
+ protected:
+ Lhs& m_matrix;
+ const BinaryOp& m_functor;
+
+ private:
+ SelfCwiseBinaryOp& operator=(const SelfCwiseBinaryOp&);
+};
+
+template<typename Derived>
+inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
+{
+ typedef typename Derived::PlainObject PlainObject;
+ SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+ tmp = PlainObject::Constant(rows(),cols(),other);
+ return derived();
+}
+
+template<typename Derived>
+inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
+{
+ typedef typename internal::conditional<NumTraits<Scalar>::IsInteger,
+ internal::scalar_quotient_op<Scalar>,
+ internal::scalar_product_op<Scalar> >::type BinOp;
+ typedef typename Derived::PlainObject PlainObject;
+ SelfCwiseBinaryOp<BinOp, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+ Scalar actual_other;
+ if(NumTraits<Scalar>::IsInteger) actual_other = other;
+ else actual_other = Scalar(1)/other;
+ tmp = PlainObject::Constant(rows(),cols(), actual_other);
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFCWISEBINARYOP_H
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
new file mode 100644
index 0000000..ef17f28
--- /dev/null
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -0,0 +1,260 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVETRIANGULAR_H
+#define EIGEN_SOLVETRIANGULAR_H
+
+namespace Eigen {
+
+namespace internal {
+
+// Forward declarations:
+// The following two routines are implemented in the products/TriangularSolver*.h files
+template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector;
+
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
+struct triangular_solve_matrix;
+
+// small helper struct extracting some traits on the underlying solver operation
+template<typename Lhs, typename Rhs, int Side>
+class trsolve_traits
+{
+ private:
+ enum {
+ RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
+ };
+ public:
+ enum {
+ Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
+ ? CompleteUnrolling : NoUnrolling,
+ RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
+ };
+};
+
+template<typename Lhs, typename Rhs,
+ int Side, // can be OnTheLeft/OnTheRight
+ int Mode, // can be Upper/Lower | UnitDiag
+ int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
+ int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
+ >
+struct triangular_solver_selector;
+
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
+{
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::ExtractType ActualLhsType;
+ typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
+ static void run(const Lhs& lhs, Rhs& rhs)
+ {
+ ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
+
+ // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
+
+ bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
+ (useRhsDirectly ? rhs.data() : 0));
+
+ if(!useRhsDirectly)
+ MappedRhs(actualRhs,rhs.size()) = rhs;
+
+ triangular_solve_vector<LhsScalar, RhsScalar, typename Lhs::Index, Side, Mode, LhsProductTraits::NeedToConjugate,
+ (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
+ ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
+
+ if(!useRhsDirectly)
+ rhs = MappedRhs(actualRhs, rhs.size());
+ }
+};
+
+// the rhs is a matrix
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef typename Rhs::Index Index;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
+
+ static void run(const Lhs& lhs, Rhs& rhs)
+ {
+ typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
+
+ const Index size = lhs.rows();
+ const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
+
+ typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
+
+ BlockingType blocking(rhs.rows(), rhs.cols(), size);
+
+ triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
+ (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
+ ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
+ }
+};
+
+/***************************************************************************
+* meta-unrolling implementation
+***************************************************************************/
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size,
+ bool Stop = Index==Size>
+struct triangular_solver_unroller;
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> {
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ I = IsLower ? Index : Size - Index - 1,
+ S = IsLower ? 0 : I+1
+ };
+ static void run(const Lhs& lhs, Rhs& rhs)
+ {
+ if (Index>0)
+ rhs.coeffRef(I) -= lhs.row(I).template segment<Index>(S).transpose()
+ .cwiseProduct(rhs.template segment<Index>(S)).sum();
+
+ if(!(Mode & UnitDiag))
+ rhs.coeffRef(I) /= lhs.coeff(I,I);
+
+ triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> {
+ static void run(const Lhs&, Rhs&) {}
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
+ static void run(const Lhs& lhs, Rhs& rhs)
+ { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
+ static void run(const Lhs& lhs, Rhs& rhs)
+ {
+ Transpose<const Lhs> trLhs(lhs);
+ Transpose<Rhs> trRhs(rhs);
+
+ triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ 0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* TriangularView methods
+***************************************************************************/
+
+/** "in-place" version of TriangularView::solve() where the result is written in \a other
+ *
+ * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
+ * This function will const_cast it, so constness isn't honored here.
+ *
+ * See TriangularView:solve() for the details.
+ */
+template<typename MatrixType, unsigned int Mode>
+template<int Side, typename OtherDerived>
+void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
+{
+ OtherDerived& other = _other.const_cast_derived();
+ eigen_assert( cols() == rows() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
+ eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+
+ enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit && OtherDerived::IsVectorAtCompileTime };
+ typedef typename internal::conditional<copy,
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
+ OtherCopy otherCopy(other);
+
+ internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
+ Side, Mode>::run(nestedExpression(), otherCopy);
+
+ if (copy)
+ other = otherCopy;
+}
+
+/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
+ *
+ * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
+ * \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
+ * \a Side==OnTheRight.
+ *
+ * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
+ * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
+ * is an upper (resp. lower) triangular matrix.
+ *
+ * Example: \include MatrixBase_marked.cpp
+ * Output: \verbinclude MatrixBase_marked.out
+ *
+ * This function returns an expression of the inverse-multiply and can works in-place if it is assigned
+ * to the same matrix or vector \a other.
+ *
+ * For users coming from BLAS, this function (and more specifically solveInPlace()) offer
+ * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
+ *
+ * \sa TriangularView::solveInPlace()
+ */
+template<typename Derived, unsigned int Mode>
+template<int Side, typename Other>
+const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
+TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const
+{
+ return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
+}
+
+namespace internal {
+
+
+template<int Side, typename TriangularType, typename Rhs>
+struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
+};
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
+ : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
+ typedef ReturnByValue<triangular_solve_retval> Base;
+ typedef typename Base::Index Index;
+
+ triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
+ : m_triangularMatrix(tri), m_rhs(rhs)
+ {}
+
+ inline Index rows() const { return m_rhs.rows(); }
+ inline Index cols() const { return m_rhs.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ if(!(is_same<RhsNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_rhs)))
+ dst = m_rhs;
+ m_triangularMatrix.template solveInPlace<Side>(dst);
+ }
+
+ protected:
+ const TriangularType& m_triangularMatrix;
+ typename Rhs::Nested m_rhs;
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVETRIANGULAR_H
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
new file mode 100644
index 0000000..389d942
--- /dev/null
+++ b/Eigen/src/Core/StableNorm.h
@@ -0,0 +1,203 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STABLENORM_H
+#define EIGEN_STABLENORM_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename ExpressionType, typename Scalar>
+inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
+{
+ using std::max;
+ Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
+
+ if (maxCoeff>scale)
+ {
+ ssq = ssq * numext::abs2(scale/maxCoeff);
+ Scalar tmp = Scalar(1)/maxCoeff;
+ if(tmp > NumTraits<Scalar>::highest())
+ {
+ invScale = NumTraits<Scalar>::highest();
+ scale = Scalar(1)/invScale;
+ }
+ else
+ {
+ scale = maxCoeff;
+ invScale = tmp;
+ }
+ }
+
+ // TODO if the maxCoeff is much much smaller than the current scale,
+ // then we can neglect this sub vector
+ if(scale>Scalar(0)) // if scale==0, then bl is 0
+ ssq += (bl*invScale).squaredNorm();
+}
+
+template<typename Derived>
+inline typename NumTraits<typename traits<Derived>::Scalar>::Real
+blueNorm_impl(const EigenBase<Derived>& _vec)
+{
+ typedef typename Derived::RealScalar RealScalar;
+ typedef typename Derived::Index Index;
+ using std::pow;
+ using std::min;
+ using std::max;
+ using std::sqrt;
+ using std::abs;
+ const Derived& vec(_vec.derived());
+ static bool initialized = false;
+ static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
+ if(!initialized)
+ {
+ int ibeta, it, iemin, iemax, iexp;
+ RealScalar eps;
+ // This program calculates the machine-dependent constants
+ // bl, b2, slm, s2m, relerr overfl
+ // from the "basic" machine-dependent numbers
+ // nbig, ibeta, it, iemin, iemax, rbig.
+ // The following define the basic machine-dependent constants.
+ // For portability, the PORT subprograms "ilmaeh" and "rlmach"
+ // are used. For any specific computer, each of the assignment
+ // statements can be replaced
+ ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
+ it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
+ iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
+ iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
+ rbig = (std::numeric_limits<RealScalar>::max)(); // largest floating-point number
+
+ iexp = -((1-iemin)/2);
+ b1 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // lower boundary of midrange
+ iexp = (iemax + 1 - it)/2;
+ b2 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // upper boundary of midrange
+
+ iexp = (2-iemin)/2;
+ s1m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for lower range
+ iexp = - ((iemax+it)/2);
+ s2m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for upper range
+
+ overfl = rbig*s2m; // overflow boundary for abig
+ eps = RealScalar(pow(double(ibeta), 1-it));
+ relerr = sqrt(eps); // tolerance for neglecting asml
+ initialized = true;
+ }
+ Index n = vec.size();
+ RealScalar ab2 = b2 / RealScalar(n);
+ RealScalar asml = RealScalar(0);
+ RealScalar amed = RealScalar(0);
+ RealScalar abig = RealScalar(0);
+ for(typename Derived::InnerIterator it(vec, 0); it; ++it)
+ {
+ RealScalar ax = abs(it.value());
+ if(ax > ab2) abig += numext::abs2(ax*s2m);
+ else if(ax < b1) asml += numext::abs2(ax*s1m);
+ else amed += numext::abs2(ax);
+ }
+ if(abig > RealScalar(0))
+ {
+ abig = sqrt(abig);
+ if(abig > overfl)
+ {
+ return rbig;
+ }
+ if(amed > RealScalar(0))
+ {
+ abig = abig/s2m;
+ amed = sqrt(amed);
+ }
+ else
+ return abig/s2m;
+ }
+ else if(asml > RealScalar(0))
+ {
+ if (amed > RealScalar(0))
+ {
+ abig = sqrt(amed);
+ amed = sqrt(asml) / s1m;
+ }
+ else
+ return sqrt(asml)/s1m;
+ }
+ else
+ return sqrt(amed);
+ asml = (min)(abig, amed);
+ abig = (max)(abig, amed);
+ if(asml <= abig*relerr)
+ return abig;
+ else
+ return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
+}
+
+} // end namespace internal
+
+/** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
+ * This version use a blockwise two passes algorithm:
+ * 1 - find the absolute largest coefficient \c s
+ * 2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
+ *
+ * For architecture/scalar types supporting vectorization, this version
+ * is faster than blueNorm(). Otherwise the blueNorm() is much faster.
+ *
+ * \sa norm(), blueNorm(), hypotNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::stableNorm() const
+{
+ using std::min;
+ using std::sqrt;
+ const Index blockSize = 4096;
+ RealScalar scale(0);
+ RealScalar invScale(1);
+ RealScalar ssq(0); // sum of square
+ enum {
+ Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? 1 : 0
+ };
+ Index n = size();
+ Index bi = internal::first_aligned(derived());
+ if (bi>0)
+ internal::stable_norm_kernel(this->head(bi), ssq, scale, invScale);
+ for (; bi<n; bi+=blockSize)
+ internal::stable_norm_kernel(this->segment(bi,(min)(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
+ return scale * sqrt(ssq);
+}
+
+/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
+ * A Portable Fortran Program to Find the Euclidean Norm of a Vector,
+ * ACM TOMS, Vol 4, Issue 1, 1978.
+ *
+ * For architecture/scalar types without vectorization, this version
+ * is much faster than stableNorm(). Otherwise the stableNorm() is faster.
+ *
+ * \sa norm(), stableNorm(), hypotNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::blueNorm() const
+{
+ return internal::blueNorm_impl(*this);
+}
+
+/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
+ * This version use a concatenation of hypot() calls, and it is very slow.
+ *
+ * \sa norm(), stableNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::hypotNorm() const
+{
+ return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_STABLENORM_H
diff --git a/Eigen/src/Core/Stride.h b/Eigen/src/Core/Stride.h
new file mode 100644
index 0000000..1e3f5fe
--- /dev/null
+++ b/Eigen/src/Core/Stride.h
@@ -0,0 +1,108 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STRIDE_H
+#define EIGEN_STRIDE_H
+
+namespace Eigen {
+
+/** \class Stride
+ * \ingroup Core_Module
+ *
+ * \brief Holds strides information for Map
+ *
+ * This class holds the strides information for mapping arrays with strides with class Map.
+ *
+ * It holds two values: the inner stride and the outer stride.
+ *
+ * The inner stride is the pointer increment between two consecutive entries within a given row of a
+ * row-major matrix or within a given column of a column-major matrix.
+ *
+ * The outer stride is the pointer increment between two consecutive rows of a row-major matrix or
+ * between two consecutive columns of a column-major matrix.
+ *
+ * These two values can be passed either at compile-time as template parameters, or at runtime as
+ * arguments to the constructor.
+ *
+ * Indeed, this class takes two template parameters:
+ * \param _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.
+ * \param _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.
+ *
+ * Here is an example:
+ * \include Map_general_stride.cpp
+ * Output: \verbinclude Map_general_stride.out
+ *
+ * \sa class InnerStride, class OuterStride, \ref TopicStorageOrders
+ */
+template<int _OuterStrideAtCompileTime, int _InnerStrideAtCompileTime>
+class Stride
+{
+ public:
+ typedef DenseIndex Index;
+ enum {
+ InnerStrideAtCompileTime = _InnerStrideAtCompileTime,
+ OuterStrideAtCompileTime = _OuterStrideAtCompileTime
+ };
+
+ /** Default constructor, for use when strides are fixed at compile time */
+ Stride()
+ : m_outer(OuterStrideAtCompileTime), m_inner(InnerStrideAtCompileTime)
+ {
+ eigen_assert(InnerStrideAtCompileTime != Dynamic && OuterStrideAtCompileTime != Dynamic);
+ }
+
+ /** Constructor allowing to pass the strides at runtime */
+ Stride(Index outerStride, Index innerStride)
+ : m_outer(outerStride), m_inner(innerStride)
+ {
+ eigen_assert(innerStride>=0 && outerStride>=0);
+ }
+
+ /** Copy constructor */
+ Stride(const Stride& other)
+ : m_outer(other.outer()), m_inner(other.inner())
+ {}
+
+ /** \returns the outer stride */
+ inline Index outer() const { return m_outer.value(); }
+ /** \returns the inner stride */
+ inline Index inner() const { return m_inner.value(); }
+
+ protected:
+ internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;
+ internal::variable_if_dynamic<Index, InnerStrideAtCompileTime> m_inner;
+};
+
+/** \brief Convenience specialization of Stride to specify only an inner stride
+ * See class Map for some examples */
+template<int Value = Dynamic>
+class InnerStride : public Stride<0, Value>
+{
+ typedef Stride<0, Value> Base;
+ public:
+ typedef DenseIndex Index;
+ InnerStride() : Base() {}
+ InnerStride(Index v) : Base(0, v) {}
+};
+
+/** \brief Convenience specialization of Stride to specify only an outer stride
+ * See class Map for some examples */
+template<int Value = Dynamic>
+class OuterStride : public Stride<Value, 0>
+{
+ typedef Stride<Value, 0> Base;
+ public:
+ typedef DenseIndex Index;
+ OuterStride() : Base() {}
+ OuterStride(Index v) : Base(v,0) {}
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_STRIDE_H
diff --git a/Eigen/src/Core/Swap.h b/Eigen/src/Core/Swap.h
new file mode 100644
index 0000000..bf58bd5
--- /dev/null
+++ b/Eigen/src/Core/Swap.h
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SWAP_H
+#define EIGEN_SWAP_H
+
+namespace Eigen {
+
+/** \class SwapWrapper
+ * \ingroup Core_Module
+ *
+ * \internal
+ *
+ * \brief Internal helper class for swapping two expressions
+ */
+namespace internal {
+template<typename ExpressionType>
+struct traits<SwapWrapper<ExpressionType> > : traits<ExpressionType> {};
+}
+
+template<typename ExpressionType> class SwapWrapper
+ : public internal::dense_xpr_base<SwapWrapper<ExpressionType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<SwapWrapper>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(SwapWrapper)
+ typedef typename internal::packet_traits<Scalar>::type Packet;
+
+ inline SwapWrapper(ExpressionType& xpr) : m_expression(xpr) {}
+
+ inline Index rows() const { return m_expression.rows(); }
+ inline Index cols() const { return m_expression.cols(); }
+ inline Index outerStride() const { return m_expression.outerStride(); }
+ inline Index innerStride() const { return m_expression.innerStride(); }
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<ExpressionType>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+ inline const Scalar* data() const { return m_expression.data(); }
+
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ return m_expression.const_cast_derived().coeffRef(rowId, colId);
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ inline Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_expression.coeffRef(rowId, colId);
+ }
+
+ inline Scalar& coeffRef(Index index) const
+ {
+ return m_expression.coeffRef(index);
+ }
+
+ template<typename OtherDerived>
+ void copyCoeff(Index rowId, Index colId, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(rowId >= 0 && rowId < rows()
+ && colId >= 0 && colId < cols());
+ Scalar tmp = m_expression.coeff(rowId, colId);
+ m_expression.coeffRef(rowId, colId) = _other.coeff(rowId, colId);
+ _other.coeffRef(rowId, colId) = tmp;
+ }
+
+ template<typename OtherDerived>
+ void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(index >= 0 && index < m_expression.size());
+ Scalar tmp = m_expression.coeff(index);
+ m_expression.coeffRef(index) = _other.coeff(index);
+ _other.coeffRef(index) = tmp;
+ }
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ void copyPacket(Index rowId, Index colId, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(rowId >= 0 && rowId < rows()
+ && colId >= 0 && colId < cols());
+ Packet tmp = m_expression.template packet<StoreMode>(rowId, colId);
+ m_expression.template writePacket<StoreMode>(rowId, colId,
+ _other.template packet<LoadMode>(rowId, colId)
+ );
+ _other.template writePacket<LoadMode>(rowId, colId, tmp);
+ }
+
+ template<typename OtherDerived, int StoreMode, int LoadMode>
+ void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+ {
+ OtherDerived& _other = other.const_cast_derived();
+ eigen_internal_assert(index >= 0 && index < m_expression.size());
+ Packet tmp = m_expression.template packet<StoreMode>(index);
+ m_expression.template writePacket<StoreMode>(index,
+ _other.template packet<LoadMode>(index)
+ );
+ _other.template writePacket<LoadMode>(index, tmp);
+ }
+
+ ExpressionType& expression() const { return m_expression; }
+
+ protected:
+ ExpressionType& m_expression;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SWAP_H
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
new file mode 100644
index 0000000..22096ea
--- /dev/null
+++ b/Eigen/src/Core/Transpose.h
@@ -0,0 +1,419 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSPOSE_H
+#define EIGEN_TRANSPOSE_H
+
+namespace Eigen {
+
+/** \class Transpose
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the transpose of a matrix
+ *
+ * \param MatrixType the type of the object of which we are taking the transpose
+ *
+ * This class represents an expression of the transpose of a matrix.
+ * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::transpose(), MatrixBase::adjoint()
+ */
+
+namespace internal {
+template<typename MatrixType>
+struct traits<Transpose<MatrixType> > : traits<MatrixType>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedPlain;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = MatrixType::ColsAtCompileTime,
+ ColsAtCompileTime = MatrixType::RowsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags0 = MatrixTypeNestedPlain::Flags & ~(LvalueBit | NestByRefBit),
+ Flags1 = Flags0 | FlagsLvalueBit,
+ Flags = Flags1 ^ RowMajorBit,
+ CoeffReadCost = MatrixTypeNestedPlain::CoeffReadCost,
+ InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,
+ OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret
+ };
+};
+}
+
+template<typename MatrixType, typename StorageKind> class TransposeImpl;
+
+template<typename MatrixType> class Transpose
+ : public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>
+{
+ public:
+
+ typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
+
+ inline Transpose(MatrixType& a_matrix) : m_matrix(a_matrix) {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
+
+ inline Index rows() const { return m_matrix.cols(); }
+ inline Index cols() const { return m_matrix.rows(); }
+
+ /** \returns the nested expression */
+ const typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() const { return m_matrix; }
+
+ /** \returns the nested expression */
+ typename internal::remove_all<typename MatrixType::Nested>::type&
+ nestedExpression() { return m_matrix.const_cast_derived(); }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+namespace internal {
+
+template<typename MatrixType, bool HasDirectAccess = has_direct_access<MatrixType>::ret>
+struct TransposeImpl_base
+{
+ typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+template<typename MatrixType>
+struct TransposeImpl_base<MatrixType, false>
+{
+ typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+} // end namespace internal
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
+ : public internal::TransposeImpl_base<MatrixType>::type
+{
+ public:
+
+ typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)
+
+ inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
+ inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
+
+ typedef typename internal::conditional<
+ internal::is_lvalue<MatrixType>::value,
+ Scalar,
+ const Scalar
+ >::type ScalarWithConstIfNotLvalue;
+
+ inline ScalarWithConstIfNotLvalue* data() { return derived().nestedExpression().data(); }
+ inline const Scalar* data() const { return derived().nestedExpression().data(); }
+
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index rowId, Index colId)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return derived().nestedExpression().const_cast_derived().coeffRef(colId, rowId);
+ }
+
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return derived().nestedExpression().const_cast_derived().coeffRef(index);
+ }
+
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return derived().nestedExpression().coeffRef(colId, rowId);
+ }
+
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return derived().nestedExpression().coeffRef(index);
+ }
+
+ inline CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ return derived().nestedExpression().coeff(colId, rowId);
+ }
+
+ inline CoeffReturnType coeff(Index index) const
+ {
+ return derived().nestedExpression().coeff(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index rowId, Index colId) const
+ {
+ return derived().nestedExpression().template packet<LoadMode>(colId, rowId);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index rowId, Index colId, const PacketScalar& x)
+ {
+ derived().nestedExpression().const_cast_derived().template writePacket<LoadMode>(colId, rowId, x);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return derived().nestedExpression().template packet<LoadMode>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ derived().nestedExpression().const_cast_derived().template writePacket<LoadMode>(index, x);
+ }
+};
+
+/** \returns an expression of the transpose of *this.
+ *
+ * Example: \include MatrixBase_transpose.cpp
+ * Output: \verbinclude MatrixBase_transpose.out
+ *
+ * \warning If you want to replace a matrix by its own transpose, do \b NOT do this:
+ * \code
+ * m = m.transpose(); // bug!!! caused by aliasing effect
+ * \endcode
+ * Instead, use the transposeInPlace() method:
+ * \code
+ * m.transposeInPlace();
+ * \endcode
+ * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+ * \code
+ * m = m.transpose().eval();
+ * \endcode
+ *
+ * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline Transpose<Derived>
+DenseBase<Derived>::transpose()
+{
+ return derived();
+}
+
+/** This is the const version of transpose().
+ *
+ * Make sure you read the warning for transpose() !
+ *
+ * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline typename DenseBase<Derived>::ConstTransposeReturnType
+DenseBase<Derived>::transpose() const
+{
+ return ConstTransposeReturnType(derived());
+}
+
+/** \returns an expression of the adjoint (i.e. conjugate transpose) of *this.
+ *
+ * Example: \include MatrixBase_adjoint.cpp
+ * Output: \verbinclude MatrixBase_adjoint.out
+ *
+ * \warning If you want to replace a matrix by its own adjoint, do \b NOT do this:
+ * \code
+ * m = m.adjoint(); // bug!!! caused by aliasing effect
+ * \endcode
+ * Instead, use the adjointInPlace() method:
+ * \code
+ * m.adjointInPlace();
+ * \endcode
+ * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+ * \code
+ * m = m.adjoint().eval();
+ * \endcode
+ *
+ * \sa adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::AdjointReturnType
+MatrixBase<Derived>::adjoint() const
+{
+ return this->transpose(); // in the complex case, the .conjugate() is be implicit here
+ // due to implicit conversion to return type
+}
+
+/***************************************************************************
+* "in place" transpose implementation
+***************************************************************************/
+
+namespace internal {
+
+template<typename MatrixType,
+ bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic>
+struct inplace_transpose_selector;
+
+template<typename MatrixType>
+struct inplace_transpose_selector<MatrixType,true> { // square matrix
+ static void run(MatrixType& m) {
+ m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
+ }
+};
+
+template<typename MatrixType>
+struct inplace_transpose_selector<MatrixType,false> { // non square matrix
+ static void run(MatrixType& m) {
+ if (m.rows()==m.cols())
+ m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
+ else
+ m = m.transpose().eval();
+ }
+};
+
+} // end namespace internal
+
+/** This is the "in place" version of transpose(): it replaces \c *this by its own transpose.
+ * Thus, doing
+ * \code
+ * m.transposeInPlace();
+ * \endcode
+ * has the same effect on m as doing
+ * \code
+ * m = m.transpose().eval();
+ * \endcode
+ * and is faster and also safer because in the latter line of code, forgetting the eval() results
+ * in a bug caused by \ref TopicAliasing "aliasing".
+ *
+ * Notice however that this method is only useful if you want to replace a matrix by its own transpose.
+ * If you just need the transpose of a matrix, use transpose().
+ *
+ * \note if the matrix is not square, then \c *this must be a resizable matrix.
+ * This excludes (non-square) fixed-size matrices, block-expressions and maps.
+ *
+ * \sa transpose(), adjoint(), adjointInPlace() */
+template<typename Derived>
+inline void DenseBase<Derived>::transposeInPlace()
+{
+ eigen_assert((rows() == cols() || (RowsAtCompileTime == Dynamic && ColsAtCompileTime == Dynamic))
+ && "transposeInPlace() called on a non-square non-resizable matrix");
+ internal::inplace_transpose_selector<Derived>::run(derived());
+}
+
+/***************************************************************************
+* "in place" adjoint implementation
+***************************************************************************/
+
+/** This is the "in place" version of adjoint(): it replaces \c *this by its own transpose.
+ * Thus, doing
+ * \code
+ * m.adjointInPlace();
+ * \endcode
+ * has the same effect on m as doing
+ * \code
+ * m = m.adjoint().eval();
+ * \endcode
+ * and is faster and also safer because in the latter line of code, forgetting the eval() results
+ * in a bug caused by aliasing.
+ *
+ * Notice however that this method is only useful if you want to replace a matrix by its own adjoint.
+ * If you just need the adjoint of a matrix, use adjoint().
+ *
+ * \note if the matrix is not square, then \c *this must be a resizable matrix.
+ * This excludes (non-square) fixed-size matrices, block-expressions and maps.
+ *
+ * \sa transpose(), adjoint(), transposeInPlace() */
+template<typename Derived>
+inline void MatrixBase<Derived>::adjointInPlace()
+{
+ derived() = adjoint().eval();
+}
+
+#ifndef EIGEN_NO_DEBUG
+
+// The following is to detect aliasing problems in most common cases.
+
+namespace internal {
+
+template<typename BinOp,typename NestedXpr,typename Rhs>
+struct blas_traits<SelfCwiseBinaryOp<BinOp,NestedXpr,Rhs> >
+ : blas_traits<NestedXpr>
+{
+ typedef SelfCwiseBinaryOp<BinOp,NestedXpr,Rhs> XprType;
+ static inline const XprType extract(const XprType& x) { return x; }
+};
+
+template<bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_compile_time_selector
+{
+ enum { ret = bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed };
+};
+
+template<bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_compile_time_selector<DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+ enum { ret = bool(blas_traits<DerivedA>::IsTransposed) != DestIsTransposed
+ || bool(blas_traits<DerivedB>::IsTransposed) != DestIsTransposed
+ };
+};
+
+template<typename Scalar, bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_run_time_selector
+{
+ static bool run(const Scalar* dest, const OtherDerived& src)
+ {
+ return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src));
+ }
+};
+
+template<typename Scalar, bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+ static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)
+ {
+ return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.lhs())))
+ || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.rhs())));
+ }
+};
+
+// the following selector, checkTransposeAliasing_impl, based on MightHaveTransposeAliasing,
+// is because when the condition controlling the assert is known at compile time, ICC emits a warning.
+// This is actually a good warning: in expressions that don't have any transposing, the condition is
+// known at compile time to be false, and using that, we can avoid generating the code of the assert again
+// and again for all these expressions that don't need it.
+
+template<typename Derived, typename OtherDerived,
+ bool MightHaveTransposeAliasing
+ = check_transpose_aliasing_compile_time_selector
+ <blas_traits<Derived>::IsTransposed,OtherDerived>::ret
+ >
+struct checkTransposeAliasing_impl
+{
+ static void run(const Derived& dst, const OtherDerived& other)
+ {
+ eigen_assert((!check_transpose_aliasing_run_time_selector
+ <typename Derived::Scalar,blas_traits<Derived>::IsTransposed,OtherDerived>
+ ::run(extract_data(dst), other))
+ && "aliasing detected during transposition, use transposeInPlace() "
+ "or evaluate the rhs into a temporary using .eval()");
+
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct checkTransposeAliasing_impl<Derived, OtherDerived, false>
+{
+ static void run(const Derived&, const OtherDerived&)
+ {
+ }
+};
+
+} // end namespace internal
+
+template<typename Derived>
+template<typename OtherDerived>
+void DenseBase<Derived>::checkTransposeAliasing(const OtherDerived& other) const
+{
+ internal::checkTransposeAliasing_impl<Derived, OtherDerived>::run(derived(), other);
+}
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSPOSE_H
diff --git a/Eigen/src/Core/Transpositions.h b/Eigen/src/Core/Transpositions.h
new file mode 100644
index 0000000..e4ba075
--- /dev/null
+++ b/Eigen/src/Core/Transpositions.h
@@ -0,0 +1,436 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSPOSITIONS_H
+#define EIGEN_TRANSPOSITIONS_H
+
+namespace Eigen {
+
+/** \class Transpositions
+ * \ingroup Core_Module
+ *
+ * \brief Represents a sequence of transpositions (row/column interchange)
+ *
+ * \param SizeAtCompileTime the number of transpositions, or Dynamic
+ * \param MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+ *
+ * This class represents a permutation transformation as a sequence of \em n transpositions
+ * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
+ * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
+ * the rows \c i and \c indices[i] of the matrix \c M.
+ * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
+ *
+ * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
+ * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
+ *
+ * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
+ * \code
+ * Transpositions tr;
+ * MatrixXf mat;
+ * mat = tr * mat;
+ * \endcode
+ * In this example, we detect that the matrix appears on both side, and so the transpositions
+ * are applied in-place without any temporary or extra copy.
+ *
+ * \sa class PermutationMatrix
+ */
+
+namespace internal {
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed=false> struct transposition_matrix_product_retval;
+}
+
+template<typename Derived>
+class TranspositionsBase
+{
+ typedef internal::traits<Derived> Traits;
+
+ public:
+
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar Index;
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Derived& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Derived& operator=(const TranspositionsBase& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+ #endif
+
+ /** \returns the number of transpositions */
+ inline Index size() const { return indices().size(); }
+
+ /** Direct access to the underlying index vector */
+ inline const Index& coeff(Index i) const { return indices().coeff(i); }
+ /** Direct access to the underlying index vector */
+ inline Index& coeffRef(Index i) { return indices().coeffRef(i); }
+ /** Direct access to the underlying index vector */
+ inline const Index& operator()(Index i) const { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline Index& operator()(Index i) { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline const Index& operator[](Index i) const { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline Index& operator[](Index i) { return indices()(i); }
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return derived().indices(); }
+ /** \returns a reference to the stored array representing the transpositions. */
+ IndicesType& indices() { return derived().indices(); }
+
+ /** Resizes to given size. */
+ inline void resize(int newSize)
+ {
+ indices().resize(newSize);
+ }
+
+ /** Sets \c *this to represents an identity transformation */
+ void setIdentity()
+ {
+ for(int i = 0; i < indices().size(); ++i)
+ coeffRef(i) = i;
+ }
+
+ // FIXME: do we want such methods ?
+ // might be usefull when the target matrix expression is complex, e.g.:
+ // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
+ /*
+ template<typename MatrixType>
+ void applyForwardToRows(MatrixType& mat) const
+ {
+ for(Index k=0 ; k<size() ; ++k)
+ if(m_indices(k)!=k)
+ mat.row(k).swap(mat.row(m_indices(k)));
+ }
+
+ template<typename MatrixType>
+ void applyBackwardToRows(MatrixType& mat) const
+ {
+ for(Index k=size()-1 ; k>=0 ; --k)
+ if(m_indices(k)!=k)
+ mat.row(k).swap(mat.row(m_indices(k)));
+ }
+ */
+
+ /** \returns the inverse transformation */
+ inline Transpose<TranspositionsBase> inverse() const
+ { return Transpose<TranspositionsBase>(derived()); }
+
+ /** \returns the tranpose transformation */
+ inline Transpose<TranspositionsBase> transpose() const
+ { return Transpose<TranspositionsBase>(derived()); }
+
+ protected:
+};
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
+{
+ typedef IndexType Index;
+ typedef Matrix<Index, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
+{
+ typedef internal::traits<Transpositions> Traits;
+ public:
+
+ typedef TranspositionsBase<Transpositions> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar Index;
+
+ inline Transpositions() {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ inline Transpositions(const TranspositionsBase<OtherDerived>& other)
+ : m_indices(other.indices()) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** Standard copy constructor. Defined only to prevent a default copy constructor
+ * from hiding the other templated constructor */
+ inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}
+ #endif
+
+ /** Generic constructor from expression of the transposition indices. */
+ template<typename Other>
+ explicit inline Transpositions(const MatrixBase<Other>& a_indices) : m_indices(a_indices)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Transpositions& operator=(const Transpositions& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** Constructs an uninitialized permutation matrix of given size.
+ */
+ inline Transpositions(Index size) : m_indices(size)
+ {}
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the transpositions. */
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,_PacketAccess> >
+{
+ typedef IndexType Index;
+ typedef Map<const Matrix<Index,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int PacketAccess>
+class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess>
+ : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess> >
+{
+ typedef internal::traits<Map> Traits;
+ public:
+
+ typedef TranspositionsBase<Map> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar Index;
+
+ inline Map(const Index* indicesPtr)
+ : m_indices(indicesPtr)
+ {}
+
+ inline Map(const Index* indicesPtr, Index size)
+ : m_indices(indicesPtr,size)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Map& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Map& operator=(const Map& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+
+ /** \returns a reference to the stored array representing the transpositions. */
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+namespace internal {
+template<typename _IndicesType>
+struct traits<TranspositionsWrapper<_IndicesType> >
+{
+ typedef typename _IndicesType::Scalar Index;
+ typedef _IndicesType IndicesType;
+};
+}
+
+template<typename _IndicesType>
+class TranspositionsWrapper
+ : public TranspositionsBase<TranspositionsWrapper<_IndicesType> >
+{
+ typedef internal::traits<TranspositionsWrapper> Traits;
+ public:
+
+ typedef TranspositionsBase<TranspositionsWrapper> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar Index;
+
+ inline TranspositionsWrapper(IndicesType& a_indices)
+ : m_indices(a_indices)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ TranspositionsWrapper& operator=(const TranspositionsWrapper& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+
+ /** \returns a reference to the stored array representing the transpositions. */
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ const typename IndicesType::Nested m_indices;
+};
+
+/** \returns the \a matrix with the \a transpositions applied to the columns.
+ */
+template<typename Derived, typename TranspositionsDerived>
+inline const internal::transposition_matrix_product_retval<TranspositionsDerived, Derived, OnTheRight>
+operator*(const MatrixBase<Derived>& matrix,
+ const TranspositionsBase<TranspositionsDerived> &transpositions)
+{
+ return internal::transposition_matrix_product_retval
+ <TranspositionsDerived, Derived, OnTheRight>
+ (transpositions.derived(), matrix.derived());
+}
+
+/** \returns the \a matrix with the \a transpositions applied to the rows.
+ */
+template<typename Derived, typename TranspositionDerived>
+inline const internal::transposition_matrix_product_retval
+ <TranspositionDerived, Derived, OnTheLeft>
+operator*(const TranspositionsBase<TranspositionDerived> &transpositions,
+ const MatrixBase<Derived>& matrix)
+{
+ return internal::transposition_matrix_product_retval
+ <TranspositionDerived, Derived, OnTheLeft>
+ (transpositions.derived(), matrix.derived());
+}
+
+namespace internal {
+
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
+struct traits<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
+struct transposition_matrix_product_retval
+ : public ReturnByValue<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
+{
+ typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+ typedef typename TranspositionType::Index Index;
+
+ transposition_matrix_product_retval(const TranspositionType& tr, const MatrixType& matrix)
+ : m_transpositions(tr), m_matrix(matrix)
+ {}
+
+ inline int rows() const { return m_matrix.rows(); }
+ inline int cols() const { return m_matrix.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ const int size = m_transpositions.size();
+ Index j = 0;
+
+ if(!(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix)))
+ dst = m_matrix;
+
+ for(int k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
+ if((j=m_transpositions.coeff(k))!=k)
+ {
+ if(Side==OnTheLeft)
+ dst.row(k).swap(dst.row(j));
+ else if(Side==OnTheRight)
+ dst.col(k).swap(dst.col(j));
+ }
+ }
+
+ protected:
+ const TranspositionType& m_transpositions;
+ typename MatrixType::Nested m_matrix;
+};
+
+} // end namespace internal
+
+/* Template partial specialization for transposed/inverse transpositions */
+
+template<typename TranspositionsDerived>
+class Transpose<TranspositionsBase<TranspositionsDerived> >
+{
+ typedef TranspositionsDerived TranspositionType;
+ typedef typename TranspositionType::IndicesType IndicesType;
+ public:
+
+ Transpose(const TranspositionType& t) : m_transpositions(t) {}
+
+ inline int size() const { return m_transpositions.size(); }
+
+ /** \returns the \a matrix with the inverse transpositions applied to the columns.
+ */
+ template<typename Derived> friend
+ inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>
+ operator*(const MatrixBase<Derived>& matrix, const Transpose& trt)
+ {
+ return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>(trt.m_transpositions, matrix.derived());
+ }
+
+ /** \returns the \a matrix with the inverse transpositions applied to the rows.
+ */
+ template<typename Derived>
+ inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>
+ operator*(const MatrixBase<Derived>& matrix) const
+ {
+ return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>(m_transpositions, matrix.derived());
+ }
+
+ protected:
+ const TranspositionType& m_transpositions;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSPOSITIONS_H
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
new file mode 100644
index 0000000..4d65392
--- /dev/null
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -0,0 +1,839 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULARMATRIX_H
+#define EIGEN_TRIANGULARMATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;
+
+}
+
+/** \internal
+ *
+ * \class TriangularBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for triangular part in a matrix
+ */
+template<typename Derived> class TriangularBase : public EigenBase<Derived>
+{
+ public:
+
+ enum {
+ Mode = internal::traits<Derived>::Mode,
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime
+ };
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::traits<Derived>::DenseMatrixType DenseMatrixType;
+ typedef DenseMatrixType DenseType;
+
+ inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); }
+
+ inline Index rows() const { return derived().rows(); }
+ inline Index cols() const { return derived().cols(); }
+ inline Index outerStride() const { return derived().outerStride(); }
+ inline Index innerStride() const { return derived().innerStride(); }
+
+ inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); }
+ inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }
+
+ /** \see MatrixBase::copyCoeff(row,col)
+ */
+ template<typename Other>
+ EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)
+ {
+ derived().coeffRef(row, col) = other.coeff(row, col);
+ }
+
+ inline Scalar operator()(Index row, Index col) const
+ {
+ check_coordinates(row, col);
+ return coeff(row,col);
+ }
+ inline Scalar& operator()(Index row, Index col)
+ {
+ check_coordinates(row, col);
+ return coeffRef(row,col);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+ #endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived> &other) const;
+ template<typename DenseDerived>
+ void evalToLazy(MatrixBase<DenseDerived> &other) const;
+
+ DenseMatrixType toDenseMatrix() const
+ {
+ DenseMatrixType res(rows(), cols());
+ evalToLazy(res);
+ return res;
+ }
+
+ protected:
+
+ void check_coordinates(Index row, Index col) const
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(row);
+ EIGEN_ONLY_USED_FOR_DEBUG(col);
+ eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());
+ const int mode = int(Mode) & ~SelfAdjoint;
+ EIGEN_ONLY_USED_FOR_DEBUG(mode);
+ eigen_assert((mode==Upper && col>=row)
+ || (mode==Lower && col<=row)
+ || ((mode==StrictlyUpper || mode==UnitUpper) && col>row)
+ || ((mode==StrictlyLower || mode==UnitLower) && col<row));
+ }
+
+ #ifdef EIGEN_INTERNAL_DEBUGGING
+ void check_coordinates_internal(Index row, Index col) const
+ {
+ check_coordinates(row, col);
+ }
+ #else
+ void check_coordinates_internal(Index , Index ) const {}
+ #endif
+
+};
+
+/** \class TriangularView
+ * \ingroup Core_Module
+ *
+ * \brief Base class for triangular part in a matrix
+ *
+ * \param MatrixType the type of the object in which we are taking the triangular part
+ * \param Mode the kind of triangular matrix expression to construct. Can be #Upper,
+ * #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.
+ * This is in fact a bit field; it must have either #Upper or #Lower,
+ * and additionnaly it may have #UnitDiag or #ZeroDiag or neither.
+ *
+ * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
+ * matrices one should speak of "trapezoid" parts. This class is the return type
+ * of MatrixBase::triangularView() and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::triangularView()
+ */
+namespace internal {
+template<typename MatrixType, unsigned int _Mode>
+struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>
+{
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
+ typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+ typedef MatrixType ExpressionType;
+ typedef typename MatrixType::PlainObject DenseMatrixType;
+ enum {
+ Mode = _Mode,
+ Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode,
+ CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
+ };
+};
+}
+
+template<int Mode, bool LhsIsTriangular,
+ typename Lhs, bool LhsIsVector,
+ typename Rhs, bool RhsIsVector>
+struct TriangularProduct;
+
+template<typename _MatrixType, unsigned int _Mode> class TriangularView
+ : public TriangularBase<TriangularView<_MatrixType, _Mode> >
+{
+ public:
+
+ typedef TriangularBase<TriangularView> Base;
+ typedef typename internal::traits<TriangularView>::Scalar Scalar;
+
+ typedef _MatrixType MatrixType;
+ typedef typename internal::traits<TriangularView>::DenseMatrixType DenseMatrixType;
+ typedef DenseMatrixType PlainObject;
+
+ protected:
+ typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;
+ typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
+
+ typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;
+
+ public:
+ using Base::evalToLazy;
+
+
+ typedef typename internal::traits<TriangularView>::StorageKind StorageKind;
+ typedef typename internal::traits<TriangularView>::Index Index;
+
+ enum {
+ Mode = _Mode,
+ TransposeMode = (Mode & Upper ? Lower : 0)
+ | (Mode & Lower ? Upper : 0)
+ | (Mode & (UnitDiag))
+ | (Mode & (ZeroDiag))
+ };
+
+ inline TriangularView(const MatrixType& matrix) : m_matrix(matrix)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index outerStride() const { return m_matrix.outerStride(); }
+ inline Index innerStride() const { return m_matrix.innerStride(); }
+
+ /** \sa MatrixBase::operator+=() */
+ template<typename Other> TriangularView& operator+=(const DenseBase<Other>& other) { return *this = m_matrix + other.derived(); }
+ /** \sa MatrixBase::operator-=() */
+ template<typename Other> TriangularView& operator-=(const DenseBase<Other>& other) { return *this = m_matrix - other.derived(); }
+ /** \sa MatrixBase::operator*=() */
+ TriangularView& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix * other; }
+ /** \sa MatrixBase::operator/=() */
+ TriangularView& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix / other; }
+
+ /** \sa MatrixBase::fill() */
+ void fill(const Scalar& value) { setConstant(value); }
+ /** \sa MatrixBase::setConstant() */
+ TriangularView& setConstant(const Scalar& value)
+ { return *this = MatrixType::Constant(rows(), cols(), value); }
+ /** \sa MatrixBase::setZero() */
+ TriangularView& setZero() { return setConstant(Scalar(0)); }
+ /** \sa MatrixBase::setOnes() */
+ TriangularView& setOnes() { return setConstant(Scalar(1)); }
+
+ /** \sa MatrixBase::coeff()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ inline Scalar coeff(Index row, Index col) const
+ {
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.coeff(row, col);
+ }
+
+ /** \sa MatrixBase::coeffRef()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.const_cast_derived().coeffRef(row, col);
+ }
+
+ const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+ MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
+
+ /** Assigns a triangular matrix to a triangular part of a dense matrix */
+ template<typename OtherDerived>
+ TriangularView& operator=(const TriangularBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ TriangularView& operator=(const MatrixBase<OtherDerived>& other);
+
+ TriangularView& operator=(const TriangularView& other)
+ { return *this = other.nestedExpression(); }
+
+ template<typename OtherDerived>
+ void lazyAssign(const TriangularBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ void lazyAssign(const MatrixBase<OtherDerived>& other);
+
+ /** \sa MatrixBase::conjugate() */
+ inline TriangularView<MatrixConjugateReturnType,Mode> conjugate()
+ { return m_matrix.conjugate(); }
+ /** \sa MatrixBase::conjugate() const */
+ inline const TriangularView<MatrixConjugateReturnType,Mode> conjugate() const
+ { return m_matrix.conjugate(); }
+
+ /** \sa MatrixBase::adjoint() const */
+ inline const TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> adjoint() const
+ { return m_matrix.adjoint(); }
+
+ /** \sa MatrixBase::transpose() */
+ inline TriangularView<Transpose<MatrixType>,TransposeMode> transpose()
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return m_matrix.const_cast_derived().transpose();
+ }
+ /** \sa MatrixBase::transpose() const */
+ inline const TriangularView<Transpose<MatrixType>,TransposeMode> transpose() const
+ {
+ return m_matrix.transpose();
+ }
+
+ /** Efficient triangular matrix times vector/matrix product */
+ template<typename OtherDerived>
+ TriangularProduct<Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return TriangularProduct
+ <Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1>
+ (m_matrix, rhs.derived());
+ }
+
+ /** Efficient vector/matrix times triangular matrix product */
+ template<typename OtherDerived> friend
+ TriangularProduct<Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false>
+ operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs)
+ {
+ return TriangularProduct
+ <Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false>
+ (lhs.derived(),rhs.m_matrix);
+ }
+
+ #ifdef EIGEN2_SUPPORT
+ template<typename OtherDerived>
+ struct eigen2_product_return_type
+ {
+ typedef typename TriangularView<MatrixType,Mode>::DenseMatrixType DenseMatrixType;
+ typedef typename OtherDerived::PlainObject::DenseType OtherPlainObject;
+ typedef typename ProductReturnType<DenseMatrixType, OtherPlainObject>::Type ProdRetType;
+ typedef typename ProdRetType::PlainObject type;
+ };
+ template<typename OtherDerived>
+ const typename eigen2_product_return_type<OtherDerived>::type
+ operator*(const EigenBase<OtherDerived>& rhs) const
+ {
+ typename OtherDerived::PlainObject::DenseType rhsPlainObject;
+ rhs.evalTo(rhsPlainObject);
+ return this->toDenseMatrix() * rhsPlainObject;
+ }
+ template<typename OtherMatrixType>
+ bool isApprox(const TriangularView<OtherMatrixType, Mode>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+ {
+ return this->toDenseMatrix().isApprox(other.toDenseMatrix(), precision);
+ }
+ template<typename OtherDerived>
+ bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+ {
+ return this->toDenseMatrix().isApprox(other, precision);
+ }
+ #endif // EIGEN2_SUPPORT
+
+ template<int Side, typename Other>
+ inline const internal::triangular_solve_retval<Side,TriangularView, Other>
+ solve(const MatrixBase<Other>& other) const;
+
+ template<int Side, typename OtherDerived>
+ void solveInPlace(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename Other>
+ inline const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other>
+ solve(const MatrixBase<Other>& other) const
+ { return solve<OnTheLeft>(other); }
+
+ template<typename OtherDerived>
+ void solveInPlace(const MatrixBase<OtherDerived>& other) const
+ { return solveInPlace<OnTheLeft>(other); }
+
+ const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const
+ {
+ EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
+ return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+ }
+ SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()
+ {
+ EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
+ return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+ }
+
+ template<typename OtherDerived>
+ void swap(TriangularBase<OtherDerived> const & other)
+ {
+ TriangularView<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived());
+ }
+
+ template<typename OtherDerived>
+ void swap(MatrixBase<OtherDerived> const & other)
+ {
+ SwapWrapper<MatrixType> swaper(const_cast<MatrixType&>(m_matrix));
+ TriangularView<SwapWrapper<MatrixType>,Mode>(swaper).lazyAssign(other.derived());
+ }
+
+ Scalar determinant() const
+ {
+ if (Mode & UnitDiag)
+ return 1;
+ else if (Mode & ZeroDiag)
+ return 0;
+ else
+ return m_matrix.diagonal().prod();
+ }
+
+ // TODO simplify the following:
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE TriangularView& operator=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+ {
+ setZero();
+ return assignProduct(other.derived(),1);
+ }
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE TriangularView& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+ {
+ return assignProduct(other.derived(),1);
+ }
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE TriangularView& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+ {
+ return assignProduct(other.derived(),-1);
+ }
+
+
+ template<typename ProductDerived>
+ EIGEN_STRONG_INLINE TriangularView& operator=(const ScaledProduct<ProductDerived>& other)
+ {
+ setZero();
+ return assignProduct(other.derived(),other.alpha());
+ }
+
+ template<typename ProductDerived>
+ EIGEN_STRONG_INLINE TriangularView& operator+=(const ScaledProduct<ProductDerived>& other)
+ {
+ return assignProduct(other.derived(),other.alpha());
+ }
+
+ template<typename ProductDerived>
+ EIGEN_STRONG_INLINE TriangularView& operator-=(const ScaledProduct<ProductDerived>& other)
+ {
+ return assignProduct(other.derived(),-other.alpha());
+ }
+
+ protected:
+
+ template<typename ProductDerived, typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE TriangularView& assignProduct(const ProductBase<ProductDerived, Lhs,Rhs>& prod, const Scalar& alpha);
+
+ template<int Mode, bool LhsIsTriangular,
+ typename Lhs, bool LhsIsVector,
+ typename Rhs, bool RhsIsVector>
+ EIGEN_STRONG_INLINE TriangularView& assignProduct(const TriangularProduct<Mode, LhsIsTriangular, Lhs, LhsIsVector, Rhs, RhsIsVector>& prod, const Scalar& alpha)
+ {
+ lazyAssign(alpha*prod.eval());
+ return *this;
+ }
+
+ MatrixTypeNested m_matrix;
+};
+
+/***************************************************************************
+* Implementation of triangular evaluation/assignment
+***************************************************************************/
+
+namespace internal {
+
+template<typename Derived1, typename Derived2, unsigned int Mode, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector
+{
+ enum {
+ col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+ };
+
+ typedef typename Derived1::Scalar Scalar;
+
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ triangular_assignment_selector<Derived1, Derived2, Mode, UnrollCount-1, ClearOpposite>::run(dst, src);
+
+ eigen_assert( Mode == Upper || Mode == Lower
+ || Mode == StrictlyUpper || Mode == StrictlyLower
+ || Mode == UnitUpper || Mode == UnitLower);
+ if((Mode == Upper && row <= col)
+ || (Mode == Lower && row >= col)
+ || (Mode == StrictlyUpper && row < col)
+ || (Mode == StrictlyLower && row > col)
+ || (Mode == UnitUpper && row < col)
+ || (Mode == UnitLower && row > col))
+ dst.copyCoeff(row, col, src);
+ else if(ClearOpposite)
+ {
+ if (Mode&UnitDiag && row==col)
+ dst.coeffRef(row, col) = Scalar(1);
+ else
+ dst.coeffRef(row, col) = Scalar(0);
+ }
+ }
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite>
+{
+ static inline void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Upper, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ typedef typename Derived1::Scalar Scalar;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ Index maxi = (std::min)(j, dst.rows()-1);
+ for(Index i = 0; i <= maxi; ++i)
+ dst.copyCoeff(i, j, src);
+ if (ClearOpposite)
+ for(Index i = maxi+1; i < dst.rows(); ++i)
+ dst.coeffRef(i, j) = Scalar(0);
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Lower, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ for(Index i = j; i < dst.rows(); ++i)
+ dst.copyCoeff(i, j, src);
+ Index maxi = (std::min)(j, dst.rows());
+ if (ClearOpposite)
+ for(Index i = 0; i < maxi; ++i)
+ dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, StrictlyUpper, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ typedef typename Derived1::Scalar Scalar;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ Index maxi = (std::min)(j, dst.rows());
+ for(Index i = 0; i < maxi; ++i)
+ dst.copyCoeff(i, j, src);
+ if (ClearOpposite)
+ for(Index i = maxi; i < dst.rows(); ++i)
+ dst.coeffRef(i, j) = Scalar(0);
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, StrictlyLower, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ for(Index i = j+1; i < dst.rows(); ++i)
+ dst.copyCoeff(i, j, src);
+ Index maxi = (std::min)(j, dst.rows()-1);
+ if (ClearOpposite)
+ for(Index i = 0; i <= maxi; ++i)
+ dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
+ }
+ }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, UnitUpper, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ Index maxi = (std::min)(j, dst.rows());
+ for(Index i = 0; i < maxi; ++i)
+ dst.copyCoeff(i, j, src);
+ if (ClearOpposite)
+ {
+ for(Index i = maxi+1; i < dst.rows(); ++i)
+ dst.coeffRef(i, j) = 0;
+ }
+ }
+ dst.diagonal().setOnes();
+ }
+};
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, UnitLower, Dynamic, ClearOpposite>
+{
+ typedef typename Derived1::Index Index;
+ static inline void run(Derived1 &dst, const Derived2 &src)
+ {
+ for(Index j = 0; j < dst.cols(); ++j)
+ {
+ Index maxi = (std::min)(j, dst.rows());
+ for(Index i = maxi+1; i < dst.rows(); ++i)
+ dst.copyCoeff(i, j, src);
+ if (ClearOpposite)
+ {
+ for(Index i = 0; i < maxi; ++i)
+ dst.coeffRef(i, j) = 0;
+ }
+ }
+ dst.diagonal().setOnes();
+ }
+};
+
+} // end namespace internal
+
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+inline TriangularView<MatrixType, Mode>&
+TriangularView<MatrixType, Mode>::operator=(const MatrixBase<OtherDerived>& other)
+{
+ if(OtherDerived::Flags & EvalBeforeAssigningBit)
+ {
+ typename internal::plain_matrix_type<OtherDerived>::type other_evaluated(other.rows(), other.cols());
+ other_evaluated.template triangularView<Mode>().lazyAssign(other.derived());
+ lazyAssign(other_evaluated);
+ }
+ else
+ lazyAssign(other.derived());
+ return *this;
+}
+
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived>& other)
+{
+ enum {
+ unroll = MatrixType::SizeAtCompileTime != Dynamic
+ && internal::traits<OtherDerived>::CoeffReadCost != Dynamic
+ && MatrixType::SizeAtCompileTime*internal::traits<OtherDerived>::CoeffReadCost/2 <= EIGEN_UNROLLING_LIMIT
+ };
+ eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
+
+ internal::triangular_assignment_selector
+ <MatrixType, OtherDerived, int(Mode),
+ unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
+ false // do not change the opposite triangular part
+ >::run(m_matrix.const_cast_derived(), other.derived());
+}
+
+
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+inline TriangularView<MatrixType, Mode>&
+TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& other)
+{
+ eigen_assert(Mode == int(OtherDerived::Mode));
+ if(internal::traits<OtherDerived>::Flags & EvalBeforeAssigningBit)
+ {
+ typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols());
+ other_evaluated.template triangularView<Mode>().lazyAssign(other.derived().nestedExpression());
+ lazyAssign(other_evaluated);
+ }
+ else
+ lazyAssign(other.derived().nestedExpression());
+ return *this;
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+void TriangularView<MatrixType, Mode>::lazyAssign(const TriangularBase<OtherDerived>& other)
+{
+ enum {
+ unroll = MatrixType::SizeAtCompileTime != Dynamic
+ && internal::traits<OtherDerived>::CoeffReadCost != Dynamic
+ && MatrixType::SizeAtCompileTime * internal::traits<OtherDerived>::CoeffReadCost / 2
+ <= EIGEN_UNROLLING_LIMIT
+ };
+ eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
+
+ internal::triangular_assignment_selector
+ <MatrixType, OtherDerived, int(Mode),
+ unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
+ false // preserve the opposite triangular part
+ >::run(m_matrix.const_cast_derived(), other.derived().nestedExpression());
+}
+
+/***************************************************************************
+* Implementation of TriangularBase methods
+***************************************************************************/
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+ * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
+{
+ if(internal::traits<Derived>::Flags & EvalBeforeAssigningBit)
+ {
+ typename internal::plain_matrix_type<Derived>::type other_evaluated(rows(), cols());
+ evalToLazy(other_evaluated);
+ other.derived().swap(other_evaluated);
+ }
+ else
+ evalToLazy(other.derived());
+}
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+ * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const
+{
+ enum {
+ unroll = DenseDerived::SizeAtCompileTime != Dynamic
+ && internal::traits<Derived>::CoeffReadCost != Dynamic
+ && DenseDerived::SizeAtCompileTime * internal::traits<Derived>::CoeffReadCost / 2
+ <= EIGEN_UNROLLING_LIMIT
+ };
+ other.derived().resize(this->rows(), this->cols());
+
+ internal::triangular_assignment_selector
+ <DenseDerived, typename internal::traits<Derived>::MatrixTypeNestedCleaned, Derived::Mode,
+ unroll ? int(DenseDerived::SizeAtCompileTime) : Dynamic,
+ true // clear the opposite triangular part
+ >::run(other.derived(), derived().nestedExpression());
+}
+
+/***************************************************************************
+* Implementation of TriangularView methods
+***************************************************************************/
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+#ifdef EIGEN2_SUPPORT
+
+// implementation of part<>(), including the SelfAdjoint case.
+
+namespace internal {
+template<typename MatrixType, unsigned int Mode>
+struct eigen2_part_return_type
+{
+ typedef TriangularView<MatrixType, Mode> type;
+};
+
+template<typename MatrixType>
+struct eigen2_part_return_type<MatrixType, SelfAdjoint>
+{
+ typedef SelfAdjointView<MatrixType, Upper> type;
+};
+}
+
+/** \deprecated use MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+const typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part() const
+{
+ return derived();
+}
+
+/** \deprecated use MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part()
+{
+ return derived();
+}
+#endif
+
+/**
+ * \returns an expression of a triangular view extracted from the current matrix
+ *
+ * The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
+ * \c #Lower, \c #StrictlyLower, \c #UnitLower.
+ *
+ * Example: \include MatrixBase_extract.cpp
+ * Output: \verbinclude MatrixBase_extract.out
+ *
+ * \sa class TriangularView
+ */
+template<typename Derived>
+template<unsigned int Mode>
+typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView()
+{
+ return derived();
+}
+
+/** This is the const version of MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView() const
+{
+ return derived();
+}
+
+/** \returns true if *this is approximately equal to an upper triangular matrix,
+ * within the precision given by \a prec.
+ *
+ * \sa isLowerTriangular()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
+{
+ using std::abs;
+ RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ {
+ Index maxi = (std::min)(j, rows()-1);
+ for(Index i = 0; i <= maxi; ++i)
+ {
+ RealScalar absValue = abs(coeff(i,j));
+ if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
+ }
+ }
+ RealScalar threshold = maxAbsOnUpperPart * prec;
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = j+1; i < rows(); ++i)
+ if(abs(coeff(i, j)) > threshold) return false;
+ return true;
+}
+
+/** \returns true if *this is approximately equal to a lower triangular matrix,
+ * within the precision given by \a prec.
+ *
+ * \sa isUpperTriangular()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
+{
+ using std::abs;
+ RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = j; i < rows(); ++i)
+ {
+ RealScalar absValue = abs(coeff(i,j));
+ if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
+ }
+ RealScalar threshold = maxAbsOnLowerPart * prec;
+ for(Index j = 1; j < cols(); ++j)
+ {
+ Index maxi = (std::min)(j, rows()-1);
+ for(Index i = 0; i < maxi; ++i)
+ if(abs(coeff(i, j)) > threshold) return false;
+ }
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULARMATRIX_H
diff --git a/Eigen/src/Core/VectorBlock.h b/Eigen/src/Core/VectorBlock.h
new file mode 100644
index 0000000..1a7330f
--- /dev/null
+++ b/Eigen/src/Core/VectorBlock.h
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_VECTORBLOCK_H
+#define EIGEN_VECTORBLOCK_H
+
+namespace Eigen {
+
+/** \class VectorBlock
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a fixed-size or dynamic-size sub-vector
+ *
+ * \param VectorType the type of the object in which we are taking a sub-vector
+ * \param Size size of the sub-vector we are taking at compile time (optional)
+ *
+ * This class represents an expression of either a fixed-size or dynamic-size sub-vector.
+ * It is the return type of DenseBase::segment(Index,Index) and DenseBase::segment<int>(Index) and
+ * most of the time this is the only way it is used.
+ *
+ * However, if you want to directly maniputate sub-vector expressions,
+ * for instance if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * Here is an example illustrating the dynamic case:
+ * \include class_VectorBlock.cpp
+ * Output: \verbinclude class_VectorBlock.out
+ *
+ * \note Even though this expression has dynamic size, in the case where \a VectorType
+ * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+ * it does not cause a dynamic memory allocation.
+ *
+ * Here is an example illustrating the fixed-size case:
+ * \include class_FixedVectorBlock.cpp
+ * Output: \verbinclude class_FixedVectorBlock.out
+ *
+ * \sa class Block, DenseBase::segment(Index,Index,Index,Index), DenseBase::segment(Index,Index)
+ */
+
+namespace internal {
+template<typename VectorType, int Size>
+struct traits<VectorBlock<VectorType, Size> >
+ : public traits<Block<VectorType,
+ traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ traits<VectorType>::Flags & RowMajorBit ? Size : 1> >
+{
+};
+}
+
+template<typename VectorType, int Size> class VectorBlock
+ : public Block<VectorType,
+ internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1>
+{
+ typedef Block<VectorType,
+ internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1> Base;
+ enum {
+ IsColVector = !(internal::traits<VectorType>::Flags & RowMajorBit)
+ };
+ public:
+ EIGEN_DENSE_PUBLIC_INTERFACE(VectorBlock)
+
+ using Base::operator=;
+
+ /** Dynamic-size constructor
+ */
+ inline VectorBlock(VectorType& vector, Index start, Index size)
+ : Base(vector,
+ IsColVector ? start : 0, IsColVector ? 0 : start,
+ IsColVector ? size : 1, IsColVector ? 1 : size)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);
+ }
+
+ /** Fixed-size constructor
+ */
+ inline VectorBlock(VectorType& vector, Index start)
+ : Base(vector, IsColVector ? start : 0, IsColVector ? 0 : start)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_VECTORBLOCK_H
diff --git a/Eigen/src/Core/VectorwiseOp.h b/Eigen/src/Core/VectorwiseOp.h
new file mode 100644
index 0000000..d5ab036
--- /dev/null
+++ b/Eigen/src/Core/VectorwiseOp.h
@@ -0,0 +1,642 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARTIAL_REDUX_H
+#define EIGEN_PARTIAL_REDUX_H
+
+namespace Eigen {
+
+/** \class PartialReduxExpr
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression of a partially reduxed matrix
+ *
+ * \tparam MatrixType the type of the matrix we are applying the redux operation
+ * \tparam MemberOp type of the member functor
+ * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
+ *
+ * This class represents an expression of a partial redux operator of a matrix.
+ * It is the return type of some VectorwiseOp functions,
+ * and most of the time this is the only way it is used.
+ *
+ * \sa class VectorwiseOp
+ */
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr;
+
+namespace internal {
+template<typename MatrixType, typename MemberOp, int Direction>
+struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+ : traits<MatrixType>
+{
+ typedef typename MemberOp::result_type Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename MatrixType::Scalar InputScalar;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ RowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
+ Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
+ Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
+ TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime : MatrixType::ColsAtCompileTime
+ };
+ #if EIGEN_GNUC_AT_LEAST(3,4)
+ typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
+ #else
+ typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
+ #endif
+ enum {
+ CoeffReadCost = TraversalSize==Dynamic ? Dynamic
+ : TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
+ };
+};
+}
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr : internal::no_assignment_operator,
+ public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
+ typedef typename internal::traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
+
+ PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
+ : m_matrix(mat), m_functor(func) {}
+
+ Index rows() const { return (Direction==Vertical ? 1 : m_matrix.rows()); }
+ Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
+ {
+ if (Direction==Vertical)
+ return m_functor(m_matrix.col(j));
+ else
+ return m_functor(m_matrix.row(i));
+ }
+
+ const Scalar coeff(Index index) const
+ {
+ if (Direction==Vertical)
+ return m_functor(m_matrix.col(index));
+ else
+ return m_functor(m_matrix.row(index));
+ }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const MemberOp m_functor;
+};
+
+#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST) \
+ template <typename ResultType> \
+ struct member_##MEMBER { \
+ EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER) \
+ typedef ResultType result_type; \
+ template<typename Scalar, int Size> struct Cost \
+ { enum { value = COST }; }; \
+ template<typename XprType> \
+ EIGEN_STRONG_INLINE ResultType operator()(const XprType& mat) const \
+ { return mat.MEMBER(); } \
+ }
+
+namespace internal {
+
+EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
+EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
+EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
+
+
+template <typename BinaryOp, typename Scalar>
+struct member_redux {
+ typedef typename result_of<
+ BinaryOp(Scalar)
+ >::type result_type;
+ template<typename _Scalar, int Size> struct Cost
+ { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
+ member_redux(const BinaryOp func) : m_functor(func) {}
+ template<typename Derived>
+ inline result_type operator()(const DenseBase<Derived>& mat) const
+ { return mat.redux(m_functor); }
+ const BinaryOp m_functor;
+};
+}
+
+/** \class VectorwiseOp
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing partial reduction operations
+ *
+ * \param ExpressionType the type of the object on which to do partial reductions
+ * \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
+ *
+ * This class represents a pseudo expression with partial reduction features.
+ * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
+ * and most of the time this is the only way it is used.
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
+ */
+template<typename ExpressionType, int Direction> class VectorwiseOp
+{
+ public:
+
+ typedef typename ExpressionType::Scalar Scalar;
+ typedef typename ExpressionType::RealScalar RealScalar;
+ typedef typename ExpressionType::Index Index;
+ typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+ ExpressionType, ExpressionType&>::type ExpressionTypeNested;
+ typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
+
+ template<template<typename _Scalar> class Functor,
+ typename Scalar=typename internal::traits<ExpressionType>::Scalar> struct ReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ Functor<Scalar>,
+ Direction
+ > Type;
+ };
+
+ template<typename BinaryOp> struct ReduxReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ internal::member_redux<BinaryOp,typename internal::traits<ExpressionType>::Scalar>,
+ Direction
+ > Type;
+ };
+
+ enum {
+ IsVertical = (Direction==Vertical) ? 1 : 0,
+ IsHorizontal = (Direction==Horizontal) ? 1 : 0
+ };
+
+ protected:
+
+ /** \internal
+ * \returns the i-th subvector according to the \c Direction */
+ typedef typename internal::conditional<Direction==Vertical,
+ typename ExpressionType::ColXpr,
+ typename ExpressionType::RowXpr>::type SubVector;
+ SubVector subVector(Index i)
+ {
+ return SubVector(m_matrix.derived(),i);
+ }
+
+ /** \internal
+ * \returns the number of subvectors in the direction \c Direction */
+ Index subVectors() const
+ { return Direction==Vertical?m_matrix.cols():m_matrix.rows(); }
+
+ template<typename OtherDerived> struct ExtendedType {
+ typedef Replicate<OtherDerived,
+ Direction==Vertical ? 1 : ExpressionType::RowsAtCompileTime,
+ Direction==Horizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector to match the size of \c *this */
+ template<typename OtherDerived>
+ typename ExtendedType<OtherDerived>::Type
+ extendedTo(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename ExtendedType<OtherDerived>::Type
+ (other.derived(),
+ Direction==Vertical ? 1 : m_matrix.rows(),
+ Direction==Horizontal ? 1 : m_matrix.cols());
+ }
+
+ template<typename OtherDerived> struct OppositeExtendedType {
+ typedef Replicate<OtherDerived,
+ Direction==Horizontal ? 1 : ExpressionType::RowsAtCompileTime,
+ Direction==Vertical ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector in the opposite direction to match the size of \c *this */
+ template<typename OtherDerived>
+ typename OppositeExtendedType<OtherDerived>::Type
+ extendedToOpposite(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename OppositeExtendedType<OtherDerived>::Type
+ (other.derived(),
+ Direction==Horizontal ? 1 : m_matrix.rows(),
+ Direction==Vertical ? 1 : m_matrix.cols());
+ }
+
+ public:
+
+ inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
+
+ /** \internal */
+ inline const ExpressionType& _expression() const { return m_matrix; }
+
+ /** \returns a row or column vector expression of \c *this reduxed by \a func
+ *
+ * The template parameter \a BinaryOp is the type of the functor
+ * of the custom redux operator. Note that func must be an associative operator.
+ *
+ * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
+ */
+ template<typename BinaryOp>
+ const typename ReduxReturnType<BinaryOp>::Type
+ redux(const BinaryOp& func = BinaryOp()) const
+ { return typename ReduxReturnType<BinaryOp>::Type(_expression(), func); }
+
+ /** \returns a row (or column) vector expression of the smallest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_minCoeff.cpp
+ * Output: \verbinclude PartialRedux_minCoeff.out
+ *
+ * \sa DenseBase::minCoeff() */
+ const typename ReturnType<internal::member_minCoeff>::Type minCoeff() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the largest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_maxCoeff.cpp
+ * Output: \verbinclude PartialRedux_maxCoeff.out
+ *
+ * \sa DenseBase::maxCoeff() */
+ const typename ReturnType<internal::member_maxCoeff>::Type maxCoeff() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the squared norm
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_squaredNorm.cpp
+ * Output: \verbinclude PartialRedux_squaredNorm.out
+ *
+ * \sa DenseBase::squaredNorm() */
+ const typename ReturnType<internal::member_squaredNorm,RealScalar>::Type squaredNorm() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_norm.cpp
+ * Output: \verbinclude PartialRedux_norm.out
+ *
+ * \sa DenseBase::norm() */
+ const typename ReturnType<internal::member_norm,RealScalar>::Type norm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, using
+ * blue's algorithm.
+ *
+ * \sa DenseBase::blueNorm() */
+ const typename ReturnType<internal::member_blueNorm,RealScalar>::Type blueNorm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow.
+ *
+ * \sa DenseBase::stableNorm() */
+ const typename ReturnType<internal::member_stableNorm,RealScalar>::Type stableNorm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow using a concatenation of hypot() calls.
+ *
+ * \sa DenseBase::hypotNorm() */
+ const typename ReturnType<internal::member_hypotNorm,RealScalar>::Type hypotNorm() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the sum
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_sum.cpp
+ * Output: \verbinclude PartialRedux_sum.out
+ *
+ * \sa DenseBase::sum() */
+ const typename ReturnType<internal::member_sum>::Type sum() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the mean
+ * of each column (or row) of the referenced expression.
+ *
+ * \sa DenseBase::mean() */
+ const typename ReturnType<internal::member_mean>::Type mean() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b all coefficients of each respective column (or row) are \c true.
+ *
+ * \sa DenseBase::all() */
+ const typename ReturnType<internal::member_all>::Type all() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b at \b least one coefficient of each respective column (or row) is \c true.
+ *
+ * \sa DenseBase::any() */
+ const typename ReturnType<internal::member_any>::Type any() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * the number of \c true coefficients of each respective column (or row).
+ *
+ * Example: \include PartialRedux_count.cpp
+ * Output: \verbinclude PartialRedux_count.out
+ *
+ * \sa DenseBase::count() */
+ const PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> count() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the product
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_prod.cpp
+ * Output: \verbinclude PartialRedux_prod.out
+ *
+ * \sa DenseBase::prod() */
+ const typename ReturnType<internal::member_prod>::Type prod() const
+ { return _expression(); }
+
+
+ /** \returns a matrix expression
+ * where each column (or row) are reversed.
+ *
+ * Example: \include Vectorwise_reverse.cpp
+ * Output: \verbinclude Vectorwise_reverse.out
+ *
+ * \sa DenseBase::reverse() */
+ const Reverse<ExpressionType, Direction> reverse() const
+ { return Reverse<ExpressionType, Direction>( _expression() ); }
+
+ typedef Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1> ReplicateReturnType;
+ const ReplicateReturnType replicate(Index factor) const;
+
+ /**
+ * \return an expression of the replication of each column (or row) of \c *this
+ *
+ * Example: \include DirectionWise_replicate.cpp
+ * Output: \verbinclude DirectionWise_replicate.out
+ *
+ * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
+ */
+ // NOTE implemented here because of sunstudio's compilation errors
+ template<int Factor> const Replicate<ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>
+ replicate(Index factor = Factor) const
+ {
+ return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
+ (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+ }
+
+/////////// Artithmetic operators ///////////
+
+ /** Copies the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
+ return const_cast<ExpressionType&>(m_matrix = extendedTo(other.derived()));
+ }
+
+ /** Adds the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return const_cast<ExpressionType&>(m_matrix += extendedTo(other.derived()));
+ }
+
+ /** Substracts the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return const_cast<ExpressionType&>(m_matrix -= extendedTo(other.derived()));
+ }
+
+ /** Multiples each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix *= extendedTo(other.derived());
+ return const_cast<ExpressionType&>(m_matrix);
+ }
+
+ /** Divides each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix /= extendedTo(other.derived());
+ return const_cast<ExpressionType&>(m_matrix);
+ }
+
+ /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE
+ CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator+(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix + extendedTo(other.derived());
+ }
+
+ /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
+ template<typename OtherDerived>
+ CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator-(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix - extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the product of the vector \a other
+ * by the corresponding subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE
+ CwiseBinaryOp<internal::scalar_product_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator*(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix * extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the quotient of the corresponding
+ * subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator/(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix / extendedTo(other.derived());
+ }
+
+ /** \returns an expression where each column of row of the referenced matrix are normalized.
+ * The referenced matrix is \b not modified.
+ * \sa MatrixBase::normalized(), normalize()
+ */
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>
+ normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
+
+
+ /** Normalize in-place each row or columns of the referenced matrix.
+ * \sa MatrixBase::normalize(), normalized()
+ */
+ void normalize() {
+ m_matrix = this->normalized();
+ }
+
+/////////// Geometry module ///////////
+
+ #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+ Homogeneous<ExpressionType,Direction> homogeneous() const;
+ #endif
+
+ typedef typename ExpressionType::PlainObject CrossReturnType;
+ template<typename OtherDerived>
+ const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
+
+ enum {
+ HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
+ : internal::traits<ExpressionType>::ColsAtCompileTime,
+ HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
+ };
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Block;
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Factors;
+ typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
+ const HNormalized_Block,
+ const Replicate<HNormalized_Factors,
+ Direction==Vertical ? HNormalized_SizeMinusOne : 1,
+ Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
+ HNormalizedReturnType;
+
+ const HNormalizedReturnType hnormalized() const;
+
+ protected:
+ ExpressionTypeNested m_matrix;
+};
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstColwiseReturnType
+DenseBase<Derived>::colwise() const
+{
+ return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::ColwiseReturnType
+DenseBase<Derived>::colwise()
+{
+ return derived();
+}
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * Example: \include MatrixBase_rowwise.cpp
+ * Output: \verbinclude MatrixBase_rowwise.out
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstRowwiseReturnType
+DenseBase<Derived>::rowwise() const
+{
+ return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::RowwiseReturnType
+DenseBase<Derived>::rowwise()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIAL_REDUX_H
diff --git a/Eigen/src/Core/Visitor.h b/Eigen/src/Core/Visitor.h
new file mode 100644
index 0000000..64867b7
--- /dev/null
+++ b/Eigen/src/Core/Visitor.h
@@ -0,0 +1,237 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_VISITOR_H
+#define EIGEN_VISITOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Visitor, typename Derived, int UnrollCount>
+struct visitor_impl
+{
+ enum {
+ col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+ row = (UnrollCount-1) % Derived::RowsAtCompileTime
+ };
+
+ static inline void run(const Derived &mat, Visitor& visitor)
+ {
+ visitor_impl<Visitor, Derived, UnrollCount-1>::run(mat, visitor);
+ visitor(mat.coeff(row, col), row, col);
+ }
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, 1>
+{
+ static inline void run(const Derived &mat, Visitor& visitor)
+ {
+ return visitor.init(mat.coeff(0, 0), 0, 0);
+ }
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, Dynamic>
+{
+ typedef typename Derived::Index Index;
+ static inline void run(const Derived& mat, Visitor& visitor)
+ {
+ visitor.init(mat.coeff(0,0), 0, 0);
+ for(Index i = 1; i < mat.rows(); ++i)
+ visitor(mat.coeff(i, 0), i, 0);
+ for(Index j = 1; j < mat.cols(); ++j)
+ for(Index i = 0; i < mat.rows(); ++i)
+ visitor(mat.coeff(i, j), i, j);
+ }
+};
+
+} // end namespace internal
+
+/** Applies the visitor \a visitor to the whole coefficients of the matrix or vector.
+ *
+ * The template parameter \a Visitor is the type of the visitor and provides the following interface:
+ * \code
+ * struct MyVisitor {
+ * // called for the first coefficient
+ * void init(const Scalar& value, Index i, Index j);
+ * // called for all other coefficients
+ * void operator() (const Scalar& value, Index i, Index j);
+ * };
+ * \endcode
+ *
+ * \note compared to one or two \em for \em loops, visitors offer automatic
+ * unrolling for small fixed size matrix.
+ *
+ * \sa minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()
+ */
+template<typename Derived>
+template<typename Visitor>
+void DenseBase<Derived>::visit(Visitor& visitor) const
+{
+ enum { unroll = SizeAtCompileTime != Dynamic
+ && CoeffReadCost != Dynamic
+ && (SizeAtCompileTime == 1 || internal::functor_traits<Visitor>::Cost != Dynamic)
+ && SizeAtCompileTime * CoeffReadCost + (SizeAtCompileTime-1) * internal::functor_traits<Visitor>::Cost
+ <= EIGEN_UNROLLING_LIMIT };
+ return internal::visitor_impl<Visitor, Derived,
+ unroll ? int(SizeAtCompileTime) : Dynamic
+ >::run(derived(), visitor);
+}
+
+namespace internal {
+
+/** \internal
+ * \brief Base class to implement min and max visitors
+ */
+template <typename Derived>
+struct coeff_visitor
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ Index row, col;
+ Scalar res;
+ inline void init(const Scalar& value, Index i, Index j)
+ {
+ res = value;
+ row = i;
+ col = j;
+ }
+};
+
+/** \internal
+ * \brief Visitor computing the min coefficient with its value and coordinates
+ *
+ * \sa DenseBase::minCoeff(Index*, Index*)
+ */
+template <typename Derived>
+struct min_coeff_visitor : coeff_visitor<Derived>
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ void operator() (const Scalar& value, Index i, Index j)
+ {
+ if(value < this->res)
+ {
+ this->res = value;
+ this->row = i;
+ this->col = j;
+ }
+ }
+};
+
+template<typename Scalar>
+struct functor_traits<min_coeff_visitor<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost
+ };
+};
+
+/** \internal
+ * \brief Visitor computing the max coefficient with its value and coordinates
+ *
+ * \sa DenseBase::maxCoeff(Index*, Index*)
+ */
+template <typename Derived>
+struct max_coeff_visitor : coeff_visitor<Derived>
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ void operator() (const Scalar& value, Index i, Index j)
+ {
+ if(value > this->res)
+ {
+ this->res = value;
+ this->row = i;
+ this->col = j;
+ }
+ }
+};
+
+template<typename Scalar>
+struct functor_traits<max_coeff_visitor<Scalar> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost
+ };
+};
+
+} // end namespace internal
+
+/** \returns the minimum of all coefficients of *this and puts in *row and *col its location.
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
+ */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
+{
+ internal::min_coeff_visitor<Derived> minVisitor;
+ this->visit(minVisitor);
+ *rowId = minVisitor.row;
+ if (colId) *colId = minVisitor.col;
+ return minVisitor.res;
+}
+
+/** \returns the minimum of all coefficients of *this and puts in *index its location.
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
+ */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* index) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ internal::min_coeff_visitor<Derived> minVisitor;
+ this->visit(minVisitor);
+ *index = (RowsAtCompileTime==1) ? minVisitor.col : minVisitor.row;
+ return minVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this and puts in *row and *col its location.
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+ */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* rowPtr, IndexType* colPtr) const
+{
+ internal::max_coeff_visitor<Derived> maxVisitor;
+ this->visit(maxVisitor);
+ *rowPtr = maxVisitor.row;
+ if (colPtr) *colPtr = maxVisitor.col;
+ return maxVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this and puts in *index its location.
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+ */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* index) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ internal::max_coeff_visitor<Derived> maxVisitor;
+ this->visit(maxVisitor);
+ *index = (RowsAtCompileTime==1) ? maxVisitor.col : maxVisitor.row;
+ return maxVisitor.res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_VISITOR_H
diff --git a/Eigen/src/Core/arch/AltiVec/CMakeLists.txt b/Eigen/src/Core/arch/AltiVec/CMakeLists.txt
new file mode 100644
index 0000000..9f8d2e9
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_AltiVec_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_arch_AltiVec_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/AltiVec COMPONENT Devel
+)
diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h
new file mode 100644
index 0000000..68d9a2b
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/Complex.h
@@ -0,0 +1,217 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_ALTIVEC_H
+#define EIGEN_COMPLEX_ALTIVEC_H
+
+namespace Eigen {
+
+namespace internal {
+
+static Packet4ui p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_ZERO_);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+static Packet16uc p16uc_COMPLEX_RE = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_COMPLEX_IM = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 1), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+static Packet16uc p16uc_COMPLEX_REV = vec_sld(p16uc_REVERSE, p16uc_REVERSE, 8);//{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
+static Packet16uc p16uc_COMPLEX_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);//{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_PSET_HI = (Packet16uc) vec_mergeh((Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 1));//{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_PSET_LO = (Packet16uc) vec_mergeh((Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 2), (Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 3));//{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
+
+//---------- float ----------
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+ Packet4f v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ Packet2cf res;
+ /* On AltiVec we cannot load 64-bit registers, so wa have to take care of alignment */
+ if((ptrdiff_t(&from) % 16) == 0)
+ res.v = pload<Packet4f>((const float *)&from);
+ else
+ res.v = ploadu<Packet4f>((const float *)&from);
+ res.v = vec_perm(res.v, res.v, p16uc_PSET_HI);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_add(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_sub(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf((Packet4f)vec_xor((Packet4ui)a.v, p4ui_CONJ_XOR)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ Packet4f v1, v2;
+
+ // Permute and multiply the real parts of a and b
+ v1 = vec_perm(a.v, a.v, p16uc_COMPLEX_RE);
+ // Get the imaginary parts of a
+ v2 = vec_perm(a.v, a.v, p16uc_COMPLEX_IM);
+ // multiply a_re * b
+ v1 = vec_madd(v1, b.v, p4f_ZERO);
+ // multiply a_im * b and get the conjugate result
+ v2 = vec_madd(v2, b.v, p4f_ZERO);
+ v2 = (Packet4f) vec_xor((Packet4ui)v2, p4ui_CONJ_XOR);
+ // permute back to a proper order
+ v2 = vec_perm(v2, v2, p16uc_COMPLEX_REV);
+
+ return Packet2cf(vec_add(v1, v2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_or(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_xor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v, vec_nor(b.v,b.v))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from)
+{
+ return pset1<Packet2cf>(*from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { vec_dstt((float *)addr, DST_CTRL(2,2,32), DST_CHAN); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ std::complex<float> EIGEN_ALIGN16 res[2];
+ pstore((float *)&res, a.v);
+
+ return res[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+ Packet4f rev_a;
+ rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX_REV2);
+ return Packet2cf(rev_a);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ b = (Packet4f) vec_sld(a.v, a.v, 8);
+ b = padd(a.v, b);
+ return pfirst(Packet2cf(b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
+{
+ Packet4f b1, b2;
+
+ b1 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8);
+ b2 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8);
+ b2 = (Packet4f) vec_sld(b2, b2, 8);
+ b2 = padd(b1, b2);
+
+ return Packet2cf(b2);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ Packet2cf prod;
+ b = (Packet4f) vec_sld(a.v, a.v, 8);
+ prod = pmul(a, Packet2cf(b));
+
+ return pfirst(prod);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cf>
+{
+ static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)
+ {
+ if (Offset==1)
+ {
+ first.v = vec_sld(first.v, second.v, 8);
+ }
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return internal::pmul(a, pconj(b));
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return internal::pmul(pconj(a), b);
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return pconj(internal::pmul(a, b));
+ }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ // TODO optimize it for AltiVec
+ Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
+ Packet4f s = vec_madd(b.v, b.v, p4f_ZERO);
+ return Packet2cf(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_COMPLEX_REV))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
+{
+ return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX_REV));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
new file mode 100644
index 0000000..e408996
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -0,0 +1,501 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Konstantinos Margaritis <markos@codex.gr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
+#define EIGEN_PACKET_MATH_ALTIVEC_H
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
+#endif
+
+#ifndef EIGEN_HAS_FUSE_CJMADD
+#define EIGEN_HAS_FUSE_CJMADD 1
+#endif
+
+// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
+#endif
+
+typedef __vector float Packet4f;
+typedef __vector int Packet4i;
+typedef __vector unsigned int Packet4ui;
+typedef __vector __bool int Packet4bi;
+typedef __vector short int Packet8i;
+typedef __vector unsigned char Packet16uc;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = (Packet4f) vec_splat_s32(X)
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = vec_splat_s32(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#define DST_CHAN 1
+#define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
+
+// Define global static constants:
+static Packet4f p4f_COUNTDOWN = { 3.0, 2.0, 1.0, 0.0 };
+static Packet4i p4i_COUNTDOWN = { 3, 2, 1, 0 };
+static Packet16uc p16uc_REVERSE = {12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
+static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
+static Packet16uc p16uc_DUPLICATE = {0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7};
+
+static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1);
+static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0);
+static Packet4f p4f_ZERO_ = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1);
+
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet4f type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4,
+
+ // FIXME check the Has*
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 0,
+ HasExp = 0,
+ HasSqrt = 0
+ };
+};
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet4i type;
+ enum {
+ // FIXME check the Has*
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4
+ };
+};
+
+template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4}; };
+template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4}; };
+/*
+inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
+{
+ union {
+ Packet4f v;
+ float n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
+{
+ union {
+ Packet4i v;
+ int n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
+{
+ union {
+ Packet4ui v;
+ unsigned int n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packetbi & v)
+{
+ union {
+ Packet4bi v;
+ unsigned int n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+*/
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) {
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ float EIGEN_ALIGN16 af[4];
+ af[0] = from;
+ Packet4f vc = vec_ld(0, af);
+ vc = vec_splat(vc, 0);
+ return vc;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) {
+ int EIGEN_ALIGN16 ai[4];
+ ai[0] = from;
+ Packet4i vc = vec_ld(0, ai);
+ vc = vec_splat(vc, 0);
+ return vc;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return vec_add(pset1<Packet4f>(a), p4f_COUNTDOWN); }
+template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a) { return vec_add(pset1<Packet4i>(a), p4i_COUNTDOWN); }
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_add(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_add(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_sub(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_sub(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return psub<Packet4f>(p4f_ZERO, a); }
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub<Packet4i>(p4i_ZERO, a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b,p4f_ZERO); }
+/* Commented out: it's actually slower than processing it scalar
+ *
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+ // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
+ //Set up constants, variables
+ Packet4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
+
+ // Get the absolute values
+ a1 = vec_abs(a);
+ b1 = vec_abs(b);
+
+ // Get the signs using xor
+ Packet4bi sgn = (Packet4bi) vec_cmplt(vec_xor(a, b), p4i_ZERO);
+
+ // Do the multiplication for the asbolute values.
+ bswap = (Packet4i) vec_rl((Packet4ui) b1, (Packet4ui) p4i_MINUS16 );
+ low_prod = vec_mulo((Packet8i) a1, (Packet8i)b1);
+ high_prod = vec_msum((Packet8i) a1, (Packet8i) bswap, p4i_ZERO);
+ high_prod = (Packet4i) vec_sl((Packet4ui) high_prod, (Packet4ui) p4i_MINUS16);
+ prod = vec_add( low_prod, high_prod );
+
+ // NOR the product and select only the negative elements according to the sign mask
+ prod_ = vec_nor(prod, prod);
+ prod_ = vec_sel(p4i_ZERO, prod_, sgn);
+
+ // Add 1 to the result to get the negative numbers
+ v1sel = vec_sel(p4i_ZERO, p4i_ONE, sgn);
+ prod_ = vec_add(prod_, v1sel);
+
+ // Merge the results back to the final vector.
+ prod = vec_sel(prod, prod_, sgn);
+
+ return prod;
+}
+*/
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f t, y_0, y_1, res;
+
+ // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
+ y_0 = vec_re(b);
+
+ // Do one Newton-Raphson iteration to get the needed accuracy
+ t = vec_nmsub(y_0, b, p4f_ONE);
+ y_1 = vec_madd(y_0, t, y_0);
+
+ res = vec_madd(a, y_1, p4f_ZERO);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by AltiVec");
+ return pset1<Packet4i>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ Packet16uc MSQ, LSQ;
+ Packet16uc mask;
+ MSQ = vec_ld(0, (unsigned char *)from); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)from); // least significant quadword
+ mask = vec_lvsl(0, from); // create the permute mask
+ return (Packet4f) vec_perm(MSQ, LSQ, mask); // align the data
+
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ Packet16uc MSQ, LSQ;
+ Packet16uc mask;
+ MSQ = vec_ld(0, (unsigned char *)from); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)from); // least significant quadword
+ mask = vec_lvsl(0, from); // create the permute mask
+ return (Packet4i) vec_perm(MSQ, LSQ, mask); // align the data
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ Packet4f p;
+ if((ptrdiff_t(&from) % 16) == 0) p = pload<Packet4f>(from);
+ else p = ploadu<Packet4f>(from);
+ return vec_perm(p, p, p16uc_DUPLICATE);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ Packet4i p;
+ if((ptrdiff_t(&from) % 16) == 0) p = pload<Packet4i>(from);
+ else p = ploadu<Packet4i>(from);
+ return vec_perm(p, p, p16uc_DUPLICATE);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ // Warning: not thread safe!
+ Packet16uc MSQ, LSQ, edges;
+ Packet16uc edgeAlign, align;
+
+ MSQ = vec_ld(0, (unsigned char *)to); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)to); // least significant quadword
+ edgeAlign = vec_lvsl(0, to); // permute map to extract edges
+ edges=vec_perm(LSQ,MSQ,edgeAlign); // extract the edges
+ align = vec_lvsr( 0, to ); // permute map to misalign data
+ MSQ = vec_perm(edges,(Packet16uc)from,align); // misalign the data (MSQ)
+ LSQ = vec_perm((Packet16uc)from,edges,align); // misalign the data (LSQ)
+ vec_st( LSQ, 15, (unsigned char *)to ); // Store the LSQ part first
+ vec_st( MSQ, 0, (unsigned char *)to ); // Store the MSQ part
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ // Warning: not thread safe!
+ Packet16uc MSQ, LSQ, edges;
+ Packet16uc edgeAlign, align;
+
+ MSQ = vec_ld(0, (unsigned char *)to); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)to); // least significant quadword
+ edgeAlign = vec_lvsl(0, to); // permute map to extract edges
+ edges=vec_perm(LSQ, MSQ, edgeAlign); // extract the edges
+ align = vec_lvsr( 0, to ); // permute map to misalign data
+ MSQ = vec_perm(edges, (Packet16uc) from, align); // misalign the data (MSQ)
+ LSQ = vec_perm((Packet16uc) from, edges, align); // misalign the data (LSQ)
+ vec_st( LSQ, 15, (unsigned char *)to ); // Store the LSQ part first
+ vec_st( MSQ, 0, (unsigned char *)to ); // Store the MSQ part
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
+
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return (Packet4f)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return (Packet4i)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, sum;
+ b = (Packet4f) vec_sld(a, a, 8);
+ sum = vec_add(a, b);
+ b = (Packet4f) vec_sld(sum, sum, 4);
+ sum = vec_add(sum, b);
+ return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
+{
+ Packet4f v[4], sum[4];
+
+ // It's easier and faster to transpose then add as columns
+ // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+ // Do the transpose, first set of moves
+ v[0] = vec_mergeh(vecs[0], vecs[2]);
+ v[1] = vec_mergel(vecs[0], vecs[2]);
+ v[2] = vec_mergeh(vecs[1], vecs[3]);
+ v[3] = vec_mergel(vecs[1], vecs[3]);
+ // Get the resulting vectors
+ sum[0] = vec_mergeh(v[0], v[2]);
+ sum[1] = vec_mergel(v[0], v[2]);
+ sum[2] = vec_mergeh(v[1], v[3]);
+ sum[3] = vec_mergel(v[1], v[3]);
+
+ // Now do the summation:
+ // Lines 0+1
+ sum[0] = vec_add(sum[0], sum[1]);
+ // Lines 2+3
+ sum[1] = vec_add(sum[2], sum[3]);
+ // Add the results
+ sum[0] = vec_add(sum[0], sum[1]);
+
+ return sum[0];
+}
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i sum;
+ sum = vec_sums(a, p4i_ZERO);
+ sum = vec_sld(sum, p4i_ZERO, 12);
+ return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
+{
+ Packet4i v[4], sum[4];
+
+ // It's easier and faster to transpose then add as columns
+ // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+ // Do the transpose, first set of moves
+ v[0] = vec_mergeh(vecs[0], vecs[2]);
+ v[1] = vec_mergel(vecs[0], vecs[2]);
+ v[2] = vec_mergeh(vecs[1], vecs[3]);
+ v[3] = vec_mergel(vecs[1], vecs[3]);
+ // Get the resulting vectors
+ sum[0] = vec_mergeh(v[0], v[2]);
+ sum[1] = vec_mergel(v[0], v[2]);
+ sum[2] = vec_mergeh(v[1], v[3]);
+ sum[3] = vec_mergel(v[1], v[3]);
+
+ // Now do the summation:
+ // Lines 0+1
+ sum[0] = vec_add(sum[0], sum[1]);
+ // Lines 2+3
+ sum[1] = vec_add(sum[2], sum[3]);
+ // Add the results
+ sum[0] = vec_add(sum[0], sum[1]);
+
+ return sum[0];
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ Packet4f prod;
+ prod = pmul(a, (Packet4f)vec_sld(a, a, 8));
+ return pfirst(pmul(prod, (Packet4f)vec_sld(prod, prod, 4)));
+}
+
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, res;
+ b = vec_min(a, vec_sld(a, a, 8));
+ res = vec_min(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+ Packet4i b, res;
+ b = vec_min(a, vec_sld(a, a, 8));
+ res = vec_min(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, res;
+ b = vec_max(a, vec_sld(a, a, 8));
+ res = vec_max(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+ Packet4i b, res;
+ b = vec_max(a, vec_sld(a, a, 8));
+ res = vec_max(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet4f>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
+ {
+ if (Offset!=0)
+ first = vec_sld(first, second, Offset*4);
+ }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet4i>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
+ {
+ if (Offset!=0)
+ first = vec_sld(first, second, Offset*4);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/CMakeLists.txt b/Eigen/src/Core/arch/CMakeLists.txt
new file mode 100644
index 0000000..8456dec
--- /dev/null
+++ b/Eigen/src/Core/arch/CMakeLists.txt
@@ -0,0 +1,4 @@
+ADD_SUBDIRECTORY(SSE)
+ADD_SUBDIRECTORY(AltiVec)
+ADD_SUBDIRECTORY(NEON)
+ADD_SUBDIRECTORY(Default)
diff --git a/Eigen/src/Core/arch/Default/CMakeLists.txt b/Eigen/src/Core/arch/Default/CMakeLists.txt
new file mode 100644
index 0000000..339c091
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_Default_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_arch_Default_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/Default COMPONENT Devel
+)
diff --git a/Eigen/src/Core/arch/Default/Settings.h b/Eigen/src/Core/arch/Default/Settings.h
new file mode 100644
index 0000000..097373c
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/Settings.h
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/* All the parameters defined in this file can be specialized in the
+ * architecture specific files, and/or by the user.
+ * More to come... */
+
+#ifndef EIGEN_DEFAULT_SETTINGS_H
+#define EIGEN_DEFAULT_SETTINGS_H
+
+/** Defines the maximal loop size to enable meta unrolling of loops.
+ * Note that the value here is expressed in Eigen's own notion of "number of FLOPS",
+ * it does not correspond to the number of iterations or the number of instructions
+ */
+#ifndef EIGEN_UNROLLING_LIMIT
+#define EIGEN_UNROLLING_LIMIT 100
+#endif
+
+/** Defines the threshold between a "small" and a "large" matrix.
+ * This threshold is mainly used to select the proper product implementation.
+ */
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+/** Defines the maximal width of the blocks used in the triangular product and solver
+ * for vectors (level 2 blas xTRMV and xTRSV). The default is 8.
+ */
+#ifndef EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH
+#define EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH 8
+#endif
+
+
+/** Defines the default number of registers available for that architecture.
+ * Currently it must be 8 or 16. Other values will fail.
+ */
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8
+#endif
+
+#endif // EIGEN_DEFAULT_SETTINGS_H
diff --git a/Eigen/src/Core/arch/NEON/CMakeLists.txt b/Eigen/src/Core/arch/NEON/CMakeLists.txt
new file mode 100644
index 0000000..fd4d4af
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_NEON_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_arch_NEON_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/NEON COMPONENT Devel
+)
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
new file mode 100644
index 0000000..8d9255e
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -0,0 +1,253 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_NEON_H
+#define EIGEN_COMPLEX_NEON_H
+
+namespace Eigen {
+
+namespace internal {
+
+static uint32x4_t p4ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET4(0x00000000, 0x80000000, 0x00000000, 0x80000000);
+static uint32x2_t p2ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x00000000, 0x80000000);
+
+//---------- float ----------
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+ Packet4f v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ float32x2_t r64;
+ r64 = vld1_f32((float *)&from);
+
+ return Packet2cf(vcombine_f32(r64, r64));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+ Packet4ui b = vreinterpretq_u32_f32(a.v);
+ return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ Packet4f v1, v2;
+
+ // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+ v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));
+ // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
+ v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));
+ // Multiply the real a with b
+ v1 = vmulq_f32(v1, b.v);
+ // Multiply the imag a with b
+ v2 = vmulq_f32(v2, b.v);
+ // Conjugate v2
+ v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR));
+ // Swap real/imag elements in v2.
+ v2 = vrev64q_f32(v2);
+ // Add and return the result
+ return Packet2cf(vaddq_f32(v1, v2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { EIGEN_ARM_PREFETCH((float *)addr); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ std::complex<float> EIGEN_ALIGN16 x[2];
+ vst1q_f32((float *)x, a.v);
+ return x[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+ float32x2_t a_lo, a_hi;
+ Packet4f a_r128;
+
+ a_lo = vget_low_f32(a.v);
+ a_hi = vget_high_f32(a.v);
+ a_r128 = vcombine_f32(a_hi, a_lo);
+
+ return Packet2cf(a_r128);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)
+{
+ return Packet2cf(vrev64q_f32(a.v));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ float32x2_t a1, a2;
+ std::complex<float> s;
+
+ a1 = vget_low_f32(a.v);
+ a2 = vget_high_f32(a.v);
+ a2 = vadd_f32(a1, a2);
+ vst1_f32((float *)&s, a2);
+
+ return s;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
+{
+ Packet4f sum1, sum2, sum;
+
+ // Add the first two 64-bit float32x2_t of vecs[0]
+ sum1 = vcombine_f32(vget_low_f32(vecs[0].v), vget_low_f32(vecs[1].v));
+ sum2 = vcombine_f32(vget_high_f32(vecs[0].v), vget_high_f32(vecs[1].v));
+ sum = vaddq_f32(sum1, sum2);
+
+ return Packet2cf(sum);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ float32x2_t a1, a2, v1, v2, prod;
+ std::complex<float> s;
+
+ a1 = vget_low_f32(a.v);
+ a2 = vget_high_f32(a.v);
+ // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+ v1 = vdup_lane_f32(a1, 0);
+ // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
+ v2 = vdup_lane_f32(a1, 1);
+ // Multiply the real a with b
+ v1 = vmul_f32(v1, a2);
+ // Multiply the imag a with b
+ v2 = vmul_f32(v2, a2);
+ // Conjugate v2
+ v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR));
+ // Swap real/imag elements in v2.
+ v2 = vrev64_f32(v2);
+ // Add v1, v2
+ prod = vadd_f32(v1, v2);
+
+ vst1_f32((float *)&s, prod);
+
+ return s;
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cf>
+{
+ EIGEN_STRONG_INLINE static void run(Packet2cf& first, const Packet2cf& second)
+ {
+ if (Offset==1)
+ {
+ first.v = vextq_f32(first.v, second.v, 2);
+ }
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return internal::pmul(a, pconj(b));
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return internal::pmul(pconj(a), b);
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ return pconj(internal::pmul(a, b));
+ }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ // TODO optimize it for AltiVec
+ Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
+ Packet4f s, rev_s;
+
+ // this computes the norm
+ s = vmulq_f32(b.v, b.v);
+ rev_s = vrev64q_f32(s);
+
+ return Packet2cf(pdiv(res.v, vaddq_f32(s,rev_s)));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_NEON_H
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
new file mode 100644
index 0000000..94dfab3
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -0,0 +1,419 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Konstantinos Margaritis <markos@codex.gr>
+// Heavily based on Gael's SSE version.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_NEON_H
+#define EIGEN_PACKET_MATH_NEON_H
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+// FIXME NEON has 16 quad registers, but since the current register allocator
+// is so bad, it is much better to reduce it to 8
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8
+#endif
+
+typedef float32x4_t Packet4f;
+typedef int32x4_t Packet4i;
+typedef uint32x4_t Packet4ui;
+
+#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ const Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ const Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#if defined(__llvm__) && !defined(__clang__)
+ //Special treatment for Apple's llvm-gcc, its NEON packet types are unions
+ #define EIGEN_INIT_NEON_PACKET2(X, Y) {{X, Y}}
+ #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {{X, Y, Z, W}}
+#else
+ //Default initializer for packets
+ #define EIGEN_INIT_NEON_PACKET2(X, Y) {X, Y}
+ #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
+#endif
+
+// arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
+// which available on LLVM and GCC (at least)
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__)
+ #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#elif defined __pld
+ #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
+#elif !defined(__aarch64__)
+ #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( " pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#else
+ // by default no explicit prefetching
+ #define EIGEN_ARM_PREFETCH(ADDR)
+#endif
+
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet4f type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+
+ HasDiv = 1,
+ // FIXME check the Has*
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 0,
+ HasExp = 0,
+ HasSqrt = 0
+ };
+};
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet4i type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4
+ // FIXME check the Has*
+ };
+};
+
+#if EIGEN_GNUC_AT_MOST(4,4) && !defined(__llvm__)
+// workaround gcc 4.2, 4.3 and 4.4 compilatin issue
+EIGEN_STRONG_INLINE float32x4_t vld1q_f32(const float* x) { return ::vld1q_f32((const float32_t*)x); }
+EIGEN_STRONG_INLINE float32x2_t vld1_f32 (const float* x) { return ::vld1_f32 ((const float32_t*)x); }
+EIGEN_STRONG_INLINE void vst1q_f32(float* to, float32x4_t from) { ::vst1q_f32((float32_t*)to,from); }
+EIGEN_STRONG_INLINE void vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); }
+#endif
+
+template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4}; };
+template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4}; };
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return vdupq_n_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return vdupq_n_s32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a)
+{
+ Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+ return vaddq_f32(pset1<Packet4f>(a), countdown);
+}
+template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a)
+{
+ Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+ return vaddq_s32(pset1<Packet4i>(a), countdown);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f inv, restep, div;
+
+ // NEON does not offer a divide instruction, we have to do a reciprocal approximation
+ // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
+ // a reciprocal estimate AND a reciprocal step -which saves a few instructions
+ // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
+ // Newton-Raphson and vrecpsq_f32()
+ inv = vrecpeq_f32(b);
+
+ // This returns a differential, by which we will have to multiply inv to get a better
+ // approximation of 1/b.
+ restep = vrecpsq_f32(b, inv);
+ inv = vmulq_f32(restep, inv);
+
+ // Finally, multiply a by 1/b and get the wanted result of the division.
+ div = vmulq_f32(a, inv);
+
+ return div;
+}
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4i>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vmlaq_f32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return vmlaq_s32(c,a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); }
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ float32x2_t lo, hi;
+ lo = vld1_dup_f32(from);
+ hi = vld1_dup_f32(from+1);
+ return vcombine_f32(lo, hi);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ int32x2_t lo, hi;
+ lo = vld1_dup_s32(from);
+ hi = vld1_dup_s32(from+1);
+ return vcombine_s32(lo, hi);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to, from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_ARM_PREFETCH(addr); }
+
+// FIXME only store the 2 first elements ?
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int EIGEN_ALIGN16 x[4]; vst1q_s32(x, a); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
+ float32x2_t a_lo, a_hi;
+ Packet4f a_r64;
+
+ a_r64 = vrev64q_f32(a);
+ a_lo = vget_low_f32(a_r64);
+ a_hi = vget_high_f32(a_r64);
+ return vcombine_f32(a_hi, a_lo);
+}
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
+ int32x2_t a_lo, a_hi;
+ Packet4i a_r64;
+
+ a_r64 = vrev64q_s32(a);
+ a_lo = vget_low_s32(a_r64);
+ a_hi = vget_high_s32(a_r64);
+ return vcombine_s32(a_hi, a_lo);
+}
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ float32x2_t a_lo, a_hi, sum;
+
+ a_lo = vget_low_f32(a);
+ a_hi = vget_high_f32(a);
+ sum = vpadd_f32(a_lo, a_hi);
+ sum = vpadd_f32(sum, sum);
+ return vget_lane_f32(sum, 0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
+{
+ float32x4x2_t vtrn1, vtrn2, res1, res2;
+ Packet4f sum1, sum2, sum;
+
+ // NEON zip performs interleaving of the supplied vectors.
+ // We perform two interleaves in a row to acquire the transposed vector
+ vtrn1 = vzipq_f32(vecs[0], vecs[2]);
+ vtrn2 = vzipq_f32(vecs[1], vecs[3]);
+ res1 = vzipq_f32(vtrn1.val[0], vtrn2.val[0]);
+ res2 = vzipq_f32(vtrn1.val[1], vtrn2.val[1]);
+
+ // Do the addition of the resulting vectors
+ sum1 = vaddq_f32(res1.val[0], res1.val[1]);
+ sum2 = vaddq_f32(res2.val[0], res2.val[1]);
+ sum = vaddq_f32(sum1, sum2);
+
+ return sum;
+}
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ int32x2_t a_lo, a_hi, sum;
+
+ a_lo = vget_low_s32(a);
+ a_hi = vget_high_s32(a);
+ sum = vpadd_s32(a_lo, a_hi);
+ sum = vpadd_s32(sum, sum);
+ return vget_lane_s32(sum, 0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
+{
+ int32x4x2_t vtrn1, vtrn2, res1, res2;
+ Packet4i sum1, sum2, sum;
+
+ // NEON zip performs interleaving of the supplied vectors.
+ // We perform two interleaves in a row to acquire the transposed vector
+ vtrn1 = vzipq_s32(vecs[0], vecs[2]);
+ vtrn2 = vzipq_s32(vecs[1], vecs[3]);
+ res1 = vzipq_s32(vtrn1.val[0], vtrn2.val[0]);
+ res2 = vzipq_s32(vtrn1.val[1], vtrn2.val[1]);
+
+ // Do the addition of the resulting vectors
+ sum1 = vaddq_s32(res1.val[0], res1.val[1]);
+ sum2 = vaddq_s32(res2.val[0], res2.val[1]);
+ sum = vaddq_s32(sum1, sum2);
+
+ return sum;
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ float32x2_t a_lo, a_hi, prod;
+
+ // Get a_lo = |a1|a2| and a_hi = |a3|a4|
+ a_lo = vget_low_f32(a);
+ a_hi = vget_high_f32(a);
+ // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
+ prod = vmul_f32(a_lo, a_hi);
+ // Multiply prod with its swapped value |a2*a4|a1*a3|
+ prod = vmul_f32(prod, vrev64_f32(prod));
+
+ return vget_lane_f32(prod, 0);
+}
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ int32x2_t a_lo, a_hi, prod;
+
+ // Get a_lo = |a1|a2| and a_hi = |a3|a4|
+ a_lo = vget_low_s32(a);
+ a_hi = vget_high_s32(a);
+ // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
+ prod = vmul_s32(a_lo, a_hi);
+ // Multiply prod with its swapped value |a2*a4|a1*a3|
+ prod = vmul_s32(prod, vrev64_s32(prod));
+
+ return vget_lane_s32(prod, 0);
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ float32x2_t a_lo, a_hi, min;
+
+ a_lo = vget_low_f32(a);
+ a_hi = vget_high_f32(a);
+ min = vpmin_f32(a_lo, a_hi);
+ min = vpmin_f32(min, min);
+
+ return vget_lane_f32(min, 0);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+ int32x2_t a_lo, a_hi, min;
+
+ a_lo = vget_low_s32(a);
+ a_hi = vget_high_s32(a);
+ min = vpmin_s32(a_lo, a_hi);
+ min = vpmin_s32(min, min);
+
+ return vget_lane_s32(min, 0);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ float32x2_t a_lo, a_hi, max;
+
+ a_lo = vget_low_f32(a);
+ a_hi = vget_high_f32(a);
+ max = vpmax_f32(a_lo, a_hi);
+ max = vpmax_f32(max, max);
+
+ return vget_lane_f32(max, 0);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+ int32x2_t a_lo, a_hi, max;
+
+ a_lo = vget_low_s32(a);
+ a_hi = vget_high_s32(a);
+ max = vpmax_s32(a_lo, a_hi);
+
+ return vget_lane_s32(max, 0);
+}
+
+// this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,
+// see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074
+#define PALIGN_NEON(Offset,Type,Command) \
+template<>\
+struct palign_impl<Offset,Type>\
+{\
+ EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\
+ {\
+ if (Offset!=0)\
+ first = Command(first, second, Offset);\
+ }\
+};\
+
+PALIGN_NEON(0,Packet4f,vextq_f32)
+PALIGN_NEON(1,Packet4f,vextq_f32)
+PALIGN_NEON(2,Packet4f,vextq_f32)
+PALIGN_NEON(3,Packet4f,vextq_f32)
+PALIGN_NEON(0,Packet4i,vextq_s32)
+PALIGN_NEON(1,Packet4i,vextq_s32)
+PALIGN_NEON(2,Packet4i,vextq_s32)
+PALIGN_NEON(3,Packet4i,vextq_s32)
+
+#undef PALIGN_NEON
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_NEON_H
diff --git a/Eigen/src/Core/arch/SSE/CMakeLists.txt b/Eigen/src/Core/arch/SSE/CMakeLists.txt
new file mode 100644
index 0000000..46ea7cc
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_SSE_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_arch_SSE_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/SSE COMPONENT Devel
+)
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
new file mode 100644
index 0000000..91bba5e
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -0,0 +1,442 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_SSE_H
+#define EIGEN_COMPLEX_SSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const __m128& a) : v(a) {}
+ __m128 v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a)
+{
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
+ return Packet2cf(_mm_xor_ps(a.v,mask));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet2cf(_mm_xor_ps(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ // TODO optimize it for SSE3 and 4
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return Packet2cf(_mm_addsub_ps(_mm_mul_ps(_mm_moveldup_ps(a.v), b.v),
+ _mm_mul_ps(_mm_movehdup_ps(a.v),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+// return Packet2cf(_mm_addsub_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
+// _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+// vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+ #else
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x00000000,0x80000000,0x00000000));
+ return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
+ _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(a.v,b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&numext::real_ref(*from))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ Packet2cf res;
+#if EIGEN_GNUC_AT_MOST(4,2)
+ // Workaround annoying "may be used uninitialized in this function" warning with gcc 4.2
+ res.v = _mm_loadl_pi(_mm_set1_ps(0.0f), reinterpret_cast<const __m64*>(&from));
+#elif EIGEN_GNUC_AT_LEAST(4,6)
+ // Suppress annoying "may be used uninitialized in this function" warning with gcc >= 4.6
+ #pragma GCC diagnostic push
+ #pragma GCC diagnostic ignored "-Wuninitialized"
+ res.v = _mm_loadl_pi(res.v, (const __m64*)&from);
+ #pragma GCC diagnostic pop
+#else
+ res.v = _mm_loadl_pi(res.v, (const __m64*)&from);
+#endif
+ return Packet2cf(_mm_movelh_ps(res.v,res.v));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ #if EIGEN_GNUC_AT_MOST(4,3)
+ // Workaround gcc 4.2 ICE - this is not performance wise ideal, but who cares...
+ // This workaround also fix invalid code generation with gcc 4.3
+ EIGEN_ALIGN16 std::complex<float> res[2];
+ _mm_store_ps((float*)res, a.v);
+ return res[0];
+ #else
+ std::complex<float> res;
+ _mm_storel_pi((__m64*)&res, a.v);
+ return res;
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) { return Packet2cf(_mm_castpd_ps(preverse(_mm_castps_pd(a.v)))); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ return pfirst(Packet2cf(_mm_add_ps(a.v, _mm_movehl_ps(a.v,a.v))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
+{
+ return Packet2cf(_mm_add_ps(_mm_movelh_ps(vecs[0].v,vecs[1].v), _mm_movehl_ps(vecs[1].v,vecs[0].v)));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ return pfirst(pmul(a, Packet2cf(_mm_movehl_ps(a.v,a.v))));
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cf>
+{
+ static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)
+ {
+ if (Offset==1)
+ {
+ first.v = _mm_movehl_ps(first.v, first.v);
+ first.v = _mm_movelh_ps(first.v, second.v);
+ }
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return internal::pmul(a, pconj(b));
+ #else
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet2cf(_mm_add_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),
+ _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return internal::pmul(pconj(a), b);
+ #else
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
+ _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return pconj(internal::pmul(a, b));
+ #else
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet2cf(_mm_sub_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),
+ _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet4f, Packet2cf, false,false>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet4f& x, const Packet2cf& y, const Packet2cf& c) const
+ { return padd(c, pmul(x,y)); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet4f& x, const Packet2cf& y) const
+ { return Packet2cf(Eigen::internal::pmul(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet2cf, Packet4f, false,false>
+{
+ EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet4f& y, const Packet2cf& c) const
+ { return padd(c, pmul(x,y)); }
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& x, const Packet4f& y) const
+ { return Packet2cf(Eigen::internal::pmul(x.v, y)); }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ // TODO optimize it for SSE3 and 4
+ Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
+ __m128 s = _mm_mul_ps(b.v,b.v);
+ return Packet2cf(_mm_div_ps(res.v,_mm_add_ps(s,_mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(s), 0xb1)))));
+}
+
+EIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)
+{
+ return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));
+}
+
+
+//---------- double ----------
+struct Packet1cd
+{
+ EIGEN_STRONG_INLINE Packet1cd() {}
+ EIGEN_STRONG_INLINE explicit Packet1cd(const __m128d& a) : v(a) {}
+ __m128d v;
+};
+
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet1cd type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1}; };
+
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)
+{
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+ return Packet1cd(_mm_xor_pd(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ // TODO optimize it for SSE3 and 4
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return Packet1cd(_mm_addsub_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
+ _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0))));
+ #else
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
+ return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
+ _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0)), mask)));
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_and_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_or_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_xor_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_andnot_pd(a.v,b.v)); }
+
+// FIXME force unaligned load, this is a temporary fix
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
+{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
+
+// FIXME force unaligned store, this is a temporary fix
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
+{
+ EIGEN_ALIGN16 double res[2];
+ _mm_store_pd(res, a.v);
+ return std::complex<double>(res[0],res[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)
+{
+ return vecs[0];
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet1cd>
+{
+ static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)
+ {
+ // FIXME is it sure we never have to align a Packet1cd?
+ // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...
+ }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, false,true>
+{
+ EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return internal::pmul(a, pconj(b));
+ #else
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+ return Packet1cd(_mm_add_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),
+ _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0))));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, true,false>
+{
+ EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return internal::pmul(pconj(a), b);
+ #else
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+ return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
+ _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0)), mask)));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
+{
+ EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+ { return padd(pmul(x,y),c); }
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+ {
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return pconj(internal::pmul(a, b));
+ #else
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+ return Packet1cd(_mm_sub_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),
+ _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0))));
+ #endif
+ }
+};
+
+template<> struct conj_helper<Packet2d, Packet1cd, false,false>
+{
+ EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet2d& x, const Packet1cd& y, const Packet1cd& c) const
+ { return padd(c, pmul(x,y)); }
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet2d& x, const Packet1cd& y) const
+ { return Packet1cd(Eigen::internal::pmul(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet1cd, Packet2d, false,false>
+{
+ EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet2d& y, const Packet1cd& c) const
+ { return padd(c, pmul(x,y)); }
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& x, const Packet2d& y) const
+ { return Packet1cd(Eigen::internal::pmul(x.v, y)); }
+};
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ // TODO optimize it for SSE3 and 4
+ Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
+ __m128d s = _mm_mul_pd(b.v,b.v);
+ return Packet1cd(_mm_div_pd(res.v, _mm_add_pd(s,_mm_shuffle_pd(s, s, 0x1))));
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+{
+ return Packet1cd(preverse(x.v));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h
new file mode 100644
index 0000000..d16f30b
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/MathFunctions.h
@@ -0,0 +1,475 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* The sin, cos, exp, and log functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
+#define EIGEN_MATH_FUNCTIONS_SSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f plog<Packet4f>(const Packet4f& _x)
+{
+ Packet4f x = _x;
+ _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+ _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+ _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+
+ _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
+
+ /* the smallest non denormalized float number */
+ _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
+ _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);//-1.f/0.f);
+
+ /* natural logarithm computed for 4 simultaneous float
+ return NaN for x <= 0
+ */
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+
+
+ Packet4i emm0;
+
+ Packet4f invalid_mask = _mm_cmpnge_ps(x, _mm_setzero_ps()); // not greater equal is true if x is NaN
+ Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
+
+ x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */
+ emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
+
+ /* keep only the fractional part */
+ x = _mm_and_ps(x, p4f_inv_mant_mask);
+ x = _mm_or_ps(x, p4f_half);
+
+ emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
+ Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
+
+ /* part2:
+ if( x < SQRTHF ) {
+ e -= 1;
+ x = x + x - 1.0;
+ } else { x = x - 1.0; }
+ */
+ Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
+ Packet4f tmp = _mm_and_ps(x, mask);
+ x = psub(x, p4f_1);
+ e = psub(e, _mm_and_ps(p4f_1, mask));
+ x = padd(x, tmp);
+
+ Packet4f x2 = pmul(x,x);
+ Packet4f x3 = pmul(x2,x);
+
+ Packet4f y, y1, y2;
+ y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
+ y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
+ y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
+ y = pmadd(y , x, p4f_cephes_log_p2);
+ y1 = pmadd(y1, x, p4f_cephes_log_p5);
+ y2 = pmadd(y2, x, p4f_cephes_log_p8);
+ y = pmadd(y, x3, y1);
+ y = pmadd(y, x3, y2);
+ y = pmul(y, x3);
+
+ y1 = pmul(e, p4f_cephes_log_q1);
+ tmp = pmul(x2, p4f_half);
+ y = padd(y, y1);
+ x = psub(x, tmp);
+ y2 = pmul(e, p4f_cephes_log_q2);
+ x = padd(x, y);
+ x = padd(x, y2);
+ // negative arg will be NAN, 0 will be -INF
+ return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),
+ _mm_and_ps(iszero_mask, p4f_minus_inf));
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f pexp<Packet4f>(const Packet4f& _x)
+{
+ Packet4f x = _x;
+ _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+ _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+ _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+
+
+ _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
+ _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
+
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
+
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
+
+ Packet4f tmp = _mm_setzero_ps(), fx;
+ Packet4i emm0;
+
+ // clamp x
+ x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
+
+ /* express exp(x) as exp(g + n*log(2)) */
+ fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
+
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ fx = _mm_floor_ps(fx);
+#else
+ emm0 = _mm_cvttps_epi32(fx);
+ tmp = _mm_cvtepi32_ps(emm0);
+ /* if greater, substract 1 */
+ Packet4f mask = _mm_cmpgt_ps(tmp, fx);
+ mask = _mm_and_ps(mask, p4f_1);
+ fx = psub(tmp, mask);
+#endif
+
+ tmp = pmul(fx, p4f_cephes_exp_C1);
+ Packet4f z = pmul(fx, p4f_cephes_exp_C2);
+ x = psub(x, tmp);
+ x = psub(x, z);
+
+ z = pmul(x,x);
+
+ Packet4f y = p4f_cephes_exp_p0;
+ y = pmadd(y, x, p4f_cephes_exp_p1);
+ y = pmadd(y, x, p4f_cephes_exp_p2);
+ y = pmadd(y, x, p4f_cephes_exp_p3);
+ y = pmadd(y, x, p4f_cephes_exp_p4);
+ y = pmadd(y, x, p4f_cephes_exp_p5);
+ y = pmadd(y, z, x);
+ y = padd(y, p4f_1);
+
+ // build 2^n
+ emm0 = _mm_cvttps_epi32(fx);
+ emm0 = _mm_add_epi32(emm0, p4i_0x7f);
+ emm0 = _mm_slli_epi32(emm0, 23);
+ return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x);
+}
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d pexp<Packet2d>(const Packet2d& _x)
+{
+ Packet2d x = _x;
+
+ _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
+ _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
+ _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
+
+ _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
+ _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
+
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
+
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
+
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
+
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
+ _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
+ static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
+
+ Packet2d tmp = _mm_setzero_pd(), fx;
+ Packet4i emm0;
+
+ // clamp x
+ x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
+ /* express exp(x) as exp(g + n*log(2)) */
+ fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
+
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ fx = _mm_floor_pd(fx);
+#else
+ emm0 = _mm_cvttpd_epi32(fx);
+ tmp = _mm_cvtepi32_pd(emm0);
+ /* if greater, substract 1 */
+ Packet2d mask = _mm_cmpgt_pd(tmp, fx);
+ mask = _mm_and_pd(mask, p2d_1);
+ fx = psub(tmp, mask);
+#endif
+
+ tmp = pmul(fx, p2d_cephes_exp_C1);
+ Packet2d z = pmul(fx, p2d_cephes_exp_C2);
+ x = psub(x, tmp);
+ x = psub(x, z);
+
+ Packet2d x2 = pmul(x,x);
+
+ Packet2d px = p2d_cephes_exp_p0;
+ px = pmadd(px, x2, p2d_cephes_exp_p1);
+ px = pmadd(px, x2, p2d_cephes_exp_p2);
+ px = pmul (px, x);
+
+ Packet2d qx = p2d_cephes_exp_q0;
+ qx = pmadd(qx, x2, p2d_cephes_exp_q1);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q2);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q3);
+
+ x = pdiv(px,psub(qx,px));
+ x = pmadd(p2d_2,x,p2d_1);
+
+ // build 2^n
+ emm0 = _mm_cvttpd_epi32(fx);
+ emm0 = _mm_add_epi32(emm0, p4i_1023_0);
+ emm0 = _mm_slli_epi32(emm0, 20);
+ emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
+ return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);
+}
+
+/* evaluation of 4 sines at onces, using SSE2 intrinsics.
+
+ The code is the exact rewriting of the cephes sinf function.
+ Precision is excellent as long as x < 8192 (I did not bother to
+ take into account the special handling they have for greater values
+ -- it does not return garbage for arguments over 8192, though, but
+ the extra precision is missing).
+
+ Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+ surprising but correct result.
+*/
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f psin<Packet4f>(const Packet4f& _x)
+{
+ Packet4f x = _x;
+ _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+ _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+
+ _EIGEN_DECLARE_CONST_Packet4i(1, 1);
+ _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
+ _EIGEN_DECLARE_CONST_Packet4i(2, 2);
+ _EIGEN_DECLARE_CONST_Packet4i(4, 4);
+
+ _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
+
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
+
+ Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
+
+ Packet4i emm0, emm2;
+ sign_bit = x;
+ /* take the absolute value */
+ x = pabs(x);
+
+ /* take the modulo */
+
+ /* extract the sign bit (upper one) */
+ sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
+
+ /* scale by 4/Pi */
+ y = pmul(x, p4f_cephes_FOPI);
+
+ /* store the integer part of y in mm0 */
+ emm2 = _mm_cvttps_epi32(y);
+ /* j=(j+1) & (~1) (see the cephes sources) */
+ emm2 = _mm_add_epi32(emm2, p4i_1);
+ emm2 = _mm_and_si128(emm2, p4i_not1);
+ y = _mm_cvtepi32_ps(emm2);
+ /* get the swap sign flag */
+ emm0 = _mm_and_si128(emm2, p4i_4);
+ emm0 = _mm_slli_epi32(emm0, 29);
+ /* get the polynom selection mask
+ there is one polynom for 0 <= x <= Pi/4
+ and another one for Pi/4<x<=Pi/2
+
+ Both branches will be computed.
+ */
+ emm2 = _mm_and_si128(emm2, p4i_2);
+ emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+
+ Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
+ Packet4f poly_mask = _mm_castsi128_ps(emm2);
+ sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
+
+ /* The magic pass: "Extended precision modular arithmetic"
+ x = ((x - y * DP1) - y * DP2) - y * DP3; */
+ xmm1 = pmul(y, p4f_minus_cephes_DP1);
+ xmm2 = pmul(y, p4f_minus_cephes_DP2);
+ xmm3 = pmul(y, p4f_minus_cephes_DP3);
+ x = padd(x, xmm1);
+ x = padd(x, xmm2);
+ x = padd(x, xmm3);
+
+ /* Evaluate the first polynom (0 <= x <= Pi/4) */
+ y = p4f_coscof_p0;
+ Packet4f z = _mm_mul_ps(x,x);
+
+ y = pmadd(y, z, p4f_coscof_p1);
+ y = pmadd(y, z, p4f_coscof_p2);
+ y = pmul(y, z);
+ y = pmul(y, z);
+ Packet4f tmp = pmul(z, p4f_half);
+ y = psub(y, tmp);
+ y = padd(y, p4f_1);
+
+ /* Evaluate the second polynom (Pi/4 <= x <= 0) */
+
+ Packet4f y2 = p4f_sincof_p0;
+ y2 = pmadd(y2, z, p4f_sincof_p1);
+ y2 = pmadd(y2, z, p4f_sincof_p2);
+ y2 = pmul(y2, z);
+ y2 = pmul(y2, x);
+ y2 = padd(y2, x);
+
+ /* select the correct result from the two polynoms */
+ y2 = _mm_and_ps(poly_mask, y2);
+ y = _mm_andnot_ps(poly_mask, y);
+ y = _mm_or_ps(y,y2);
+ /* update the sign */
+ return _mm_xor_ps(y, sign_bit);
+}
+
+/* almost the same as psin */
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f pcos<Packet4f>(const Packet4f& _x)
+{
+ Packet4f x = _x;
+ _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+ _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+
+ _EIGEN_DECLARE_CONST_Packet4i(1, 1);
+ _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
+ _EIGEN_DECLARE_CONST_Packet4i(2, 2);
+ _EIGEN_DECLARE_CONST_Packet4i(4, 4);
+
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
+ _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
+ _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
+ _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
+
+ Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
+ Packet4i emm0, emm2;
+
+ x = pabs(x);
+
+ /* scale by 4/Pi */
+ y = pmul(x, p4f_cephes_FOPI);
+
+ /* get the integer part of y */
+ emm2 = _mm_cvttps_epi32(y);
+ /* j=(j+1) & (~1) (see the cephes sources) */
+ emm2 = _mm_add_epi32(emm2, p4i_1);
+ emm2 = _mm_and_si128(emm2, p4i_not1);
+ y = _mm_cvtepi32_ps(emm2);
+
+ emm2 = _mm_sub_epi32(emm2, p4i_2);
+
+ /* get the swap sign flag */
+ emm0 = _mm_andnot_si128(emm2, p4i_4);
+ emm0 = _mm_slli_epi32(emm0, 29);
+ /* get the polynom selection mask */
+ emm2 = _mm_and_si128(emm2, p4i_2);
+ emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+
+ Packet4f sign_bit = _mm_castsi128_ps(emm0);
+ Packet4f poly_mask = _mm_castsi128_ps(emm2);
+
+ /* The magic pass: "Extended precision modular arithmetic"
+ x = ((x - y * DP1) - y * DP2) - y * DP3; */
+ xmm1 = pmul(y, p4f_minus_cephes_DP1);
+ xmm2 = pmul(y, p4f_minus_cephes_DP2);
+ xmm3 = pmul(y, p4f_minus_cephes_DP3);
+ x = padd(x, xmm1);
+ x = padd(x, xmm2);
+ x = padd(x, xmm3);
+
+ /* Evaluate the first polynom (0 <= x <= Pi/4) */
+ y = p4f_coscof_p0;
+ Packet4f z = pmul(x,x);
+
+ y = pmadd(y,z,p4f_coscof_p1);
+ y = pmadd(y,z,p4f_coscof_p2);
+ y = pmul(y, z);
+ y = pmul(y, z);
+ Packet4f tmp = _mm_mul_ps(z, p4f_half);
+ y = psub(y, tmp);
+ y = padd(y, p4f_1);
+
+ /* Evaluate the second polynom (Pi/4 <= x <= 0) */
+ Packet4f y2 = p4f_sincof_p0;
+ y2 = pmadd(y2, z, p4f_sincof_p1);
+ y2 = pmadd(y2, z, p4f_sincof_p2);
+ y2 = pmul(y2, z);
+ y2 = pmadd(y2, x, x);
+
+ /* select the correct result from the two polynoms */
+ y2 = _mm_and_ps(poly_mask, y2);
+ y = _mm_andnot_ps(poly_mask, y);
+ y = _mm_or_ps(y,y2);
+
+ /* update the sign */
+ return _mm_xor_ps(y, sign_bit);
+}
+
+#if EIGEN_FAST_MATH
+
+// This is based on Quake3's fast inverse square root.
+// For detail see here: http://www.beyond3d.com/content/articles/8/
+// It lacks 1 (or 2 bits in some rare cases) of precision, and does not handle negative, +inf, or denormalized numbers correctly.
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f psqrt<Packet4f>(const Packet4f& _x)
+{
+ Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
+
+ /* select only the inverse sqrt of non-zero inputs */
+ Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));
+ Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
+
+ x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
+ return pmul(_x,x);
+}
+
+#else
+
+template<> EIGEN_STRONG_INLINE Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
+
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
new file mode 100644
index 0000000..fc8ae50
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -0,0 +1,649 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_SSE_H
+#define EIGEN_PACKET_MATH_SSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))
+#endif
+
+typedef __m128 Packet4f;
+typedef __m128i Packet4i;
+typedef __m128d Packet2d;
+
+template<> struct is_arithmetic<__m128> { enum { value = true }; };
+template<> struct is_arithmetic<__m128i> { enum { value = true }; };
+template<> struct is_arithmetic<__m128d> { enum { value = true }; };
+
+#define vec4f_swizzle1(v,p,q,r,s) \
+ (_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), ((s)<<6|(r)<<4|(q)<<2|(p)))))
+
+#define vec4i_swizzle1(v,p,q,r,s) \
+ (_mm_shuffle_epi32( v, ((s)<<6|(r)<<4|(q)<<2|(p))))
+
+#define vec2d_swizzle1(v,p,q) \
+ (_mm_castsi128_pd(_mm_shuffle_epi32( _mm_castpd_si128(v), ((q*2+1)<<6|(q*2)<<4|(p*2+1)<<2|(p*2)))))
+
+#define vec4f_swizzle2(a,b,p,q,r,s) \
+ (_mm_shuffle_ps( (a), (b), ((s)<<6|(r)<<4|(q)<<2|(p))))
+
+#define vec4i_swizzle2(a,b,p,q,r,s) \
+ (_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), ((s)<<6|(r)<<4|(q)<<2|(p))))))
+
+#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ const Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
+ const Packet2d p2d_##NAME = pset1<Packet2d>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = _mm_castsi128_ps(pset1<Packet4i>(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ const Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet4f type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4,
+
+ HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1
+ };
+};
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet2d type;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=2,
+
+ HasDiv = 1,
+ HasExp = 1,
+ HasSqrt = 1
+ };
+};
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet4i type;
+ enum {
+ // FIXME check the Has*
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4
+ };
+};
+
+template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4}; };
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2}; };
+template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4}; };
+
+#if defined(_MSC_VER) && (_MSC_VER==1500)
+// Workaround MSVC 9 internal compiler error.
+// TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode
+// TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set_ps(from,from,from,from); }
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from,from); }
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set_epi32(from,from,from,from); }
+#else
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set1_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set1_epi32(from); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
+template<> EIGEN_STRONG_INLINE Packet2d plset<double>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
+template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
+{
+ const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
+ return _mm_xor_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
+{
+ const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
+ return _mm_xor_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
+{
+ return psub(_mm_setr_epi32(0,0,0,0), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_mullo_epi32(a,b);
+#else
+ // this version is slightly faster than 4 scalar products
+ return vec4i_swizzle1(
+ vec4i_swizzle2(
+ _mm_mul_epu32(a,b),
+ _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),
+ vec4i_swizzle1(b,1,0,3,2)),
+ 0,2,0,2),
+ 0,2,1,3);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by SSE");
+ return pset1<Packet4i>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_min_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_min_epi32(a,b);
+#else
+ // after some bench, this version *is* faster than a scalar implementation
+ Packet4i mask = _mm_cmplt_epi32(a,b);
+ return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_max_epi32(a,b);
+#else
+ // after some bench, this version *is* faster than a scalar implementation
+ Packet4i mask = _mm_cmpgt_epi32(a,b);
+ return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const Packet4i*>(from)); }
+
+#if defined(_MSC_VER)
+ template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ #if (_MSC_VER==1600)
+ // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps
+ // (i.e., it does not generate an unaligned load!!
+ // TODO On most architectures this version should also be faster than a single _mm_loadu_ps
+ // so we could also enable it for MSVC08 but first we have to make this later does not generate crap when doing so...
+ __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));
+ res = _mm_loadh_pi(res, (const __m64*)(from+2));
+ return res;
+ #else
+ return _mm_loadu_ps(from);
+ #endif
+ }
+ template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_pd(from); }
+ template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from)); }
+#else
+// Fast unaligned loads. Note that here we cannot directly use intrinsics: this would
+// require pointer casting to incompatible pointer types and leads to invalid code
+// because of the strict aliasing rule. The "dummy" stuff are required to enforce
+// a correct instruction dependency.
+// TODO: do the same for MSVC (ICC is compatible)
+// NOTE: with the code below, MSVC's compiler crashes!
+
+#if defined(__GNUC__) && defined(__i386__)
+ // bug 195: gcc/i386 emits weird x87 fldl/fstpl instructions for _mm_load_sd
+ #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
+#elif defined(__clang__)
+ // bug 201: Segfaults in __mm_loadh_pd with clang 2.8
+ #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
+#else
+ #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 0
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
+ return _mm_loadu_ps(from);
+#else
+ __m128d res;
+ res = _mm_load_sd((const double*)(from)) ;
+ res = _mm_loadh_pd(res, (const double*)(from+2)) ;
+ return _mm_castpd_ps(res);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
+ return _mm_loadu_pd(from);
+#else
+ __m128d res;
+ res = _mm_load_sd(from) ;
+ res = _mm_loadh_pd(res,from+1);
+ return res;
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
+ return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from));
+#else
+ __m128d res;
+ res = _mm_load_sd((const double*)(from)) ;
+ res = _mm_loadh_pd(res, (const double*)(from+2)) ;
+ return _mm_castpd_si128(res);
+#endif
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
+}
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
+{ return pset1<Packet2d>(from[0]); }
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ Packet4i tmp;
+ tmp = _mm_loadl_epi64(reinterpret_cast<const Packet4i*>(from));
+ return vec4i_swizzle1(tmp, 0, 0, 1, 1);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<Packet4i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE
+ _mm_storel_pd((to), from);
+ _mm_storeh_pd((to+1), from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), _mm_castps_pd(from)); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), _mm_castsi128_pd(from)); }
+
+// some compilers might be tempted to perform multiple moves instead of using a vector path.
+template<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
+{
+ Packet4f pa = _mm_set_ss(a);
+ pstore(to, vec4f_swizzle1(pa,0,0,0,0));
+}
+// some compilers might be tempted to perform multiple moves instead of using a vector path.
+template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
+{
+ Packet2d pa = _mm_set_sd(a);
+ pstore(to, vec2d_swizzle1(pa,0,0));
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+#if defined(_MSC_VER) && defined(_WIN64) && !defined(__INTEL_COMPILER)
+// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
+// Direct of the struct members fixed bug #62.
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#elif defined(_MSC_VER) && !defined(__INTEL_COMPILER)
+// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#else
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{ return _mm_shuffle_ps(a,a,0x1B); }
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{ return _mm_shuffle_pd(a,a,0x1); }
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{ return _mm_shuffle_epi32(a,0x1B); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
+{
+ const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
+ return _mm_and_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
+{
+ const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
+ return _mm_and_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
+{
+ #ifdef EIGEN_VECTORIZE_SSSE3
+ return _mm_abs_epi32(a);
+ #else
+ Packet4i aux = _mm_srai_epi32(a,31);
+ return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
+ #endif
+}
+
+EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
+{
+ vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
+ vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
+ vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
+ vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
+}
+
+#ifdef EIGEN_VECTORIZE_SSE3
+// TODO implement SSE2 versions as well as integer versions
+template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
+{
+ return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));
+}
+template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
+{
+ return _mm_hadd_pd(vecs[0], vecs[1]);
+}
+// SSSE3 version:
+// EIGEN_STRONG_INLINE Packet4i preduxp(const Packet4i* vecs)
+// {
+// return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));
+// }
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp0 = _mm_hadd_ps(a,a);
+ return pfirst(_mm_hadd_ps(tmp0, tmp0));
+}
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return pfirst(_mm_hadd_pd(a, a)); }
+
+// SSSE3 version:
+// EIGEN_STRONG_INLINE float predux(const Packet4i& a)
+// {
+// Packet4i tmp0 = _mm_hadd_epi32(a,a);
+// return pfirst(_mm_hadd_epi32(tmp0, tmp0));
+// }
+#else
+// SSE2 versions
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
+ return pfirst(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{
+ return pfirst(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
+{
+ Packet4f tmp0, tmp1, tmp2;
+ tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);
+ tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);
+ tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);
+ tmp0 = _mm_add_ps(tmp0, tmp1);
+ tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);
+ tmp1 = _mm_add_ps(tmp1, tmp2);
+ tmp2 = _mm_movehl_ps(tmp1, tmp0);
+ tmp0 = _mm_movelh_ps(tmp0, tmp1);
+ return _mm_add_ps(tmp0, tmp2);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
+{
+ return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));
+}
+#endif // SSE3
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
+ return pfirst(tmp) + pfirst(_mm_shuffle_epi32(tmp, 1));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
+{
+ Packet4i tmp0, tmp1, tmp2;
+ tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);
+ tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);
+ tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);
+ tmp0 = _mm_add_epi32(tmp0, tmp1);
+ tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);
+ tmp1 = _mm_add_epi32(tmp1, tmp2);
+ tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);
+ tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);
+ return _mm_add_epi32(tmp0, tmp2);
+}
+
+// Other reduction functions:
+
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
+ return pfirst(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{
+ return pfirst(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., reusing pmul is very slow !)
+ // TODO try to call _mm_mul_epu32 directly
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ return (aux[0] * aux[1]) * (aux[2] * aux[3]);;
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
+ return pfirst(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{
+ return pfirst(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., it does not like using std::min after the pstore !!)
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
+ int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
+ return aux0<aux2 ? aux0 : aux2;
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
+ return pfirst(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{
+ return pfirst(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., it does not like using std::min after the pstore !!)
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
+ int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
+ return aux0>aux2 ? aux0 : aux2;
+}
+
+#if (defined __GNUC__)
+// template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)
+// {
+// Packet4f res = b;
+// asm("mulps %[a], %[b] \n\taddps %[c], %[b]" : [b] "+x" (res) : [a] "x" (a), [c] "x" (c));
+// return res;
+// }
+// EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i& a, const Packet4i& b, const int i)
+// {
+// Packet4i res = a;
+// asm("palignr %[i], %[a], %[b] " : [b] "+x" (res) : [a] "x" (a), [i] "i" (i));
+// return res;
+// }
+#endif
+
+#ifdef EIGEN_VECTORIZE_SSSE3
+// SSSE3 versions
+template<int Offset>
+struct palign_impl<Offset,Packet4f>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
+ {
+ if (Offset!=0)
+ first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));
+ }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet4i>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
+ {
+ if (Offset!=0)
+ first = _mm_alignr_epi8(second,first, Offset*4);
+ }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet2d>
+{
+ static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
+ {
+ if (Offset==1)
+ first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));
+ }
+};
+#else
+// SSE2 versions
+template<int Offset>
+struct palign_impl<Offset,Packet4f>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
+ {
+ if (Offset==1)
+ {
+ first = _mm_move_ss(first,second);
+ first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));
+ }
+ else if (Offset==2)
+ {
+ first = _mm_movehl_ps(first,first);
+ first = _mm_movelh_ps(first,second);
+ }
+ else if (Offset==3)
+ {
+ first = _mm_move_ss(first,second);
+ first = _mm_shuffle_ps(first,second,0x93);
+ }
+ }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet4i>
+{
+ static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
+ {
+ if (Offset==1)
+ {
+ first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+ first = _mm_shuffle_epi32(first,0x39);
+ }
+ else if (Offset==2)
+ {
+ first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));
+ first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+ }
+ else if (Offset==3)
+ {
+ first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+ first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));
+ }
+ }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet2d>
+{
+ static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
+ {
+ if (Offset==1)
+ {
+ first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));
+ first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));
+ }
+ }
+};
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_SSE_H
diff --git a/Eigen/src/Core/products/CMakeLists.txt b/Eigen/src/Core/products/CMakeLists.txt
new file mode 100644
index 0000000..21fc94a
--- /dev/null
+++ b/Eigen/src/Core/products/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_Product_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_Product_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/products COMPONENT Devel
+ )
diff --git a/Eigen/src/Core/products/CoeffBasedProduct.h b/Eigen/src/Core/products/CoeffBasedProduct.h
new file mode 100644
index 0000000..2a9d65b
--- /dev/null
+++ b/Eigen/src/Core/products/CoeffBasedProduct.h
@@ -0,0 +1,476 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COEFFBASED_PRODUCT_H
+#define EIGEN_COEFFBASED_PRODUCT_H
+
+namespace Eigen {
+
+namespace internal {
+
+/*********************************************************************************
+* Coefficient based product implementation.
+* It is designed for the following use cases:
+* - small fixed sizes
+* - lazy products
+*********************************************************************************/
+
+/* Since the all the dimensions of the product are small, here we can rely
+ * on the generic Assign mechanism to evaluate the product per coeff (or packet).
+ *
+ * Note that here the inner-loops should always be unrolled.
+ */
+
+template<int Traversal, int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl;
+
+template<int StorageOrder, int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl;
+
+template<typename LhsNested, typename RhsNested, int NestingFlags>
+struct traits<CoeffBasedProduct<LhsNested,RhsNested,NestingFlags> >
+{
+ typedef MatrixXpr XprKind;
+ typedef typename remove_all<LhsNested>::type _LhsNested;
+ typedef typename remove_all<RhsNested>::type _RhsNested;
+ typedef typename scalar_product_traits<typename _LhsNested::Scalar, typename _RhsNested::Scalar>::ReturnType Scalar;
+ typedef typename promote_storage_type<typename traits<_LhsNested>::StorageKind,
+ typename traits<_RhsNested>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<_LhsNested>::Index,
+ typename traits<_RhsNested>::Index>::type Index;
+
+ enum {
+ LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+ RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+ LhsFlags = _LhsNested::Flags,
+ RhsFlags = _RhsNested::Flags,
+
+ RowsAtCompileTime = _LhsNested::RowsAtCompileTime,
+ ColsAtCompileTime = _RhsNested::ColsAtCompileTime,
+ InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime),
+
+ MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,
+
+ LhsRowMajor = LhsFlags & RowMajorBit,
+ RhsRowMajor = RhsFlags & RowMajorBit,
+
+ SameType = is_same<typename _LhsNested::Scalar,typename _RhsNested::Scalar>::value,
+
+ CanVectorizeRhs = RhsRowMajor && (RhsFlags & PacketAccessBit)
+ && (ColsAtCompileTime == Dynamic
+ || ( (ColsAtCompileTime % packet_traits<Scalar>::size) == 0
+ && (RhsFlags&AlignedBit)
+ )
+ ),
+
+ CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit)
+ && (RowsAtCompileTime == Dynamic
+ || ( (RowsAtCompileTime % packet_traits<Scalar>::size) == 0
+ && (LhsFlags&AlignedBit)
+ )
+ ),
+
+ EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+ : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+ : (RhsRowMajor && !CanVectorizeLhs),
+
+ Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & ~RowMajorBit)
+ | (EvalToRowMajor ? RowMajorBit : 0)
+ | NestingFlags
+ | (LhsFlags & RhsFlags & AlignedBit)
+ // TODO enable vectorization for mixed types
+ | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0),
+
+ CoeffReadCost = InnerSize == Dynamic ? Dynamic
+ : InnerSize == 0 ? 0
+ : InnerSize * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
+ + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
+
+ /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside
+ * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner
+ * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect
+ * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI.
+ */
+ CanVectorizeInner = SameType
+ && LhsRowMajor
+ && (!RhsRowMajor)
+ && (LhsFlags & RhsFlags & ActualPacketAccessBit)
+ && (LhsFlags & RhsFlags & AlignedBit)
+ && (InnerSize % packet_traits<Scalar>::size == 0)
+ };
+};
+
+} // end namespace internal
+
+template<typename LhsNested, typename RhsNested, int NestingFlags>
+class CoeffBasedProduct
+ : internal::no_assignment_operator,
+ public MatrixBase<CoeffBasedProduct<LhsNested, RhsNested, NestingFlags> >
+{
+ public:
+
+ typedef MatrixBase<CoeffBasedProduct> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(CoeffBasedProduct)
+ typedef typename Base::PlainObject PlainObject;
+
+ private:
+
+ typedef typename internal::traits<CoeffBasedProduct>::_LhsNested _LhsNested;
+ typedef typename internal::traits<CoeffBasedProduct>::_RhsNested _RhsNested;
+
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ InnerSize = internal::traits<CoeffBasedProduct>::InnerSize,
+ Unroll = CoeffReadCost != Dynamic && CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
+ CanVectorizeInner = internal::traits<CoeffBasedProduct>::CanVectorizeInner
+ };
+
+ typedef internal::product_coeff_impl<CanVectorizeInner ? InnerVectorizedTraversal : DefaultTraversal,
+ Unroll ? InnerSize : Dynamic,
+ _LhsNested, _RhsNested, Scalar> ScalarCoeffImpl;
+
+ typedef CoeffBasedProduct<LhsNested,RhsNested,NestByRefBit> LazyCoeffBasedProductType;
+
+ public:
+
+ inline CoeffBasedProduct(const CoeffBasedProduct& other)
+ : Base(), m_lhs(other.m_lhs), m_rhs(other.m_rhs)
+ {}
+
+ template<typename Lhs, typename Rhs>
+ inline CoeffBasedProduct(const Lhs& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {
+ // we don't allow taking products of matrices of different real types, as that wouldn't be vectorizable.
+ // We still allow to mix T and complex<T>.
+ EIGEN_STATIC_ASSERT((internal::scalar_product_traits<typename Lhs::RealScalar, typename Rhs::RealScalar>::Defined),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ eigen_assert(lhs.cols() == rhs.rows()
+ && "invalid matrix product"
+ && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_lhs.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_rhs.cols(); }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+ {
+ Scalar res;
+ ScalarCoeffImpl::run(row, col, m_lhs, m_rhs, res);
+ return res;
+ }
+
+ /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,
+ * which is why we don't set the LinearAccessBit.
+ */
+ EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+ {
+ Scalar res;
+ const Index row = RowsAtCompileTime == 1 ? 0 : index;
+ const Index col = RowsAtCompileTime == 1 ? index : 0;
+ ScalarCoeffImpl::run(row, col, m_lhs, m_rhs, res);
+ return res;
+ }
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE const PacketScalar packet(Index row, Index col) const
+ {
+ PacketScalar res;
+ internal::product_packet_impl<Flags&RowMajorBit ? RowMajor : ColMajor,
+ Unroll ? InnerSize : Dynamic,
+ _LhsNested, _RhsNested, PacketScalar, LoadMode>
+ ::run(row, col, m_lhs, m_rhs, res);
+ return res;
+ }
+
+ // Implicit conversion to the nested type (trigger the evaluation of the product)
+ EIGEN_STRONG_INLINE operator const PlainObject& () const
+ {
+ m_result.lazyAssign(*this);
+ return m_result;
+ }
+
+ const _LhsNested& lhs() const { return m_lhs; }
+ const _RhsNested& rhs() const { return m_rhs; }
+
+ const Diagonal<const LazyCoeffBasedProductType,0> diagonal() const
+ { return reinterpret_cast<const LazyCoeffBasedProductType&>(*this); }
+
+ template<int DiagonalIndex>
+ const Diagonal<const LazyCoeffBasedProductType,DiagonalIndex> diagonal() const
+ { return reinterpret_cast<const LazyCoeffBasedProductType&>(*this); }
+
+ const Diagonal<const LazyCoeffBasedProductType,Dynamic> diagonal(Index index) const
+ { return reinterpret_cast<const LazyCoeffBasedProductType&>(*this).diagonal(index); }
+
+ protected:
+ typename internal::add_const_on_value_type<LhsNested>::type m_lhs;
+ typename internal::add_const_on_value_type<RhsNested>::type m_rhs;
+
+ mutable PlainObject m_result;
+};
+
+namespace internal {
+
+// here we need to overload the nested rule for products
+// such that the nested type is a const reference to a plain matrix
+template<typename Lhs, typename Rhs, int N, typename PlainObject>
+struct nested<CoeffBasedProduct<Lhs,Rhs,EvalBeforeNestingBit|EvalBeforeAssigningBit>, N, PlainObject>
+{
+ typedef PlainObject const& type;
+};
+
+/***************************************************************************
+* Normal product .coeff() implementation (with meta-unrolling)
+***************************************************************************/
+
+/**************************************
+*** Scalar path - no vectorization ***
+**************************************/
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+ {
+ product_coeff_impl<DefaultTraversal, UnrollingIndex-1, Lhs, Rhs, RetScalar>::run(row, col, lhs, rhs, res);
+ res += lhs.coeff(row, UnrollingIndex-1) * rhs.coeff(UnrollingIndex-1, col);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, 1, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+ {
+ res = lhs.coeff(row, 0) * rhs.coeff(0, col);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+ {
+ res = RetScalar(0);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, Dynamic, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar& res)
+ {
+ res = (lhs.row(row).transpose().cwiseProduct( rhs.col(col) )).sum();
+ }
+};
+
+/*******************************************
+*** Scalar path with inner vectorization ***
+*******************************************/
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet>
+struct product_coeff_vectorized_unroller
+{
+ typedef typename Lhs::Index Index;
+ enum { PacketSize = packet_traits<typename Lhs::Scalar>::size };
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, typename Lhs::PacketScalar &pres)
+ {
+ product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
+ pres = padd(pres, pmul( lhs.template packet<Aligned>(row, UnrollingIndex) , rhs.template packet<Aligned>(UnrollingIndex, col) ));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet>
+struct product_coeff_vectorized_unroller<0, Lhs, Rhs, Packet>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, typename Lhs::PacketScalar &pres)
+ {
+ pres = pmul(lhs.template packet<Aligned>(row, 0) , rhs.template packet<Aligned>(0, col));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<InnerVectorizedTraversal, 0, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+ {
+ res = 0;
+ }
+};
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::PacketScalar Packet;
+ typedef typename Lhs::Index Index;
+ enum { PacketSize = packet_traits<typename Lhs::Scalar>::size };
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+ {
+ Packet pres;
+ product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
+ res = predux(pres);
+ }
+};
+
+template<typename Lhs, typename Rhs, int LhsRows = Lhs::RowsAtCompileTime, int RhsCols = Rhs::ColsAtCompileTime>
+struct product_coeff_vectorized_dyn_selector
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+ {
+ res = lhs.row(row).transpose().cwiseProduct(rhs.col(col)).sum();
+ }
+};
+
+// NOTE the 3 following specializations are because taking .col(0) on a vector is a bit slower
+// NOTE maybe they are now useless since we have a specialization for Block<Matrix>
+template<typename Lhs, typename Rhs, int RhsCols>
+struct product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,RhsCols>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+ {
+ res = lhs.transpose().cwiseProduct(rhs.col(col)).sum();
+ }
+};
+
+template<typename Lhs, typename Rhs, int LhsRows>
+struct product_coeff_vectorized_dyn_selector<Lhs,Rhs,LhsRows,1>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index /*col*/, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+ {
+ res = lhs.row(row).transpose().cwiseProduct(rhs).sum();
+ }
+};
+
+template<typename Lhs, typename Rhs>
+struct product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,1>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+ {
+ res = lhs.transpose().cwiseProduct(rhs).sum();
+ }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<InnerVectorizedTraversal, Dynamic, Lhs, Rhs, RetScalar>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+ {
+ product_coeff_vectorized_dyn_selector<Lhs,Rhs>::run(row, col, lhs, rhs, res);
+ }
+};
+
+/*******************
+*** Packet path ***
+*******************/
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
+ {
+ product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
+ res = pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex-1)), rhs.template packet<LoadMode>(UnrollingIndex-1, col), res);
+ }
+};
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
+ {
+ product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
+ res = pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex-1), pset1<Packet>(rhs.coeff(UnrollingIndex-1, col)), res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
+ {
+ res = pmul(pset1<Packet>(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
+ {
+ res = pmul(lhs.template packet<LoadMode>(row, 0), pset1<Packet>(rhs.coeff(0, col)));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+ {
+ res = pset1<Packet>(0);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+ {
+ res = pset1<Packet>(0);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
+ {
+ res = pset1<Packet>(0);
+ for(Index i = 0; i < lhs.cols(); ++i)
+ res = pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
+{
+ typedef typename Lhs::Index Index;
+ static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
+ {
+ res = pset1<Packet>(0);
+ for(Index i = 0; i < lhs.cols(); ++i)
+ res = pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COEFFBASED_PRODUCT_H
diff --git a/Eigen/src/Core/products/GeneralBlockPanelKernel.h b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
new file mode 100644
index 0000000..bcdca5b
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
@@ -0,0 +1,1341 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_BLOCK_PANEL_H
+#define EIGEN_GENERAL_BLOCK_PANEL_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false>
+class gebp_traits;
+
+
+/** \internal \returns b if a<=0, and returns a otherwise. */
+inline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a, std::ptrdiff_t b)
+{
+ return a<=0 ? b : a;
+}
+
+/** \internal */
+inline void manage_caching_sizes(Action action, std::ptrdiff_t* l1=0, std::ptrdiff_t* l2=0)
+{
+ static std::ptrdiff_t m_l1CacheSize = 0;
+ static std::ptrdiff_t m_l2CacheSize = 0;
+ if(m_l2CacheSize==0)
+ {
+ m_l1CacheSize = manage_caching_sizes_helper(queryL1CacheSize(),8 * 1024);
+ m_l2CacheSize = manage_caching_sizes_helper(queryTopLevelCacheSize(),1*1024*1024);
+ }
+
+ if(action==SetAction)
+ {
+ // set the cpu cache size and cache all block sizes from a global cache size in byte
+ eigen_internal_assert(l1!=0 && l2!=0);
+ m_l1CacheSize = *l1;
+ m_l2CacheSize = *l2;
+ }
+ else if(action==GetAction)
+ {
+ eigen_internal_assert(l1!=0 && l2!=0);
+ *l1 = m_l1CacheSize;
+ *l2 = m_l2CacheSize;
+ }
+ else
+ {
+ eigen_internal_assert(false);
+ }
+}
+
+/** \brief Computes the blocking parameters for a m x k times k x n matrix product
+ *
+ * \param[in,out] k Input: the third dimension of the product. Output: the blocking size along the same dimension.
+ * \param[in,out] m Input: the number of rows of the left hand side. Output: the blocking size along the same dimension.
+ * \param[in,out] n Input: the number of columns of the right hand side. Output: the blocking size along the same dimension.
+ *
+ * Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
+ * this function computes the blocking size parameters along the respective dimensions
+ * for matrix products and related algorithms. The blocking sizes depends on various
+ * parameters:
+ * - the L1 and L2 cache sizes,
+ * - the register level blocking sizes defined by gebp_traits,
+ * - the number of scalars that fit into a packet (when vectorization is enabled).
+ *
+ * \sa setCpuCacheSizes */
+template<typename LhsScalar, typename RhsScalar, int KcFactor, typename SizeType>
+void computeProductBlockingSizes(SizeType& k, SizeType& m, SizeType& n)
+{
+ EIGEN_UNUSED_VARIABLE(n);
+ // Explanations:
+ // Let's recall the product algorithms form kc x nc horizontal panels B' on the rhs and
+ // mc x kc blocks A' on the lhs. A' has to fit into L2 cache. Moreover, B' is processed
+ // per kc x nr vertical small panels where nr is the blocking size along the n dimension
+ // at the register level. For vectorization purpose, these small vertical panels are unpacked,
+ // e.g., each coefficient is replicated to fit a packet. This small vertical panel has to
+ // stay in L1 cache.
+ std::ptrdiff_t l1, l2;
+
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+ enum {
+ kdiv = KcFactor * 2 * Traits::nr
+ * Traits::RhsProgress * sizeof(RhsScalar),
+ mr = gebp_traits<LhsScalar,RhsScalar>::mr,
+ mr_mask = (0xffffffff/mr)*mr
+ };
+
+ manage_caching_sizes(GetAction, &l1, &l2);
+ k = std::min<SizeType>(k, l1/kdiv);
+ SizeType _m = k>0 ? l2/(4 * sizeof(LhsScalar) * k) : 0;
+ if(_m<m) m = _m & mr_mask;
+}
+
+template<typename LhsScalar, typename RhsScalar, typename SizeType>
+inline void computeProductBlockingSizes(SizeType& k, SizeType& m, SizeType& n)
+{
+ computeProductBlockingSizes<LhsScalar,RhsScalar,1>(k, m, n);
+}
+
+#ifdef EIGEN_HAS_FUSE_CJMADD
+ #define MADD(CJ,A,B,C,T) C = CJ.pmadd(A,B,C);
+#else
+
+ // FIXME (a bit overkill maybe ?)
+
+ template<typename CJ, typename A, typename B, typename C, typename T> struct gebp_madd_selector {
+ EIGEN_ALWAYS_INLINE static void run(const CJ& cj, A& a, B& b, C& c, T& /*t*/)
+ {
+ c = cj.pmadd(a,b,c);
+ }
+ };
+
+ template<typename CJ, typename T> struct gebp_madd_selector<CJ,T,T,T,T> {
+ EIGEN_ALWAYS_INLINE static void run(const CJ& cj, T& a, T& b, T& c, T& t)
+ {
+ t = b; t = cj.pmul(a,t); c = padd(c,t);
+ }
+ };
+
+ template<typename CJ, typename A, typename B, typename C, typename T>
+ EIGEN_STRONG_INLINE void gebp_madd(const CJ& cj, A& a, B& b, C& c, T& t)
+ {
+ gebp_madd_selector<CJ,A,B,C,T>::run(cj,a,b,c,t);
+ }
+
+ #define MADD(CJ,A,B,C,T) gebp_madd(CJ,A,B,C,T);
+// #define MADD(CJ,A,B,C,T) T = B; T = CJ.pmul(A,T); C = padd(C,T);
+#endif
+
+/* Vectorization logic
+ * real*real: unpack rhs to constant packets, ...
+ *
+ * cd*cd : unpack rhs to (b_r,b_r), (b_i,b_i), mul to get (a_r b_r,a_i b_r) (a_r b_i,a_i b_i),
+ * storing each res packet into two packets (2x2),
+ * at the end combine them: swap the second and addsub them
+ * cf*cf : same but with 2x4 blocks
+ * cplx*real : unpack rhs to constant packets, ...
+ * real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual
+ */
+template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs>
+class gebp_traits
+{
+public:
+ typedef _LhsScalar LhsScalar;
+ typedef _RhsScalar RhsScalar;
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ enum {
+ ConjLhs = _ConjLhs,
+ ConjRhs = _ConjRhs,
+ Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
+ LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
+ RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+
+ // register block size along the N direction (must be either 2 or 4)
+ nr = NumberOfRegisters/4,
+
+ // register block size along the M direction (currently, this one cannot be modified)
+ mr = 2 * LhsPacketSize,
+
+ WorkSpaceFactor = nr * RhsPacketSize,
+
+ LhsProgress = LhsPacketSize,
+ RhsProgress = RhsPacketSize
+ };
+
+ typedef typename packet_traits<LhsScalar>::type _LhsPacket;
+ typedef typename packet_traits<RhsScalar>::type _RhsPacket;
+ typedef typename packet_traits<ResScalar>::type _ResPacket;
+
+ typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
+ typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
+ typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
+
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
+ {
+ for(DenseIndex k=0; k<n; k++)
+ pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = pload<RhsPacket>(b);
+ }
+
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = pload<LhsPacket>(a);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, AccPacket& tmp) const
+ {
+ tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);
+ }
+
+ EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ r = pmadd(c,alpha,r);
+ }
+
+protected:
+// conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
+// conj_helper<LhsPacket,RhsPacket,ConjLhs,ConjRhs> pcj;
+};
+
+template<typename RealScalar, bool _ConjLhs>
+class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false>
+{
+public:
+ typedef std::complex<RealScalar> LhsScalar;
+ typedef RealScalar RhsScalar;
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ enum {
+ ConjLhs = _ConjLhs,
+ ConjRhs = false,
+ Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
+ LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
+ RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ nr = NumberOfRegisters/4,
+ mr = 2 * LhsPacketSize,
+ WorkSpaceFactor = nr*RhsPacketSize,
+
+ LhsProgress = LhsPacketSize,
+ RhsProgress = RhsPacketSize
+ };
+
+ typedef typename packet_traits<LhsScalar>::type _LhsPacket;
+ typedef typename packet_traits<RhsScalar>::type _RhsPacket;
+ typedef typename packet_traits<ResScalar>::type _ResPacket;
+
+ typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
+ typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
+ typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
+
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
+ {
+ for(DenseIndex k=0; k<n; k++)
+ pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = pload<RhsPacket>(b);
+ }
+
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = pload<LhsPacket>(a);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
+ {
+ madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
+ {
+ tmp = b; tmp = pmul(a.v,tmp); c.v = padd(c.v,tmp);
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
+ {
+ c += a * b;
+ }
+
+ EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ r = cj.pmadd(c,alpha,r);
+ }
+
+protected:
+ conj_helper<ResPacket,ResPacket,ConjLhs,false> cj;
+};
+
+template<typename RealScalar, bool _ConjLhs, bool _ConjRhs>
+class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs >
+{
+public:
+ typedef std::complex<RealScalar> Scalar;
+ typedef std::complex<RealScalar> LhsScalar;
+ typedef std::complex<RealScalar> RhsScalar;
+ typedef std::complex<RealScalar> ResScalar;
+
+ enum {
+ ConjLhs = _ConjLhs,
+ ConjRhs = _ConjRhs,
+ Vectorizable = packet_traits<RealScalar>::Vectorizable
+ && packet_traits<Scalar>::Vectorizable,
+ RealPacketSize = Vectorizable ? packet_traits<RealScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+
+ nr = 2,
+ mr = 2 * ResPacketSize,
+ WorkSpaceFactor = Vectorizable ? 2*nr*RealPacketSize : nr,
+
+ LhsProgress = ResPacketSize,
+ RhsProgress = Vectorizable ? 2*ResPacketSize : 1
+ };
+
+ typedef typename packet_traits<RealScalar>::type RealPacket;
+ typedef typename packet_traits<Scalar>::type ScalarPacket;
+ struct DoublePacket
+ {
+ RealPacket first;
+ RealPacket second;
+ };
+
+ typedef typename conditional<Vectorizable,RealPacket, Scalar>::type LhsPacket;
+ typedef typename conditional<Vectorizable,DoublePacket,Scalar>::type RhsPacket;
+ typedef typename conditional<Vectorizable,ScalarPacket,Scalar>::type ResPacket;
+ typedef typename conditional<Vectorizable,DoublePacket,Scalar>::type AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(Scalar& p) { p = Scalar(0); }
+
+ EIGEN_STRONG_INLINE void initAcc(DoublePacket& p)
+ {
+ p.first = pset1<RealPacket>(RealScalar(0));
+ p.second = pset1<RealPacket>(RealScalar(0));
+ }
+
+ /* Unpack the rhs coeff such that each complex coefficient is spread into
+ * two packects containing respectively the real and imaginary coefficient
+ * duplicated as many time as needed: (x+iy) => [x, ..., x] [y, ..., y]
+ */
+ EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const Scalar* rhs, Scalar* b)
+ {
+ for(DenseIndex k=0; k<n; k++)
+ {
+ if(Vectorizable)
+ {
+ pstore1<RealPacket>((RealScalar*)&b[k*ResPacketSize*2+0], real(rhs[k]));
+ pstore1<RealPacket>((RealScalar*)&b[k*ResPacketSize*2+ResPacketSize], imag(rhs[k]));
+ }
+ else
+ b[k] = rhs[k];
+ }
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, ResPacket& dest) const { dest = *b; }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, DoublePacket& dest) const
+ {
+ dest.first = pload<RealPacket>((const RealScalar*)b);
+ dest.second = pload<RealPacket>((const RealScalar*)(b+ResPacketSize));
+ }
+
+ // nothing special here
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = pload<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, DoublePacket& c, RhsPacket& /*tmp*/) const
+ {
+ c.first = padd(pmul(a,b.first), c.first);
+ c.second = padd(pmul(a,b.second),c.second);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, ResPacket& c, RhsPacket& /*tmp*/) const
+ {
+ c = cj.pmadd(a,b,c);
+ }
+
+ EIGEN_STRONG_INLINE void acc(const Scalar& c, const Scalar& alpha, Scalar& r) const { r += alpha * c; }
+
+ EIGEN_STRONG_INLINE void acc(const DoublePacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ // assemble c
+ ResPacket tmp;
+ if((!ConjLhs)&&(!ConjRhs))
+ {
+ tmp = pcplxflip(pconj(ResPacket(c.second)));
+ tmp = padd(ResPacket(c.first),tmp);
+ }
+ else if((!ConjLhs)&&(ConjRhs))
+ {
+ tmp = pconj(pcplxflip(ResPacket(c.second)));
+ tmp = padd(ResPacket(c.first),tmp);
+ }
+ else if((ConjLhs)&&(!ConjRhs))
+ {
+ tmp = pcplxflip(ResPacket(c.second));
+ tmp = padd(pconj(ResPacket(c.first)),tmp);
+ }
+ else if((ConjLhs)&&(ConjRhs))
+ {
+ tmp = pcplxflip(ResPacket(c.second));
+ tmp = psub(pconj(ResPacket(c.first)),tmp);
+ }
+
+ r = pmadd(tmp,alpha,r);
+ }
+
+protected:
+ conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
+};
+
+template<typename RealScalar, bool _ConjRhs>
+class gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs >
+{
+public:
+ typedef std::complex<RealScalar> Scalar;
+ typedef RealScalar LhsScalar;
+ typedef Scalar RhsScalar;
+ typedef Scalar ResScalar;
+
+ enum {
+ ConjLhs = false,
+ ConjRhs = _ConjRhs,
+ Vectorizable = packet_traits<RealScalar>::Vectorizable
+ && packet_traits<Scalar>::Vectorizable,
+ LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
+ RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ nr = 4,
+ mr = 2*ResPacketSize,
+ WorkSpaceFactor = nr*RhsPacketSize,
+
+ LhsProgress = ResPacketSize,
+ RhsProgress = ResPacketSize
+ };
+
+ typedef typename packet_traits<LhsScalar>::type _LhsPacket;
+ typedef typename packet_traits<RhsScalar>::type _RhsPacket;
+ typedef typename packet_traits<ResScalar>::type _ResPacket;
+
+ typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
+ typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
+ typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
+
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
+ {
+ for(DenseIndex k=0; k<n; k++)
+ pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = pload<RhsPacket>(b);
+ }
+
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = ploaddup<LhsPacket>(a);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
+ {
+ madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
+ {
+ tmp = b; tmp.v = pmul(a,tmp.v); c = padd(c,tmp);
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
+ {
+ c += a * b;
+ }
+
+ EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ r = cj.pmadd(alpha,c,r);
+ }
+
+protected:
+ conj_helper<ResPacket,ResPacket,false,ConjRhs> cj;
+};
+
+/* optimized GEneral packed Block * packed Panel product kernel
+ *
+ * Mixing type logic: C += A * B
+ * | A | B | comments
+ * |real |cplx | no vectorization yet, would require to pack A with duplication
+ * |cplx |real | easy vectorization
+ */
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel
+{
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
+ typedef typename Traits::ResScalar ResScalar;
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+ typedef typename Traits::AccPacket AccPacket;
+
+ enum {
+ Vectorizable = Traits::Vectorizable,
+ LhsProgress = Traits::LhsProgress,
+ RhsProgress = Traits::RhsProgress,
+ ResPacketSize = Traits::ResPacketSize
+ };
+
+ EIGEN_DONT_INLINE
+ void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index rows, Index depth, Index cols, ResScalar alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0, RhsScalar* unpackedB=0);
+};
+
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_DONT_INLINE
+void gebp_kernel<LhsScalar,RhsScalar,Index,mr,nr,ConjugateLhs,ConjugateRhs>
+ ::operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index rows, Index depth, Index cols, ResScalar alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB, RhsScalar* unpackedB)
+ {
+ Traits traits;
+
+ if(strideA==-1) strideA = depth;
+ if(strideB==-1) strideB = depth;
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+// conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
+ Index packet_cols = (cols/nr) * nr;
+ const Index peeled_mc = (rows/mr)*mr;
+ // FIXME:
+ const Index peeled_mc2 = peeled_mc + (rows-peeled_mc >= LhsProgress ? LhsProgress : 0);
+ const Index peeled_kc = (depth/4)*4;
+
+ if(unpackedB==0)
+ unpackedB = const_cast<RhsScalar*>(blockB - strideB * nr * RhsProgress);
+
+ // loops on each micro vertical panel of rhs (depth x nr)
+ for(Index j2=0; j2<packet_cols; j2+=nr)
+ {
+ traits.unpackRhs(depth*nr,&blockB[j2*strideB+offsetB*nr],unpackedB);
+
+ // loops on each largest micro horizontal panel of lhs (mr x depth)
+ // => we select a mr x nr micro block of res which is entirely
+ // stored into mr/packet_size x nr registers.
+ for(Index i=0; i<peeled_mc; i+=mr)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*mr];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3, C4, C5, C6, C7;
+ traits.initAcc(C0);
+ traits.initAcc(C1);
+ if(nr==4) traits.initAcc(C2);
+ if(nr==4) traits.initAcc(C3);
+ traits.initAcc(C4);
+ traits.initAcc(C5);
+ if(nr==4) traits.initAcc(C6);
+ if(nr==4) traits.initAcc(C7);
+
+ ResScalar* r0 = &res[(j2+0)*resStride + i];
+ ResScalar* r1 = r0 + resStride;
+ ResScalar* r2 = r1 + resStride;
+ ResScalar* r3 = r2 + resStride;
+
+ prefetch(r0+16);
+ prefetch(r1+16);
+ prefetch(r2+16);
+ prefetch(r3+16);
+
+ // performs "inner" product
+ // TODO let's check wether the folowing peeled loop could not be
+ // optimized via optimal prefetching from one loop to the other
+ const RhsScalar* blB = unpackedB;
+ for(Index k=0; k<peeled_kc; k+=4)
+ {
+ if(nr==2)
+ {
+ LhsPacket A0, A1;
+ RhsPacket B_0;
+ RhsPacket T0;
+
+EIGEN_ASM_COMMENT("mybegin2");
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadLhs(&blA[1*LhsProgress], A1);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B_0);
+ traits.madd(A0,B_0,C1,T0);
+ traits.madd(A1,B_0,C5,B_0);
+
+ traits.loadLhs(&blA[2*LhsProgress], A0);
+ traits.loadLhs(&blA[3*LhsProgress], A1);
+ traits.loadRhs(&blB[2*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[3*RhsProgress], B_0);
+ traits.madd(A0,B_0,C1,T0);
+ traits.madd(A1,B_0,C5,B_0);
+
+ traits.loadLhs(&blA[4*LhsProgress], A0);
+ traits.loadLhs(&blA[5*LhsProgress], A1);
+ traits.loadRhs(&blB[4*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[5*RhsProgress], B_0);
+ traits.madd(A0,B_0,C1,T0);
+ traits.madd(A1,B_0,C5,B_0);
+
+ traits.loadLhs(&blA[6*LhsProgress], A0);
+ traits.loadLhs(&blA[7*LhsProgress], A1);
+ traits.loadRhs(&blB[6*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[7*RhsProgress], B_0);
+ traits.madd(A0,B_0,C1,T0);
+ traits.madd(A1,B_0,C5,B_0);
+EIGEN_ASM_COMMENT("myend");
+ }
+ else
+ {
+EIGEN_ASM_COMMENT("mybegin4");
+ LhsPacket A0, A1;
+ RhsPacket B_0, B1, B2, B3;
+ RhsPacket T0;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadLhs(&blA[1*LhsProgress], A1);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+
+ traits.madd(A0,B_0,C0,T0);
+ traits.loadRhs(&blB[2*RhsProgress], B2);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[3*RhsProgress], B3);
+ traits.loadRhs(&blB[4*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,T0);
+ traits.madd(A1,B1,C5,B1);
+ traits.loadRhs(&blB[5*RhsProgress], B1);
+ traits.madd(A0,B2,C2,T0);
+ traits.madd(A1,B2,C6,B2);
+ traits.loadRhs(&blB[6*RhsProgress], B2);
+ traits.madd(A0,B3,C3,T0);
+ traits.loadLhs(&blA[2*LhsProgress], A0);
+ traits.madd(A1,B3,C7,B3);
+ traits.loadLhs(&blA[3*LhsProgress], A1);
+ traits.loadRhs(&blB[7*RhsProgress], B3);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[8*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,T0);
+ traits.madd(A1,B1,C5,B1);
+ traits.loadRhs(&blB[9*RhsProgress], B1);
+ traits.madd(A0,B2,C2,T0);
+ traits.madd(A1,B2,C6,B2);
+ traits.loadRhs(&blB[10*RhsProgress], B2);
+ traits.madd(A0,B3,C3,T0);
+ traits.loadLhs(&blA[4*LhsProgress], A0);
+ traits.madd(A1,B3,C7,B3);
+ traits.loadLhs(&blA[5*LhsProgress], A1);
+ traits.loadRhs(&blB[11*RhsProgress], B3);
+
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[12*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,T0);
+ traits.madd(A1,B1,C5,B1);
+ traits.loadRhs(&blB[13*RhsProgress], B1);
+ traits.madd(A0,B2,C2,T0);
+ traits.madd(A1,B2,C6,B2);
+ traits.loadRhs(&blB[14*RhsProgress], B2);
+ traits.madd(A0,B3,C3,T0);
+ traits.loadLhs(&blA[6*LhsProgress], A0);
+ traits.madd(A1,B3,C7,B3);
+ traits.loadLhs(&blA[7*LhsProgress], A1);
+ traits.loadRhs(&blB[15*RhsProgress], B3);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.madd(A0,B1,C1,T0);
+ traits.madd(A1,B1,C5,B1);
+ traits.madd(A0,B2,C2,T0);
+ traits.madd(A1,B2,C6,B2);
+ traits.madd(A0,B3,C3,T0);
+ traits.madd(A1,B3,C7,B3);
+ }
+
+ blB += 4*nr*RhsProgress;
+ blA += 4*mr;
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ if(nr==2)
+ {
+ LhsPacket A0, A1;
+ RhsPacket B_0;
+ RhsPacket T0;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadLhs(&blA[1*LhsProgress], A1);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B_0);
+ traits.madd(A0,B_0,C1,T0);
+ traits.madd(A1,B_0,C5,B_0);
+ }
+ else
+ {
+ LhsPacket A0, A1;
+ RhsPacket B_0, B1, B2, B3;
+ RhsPacket T0;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadLhs(&blA[1*LhsProgress], A1);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+
+ traits.madd(A0,B_0,C0,T0);
+ traits.loadRhs(&blB[2*RhsProgress], B2);
+ traits.madd(A1,B_0,C4,B_0);
+ traits.loadRhs(&blB[3*RhsProgress], B3);
+ traits.madd(A0,B1,C1,T0);
+ traits.madd(A1,B1,C5,B1);
+ traits.madd(A0,B2,C2,T0);
+ traits.madd(A1,B2,C6,B2);
+ traits.madd(A0,B3,C3,T0);
+ traits.madd(A1,B3,C7,B3);
+ }
+
+ blB += nr*RhsProgress;
+ blA += mr;
+ }
+
+ if(nr==4)
+ {
+ ResPacket R0, R1, R2, R3, R4, R5, R6;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = ploadu<ResPacket>(r0);
+ R1 = ploadu<ResPacket>(r1);
+ R2 = ploadu<ResPacket>(r2);
+ R3 = ploadu<ResPacket>(r3);
+ R4 = ploadu<ResPacket>(r0 + ResPacketSize);
+ R5 = ploadu<ResPacket>(r1 + ResPacketSize);
+ R6 = ploadu<ResPacket>(r2 + ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ pstoreu(r0, R0);
+ R0 = ploadu<ResPacket>(r3 + ResPacketSize);
+
+ traits.acc(C1, alphav, R1);
+ traits.acc(C2, alphav, R2);
+ traits.acc(C3, alphav, R3);
+ traits.acc(C4, alphav, R4);
+ traits.acc(C5, alphav, R5);
+ traits.acc(C6, alphav, R6);
+ traits.acc(C7, alphav, R0);
+
+ pstoreu(r1, R1);
+ pstoreu(r2, R2);
+ pstoreu(r3, R3);
+ pstoreu(r0 + ResPacketSize, R4);
+ pstoreu(r1 + ResPacketSize, R5);
+ pstoreu(r2 + ResPacketSize, R6);
+ pstoreu(r3 + ResPacketSize, R0);
+ }
+ else
+ {
+ ResPacket R0, R1, R4;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = ploadu<ResPacket>(r0);
+ R1 = ploadu<ResPacket>(r1);
+ R4 = ploadu<ResPacket>(r0 + ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ pstoreu(r0, R0);
+ R0 = ploadu<ResPacket>(r1 + ResPacketSize);
+ traits.acc(C1, alphav, R1);
+ traits.acc(C4, alphav, R4);
+ traits.acc(C5, alphav, R0);
+ pstoreu(r1, R1);
+ pstoreu(r0 + ResPacketSize, R4);
+ pstoreu(r1 + ResPacketSize, R0);
+ }
+
+ }
+
+ if(rows-peeled_mc>=LhsProgress)
+ {
+ Index i = peeled_mc;
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*LhsProgress];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3;
+ traits.initAcc(C0);
+ traits.initAcc(C1);
+ if(nr==4) traits.initAcc(C2);
+ if(nr==4) traits.initAcc(C3);
+
+ // performs "inner" product
+ const RhsScalar* blB = unpackedB;
+ for(Index k=0; k<peeled_kc; k+=4)
+ {
+ if(nr==2)
+ {
+ LhsPacket A0;
+ RhsPacket B_0, B1;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[2*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadLhs(&blA[1*LhsProgress], A0);
+ traits.loadRhs(&blB[3*RhsProgress], B1);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[4*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadLhs(&blA[2*LhsProgress], A0);
+ traits.loadRhs(&blB[5*RhsProgress], B1);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[6*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadLhs(&blA[3*LhsProgress], A0);
+ traits.loadRhs(&blB[7*RhsProgress], B1);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.madd(A0,B1,C1,B1);
+ }
+ else
+ {
+ LhsPacket A0;
+ RhsPacket B_0, B1, B2, B3;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[2*RhsProgress], B2);
+ traits.loadRhs(&blB[3*RhsProgress], B3);
+ traits.loadRhs(&blB[4*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadRhs(&blB[5*RhsProgress], B1);
+ traits.madd(A0,B2,C2,B2);
+ traits.loadRhs(&blB[6*RhsProgress], B2);
+ traits.madd(A0,B3,C3,B3);
+ traits.loadLhs(&blA[1*LhsProgress], A0);
+ traits.loadRhs(&blB[7*RhsProgress], B3);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[8*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadRhs(&blB[9*RhsProgress], B1);
+ traits.madd(A0,B2,C2,B2);
+ traits.loadRhs(&blB[10*RhsProgress], B2);
+ traits.madd(A0,B3,C3,B3);
+ traits.loadLhs(&blA[2*LhsProgress], A0);
+ traits.loadRhs(&blB[11*RhsProgress], B3);
+
+ traits.madd(A0,B_0,C0,B_0);
+ traits.loadRhs(&blB[12*RhsProgress], B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.loadRhs(&blB[13*RhsProgress], B1);
+ traits.madd(A0,B2,C2,B2);
+ traits.loadRhs(&blB[14*RhsProgress], B2);
+ traits.madd(A0,B3,C3,B3);
+
+ traits.loadLhs(&blA[3*LhsProgress], A0);
+ traits.loadRhs(&blB[15*RhsProgress], B3);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.madd(A0,B2,C2,B2);
+ traits.madd(A0,B3,C3,B3);
+ }
+
+ blB += nr*4*RhsProgress;
+ blA += 4*LhsProgress;
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ if(nr==2)
+ {
+ LhsPacket A0;
+ RhsPacket B_0, B1;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+ traits.madd(A0,B_0,C0,B_0);
+ traits.madd(A0,B1,C1,B1);
+ }
+ else
+ {
+ LhsPacket A0;
+ RhsPacket B_0, B1, B2, B3;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.loadRhs(&blB[1*RhsProgress], B1);
+ traits.loadRhs(&blB[2*RhsProgress], B2);
+ traits.loadRhs(&blB[3*RhsProgress], B3);
+
+ traits.madd(A0,B_0,C0,B_0);
+ traits.madd(A0,B1,C1,B1);
+ traits.madd(A0,B2,C2,B2);
+ traits.madd(A0,B3,C3,B3);
+ }
+
+ blB += nr*RhsProgress;
+ blA += LhsProgress;
+ }
+
+ ResPacket R0, R1, R2, R3;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ ResScalar* r0 = &res[(j2+0)*resStride + i];
+ ResScalar* r1 = r0 + resStride;
+ ResScalar* r2 = r1 + resStride;
+ ResScalar* r3 = r2 + resStride;
+
+ R0 = ploadu<ResPacket>(r0);
+ R1 = ploadu<ResPacket>(r1);
+ if(nr==4) R2 = ploadu<ResPacket>(r2);
+ if(nr==4) R3 = ploadu<ResPacket>(r3);
+
+ traits.acc(C0, alphav, R0);
+ traits.acc(C1, alphav, R1);
+ if(nr==4) traits.acc(C2, alphav, R2);
+ if(nr==4) traits.acc(C3, alphav, R3);
+
+ pstoreu(r0, R0);
+ pstoreu(r1, R1);
+ if(nr==4) pstoreu(r2, R2);
+ if(nr==4) pstoreu(r3, R3);
+ }
+ for(Index i=peeled_mc2; i<rows; i++)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA];
+ prefetch(&blA[0]);
+
+ // gets a 1 x nr res block as registers
+ ResScalar C0(0), C1(0), C2(0), C3(0);
+ // TODO directly use blockB ???
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
+ for(Index k=0; k<depth; k++)
+ {
+ if(nr==2)
+ {
+ LhsScalar A0;
+ RhsScalar B_0, B1;
+
+ A0 = blA[k];
+ B_0 = blB[0];
+ B1 = blB[1];
+ MADD(cj,A0,B_0,C0,B_0);
+ MADD(cj,A0,B1,C1,B1);
+ }
+ else
+ {
+ LhsScalar A0;
+ RhsScalar B_0, B1, B2, B3;
+
+ A0 = blA[k];
+ B_0 = blB[0];
+ B1 = blB[1];
+ B2 = blB[2];
+ B3 = blB[3];
+
+ MADD(cj,A0,B_0,C0,B_0);
+ MADD(cj,A0,B1,C1,B1);
+ MADD(cj,A0,B2,C2,B2);
+ MADD(cj,A0,B3,C3,B3);
+ }
+
+ blB += nr;
+ }
+ res[(j2+0)*resStride + i] += alpha*C0;
+ res[(j2+1)*resStride + i] += alpha*C1;
+ if(nr==4) res[(j2+2)*resStride + i] += alpha*C2;
+ if(nr==4) res[(j2+3)*resStride + i] += alpha*C3;
+ }
+ }
+ // process remaining rhs/res columns one at a time
+ // => do the same but with nr==1
+ for(Index j2=packet_cols; j2<cols; j2++)
+ {
+ // unpack B
+ traits.unpackRhs(depth, &blockB[j2*strideB+offsetB], unpackedB);
+
+ for(Index i=0; i<peeled_mc; i+=mr)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*mr];
+ prefetch(&blA[0]);
+
+ // TODO move the res loads to the stores
+
+ // get res block as registers
+ AccPacket C0, C4;
+ traits.initAcc(C0);
+ traits.initAcc(C4);
+
+ const RhsScalar* blB = unpackedB;
+ for(Index k=0; k<depth; k++)
+ {
+ LhsPacket A0, A1;
+ RhsPacket B_0;
+ RhsPacket T0;
+
+ traits.loadLhs(&blA[0*LhsProgress], A0);
+ traits.loadLhs(&blA[1*LhsProgress], A1);
+ traits.loadRhs(&blB[0*RhsProgress], B_0);
+ traits.madd(A0,B_0,C0,T0);
+ traits.madd(A1,B_0,C4,B_0);
+
+ blB += RhsProgress;
+ blA += 2*LhsProgress;
+ }
+ ResPacket R0, R4;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ ResScalar* r0 = &res[(j2+0)*resStride + i];
+
+ R0 = ploadu<ResPacket>(r0);
+ R4 = ploadu<ResPacket>(r0+ResPacketSize);
+
+ traits.acc(C0, alphav, R0);
+ traits.acc(C4, alphav, R4);
+
+ pstoreu(r0, R0);
+ pstoreu(r0+ResPacketSize, R4);
+ }
+ if(rows-peeled_mc>=LhsProgress)
+ {
+ Index i = peeled_mc;
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*LhsProgress];
+ prefetch(&blA[0]);
+
+ AccPacket C0;
+ traits.initAcc(C0);
+
+ const RhsScalar* blB = unpackedB;
+ for(Index k=0; k<depth; k++)
+ {
+ LhsPacket A0;
+ RhsPacket B_0;
+ traits.loadLhs(blA, A0);
+ traits.loadRhs(blB, B_0);
+ traits.madd(A0, B_0, C0, B_0);
+ blB += RhsProgress;
+ blA += LhsProgress;
+ }
+
+ ResPacket alphav = pset1<ResPacket>(alpha);
+ ResPacket R0 = ploadu<ResPacket>(&res[(j2+0)*resStride + i]);
+ traits.acc(C0, alphav, R0);
+ pstoreu(&res[(j2+0)*resStride + i], R0);
+ }
+ for(Index i=peeled_mc2; i<rows; i++)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA];
+ prefetch(&blA[0]);
+
+ // gets a 1 x 1 res block as registers
+ ResScalar C0(0);
+ // FIXME directly use blockB ??
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+ for(Index k=0; k<depth; k++)
+ {
+ LhsScalar A0 = blA[k];
+ RhsScalar B_0 = blB[k];
+ MADD(cj, A0, B_0, C0, B_0);
+ }
+ res[(j2+0)*resStride + i] += alpha*C0;
+ }
+ }
+ }
+
+
+#undef CJMADD
+
+// pack a block of the lhs
+// The traversal is as follow (mr==4):
+// 0 4 8 12 ...
+// 1 5 9 13 ...
+// 2 6 10 14 ...
+// 3 7 11 15 ...
+//
+// 16 20 24 28 ...
+// 17 21 25 29 ...
+// 18 22 26 30 ...
+// 19 23 27 31 ...
+//
+// 32 33 34 35 ...
+// 36 36 38 39 ...
+template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs
+{
+ EIGEN_DONT_INLINE void operator()(Scalar* blockA, const Scalar* EIGEN_RESTRICT _lhs, Index lhsStride, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, Pack1, Pack2, StorageOrder, Conjugate, PanelMode>
+ ::operator()(Scalar* blockA, const Scalar* EIGEN_RESTRICT _lhs, Index lhsStride, Index depth, Index rows, Index stride, Index offset)
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ enum { PacketSize = packet_traits<Scalar>::size };
+
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
+ EIGEN_UNUSED_VARIABLE(stride)
+ EIGEN_UNUSED_VARIABLE(offset)
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ eigen_assert( (StorageOrder==RowMajor) || ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) );
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ const_blas_data_mapper<Scalar, Index, StorageOrder> lhs(_lhs,lhsStride);
+ Index count = 0;
+ Index peeled_mc = (rows/Pack1)*Pack1;
+ for(Index i=0; i<peeled_mc; i+=Pack1)
+ {
+ if(PanelMode) count += Pack1 * offset;
+
+ if(StorageOrder==ColMajor)
+ {
+ for(Index k=0; k<depth; k++)
+ {
+ Packet A, B, C, D;
+ if(Pack1>=1*PacketSize) A = ploadu<Packet>(&lhs(i+0*PacketSize, k));
+ if(Pack1>=2*PacketSize) B = ploadu<Packet>(&lhs(i+1*PacketSize, k));
+ if(Pack1>=3*PacketSize) C = ploadu<Packet>(&lhs(i+2*PacketSize, k));
+ if(Pack1>=4*PacketSize) D = ploadu<Packet>(&lhs(i+3*PacketSize, k));
+ if(Pack1>=1*PacketSize) { pstore(blockA+count, cj.pconj(A)); count+=PacketSize; }
+ if(Pack1>=2*PacketSize) { pstore(blockA+count, cj.pconj(B)); count+=PacketSize; }
+ if(Pack1>=3*PacketSize) { pstore(blockA+count, cj.pconj(C)); count+=PacketSize; }
+ if(Pack1>=4*PacketSize) { pstore(blockA+count, cj.pconj(D)); count+=PacketSize; }
+ }
+ }
+ else
+ {
+ for(Index k=0; k<depth; k++)
+ {
+ // TODO add a vectorized transpose here
+ Index w=0;
+ for(; w<Pack1-3; w+=4)
+ {
+ Scalar a(cj(lhs(i+w+0, k))),
+ b(cj(lhs(i+w+1, k))),
+ c(cj(lhs(i+w+2, k))),
+ d(cj(lhs(i+w+3, k)));
+ blockA[count++] = a;
+ blockA[count++] = b;
+ blockA[count++] = c;
+ blockA[count++] = d;
+ }
+ if(Pack1%4)
+ for(;w<Pack1;++w)
+ blockA[count++] = cj(lhs(i+w, k));
+ }
+ }
+ if(PanelMode) count += Pack1 * (stride-offset-depth);
+ }
+ if(rows-peeled_mc>=Pack2)
+ {
+ if(PanelMode) count += Pack2*offset;
+ for(Index k=0; k<depth; k++)
+ for(Index w=0; w<Pack2; w++)
+ blockA[count++] = cj(lhs(peeled_mc+w, k));
+ if(PanelMode) count += Pack2 * (stride-offset-depth);
+ peeled_mc += Pack2;
+ }
+ for(Index i=peeled_mc; i<rows; i++)
+ {
+ if(PanelMode) count += offset;
+ for(Index k=0; k<depth; k++)
+ blockA[count++] = cj(lhs(i, k));
+ if(PanelMode) count += (stride-offset-depth);
+ }
+}
+
+// copy a complete panel of the rhs
+// this version is optimized for column major matrices
+// The traversal order is as follow: (nr==4):
+// 0 1 2 3 12 13 14 15 24 27
+// 4 5 6 7 16 17 18 19 25 28
+// 8 9 10 11 20 21 22 23 26 29
+// . . . . . . . . . .
+template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, nr, ColMajor, Conjugate, PanelMode>
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ enum { PacketSize = packet_traits<Scalar>::size };
+ EIGEN_DONT_INLINE void operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
+{
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride)
+ EIGEN_UNUSED_VARIABLE(offset)
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols = (cols/nr) * nr;
+ Index count = 0;
+ for(Index j2=0; j2<packet_cols; j2+=nr)
+ {
+ // skip what we have before
+ if(PanelMode) count += nr * offset;
+ const Scalar* b0 = &rhs[(j2+0)*rhsStride];
+ const Scalar* b1 = &rhs[(j2+1)*rhsStride];
+ const Scalar* b2 = &rhs[(j2+2)*rhsStride];
+ const Scalar* b3 = &rhs[(j2+3)*rhsStride];
+ for(Index k=0; k<depth; k++)
+ {
+ blockB[count+0] = cj(b0[k]);
+ blockB[count+1] = cj(b1[k]);
+ if(nr==4) blockB[count+2] = cj(b2[k]);
+ if(nr==4) blockB[count+3] = cj(b3[k]);
+ count += nr;
+ }
+ // skip what we have after
+ if(PanelMode) count += nr * (stride-offset-depth);
+ }
+
+ // copy the remaining columns one at a time (nr==1)
+ for(Index j2=packet_cols; j2<cols; ++j2)
+ {
+ if(PanelMode) count += offset;
+ const Scalar* b0 = &rhs[(j2+0)*rhsStride];
+ for(Index k=0; k<depth; k++)
+ {
+ blockB[count] = cj(b0[k]);
+ count += 1;
+ }
+ if(PanelMode) count += (stride-offset-depth);
+ }
+}
+
+// this version is optimized for row major matrices
+template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, nr, RowMajor, Conjugate, PanelMode>
+{
+ enum { PacketSize = packet_traits<Scalar>::size };
+ EIGEN_DONT_INLINE void operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, RowMajor, Conjugate, PanelMode>
+ ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
+{
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride)
+ EIGEN_UNUSED_VARIABLE(offset)
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols = (cols/nr) * nr;
+ Index count = 0;
+ for(Index j2=0; j2<packet_cols; j2+=nr)
+ {
+ // skip what we have before
+ if(PanelMode) count += nr * offset;
+ for(Index k=0; k<depth; k++)
+ {
+ const Scalar* b0 = &rhs[k*rhsStride + j2];
+ blockB[count+0] = cj(b0[0]);
+ blockB[count+1] = cj(b0[1]);
+ if(nr==4) blockB[count+2] = cj(b0[2]);
+ if(nr==4) blockB[count+3] = cj(b0[3]);
+ count += nr;
+ }
+ // skip what we have after
+ if(PanelMode) count += nr * (stride-offset-depth);
+ }
+ // copy the remaining columns one at a time (nr==1)
+ for(Index j2=packet_cols; j2<cols; ++j2)
+ {
+ if(PanelMode) count += offset;
+ const Scalar* b0 = &rhs[j2];
+ for(Index k=0; k<depth; k++)
+ {
+ blockB[count] = cj(b0[k*rhsStride]);
+ count += 1;
+ }
+ if(PanelMode) count += stride-offset-depth;
+ }
+}
+
+} // end namespace internal
+
+/** \returns the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
+ * \sa setCpuCacheSize */
+inline std::ptrdiff_t l1CacheSize()
+{
+ std::ptrdiff_t l1, l2;
+ internal::manage_caching_sizes(GetAction, &l1, &l2);
+ return l1;
+}
+
+/** \returns the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
+ * \sa setCpuCacheSize */
+inline std::ptrdiff_t l2CacheSize()
+{
+ std::ptrdiff_t l1, l2;
+ internal::manage_caching_sizes(GetAction, &l1, &l2);
+ return l2;
+}
+
+/** Set the cpu L1 and L2 cache sizes (in bytes).
+ * These values are use to adjust the size of the blocks
+ * for the algorithms working per blocks.
+ *
+ * \sa computeProductBlockingSizes */
+inline void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2)
+{
+ internal::manage_caching_sizes(SetAction, &l1, &l2);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_BLOCK_PANEL_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix.h b/Eigen/src/Core/products/GeneralMatrixMatrix.h
new file mode 100644
index 0000000..3f5ffcf
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix.h
@@ -0,0 +1,427 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename _LhsScalar, typename _RhsScalar> class level3_blocking;
+
+/* Specialization for a row-major destination matrix => simple transposition of the product */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols, Index depth,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsStride,
+ ResScalar* res, Index resStride,
+ ResScalar alpha,
+ level3_blocking<RhsScalar,LhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+ {
+ // transpose the product such that the result is column major
+ general_matrix_matrix_product<Index,
+ RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
+ LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
+ ColMajor>
+ ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info);
+ }
+};
+
+/* Specialization for a col-major destination matrix
+ * => Blocking algorithm following Goto's paper */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor>
+{
+
+typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+static void run(Index rows, Index cols, Index depth,
+ const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsStride,
+ ResScalar* res, Index resStride,
+ ResScalar alpha,
+ level3_blocking<LhsScalar,RhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+{
+ const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ //Index nc = blocking.nc(); // cache block size along the N direction
+
+ gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
+ gebp_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
+
+#ifdef EIGEN_HAS_OPENMP
+ if(info)
+ {
+ // this is the parallel version!
+ Index tid = omp_get_thread_num();
+ Index threads = omp_get_num_threads();
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, 0);
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, w, sizeW, 0);
+
+ RhsScalar* blockB = blocking.blockB();
+ eigen_internal_assert(blockB!=0);
+
+ // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
+ for(Index k=0; k<depth; k+=kc)
+ {
+ const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
+
+ // In order to reduce the chance that a thread has to wait for the other,
+ // let's start by packing A'.
+ pack_lhs(blockA, &lhs(0,k), lhsStride, actual_kc, mc);
+
+ // Pack B_k to B' in a parallel fashion:
+ // each thread packs the sub block B_k,j to B'_j where j is the thread id.
+
+ // However, before copying to B'_j, we have to make sure that no other thread is still using it,
+ // i.e., we test that info[tid].users equals 0.
+ // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
+ while(info[tid].users!=0) {}
+ info[tid].users += threads;
+
+ pack_rhs(blockB+info[tid].rhs_start*actual_kc, &rhs(k,info[tid].rhs_start), rhsStride, actual_kc, info[tid].rhs_length);
+
+ // Notify the other threads that the part B'_j is ready to go.
+ info[tid].sync = k;
+
+ // Computes C_i += A' * B' per B'_j
+ for(Index shift=0; shift<threads; ++shift)
+ {
+ Index j = (tid+shift)%threads;
+
+ // At this point we have to make sure that B'_j has been updated by the thread j,
+ // we use testAndSetOrdered to mimic a volatile access.
+ // However, no need to wait for the B' part which has been updated by the current thread!
+ if(shift>0)
+ while(info[j].sync!=k) {}
+
+ gebp(res+info[j].rhs_start*resStride, resStride, blockA, blockB+info[j].rhs_start*actual_kc, mc, actual_kc, info[j].rhs_length, alpha, -1,-1,0,0, w);
+ }
+
+ // Then keep going as usual with the remaining A'
+ for(Index i=mc; i<rows; i+=mc)
+ {
+ const Index actual_mc = (std::min)(i+mc,rows)-i;
+
+ // pack A_i,k to A'
+ pack_lhs(blockA, &lhs(i,k), lhsStride, actual_kc, actual_mc);
+
+ // C_i += A' * B'
+ gebp(res+i, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1,-1,0,0, w);
+ }
+
+ // Release all the sub blocks B'_j of B' for the current thread,
+ // i.e., we simply decrement the number of users by 1
+ for(Index j=0; j<threads; ++j)
+ #pragma omp atomic
+ --(info[j].users);
+ }
+ }
+ else
+#endif // EIGEN_HAS_OPENMP
+ {
+ EIGEN_UNUSED_VARIABLE(info);
+
+ // this is the sequential version!
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockW, sizeW, blocking.blockW());
+
+ // For each horizontal panel of the rhs, and corresponding panel of the lhs...
+ // (==GEMM_VAR1)
+ for(Index k2=0; k2<depth; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,depth)-k2;
+
+ // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
+ // => Pack rhs's panel into a sequential chunk of memory (L2 caching)
+ // Note that this panel will be read as many times as the number of blocks in the lhs's
+ // vertical panel which is, in practice, a very low number.
+ pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
+
+ // For each mc x kc block of the lhs's vertical panel...
+ // (==GEPP_VAR1)
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,rows)-i2;
+
+ // We pack the lhs's block into a sequential chunk of memory (L1 caching)
+ // Note that this block will be read a very high number of times, which is equal to the number of
+ // micro vertical panel of the large rhs's panel (e.g., cols/4 times).
+ pack_lhs(blockA, &lhs(i2,k2), lhsStride, actual_kc, actual_mc);
+
+ // Everything is packed, we can now call the block * panel kernel:
+ gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
+ }
+ }
+ }
+}
+
+};
+
+/*********************************************************************************
+* Specialization of GeneralProduct<> for "large" GEMM, i.e.,
+* implementation of the high level wrapper to general_matrix_matrix_product
+**********************************************************************************/
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,GemmProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> >
+{};
+
+template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
+struct gemm_functor
+{
+ gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha,
+ BlockingType& blocking)
+ : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
+ {}
+
+ void initParallelSession() const
+ {
+ m_blocking.allocateB();
+ }
+
+ void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
+ {
+ if(cols==-1)
+ cols = m_rhs.cols();
+
+ Gemm::run(rows, cols, m_lhs.cols(),
+ /*(const Scalar*)*/&m_lhs.coeffRef(row,0), m_lhs.outerStride(),
+ /*(const Scalar*)*/&m_rhs.coeffRef(0,col), m_rhs.outerStride(),
+ (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(),
+ m_actualAlpha, m_blocking, info);
+ }
+
+ protected:
+ const Lhs& m_lhs;
+ const Rhs& m_rhs;
+ Dest& m_dest;
+ Scalar m_actualAlpha;
+ BlockingType& m_blocking;
+};
+
+template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
+bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
+
+template<typename _LhsScalar, typename _RhsScalar>
+class level3_blocking
+{
+ typedef _LhsScalar LhsScalar;
+ typedef _RhsScalar RhsScalar;
+
+ protected:
+ LhsScalar* m_blockA;
+ RhsScalar* m_blockB;
+ RhsScalar* m_blockW;
+
+ DenseIndex m_mc;
+ DenseIndex m_nc;
+ DenseIndex m_kc;
+
+ public:
+
+ level3_blocking()
+ : m_blockA(0), m_blockB(0), m_blockW(0), m_mc(0), m_nc(0), m_kc(0)
+ {}
+
+ inline DenseIndex mc() const { return m_mc; }
+ inline DenseIndex nc() const { return m_nc; }
+ inline DenseIndex kc() const { return m_kc; }
+
+ inline LhsScalar* blockA() { return m_blockA; }
+ inline RhsScalar* blockB() { return m_blockB; }
+ inline RhsScalar* blockW() { return m_blockW; }
+};
+
+template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true>
+ : public level3_blocking<
+ typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
+ typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor,
+ ActualRows = Transpose ? MaxCols : MaxRows,
+ ActualCols = Transpose ? MaxRows : MaxCols
+ };
+ typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
+ typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+ enum {
+ SizeA = ActualRows * MaxDepth,
+ SizeB = ActualCols * MaxDepth,
+ SizeW = MaxDepth * Traits::WorkSpaceFactor
+ };
+
+ EIGEN_ALIGN16 LhsScalar m_staticA[SizeA];
+ EIGEN_ALIGN16 RhsScalar m_staticB[SizeB];
+ EIGEN_ALIGN16 RhsScalar m_staticW[SizeW];
+
+ public:
+
+ gemm_blocking_space(DenseIndex /*rows*/, DenseIndex /*cols*/, DenseIndex /*depth*/)
+ {
+ this->m_mc = ActualRows;
+ this->m_nc = ActualCols;
+ this->m_kc = MaxDepth;
+ this->m_blockA = m_staticA;
+ this->m_blockB = m_staticB;
+ this->m_blockW = m_staticW;
+ }
+
+ inline void allocateA() {}
+ inline void allocateB() {}
+ inline void allocateW() {}
+ inline void allocateAll() {}
+};
+
+template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>
+ : public level3_blocking<
+ typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
+ typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor
+ };
+ typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
+ typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ DenseIndex m_sizeA;
+ DenseIndex m_sizeB;
+ DenseIndex m_sizeW;
+
+ public:
+
+ gemm_blocking_space(DenseIndex rows, DenseIndex cols, DenseIndex depth)
+ {
+ this->m_mc = Transpose ? cols : rows;
+ this->m_nc = Transpose ? rows : cols;
+ this->m_kc = depth;
+
+ computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc);
+ m_sizeA = this->m_mc * this->m_kc;
+ m_sizeB = this->m_kc * this->m_nc;
+ m_sizeW = this->m_kc*Traits::WorkSpaceFactor;
+ }
+
+ void allocateA()
+ {
+ if(this->m_blockA==0)
+ this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
+ }
+
+ void allocateB()
+ {
+ if(this->m_blockB==0)
+ this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
+ }
+
+ void allocateW()
+ {
+ if(this->m_blockW==0)
+ this->m_blockW = aligned_new<RhsScalar>(m_sizeW);
+ }
+
+ void allocateAll()
+ {
+ allocateA();
+ allocateB();
+ allocateW();
+ }
+
+ ~gemm_blocking_space()
+ {
+ aligned_delete(this->m_blockA, m_sizeA);
+ aligned_delete(this->m_blockB, m_sizeB);
+ aligned_delete(this->m_blockW, m_sizeW);
+ }
+};
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, GemmProduct>
+ : public ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs>
+{
+ enum {
+ MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)
+ };
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef Scalar ResScalar;
+
+ GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {
+ typedef internal::scalar_product_op<LhsScalar,RhsScalar> BinOp;
+ EIGEN_CHECK_BINARY_COMPATIBILIY(BinOp,LhsScalar,RhsScalar);
+ }
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
+
+ typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
+ typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+ * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
+ Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
+
+ typedef internal::gemm_functor<
+ Scalar, Index,
+ internal::general_matrix_matrix_product<
+ Index,
+ LhsScalar, (_ActualLhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
+ RhsScalar, (_ActualRhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
+ (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>,
+ _ActualLhsType, _ActualRhsType, Dest, BlockingType> GemmFunctor;
+
+ BlockingType blocking(dst.rows(), dst.cols(), lhs.cols());
+
+ internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>(GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), this->rows(), this->cols(), Dest::Flags&RowMajorBit);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
new file mode 100644
index 0000000..5c37639
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
@@ -0,0 +1,278 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
+
+namespace Eigen {
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update;
+
+namespace internal {
+
+/**********************************************************************
+* This file implements a general A * B product while
+* evaluating only one triangular part of the product.
+* This is more general version of self adjoint product (C += A A^T)
+* as the level 3 SYRK Blas routine.
+**********************************************************************/
+
+// forward declarations (defined at the end of this file)
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
+struct tribb_kernel;
+
+/* Optimized matrix-matrix product evaluating only one triangular half */
+template <typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder, int UpLo, int Version = Specialized>
+struct general_matrix_matrix_triangular_product;
+
+// as usual if the result is row major => we transpose the product
+template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
+struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
+ {
+ general_matrix_matrix_triangular_product<Index,
+ RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
+ LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
+ ColMajor, UpLo==Lower?Upper:Lower>
+ ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
+ }
+};
+
+template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
+struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
+ {
+ const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ Index kc = depth; // cache block size along the K direction
+ Index mc = size; // cache block size along the M direction
+ Index nc = size; // cache block size along the N direction
+ computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc);
+ // !!! mc must be a multiple of nr:
+ if(mc > Traits::nr)
+ mc = (mc/Traits::nr)*Traits::nr;
+
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+ std::size_t sizeB = sizeW + kc*size;
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0);
+ RhsScalar* blockB = allocatedBlockB + sizeW;
+
+ gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
+ gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
+ tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
+
+ for(Index k2=0; k2<depth; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,depth)-k2;
+
+ // note that the actual rhs is the transpose/adjoint of mat
+ pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size);
+
+ for(Index i2=0; i2<size; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,size)-i2;
+
+ pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
+
+ // the selected actual_mc * size panel of res is split into three different part:
+ // 1 - before the diagonal => processed with gebp or skipped
+ // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
+ // 3 - after the diagonal => processed with gebp or skipped
+ if (UpLo==Lower)
+ gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha,
+ -1, -1, 0, 0, allocatedBlockB);
+
+ sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB);
+
+ if (UpLo==Upper)
+ {
+ Index j2 = i2+actual_mc;
+ gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha,
+ -1, -1, 0, 0, allocatedBlockB);
+ }
+ }
+ }
+ }
+};
+
+// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
+// This kernel is built on top of the gebp kernel:
+// - the current destination block is processed per panel of actual_mc x BlockSize
+// where BlockSize is set to the minimal value allowing gebp to be as fast as possible
+// - then, as usual, each panel is split into three parts along the diagonal,
+// the sub blocks above and below the diagonal are processed as usual,
+// while the triangular block overlapping the diagonal is evaluated into a
+// small temporary buffer which is then accumulated into the result using a
+// triangular traversal.
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
+struct tribb_kernel
+{
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
+ typedef typename Traits::ResScalar ResScalar;
+
+ enum {
+ BlockSize = EIGEN_PLAIN_ENUM_MAX(mr,nr)
+ };
+ void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha, RhsScalar* workspace)
+ {
+ gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
+ Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
+
+ // let's process the block per panel of actual_mc x BlockSize,
+ // again, each is split into three parts, etc.
+ for (Index j=0; j<size; j+=BlockSize)
+ {
+ Index actualBlockSize = std::min<Index>(BlockSize,size - j);
+ const RhsScalar* actual_b = blockB+j*depth;
+
+ if(UpLo==Upper)
+ gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha,
+ -1, -1, 0, 0, workspace);
+
+ // selfadjoint micro block
+ {
+ Index i = j;
+ buffer.setZero();
+ // 1 - apply the kernel on the temporary buffer
+ gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
+ -1, -1, 0, 0, workspace);
+ // 2 - triangular accumulation
+ for(Index j1=0; j1<actualBlockSize; ++j1)
+ {
+ ResScalar* r = res + (j+j1)*resStride + i;
+ for(Index i1=UpLo==Lower ? j1 : 0;
+ UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
+ r[i1] += buffer(i1,j1);
+ }
+ }
+
+ if(UpLo==Lower)
+ {
+ Index i = j+actualBlockSize;
+ gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha,
+ -1, -1, 0, 0, workspace);
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+// high level API
+
+template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
+struct general_product_to_triangular_selector;
+
+
+template<typename MatrixType, typename ProductType, int UpLo>
+struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
+{
+ static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
+ typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
+ typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+
+ typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
+ typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
+ typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
+
+ enum {
+ StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
+ UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
+ };
+
+ internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
+ (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
+ if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
+
+ internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
+ (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
+ if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+
+
+ selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
+ LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
+ ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
+ }
+};
+
+template<typename MatrixType, typename ProductType, int UpLo>
+struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
+{
+ static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Index Index;
+
+ typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
+ typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
+ typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+
+ typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
+ typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
+ typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
+
+ internal::general_matrix_matrix_triangular_product<Index,
+ typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+ typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+ MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
+ ::run(mat.cols(), actualLhs.cols(),
+ &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
+ mat.data(), mat.outerStride(), actualAlpha);
+ }
+};
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename ProductDerived, typename _Lhs, typename _Rhs>
+TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha)
+{
+ general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha);
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_MKL.h b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_MKL.h
new file mode 100644
index 0000000..3deed06
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_MKL.h
@@ -0,0 +1,146 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Level 3 BLAS SYRK/HERK implementation.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Index, typename Scalar, int AStorageOrder, bool ConjugateA, int ResStorageOrder, int UpLo>
+struct general_matrix_matrix_rankupdate :
+ general_matrix_matrix_triangular_product<
+ Index,Scalar,AStorageOrder,ConjugateA,Scalar,AStorageOrder,ConjugateA,ResStorageOrder,UpLo,BuiltIn> {};
+
+
+// try to go to BLAS specialization
+#define EIGEN_MKL_RANKUPDATE_SPECIALIZE(Scalar) \
+template <typename Index, int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs, int UpLo> \
+struct general_matrix_matrix_triangular_product<Index,Scalar,LhsStorageOrder,ConjugateLhs, \
+ Scalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Specialized> { \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const Scalar* lhs, Index lhsStride, \
+ const Scalar* rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha) \
+ { \
+ if (lhs==rhs) { \
+ general_matrix_matrix_rankupdate<Index,Scalar,LhsStorageOrder,ConjugateLhs,ColMajor,UpLo> \
+ ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha); \
+ } else { \
+ general_matrix_matrix_triangular_product<Index, \
+ Scalar, LhsStorageOrder, ConjugateLhs, \
+ Scalar, RhsStorageOrder, ConjugateRhs, \
+ ColMajor, UpLo, BuiltIn> \
+ ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha); \
+ } \
+ } \
+};
+
+EIGEN_MKL_RANKUPDATE_SPECIALIZE(double)
+//EIGEN_MKL_RANKUPDATE_SPECIALIZE(dcomplex)
+EIGEN_MKL_RANKUPDATE_SPECIALIZE(float)
+//EIGEN_MKL_RANKUPDATE_SPECIALIZE(scomplex)
+
+// SYRK for float/double
+#define EIGEN_MKL_RANKUPDATE_R(EIGTYPE, MKLTYPE, MKLFUNC) \
+template <typename Index, int AStorageOrder, bool ConjugateA, int UpLo> \
+struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
+ enum { \
+ IsLower = (UpLo&Lower) == Lower, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((AStorageOrder==ColMajor) && ConjugateA) ? 1 : 0 \
+ }; \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* rhs, Index rhsStride, EIGTYPE* res, Index resStride, EIGTYPE alpha) \
+ { \
+ /* typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs;*/ \
+\
+ MKL_INT lda=lhsStride, ldc=resStride, n=size, k=depth; \
+ char uplo=(IsLower) ? 'L' : 'U', trans=(AStorageOrder==RowMajor) ? 'T':'N'; \
+ MKLTYPE alpha_, beta_; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
+ MKLFUNC(&uplo, &trans, &n, &k, &alpha_, lhs, &lda, &beta_, res, &ldc); \
+ } \
+};
+
+// HERK for complex data
+#define EIGEN_MKL_RANKUPDATE_C(EIGTYPE, MKLTYPE, RTYPE, MKLFUNC) \
+template <typename Index, int AStorageOrder, bool ConjugateA, int UpLo> \
+struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
+ enum { \
+ IsLower = (UpLo&Lower) == Lower, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = (((AStorageOrder==ColMajor) && ConjugateA) || ((AStorageOrder==RowMajor) && !ConjugateA)) ? 1 : 0 \
+ }; \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* rhs, Index rhsStride, EIGTYPE* res, Index resStride, EIGTYPE alpha) \
+ { \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, AStorageOrder> MatrixType; \
+\
+ MKL_INT lda=lhsStride, ldc=resStride, n=size, k=depth; \
+ char uplo=(IsLower) ? 'L' : 'U', trans=(AStorageOrder==RowMajor) ? 'C':'N'; \
+ RTYPE alpha_, beta_; \
+ const EIGTYPE* a_ptr; \
+\
+/* Set alpha_ & beta_ */ \
+/* assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); */\
+/* assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1));*/ \
+ alpha_ = alpha.real(); \
+ beta_ = 1.0; \
+/* Copy with conjugation in some cases*/ \
+ MatrixType a; \
+ if (conjA) { \
+ Map<const MatrixType, 0, OuterStride<> > mapA(lhs,n,k,OuterStride<>(lhsStride)); \
+ a = mapA.conjugate(); \
+ lda = a.outerStride(); \
+ a_ptr = a.data(); \
+ } else a_ptr=lhs; \
+ MKLFUNC(&uplo, &trans, &n, &k, &alpha_, (MKLTYPE*)a_ptr, &lda, &beta_, (MKLTYPE*)res, &ldc); \
+ } \
+};
+
+
+EIGEN_MKL_RANKUPDATE_R(double, double, dsyrk)
+EIGEN_MKL_RANKUPDATE_R(float, float, ssyrk)
+
+//EIGEN_MKL_RANKUPDATE_C(dcomplex, MKL_Complex16, double, zherk)
+//EIGEN_MKL_RANKUPDATE_C(scomplex, MKL_Complex8, double, cherk)
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix_MKL.h b/Eigen/src/Core/products/GeneralMatrixMatrix_MKL.h
new file mode 100644
index 0000000..060af32
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix_MKL.h
@@ -0,0 +1,118 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * General matrix-matrix product functionality based on ?GEMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements general matrix-matrix multiplication using BLAS
+* gemm function via partial specialization of
+* general_matrix_matrix_product::run(..) method for float, double,
+* std::complex<float> and std::complex<double> types
+**********************************************************************/
+
+// gemm specialization
+
+#define GEMM_SPECIALIZATION(EIGTYPE, EIGPREFIX, MKLTYPE, MKLPREFIX) \
+template< \
+ typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor> \
+{ \
+static void run(Index rows, Index cols, Index depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha, \
+ level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/, \
+ GemmParallelInfo<Index>* /*info = 0*/) \
+{ \
+ using std::conj; \
+\
+ char transa, transb; \
+ MKL_INT m, n, k, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ MKLTYPE alpha_, beta_; \
+ MatrixX##EIGPREFIX a_tmp, b_tmp; \
+ EIGTYPE myone(1);\
+\
+/* Set transpose options */ \
+ transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
+ transb = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set m, n, k */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)cols; \
+ k = (MKL_INT)depth; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = (MKL_INT)lhsStride; \
+ ldb = (MKL_INT)rhsStride; \
+ ldc = (MKL_INT)resStride; \
+\
+/* Set a, b, c */ \
+ if ((LhsStorageOrder==ColMajor) && (ConjugateLhs)) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,k,OuterStride<>(lhsStride)); \
+ a_tmp = lhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else a = _lhs; \
+\
+ if ((RhsStorageOrder==ColMajor) && (ConjugateRhs)) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,k,n,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.conjugate(); \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+ } else b = _rhs; \
+\
+ MKLPREFIX##gemm(&transa, &transb, &m, &n, &k, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+}};
+
+GEMM_SPECIALIZATION(double, d, double, d)
+GEMM_SPECIALIZATION(float, f, float, s)
+GEMM_SPECIALIZATION(dcomplex, cd, MKL_Complex16, z)
+GEMM_SPECIALIZATION(scomplex, cf, MKL_Complex8, c)
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
new file mode 100644
index 0000000..0938770
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -0,0 +1,566 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+/* Optimized col-major matrix * vector product:
+ * This algorithm processes 4 columns at onces that allows to both reduce
+ * the number of load/stores of the result by a factor 4 and to reduce
+ * the instruction dependency. Moreover, we know that all bands have the
+ * same alignment pattern.
+ *
+ * Mixing type logic: C += alpha * A * B
+ * | A | B |alpha| comments
+ * |real |cplx |cplx | no vectorization
+ * |real |cplx |real | alpha is converted to a cplx when calling the run function, no vectorization
+ * |cplx |real |cplx | invalid, the caller has to do tmp: = A * B; C += alpha*tmp
+ * |cplx |real |real | optimal case, vectorization possible via real-cplx mul
+ */
+template<typename Index, typename LhsScalar, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version>
+struct general_matrix_vector_product<Index,LhsScalar,ColMajor,ConjugateLhs,RhsScalar,ConjugateRhs,Version>
+{
+typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+enum {
+ Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
+ && int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),
+ LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
+ RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1
+};
+
+typedef typename packet_traits<LhsScalar>::type _LhsPacket;
+typedef typename packet_traits<RhsScalar>::type _RhsPacket;
+typedef typename packet_traits<ResScalar>::type _ResPacket;
+
+typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
+typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
+typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
+
+EIGEN_DONT_INLINE static void run(
+ Index rows, Index cols,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsIncr,
+ ResScalar* res, Index resIncr, RhsScalar alpha);
+};
+
+template<typename Index, typename LhsScalar, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,ConjugateLhs,RhsScalar,ConjugateRhs,Version>::run(
+ Index rows, Index cols,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsIncr,
+ ResScalar* res, Index resIncr, RhsScalar alpha)
+{
+ EIGEN_UNUSED_VARIABLE(resIncr)
+ eigen_internal_assert(resIncr==1);
+ #ifdef _EIGEN_ACCUMULATE_PACKETS
+ #error _EIGEN_ACCUMULATE_PACKETS has already been defined
+ #endif
+ #define _EIGEN_ACCUMULATE_PACKETS(A0,A13,A2) \
+ pstore(&res[j], \
+ padd(pload<ResPacket>(&res[j]), \
+ padd( \
+ padd(pcj.pmul(EIGEN_CAT(ploa , A0)<LhsPacket>(&lhs0[j]), ptmp0), \
+ pcj.pmul(EIGEN_CAT(ploa , A13)<LhsPacket>(&lhs1[j]), ptmp1)), \
+ padd(pcj.pmul(EIGEN_CAT(ploa , A2)<LhsPacket>(&lhs2[j]), ptmp2), \
+ pcj.pmul(EIGEN_CAT(ploa , A13)<LhsPacket>(&lhs3[j]), ptmp3)) )))
+
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+ conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
+ if(ConjugateRhs)
+ alpha = numext::conj(alpha);
+
+ enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };
+ const Index columnsAtOnce = 4;
+ const Index peels = 2;
+ const Index LhsPacketAlignedMask = LhsPacketSize-1;
+ const Index ResPacketAlignedMask = ResPacketSize-1;
+// const Index PeelAlignedMask = ResPacketSize*peels-1;
+ const Index size = rows;
+
+ // How many coeffs of the result do we have to skip to be aligned.
+ // Here we assume data are at least aligned on the base scalar type.
+ Index alignedStart = internal::first_aligned(res,size);
+ Index alignedSize = ResPacketSize>1 ? alignedStart + ((size-alignedStart) & ~ResPacketAlignedMask) : 0;
+ const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
+
+ const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;
+ Index alignmentPattern = alignmentStep==0 ? AllAligned
+ : alignmentStep==(LhsPacketSize/2) ? EvenAligned
+ : FirstAligned;
+
+ // we cannot assume the first element is aligned because of sub-matrices
+ const Index lhsAlignmentOffset = internal::first_aligned(lhs,size);
+
+ // find how many columns do we have to skip to be aligned with the result (if possible)
+ Index skipColumns = 0;
+ // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
+ if( (size_t(lhs)%sizeof(LhsScalar)) || (size_t(res)%sizeof(ResScalar)) )
+ {
+ alignedSize = 0;
+ alignedStart = 0;
+ }
+ else if (LhsPacketSize>1)
+ {
+ eigen_internal_assert(size_t(lhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || size<LhsPacketSize);
+
+ while (skipColumns<LhsPacketSize &&
+ alignedStart != ((lhsAlignmentOffset + alignmentStep*skipColumns)%LhsPacketSize))
+ ++skipColumns;
+ if (skipColumns==LhsPacketSize)
+ {
+ // nothing can be aligned, no need to skip any column
+ alignmentPattern = NoneAligned;
+ skipColumns = 0;
+ }
+ else
+ {
+ skipColumns = (std::min)(skipColumns,cols);
+ // note that the skiped columns are processed later.
+ }
+
+ eigen_internal_assert( (alignmentPattern==NoneAligned)
+ || (skipColumns + columnsAtOnce >= cols)
+ || LhsPacketSize > size
+ || (size_t(lhs+alignedStart+lhsStride*skipColumns)%sizeof(LhsPacket))==0);
+ }
+ else if(Vectorizable)
+ {
+ alignedStart = 0;
+ alignedSize = size;
+ alignmentPattern = AllAligned;
+ }
+
+ Index offset1 = (FirstAligned && alignmentStep==1?3:1);
+ Index offset3 = (FirstAligned && alignmentStep==1?1:3);
+
+ Index columnBound = ((cols-skipColumns)/columnsAtOnce)*columnsAtOnce + skipColumns;
+ for (Index i=skipColumns; i<columnBound; i+=columnsAtOnce)
+ {
+ RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs[i*rhsIncr]),
+ ptmp1 = pset1<RhsPacket>(alpha*rhs[(i+offset1)*rhsIncr]),
+ ptmp2 = pset1<RhsPacket>(alpha*rhs[(i+2)*rhsIncr]),
+ ptmp3 = pset1<RhsPacket>(alpha*rhs[(i+offset3)*rhsIncr]);
+
+ // this helps a lot generating better binary code
+ const LhsScalar *lhs0 = lhs + i*lhsStride, *lhs1 = lhs + (i+offset1)*lhsStride,
+ *lhs2 = lhs + (i+2)*lhsStride, *lhs3 = lhs + (i+offset3)*lhsStride;
+
+ if (Vectorizable)
+ {
+ /* explicit vectorization */
+ // process initial unaligned coeffs
+ for (Index j=0; j<alignedStart; ++j)
+ {
+ res[j] = cj.pmadd(lhs0[j], pfirst(ptmp0), res[j]);
+ res[j] = cj.pmadd(lhs1[j], pfirst(ptmp1), res[j]);
+ res[j] = cj.pmadd(lhs2[j], pfirst(ptmp2), res[j]);
+ res[j] = cj.pmadd(lhs3[j], pfirst(ptmp3), res[j]);
+ }
+
+ if (alignedSize>alignedStart)
+ {
+ switch(alignmentPattern)
+ {
+ case AllAligned:
+ for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,d,d);
+ break;
+ case EvenAligned:
+ for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,du,d);
+ break;
+ case FirstAligned:
+ {
+ Index j = alignedStart;
+ if(peels>1)
+ {
+ LhsPacket A00, A01, A02, A03, A10, A11, A12, A13;
+ ResPacket T0, T1;
+
+ A01 = pload<LhsPacket>(&lhs1[alignedStart-1]);
+ A02 = pload<LhsPacket>(&lhs2[alignedStart-2]);
+ A03 = pload<LhsPacket>(&lhs3[alignedStart-3]);
+
+ for (; j<peeledSize; j+=peels*ResPacketSize)
+ {
+ A11 = pload<LhsPacket>(&lhs1[j-1+LhsPacketSize]); palign<1>(A01,A11);
+ A12 = pload<LhsPacket>(&lhs2[j-2+LhsPacketSize]); palign<2>(A02,A12);
+ A13 = pload<LhsPacket>(&lhs3[j-3+LhsPacketSize]); palign<3>(A03,A13);
+
+ A00 = pload<LhsPacket>(&lhs0[j]);
+ A10 = pload<LhsPacket>(&lhs0[j+LhsPacketSize]);
+ T0 = pcj.pmadd(A00, ptmp0, pload<ResPacket>(&res[j]));
+ T1 = pcj.pmadd(A10, ptmp0, pload<ResPacket>(&res[j+ResPacketSize]));
+
+ T0 = pcj.pmadd(A01, ptmp1, T0);
+ A01 = pload<LhsPacket>(&lhs1[j-1+2*LhsPacketSize]); palign<1>(A11,A01);
+ T0 = pcj.pmadd(A02, ptmp2, T0);
+ A02 = pload<LhsPacket>(&lhs2[j-2+2*LhsPacketSize]); palign<2>(A12,A02);
+ T0 = pcj.pmadd(A03, ptmp3, T0);
+ pstore(&res[j],T0);
+ A03 = pload<LhsPacket>(&lhs3[j-3+2*LhsPacketSize]); palign<3>(A13,A03);
+ T1 = pcj.pmadd(A11, ptmp1, T1);
+ T1 = pcj.pmadd(A12, ptmp2, T1);
+ T1 = pcj.pmadd(A13, ptmp3, T1);
+ pstore(&res[j+ResPacketSize],T1);
+ }
+ }
+ for (; j<alignedSize; j+=ResPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,du,du);
+ break;
+ }
+ default:
+ for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(du,du,du);
+ break;
+ }
+ }
+ } // end explicit vectorization
+
+ /* process remaining coeffs (or all if there is no explicit vectorization) */
+ for (Index j=alignedSize; j<size; ++j)
+ {
+ res[j] = cj.pmadd(lhs0[j], pfirst(ptmp0), res[j]);
+ res[j] = cj.pmadd(lhs1[j], pfirst(ptmp1), res[j]);
+ res[j] = cj.pmadd(lhs2[j], pfirst(ptmp2), res[j]);
+ res[j] = cj.pmadd(lhs3[j], pfirst(ptmp3), res[j]);
+ }
+ }
+
+ // process remaining first and last columns (at most columnsAtOnce-1)
+ Index end = cols;
+ Index start = columnBound;
+ do
+ {
+ for (Index k=start; k<end; ++k)
+ {
+ RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs[k*rhsIncr]);
+ const LhsScalar* lhs0 = lhs + k*lhsStride;
+
+ if (Vectorizable)
+ {
+ /* explicit vectorization */
+ // process first unaligned result's coeffs
+ for (Index j=0; j<alignedStart; ++j)
+ res[j] += cj.pmul(lhs0[j], pfirst(ptmp0));
+ // process aligned result's coeffs
+ if ((size_t(lhs0+alignedStart)%sizeof(LhsPacket))==0)
+ for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
+ pstore(&res[i], pcj.pmadd(pload<LhsPacket>(&lhs0[i]), ptmp0, pload<ResPacket>(&res[i])));
+ else
+ for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
+ pstore(&res[i], pcj.pmadd(ploadu<LhsPacket>(&lhs0[i]), ptmp0, pload<ResPacket>(&res[i])));
+ }
+
+ // process remaining scalars (or all if no explicit vectorization)
+ for (Index i=alignedSize; i<size; ++i)
+ res[i] += cj.pmul(lhs0[i], pfirst(ptmp0));
+ }
+ if (skipColumns)
+ {
+ start = 0;
+ end = skipColumns;
+ skipColumns = 0;
+ }
+ else
+ break;
+ } while(Vectorizable);
+ #undef _EIGEN_ACCUMULATE_PACKETS
+}
+
+/* Optimized row-major matrix * vector product:
+ * This algorithm processes 4 rows at onces that allows to both reduce
+ * the number of load/stores of the result by a factor 4 and to reduce
+ * the instruction dependency. Moreover, we know that all bands have the
+ * same alignment pattern.
+ *
+ * Mixing type logic:
+ * - alpha is always a complex (or converted to a complex)
+ * - no vectorization
+ */
+template<typename Index, typename LhsScalar, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version>
+struct general_matrix_vector_product<Index,LhsScalar,RowMajor,ConjugateLhs,RhsScalar,ConjugateRhs,Version>
+{
+typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+enum {
+ Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
+ && int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),
+ LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
+ RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
+ ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1
+};
+
+typedef typename packet_traits<LhsScalar>::type _LhsPacket;
+typedef typename packet_traits<RhsScalar>::type _RhsPacket;
+typedef typename packet_traits<ResScalar>::type _ResPacket;
+
+typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
+typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
+typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
+
+EIGEN_DONT_INLINE static void run(
+ Index rows, Index cols,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsIncr,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha);
+};
+
+template<typename Index, typename LhsScalar, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,RowMajor,ConjugateLhs,RhsScalar,ConjugateRhs,Version>::run(
+ Index rows, Index cols,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsIncr,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ EIGEN_UNUSED_VARIABLE(rhsIncr);
+ eigen_internal_assert(rhsIncr==1);
+ #ifdef _EIGEN_ACCUMULATE_PACKETS
+ #error _EIGEN_ACCUMULATE_PACKETS has already been defined
+ #endif
+
+ #define _EIGEN_ACCUMULATE_PACKETS(A0,A13,A2) {\
+ RhsPacket b = pload<RhsPacket>(&rhs[j]); \
+ ptmp0 = pcj.pmadd(EIGEN_CAT(ploa,A0) <LhsPacket>(&lhs0[j]), b, ptmp0); \
+ ptmp1 = pcj.pmadd(EIGEN_CAT(ploa,A13)<LhsPacket>(&lhs1[j]), b, ptmp1); \
+ ptmp2 = pcj.pmadd(EIGEN_CAT(ploa,A2) <LhsPacket>(&lhs2[j]), b, ptmp2); \
+ ptmp3 = pcj.pmadd(EIGEN_CAT(ploa,A13)<LhsPacket>(&lhs3[j]), b, ptmp3); }
+
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+ conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
+
+ enum { AllAligned=0, EvenAligned=1, FirstAligned=2, NoneAligned=3 };
+ const Index rowsAtOnce = 4;
+ const Index peels = 2;
+ const Index RhsPacketAlignedMask = RhsPacketSize-1;
+ const Index LhsPacketAlignedMask = LhsPacketSize-1;
+// const Index PeelAlignedMask = RhsPacketSize*peels-1;
+ const Index depth = cols;
+
+ // How many coeffs of the result do we have to skip to be aligned.
+ // Here we assume data are at least aligned on the base scalar type
+ // if that's not the case then vectorization is discarded, see below.
+ Index alignedStart = internal::first_aligned(rhs, depth);
+ Index alignedSize = RhsPacketSize>1 ? alignedStart + ((depth-alignedStart) & ~RhsPacketAlignedMask) : 0;
+ const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
+
+ const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;
+ Index alignmentPattern = alignmentStep==0 ? AllAligned
+ : alignmentStep==(LhsPacketSize/2) ? EvenAligned
+ : FirstAligned;
+
+ // we cannot assume the first element is aligned because of sub-matrices
+ const Index lhsAlignmentOffset = internal::first_aligned(lhs,depth);
+
+ // find how many rows do we have to skip to be aligned with rhs (if possible)
+ Index skipRows = 0;
+ // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
+ if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) || (size_t(lhs)%sizeof(LhsScalar)) || (size_t(rhs)%sizeof(RhsScalar)) )
+ {
+ alignedSize = 0;
+ alignedStart = 0;
+ }
+ else if (LhsPacketSize>1)
+ {
+ eigen_internal_assert(size_t(lhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || depth<LhsPacketSize);
+
+ while (skipRows<LhsPacketSize &&
+ alignedStart != ((lhsAlignmentOffset + alignmentStep*skipRows)%LhsPacketSize))
+ ++skipRows;
+ if (skipRows==LhsPacketSize)
+ {
+ // nothing can be aligned, no need to skip any column
+ alignmentPattern = NoneAligned;
+ skipRows = 0;
+ }
+ else
+ {
+ skipRows = (std::min)(skipRows,Index(rows));
+ // note that the skiped columns are processed later.
+ }
+ eigen_internal_assert( alignmentPattern==NoneAligned
+ || LhsPacketSize==1
+ || (skipRows + rowsAtOnce >= rows)
+ || LhsPacketSize > depth
+ || (size_t(lhs+alignedStart+lhsStride*skipRows)%sizeof(LhsPacket))==0);
+ }
+ else if(Vectorizable)
+ {
+ alignedStart = 0;
+ alignedSize = depth;
+ alignmentPattern = AllAligned;
+ }
+
+ Index offset1 = (FirstAligned && alignmentStep==1?3:1);
+ Index offset3 = (FirstAligned && alignmentStep==1?1:3);
+
+ Index rowBound = ((rows-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;
+ for (Index i=skipRows; i<rowBound; i+=rowsAtOnce)
+ {
+ EIGEN_ALIGN16 ResScalar tmp0 = ResScalar(0);
+ ResScalar tmp1 = ResScalar(0), tmp2 = ResScalar(0), tmp3 = ResScalar(0);
+
+ // this helps the compiler generating good binary code
+ const LhsScalar *lhs0 = lhs + i*lhsStride, *lhs1 = lhs + (i+offset1)*lhsStride,
+ *lhs2 = lhs + (i+2)*lhsStride, *lhs3 = lhs + (i+offset3)*lhsStride;
+
+ if (Vectorizable)
+ {
+ /* explicit vectorization */
+ ResPacket ptmp0 = pset1<ResPacket>(ResScalar(0)), ptmp1 = pset1<ResPacket>(ResScalar(0)),
+ ptmp2 = pset1<ResPacket>(ResScalar(0)), ptmp3 = pset1<ResPacket>(ResScalar(0));
+
+ // process initial unaligned coeffs
+ // FIXME this loop get vectorized by the compiler !
+ for (Index j=0; j<alignedStart; ++j)
+ {
+ RhsScalar b = rhs[j];
+ tmp0 += cj.pmul(lhs0[j],b); tmp1 += cj.pmul(lhs1[j],b);
+ tmp2 += cj.pmul(lhs2[j],b); tmp3 += cj.pmul(lhs3[j],b);
+ }
+
+ if (alignedSize>alignedStart)
+ {
+ switch(alignmentPattern)
+ {
+ case AllAligned:
+ for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,d,d);
+ break;
+ case EvenAligned:
+ for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,du,d);
+ break;
+ case FirstAligned:
+ {
+ Index j = alignedStart;
+ if (peels>1)
+ {
+ /* Here we proccess 4 rows with with two peeled iterations to hide
+ * the overhead of unaligned loads. Moreover unaligned loads are handled
+ * using special shift/move operations between the two aligned packets
+ * overlaping the desired unaligned packet. This is *much* more efficient
+ * than basic unaligned loads.
+ */
+ LhsPacket A01, A02, A03, A11, A12, A13;
+ A01 = pload<LhsPacket>(&lhs1[alignedStart-1]);
+ A02 = pload<LhsPacket>(&lhs2[alignedStart-2]);
+ A03 = pload<LhsPacket>(&lhs3[alignedStart-3]);
+
+ for (; j<peeledSize; j+=peels*RhsPacketSize)
+ {
+ RhsPacket b = pload<RhsPacket>(&rhs[j]);
+ A11 = pload<LhsPacket>(&lhs1[j-1+LhsPacketSize]); palign<1>(A01,A11);
+ A12 = pload<LhsPacket>(&lhs2[j-2+LhsPacketSize]); palign<2>(A02,A12);
+ A13 = pload<LhsPacket>(&lhs3[j-3+LhsPacketSize]); palign<3>(A03,A13);
+
+ ptmp0 = pcj.pmadd(pload<LhsPacket>(&lhs0[j]), b, ptmp0);
+ ptmp1 = pcj.pmadd(A01, b, ptmp1);
+ A01 = pload<LhsPacket>(&lhs1[j-1+2*LhsPacketSize]); palign<1>(A11,A01);
+ ptmp2 = pcj.pmadd(A02, b, ptmp2);
+ A02 = pload<LhsPacket>(&lhs2[j-2+2*LhsPacketSize]); palign<2>(A12,A02);
+ ptmp3 = pcj.pmadd(A03, b, ptmp3);
+ A03 = pload<LhsPacket>(&lhs3[j-3+2*LhsPacketSize]); palign<3>(A13,A03);
+
+ b = pload<RhsPacket>(&rhs[j+RhsPacketSize]);
+ ptmp0 = pcj.pmadd(pload<LhsPacket>(&lhs0[j+LhsPacketSize]), b, ptmp0);
+ ptmp1 = pcj.pmadd(A11, b, ptmp1);
+ ptmp2 = pcj.pmadd(A12, b, ptmp2);
+ ptmp3 = pcj.pmadd(A13, b, ptmp3);
+ }
+ }
+ for (; j<alignedSize; j+=RhsPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(d,du,du);
+ break;
+ }
+ default:
+ for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
+ _EIGEN_ACCUMULATE_PACKETS(du,du,du);
+ break;
+ }
+ tmp0 += predux(ptmp0);
+ tmp1 += predux(ptmp1);
+ tmp2 += predux(ptmp2);
+ tmp3 += predux(ptmp3);
+ }
+ } // end explicit vectorization
+
+ // process remaining coeffs (or all if no explicit vectorization)
+ // FIXME this loop get vectorized by the compiler !
+ for (Index j=alignedSize; j<depth; ++j)
+ {
+ RhsScalar b = rhs[j];
+ tmp0 += cj.pmul(lhs0[j],b); tmp1 += cj.pmul(lhs1[j],b);
+ tmp2 += cj.pmul(lhs2[j],b); tmp3 += cj.pmul(lhs3[j],b);
+ }
+ res[i*resIncr] += alpha*tmp0;
+ res[(i+offset1)*resIncr] += alpha*tmp1;
+ res[(i+2)*resIncr] += alpha*tmp2;
+ res[(i+offset3)*resIncr] += alpha*tmp3;
+ }
+
+ // process remaining first and last rows (at most columnsAtOnce-1)
+ Index end = rows;
+ Index start = rowBound;
+ do
+ {
+ for (Index i=start; i<end; ++i)
+ {
+ EIGEN_ALIGN16 ResScalar tmp0 = ResScalar(0);
+ ResPacket ptmp0 = pset1<ResPacket>(tmp0);
+ const LhsScalar* lhs0 = lhs + i*lhsStride;
+ // process first unaligned result's coeffs
+ // FIXME this loop get vectorized by the compiler !
+ for (Index j=0; j<alignedStart; ++j)
+ tmp0 += cj.pmul(lhs0[j], rhs[j]);
+
+ if (alignedSize>alignedStart)
+ {
+ // process aligned rhs coeffs
+ if ((size_t(lhs0+alignedStart)%sizeof(LhsPacket))==0)
+ for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)
+ ptmp0 = pcj.pmadd(pload<LhsPacket>(&lhs0[j]), pload<RhsPacket>(&rhs[j]), ptmp0);
+ else
+ for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)
+ ptmp0 = pcj.pmadd(ploadu<LhsPacket>(&lhs0[j]), pload<RhsPacket>(&rhs[j]), ptmp0);
+ tmp0 += predux(ptmp0);
+ }
+
+ // process remaining scalars
+ // FIXME this loop get vectorized by the compiler !
+ for (Index j=alignedSize; j<depth; ++j)
+ tmp0 += cj.pmul(lhs0[j], rhs[j]);
+ res[i*resIncr] += alpha*tmp0;
+ }
+ if (skipRows)
+ {
+ start = 0;
+ end = skipRows;
+ skipRows = 0;
+ }
+ else
+ break;
+ } while(Vectorizable);
+
+ #undef _EIGEN_ACCUMULATE_PACKETS
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_H
diff --git a/Eigen/src/Core/products/GeneralMatrixVector_MKL.h b/Eigen/src/Core/products/GeneralMatrixVector_MKL.h
new file mode 100644
index 0000000..1cb9fe6
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixVector_MKL.h
@@ -0,0 +1,131 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * General matrix-vector product functionality based on ?GEMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements general matrix-vector multiplication using BLAS
+* gemv function via partial specialization of
+* general_matrix_vector_product::run(..) method for float, double,
+* std::complex<float> and std::complex<double> types
+**********************************************************************/
+
+// gemv specialization
+
+template<typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs>
+struct general_matrix_vector_product_gemv :
+ general_matrix_vector_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,ConjugateRhs,BuiltIn> {};
+
+#define EIGEN_MKL_GEMV_SPECIALIZE(Scalar) \
+template<typename Index, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product<Index,Scalar,ColMajor,ConjugateLhs,Scalar,ConjugateRhs,Specialized> { \
+static void run( \
+ Index rows, Index cols, \
+ const Scalar* lhs, Index lhsStride, \
+ const Scalar* rhs, Index rhsIncr, \
+ Scalar* res, Index resIncr, Scalar alpha) \
+{ \
+ if (ConjugateLhs) { \
+ general_matrix_vector_product<Index,Scalar,ColMajor,ConjugateLhs,Scalar,ConjugateRhs,BuiltIn>::run( \
+ rows, cols, lhs, lhsStride, rhs, rhsIncr, res, resIncr, alpha); \
+ } else { \
+ general_matrix_vector_product_gemv<Index,Scalar,ColMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \
+ rows, cols, lhs, lhsStride, rhs, rhsIncr, res, resIncr, alpha); \
+ } \
+} \
+}; \
+template<typename Index, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product<Index,Scalar,RowMajor,ConjugateLhs,Scalar,ConjugateRhs,Specialized> { \
+static void run( \
+ Index rows, Index cols, \
+ const Scalar* lhs, Index lhsStride, \
+ const Scalar* rhs, Index rhsIncr, \
+ Scalar* res, Index resIncr, Scalar alpha) \
+{ \
+ general_matrix_vector_product_gemv<Index,Scalar,RowMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \
+ rows, cols, lhs, lhsStride, rhs, rhsIncr, res, resIncr, alpha); \
+} \
+}; \
+
+EIGEN_MKL_GEMV_SPECIALIZE(double)
+EIGEN_MKL_GEMV_SPECIALIZE(float)
+EIGEN_MKL_GEMV_SPECIALIZE(dcomplex)
+EIGEN_MKL_GEMV_SPECIALIZE(scomplex)
+
+#define EIGEN_MKL_GEMV_SPECIALIZATION(EIGTYPE,MKLTYPE,MKLPREFIX) \
+template<typename Index, int LhsStorageOrder, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product_gemv<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,ConjugateRhs> \
+{ \
+typedef Matrix<EIGTYPE,Dynamic,1,ColMajor> GEMVVector;\
+\
+static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* rhs, Index rhsIncr, \
+ EIGTYPE* res, Index resIncr, EIGTYPE alpha) \
+{ \
+ MKL_INT m=rows, n=cols, lda=lhsStride, incx=rhsIncr, incy=resIncr; \
+ MKLTYPE alpha_, beta_; \
+ const EIGTYPE *x_ptr, myone(1); \
+ char trans=(LhsStorageOrder==ColMajor) ? 'N' : (ConjugateLhs) ? 'C' : 'T'; \
+ if (LhsStorageOrder==RowMajor) { \
+ m=cols; \
+ n=rows; \
+ }\
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+ GEMVVector x_tmp; \
+ if (ConjugateRhs) { \
+ Map<const GEMVVector, 0, InnerStride<> > map_x(rhs,cols,1,InnerStride<>(incx)); \
+ x_tmp=map_x.conjugate(); \
+ x_ptr=x_tmp.data(); \
+ incx=1; \
+ } else x_ptr=rhs; \
+ MKLPREFIX##gemv(&trans, &m, &n, &alpha_, (const MKLTYPE*)lhs, &lda, (const MKLTYPE*)x_ptr, &incx, &beta_, (MKLTYPE*)res, &incy); \
+}\
+};
+
+EIGEN_MKL_GEMV_SPECIALIZATION(double, double, d)
+EIGEN_MKL_GEMV_SPECIALIZATION(float, float, s)
+EIGEN_MKL_GEMV_SPECIALIZATION(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_GEMV_SPECIALIZATION(scomplex, MKL_Complex8, c)
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
diff --git a/Eigen/src/Core/products/Parallelizer.h b/Eigen/src/Core/products/Parallelizer.h
new file mode 100644
index 0000000..6937ee3
--- /dev/null
+++ b/Eigen/src/Core/products/Parallelizer.h
@@ -0,0 +1,162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARALLELIZER_H
+#define EIGEN_PARALLELIZER_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal */
+inline void manage_multi_threading(Action action, int* v)
+{
+ static EIGEN_UNUSED int m_maxThreads = -1;
+
+ if(action==SetAction)
+ {
+ eigen_internal_assert(v!=0);
+ m_maxThreads = *v;
+ }
+ else if(action==GetAction)
+ {
+ eigen_internal_assert(v!=0);
+ #ifdef EIGEN_HAS_OPENMP
+ if(m_maxThreads>0)
+ *v = m_maxThreads;
+ else
+ *v = omp_get_max_threads();
+ #else
+ *v = 1;
+ #endif
+ }
+ else
+ {
+ eigen_internal_assert(false);
+ }
+}
+
+}
+
+/** Must be call first when calling Eigen from multiple threads */
+inline void initParallel()
+{
+ int nbt;
+ internal::manage_multi_threading(GetAction, &nbt);
+ std::ptrdiff_t l1, l2;
+ internal::manage_caching_sizes(GetAction, &l1, &l2);
+}
+
+/** \returns the max number of threads reserved for Eigen
+ * \sa setNbThreads */
+inline int nbThreads()
+{
+ int ret;
+ internal::manage_multi_threading(GetAction, &ret);
+ return ret;
+}
+
+/** Sets the max number of threads reserved for Eigen
+ * \sa nbThreads */
+inline void setNbThreads(int v)
+{
+ internal::manage_multi_threading(SetAction, &v);
+}
+
+namespace internal {
+
+template<typename Index> struct GemmParallelInfo
+{
+ GemmParallelInfo() : sync(-1), users(0), rhs_start(0), rhs_length(0) {}
+
+ int volatile sync;
+ int volatile users;
+
+ Index rhs_start;
+ Index rhs_length;
+};
+
+template<bool Condition, typename Functor, typename Index>
+void parallelize_gemm(const Functor& func, Index rows, Index cols, bool transpose)
+{
+ // TODO when EIGEN_USE_BLAS is defined,
+ // we should still enable OMP for other scalar types
+#if !(defined (EIGEN_HAS_OPENMP)) || defined (EIGEN_USE_BLAS)
+ // FIXME the transpose variable is only needed to properly split
+ // the matrix product when multithreading is enabled. This is a temporary
+ // fix to support row-major destination matrices. This whole
+ // parallelizer mechanism has to be redisigned anyway.
+ EIGEN_UNUSED_VARIABLE(transpose);
+ func(0,rows, 0,cols);
+#else
+
+ // Dynamically check whether we should enable or disable OpenMP.
+ // The conditions are:
+ // - the max number of threads we can create is greater than 1
+ // - we are not already in a parallel code
+ // - the sizes are large enough
+
+ // 1- are we already in a parallel session?
+ // FIXME omp_get_num_threads()>1 only works for openmp, what if the user does not use openmp?
+ if((!Condition) || (omp_get_num_threads()>1))
+ return func(0,rows, 0,cols);
+
+ Index size = transpose ? cols : rows;
+
+ // 2- compute the maximal number of threads from the size of the product:
+ // FIXME this has to be fine tuned
+ Index max_threads = std::max<Index>(1,size / 32);
+
+ // 3 - compute the number of threads we are going to use
+ Index threads = std::min<Index>(nbThreads(), max_threads);
+
+ if(threads==1)
+ return func(0,rows, 0,cols);
+
+ Eigen::initParallel();
+ func.initParallelSession();
+
+ if(transpose)
+ std::swap(rows,cols);
+
+ GemmParallelInfo<Index>* info = new GemmParallelInfo<Index>[threads];
+
+ #pragma omp parallel num_threads(threads)
+ {
+ Index i = omp_get_thread_num();
+ // Note that the actual number of threads might be lower than the number of request ones.
+ Index actual_threads = omp_get_num_threads();
+
+ Index blockCols = (cols / actual_threads) & ~Index(0x3);
+ Index blockRows = (rows / actual_threads) & ~Index(0x7);
+
+ Index r0 = i*blockRows;
+ Index actualBlockRows = (i+1==actual_threads) ? rows-r0 : blockRows;
+
+ Index c0 = i*blockCols;
+ Index actualBlockCols = (i+1==actual_threads) ? cols-c0 : blockCols;
+
+ info[i].rhs_start = c0;
+ info[i].rhs_length = actualBlockCols;
+
+ if(transpose)
+ func(0, cols, r0, actualBlockRows, info);
+ else
+ func(r0, actualBlockRows, 0,cols, info);
+ }
+
+ delete[] info;
+#endif
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARALLELIZER_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
new file mode 100644
index 0000000..99cf9e0
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
@@ -0,0 +1,436 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_H
+#define EIGEN_SELFADJOINT_MATRIX_MATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+// pack a selfadjoint block diagonal for use with the gebp_kernel
+template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder>
+struct symm_pack_lhs
+{
+ template<int BlockRows> inline
+ void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)
+ {
+ // normal copy
+ for(Index k=0; k<i; k++)
+ for(Index w=0; w<BlockRows; w++)
+ blockA[count++] = lhs(i+w,k); // normal
+ // symmetric copy
+ Index h = 0;
+ for(Index k=i; k<i+BlockRows; k++)
+ {
+ for(Index w=0; w<h; w++)
+ blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
+
+ blockA[count++] = numext::real(lhs(k,k)); // real (diagonal)
+
+ for(Index w=h+1; w<BlockRows; w++)
+ blockA[count++] = lhs(i+w, k); // normal
+ ++h;
+ }
+ // transposed copy
+ for(Index k=i+BlockRows; k<cols; k++)
+ for(Index w=0; w<BlockRows; w++)
+ blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
+ }
+ void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
+ Index count = 0;
+ Index peeled_mc = (rows/Pack1)*Pack1;
+ for(Index i=0; i<peeled_mc; i+=Pack1)
+ {
+ pack<Pack1>(blockA, lhs, cols, i, count);
+ }
+
+ if(rows-peeled_mc>=Pack2)
+ {
+ pack<Pack2>(blockA, lhs, cols, peeled_mc, count);
+ peeled_mc += Pack2;
+ }
+
+ // do the same with mr==1
+ for(Index i=peeled_mc; i<rows; i++)
+ {
+ for(Index k=0; k<i; k++)
+ blockA[count++] = lhs(i, k); // normal
+
+ blockA[count++] = numext::real(lhs(i, i)); // real (diagonal)
+
+ for(Index k=i+1; k<cols; k++)
+ blockA[count++] = numext::conj(lhs(k, i)); // transposed
+ }
+ }
+};
+
+template<typename Scalar, typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs
+{
+ enum { PacketSize = packet_traits<Scalar>::size };
+ void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ Index end_k = k2 + rows;
+ Index count = 0;
+ const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
+ Index packet_cols = (cols/nr)*nr;
+
+ // first part: normal case
+ for(Index j2=0; j2<k2; j2+=nr)
+ {
+ for(Index k=k2; k<end_k; k++)
+ {
+ blockB[count+0] = rhs(k,j2+0);
+ blockB[count+1] = rhs(k,j2+1);
+ if (nr==4)
+ {
+ blockB[count+2] = rhs(k,j2+2);
+ blockB[count+3] = rhs(k,j2+3);
+ }
+ count += nr;
+ }
+ }
+
+ // second part: diagonal block
+ for(Index j2=k2; j2<(std::min)(k2+rows,packet_cols); j2+=nr)
+ {
+ // again we can split vertically in three different parts (transpose, symmetric, normal)
+ // transpose
+ for(Index k=k2; k<j2; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ if (nr==4)
+ {
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ }
+ count += nr;
+ }
+ // symmetric
+ Index h = 0;
+ for(Index k=j2; k<j2+nr; k++)
+ {
+ // normal
+ for (Index w=0 ; w<h; ++w)
+ blockB[count+w] = rhs(k,j2+w);
+
+ blockB[count+h] = numext::real(rhs(k,k));
+
+ // transpose
+ for (Index w=h+1 ; w<nr; ++w)
+ blockB[count+w] = numext::conj(rhs(j2+w,k));
+ count += nr;
+ ++h;
+ }
+ // normal
+ for(Index k=j2+nr; k<end_k; k++)
+ {
+ blockB[count+0] = rhs(k,j2+0);
+ blockB[count+1] = rhs(k,j2+1);
+ if (nr==4)
+ {
+ blockB[count+2] = rhs(k,j2+2);
+ blockB[count+3] = rhs(k,j2+3);
+ }
+ count += nr;
+ }
+ }
+
+ // third part: transposed
+ for(Index j2=k2+rows; j2<packet_cols; j2+=nr)
+ {
+ for(Index k=k2; k<end_k; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ if (nr==4)
+ {
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ }
+ count += nr;
+ }
+ }
+
+ // copy the remaining columns one at a time (=> the same with nr==1)
+ for(Index j2=packet_cols; j2<cols; ++j2)
+ {
+ // transpose
+ Index half = (std::min)(end_k,j2);
+ for(Index k=k2; k<half; k++)
+ {
+ blockB[count] = numext::conj(rhs(j2,k));
+ count += 1;
+ }
+
+ if(half==j2 && half<k2+rows)
+ {
+ blockB[count] = numext::real(rhs(j2,j2));
+ count += 1;
+ }
+ else
+ half--;
+
+ // normal
+ for(Index k=half+1; k<k2+rows; k++)
+ {
+ blockB[count] = rhs(k,j2);
+ count += 1;
+ }
+ }
+ }
+};
+
+/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
+ * the general matrix matrix product.
+ */
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
+ int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
+ int ResStorageOrder>
+struct product_selfadjoint_matrix;
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
+ int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor>
+{
+
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha)
+ {
+ product_selfadjoint_matrix<Scalar, Index,
+ EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
+ RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsSelfAdjoint,ConjugateRhs),
+ EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
+ LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),
+ ColMajor>
+ ::run(cols, rows, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
+ }
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>
+{
+
+ static EIGEN_DONT_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha);
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs>
+EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>::run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha)
+ {
+ Index size = rows;
+
+ const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+
+ Index kc = size; // cache block size along the K direction
+ Index mc = rows; // cache block size along the M direction
+ Index nc = cols; // cache block size along the N direction
+ computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
+ // kc must smaller than mc
+ kc = (std::min)(kc,mc);
+
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+ std::size_t sizeB = sizeW + kc*cols;
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
+ ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
+ Scalar* blockB = allocatedBlockB + sizeW;
+
+ gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
+
+ for(Index k2=0; k2<size; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,size)-k2;
+
+ // we have selected one row panel of rhs and one column panel of lhs
+ // pack rhs's panel into a sequential chunk of memory
+ // and expand each coeff to a constant packet for further reuse
+ pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
+
+ // the select lhs's panel has to be split in three different parts:
+ // 1 - the transposed panel above the diagonal block => transposed packed copy
+ // 2 - the diagonal block => special packed copy
+ // 3 - the panel below the diagonal block => generic packed copy
+ for(Index i2=0; i2<k2; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,k2)-i2;
+ // transposed packed copy
+ pack_lhs_transposed(blockA, &lhs(k2, i2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ // the block diagonal
+ {
+ const Index actual_mc = (std::min)(k2+kc,size)-k2;
+ // symmetric packed copy
+ pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res+k2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+
+ for(Index i2=k2+kc; i2<size; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,size)-i2;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()
+ (blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ }
+ }
+
+// matrix * selfadjoint product
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>
+{
+
+ static EIGEN_DONT_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha);
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs>
+EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>::run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha)
+ {
+ Index size = cols;
+
+ const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+
+ Index kc = size; // cache block size along the K direction
+ Index mc = rows; // cache block size along the M direction
+ Index nc = cols; // cache block size along the N direction
+ computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+ std::size_t sizeB = sizeW + kc*cols;
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
+ ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
+ Scalar* blockB = allocatedBlockB + sizeW;
+
+ gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+
+ for(Index k2=0; k2<size; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,size)-k2;
+
+ pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
+
+ // => GEPP
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,rows)-i2;
+ pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ }
+ }
+
+} // end namespace internal
+
+/***************************************************************************
+* Wrapper to product_selfadjoint_matrix
+***************************************************************************/
+
+namespace internal {
+template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
+struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false> >
+ : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs> >
+{};
+}
+
+template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
+struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>
+ : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
+
+ SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ enum {
+ LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
+ LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,
+ RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
+ RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint
+ };
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
+
+ typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
+ typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+ * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+ internal::product_selfadjoint_matrix<Scalar, Index,
+ EIGEN_LOGICAL_XOR(LhsIsUpper,
+ internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
+ NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
+ EIGEN_LOGICAL_XOR(RhsIsUpper,
+ internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
+ NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),
+ internal::traits<Dest>::Flags&RowMajorBit ? RowMajor : ColMajor>
+ ::run(
+ lhs.rows(), rhs.cols(), // sizes
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
+ &dst.coeffRef(0,0), dst.outerStride(), // result info
+ actualAlpha // alpha
+ );
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix_MKL.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix_MKL.h
new file mode 100644
index 0000000..dfa687f
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix_MKL.h
@@ -0,0 +1,295 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Self adjoint matrix * matrix product functionality based on ?SYMM/?HEMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
+#define EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+
+/* Optimized selfadjoint matrix * matrix (?SYMM/?HEMM) product */
+
+#define EIGEN_MKL_SYMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor> \
+{\
+\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha) \
+ { \
+ char side='L', uplo='L'; \
+ MKL_INT m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ MKLTYPE alpha_, beta_; \
+ MatrixX##EIGPREFIX b_tmp; \
+ EIGTYPE myone(1);\
+\
+/* Set transpose options */ \
+/* Set m, n, k */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)cols; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = (MKL_INT)lhsStride; \
+ ldb = (MKL_INT)rhsStride; \
+ ldc = (MKL_INT)resStride; \
+\
+/* Set a, b, c */ \
+ if (LhsStorageOrder==RowMajor) uplo='U'; \
+ a = _lhs; \
+\
+ if (RhsStorageOrder==RowMajor) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.adjoint(); \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+ } else b = _rhs; \
+\
+ MKLPREFIX##symm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+\
+ } \
+};
+
+
+#define EIGEN_MKL_HEMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor> \
+{\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha) \
+ { \
+ char side='L', uplo='L'; \
+ MKL_INT m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ MKLTYPE alpha_, beta_; \
+ MatrixX##EIGPREFIX b_tmp; \
+ Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> a_tmp; \
+ EIGTYPE myone(1); \
+\
+/* Set transpose options */ \
+/* Set m, n, k */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)cols; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = (MKL_INT)lhsStride; \
+ ldb = (MKL_INT)rhsStride; \
+ ldc = (MKL_INT)resStride; \
+\
+/* Set a, b, c */ \
+ if (((LhsStorageOrder==ColMajor) && ConjugateLhs) || ((LhsStorageOrder==RowMajor) && (!ConjugateLhs))) { \
+ Map<const Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder>, 0, OuterStride<> > lhs(_lhs,m,m,OuterStride<>(lhsStride)); \
+ a_tmp = lhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else a = _lhs; \
+ if (LhsStorageOrder==RowMajor) uplo='U'; \
+\
+ if (RhsStorageOrder==ColMajor && (!ConjugateRhs)) { \
+ b = _rhs; } \
+ else { \
+ if (RhsStorageOrder==ColMajor && ConjugateRhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,m,n,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.conjugate(); \
+ } else \
+ if (ConjugateRhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.adjoint(); \
+ } else { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.transpose(); \
+ } \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+ } \
+\
+ MKLPREFIX##hemm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+\
+ } \
+};
+
+EIGEN_MKL_SYMM_L(double, double, d, d)
+EIGEN_MKL_SYMM_L(float, float, f, s)
+EIGEN_MKL_HEMM_L(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_HEMM_L(scomplex, MKL_Complex8, cf, c)
+
+
+/* Optimized matrix * selfadjoint matrix (?SYMM/?HEMM) product */
+
+#define EIGEN_MKL_SYMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor> \
+{\
+\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha) \
+ { \
+ char side='R', uplo='L'; \
+ MKL_INT m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ MKLTYPE alpha_, beta_; \
+ MatrixX##EIGPREFIX b_tmp; \
+ EIGTYPE myone(1);\
+\
+/* Set m, n, k */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)cols; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = (MKL_INT)rhsStride; \
+ ldb = (MKL_INT)lhsStride; \
+ ldc = (MKL_INT)resStride; \
+\
+/* Set a, b, c */ \
+ if (RhsStorageOrder==RowMajor) uplo='U'; \
+ a = _rhs; \
+\
+ if (LhsStorageOrder==RowMajor) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = lhs.adjoint(); \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+ } else b = _lhs; \
+\
+ MKLPREFIX##symm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+\
+ } \
+};
+
+
+#define EIGEN_MKL_HEMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor> \
+{\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha) \
+ { \
+ char side='R', uplo='L'; \
+ MKL_INT m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ MKLTYPE alpha_, beta_; \
+ MatrixX##EIGPREFIX b_tmp; \
+ Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> a_tmp; \
+ EIGTYPE myone(1); \
+\
+/* Set m, n, k */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)cols; \
+\
+/* Set alpha_ & beta_ */ \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = (MKL_INT)rhsStride; \
+ ldb = (MKL_INT)lhsStride; \
+ ldc = (MKL_INT)resStride; \
+\
+/* Set a, b, c */ \
+ if (((RhsStorageOrder==ColMajor) && ConjugateRhs) || ((RhsStorageOrder==RowMajor) && (!ConjugateRhs))) { \
+ Map<const Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder>, 0, OuterStride<> > rhs(_rhs,n,n,OuterStride<>(rhsStride)); \
+ a_tmp = rhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else a = _rhs; \
+ if (RhsStorageOrder==RowMajor) uplo='U'; \
+\
+ if (LhsStorageOrder==ColMajor && (!ConjugateLhs)) { \
+ b = _lhs; } \
+ else { \
+ if (LhsStorageOrder==ColMajor && ConjugateLhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,n,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.conjugate(); \
+ } else \
+ if (ConjugateLhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.adjoint(); \
+ } else { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.transpose(); \
+ } \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+ } \
+\
+ MKLPREFIX##hemm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+ } \
+};
+
+EIGEN_MKL_SYMM_R(double, double, d, d)
+EIGEN_MKL_SYMM_R(float, float, f, s)
+EIGEN_MKL_HEMM_R(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_HEMM_R(scomplex, MKL_Complex8, cf, c)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector.h b/Eigen/src/Core/products/SelfadjointMatrixVector.h
new file mode 100644
index 0000000..f698f67
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector.h
@@ -0,0 +1,281 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+/* Optimized selfadjoint matrix * vector product:
+ * This algorithm processes 2 columns at onces that allows to both reduce
+ * the number of load/stores of the result by a factor 2 and to reduce
+ * the instruction dependency.
+ */
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized>
+struct selfadjoint_matrix_vector_product;
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
+struct selfadjoint_matrix_vector_product
+
+{
+static EIGEN_DONT_INLINE void run(
+ Index size,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsIncr,
+ Scalar* res,
+ Scalar alpha);
+};
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Version>::run(
+ Index size,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsIncr,
+ Scalar* res,
+ Scalar alpha)
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ const Index PacketSize = sizeof(Packet)/sizeof(Scalar);
+
+ enum {
+ IsRowMajor = StorageOrder==RowMajor ? 1 : 0,
+ IsLower = UpLo == Lower ? 1 : 0,
+ FirstTriangular = IsRowMajor == IsLower
+ };
+
+ conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0;
+ conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1;
+ conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex, ConjugateRhs> cjd;
+
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0;
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
+
+ Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
+
+ // FIXME this copy is now handled outside product_selfadjoint_vector, so it could probably be removed.
+ // if the rhs is not sequentially stored in memory we copy it to a temporary buffer,
+ // this is because we need to extract packets
+ ei_declare_aligned_stack_constructed_variable(Scalar,rhs,size,rhsIncr==1 ? const_cast<Scalar*>(_rhs) : 0);
+ if (rhsIncr!=1)
+ {
+ const Scalar* it = _rhs;
+ for (Index i=0; i<size; ++i, it+=rhsIncr)
+ rhs[i] = *it;
+ }
+
+ Index bound = (std::max)(Index(0),size-8) & 0xfffffffe;
+ if (FirstTriangular)
+ bound = size - bound;
+
+ for (Index j=FirstTriangular ? bound : 0;
+ j<(FirstTriangular ? size : bound);j+=2)
+ {
+ const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+ const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
+
+ Scalar t0 = cjAlpha * rhs[j];
+ Packet ptmp0 = pset1<Packet>(t0);
+ Scalar t1 = cjAlpha * rhs[j+1];
+ Packet ptmp1 = pset1<Packet>(t1);
+
+ Scalar t2(0);
+ Packet ptmp2 = pset1<Packet>(t2);
+ Scalar t3(0);
+ Packet ptmp3 = pset1<Packet>(t3);
+
+ size_t starti = FirstTriangular ? 0 : j+2;
+ size_t endi = FirstTriangular ? j : size;
+ size_t alignedStart = (starti) + internal::first_aligned(&res[starti], endi-starti);
+ size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
+
+ // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
+ res[j] += cjd.pmul(numext::real(A0[j]), t0);
+ res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
+ if(FirstTriangular)
+ {
+ res[j] += cj0.pmul(A1[j], t1);
+ t3 += cj1.pmul(A1[j], rhs[j]);
+ }
+ else
+ {
+ res[j+1] += cj0.pmul(A0[j+1],t0);
+ t2 += cj1.pmul(A0[j+1], rhs[j+1]);
+ }
+
+ for (size_t i=starti; i<alignedStart; ++i)
+ {
+ res[i] += t0 * A0[i] + t1 * A1[i];
+ t2 += numext::conj(A0[i]) * rhs[i];
+ t3 += numext::conj(A1[i]) * rhs[i];
+ }
+ // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
+ // gcc 4.2 does this optimization automatically.
+ const Scalar* EIGEN_RESTRICT a0It = A0 + alignedStart;
+ const Scalar* EIGEN_RESTRICT a1It = A1 + alignedStart;
+ const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart;
+ Scalar* EIGEN_RESTRICT resIt = res + alignedStart;
+ for (size_t i=alignedStart; i<alignedEnd; i+=PacketSize)
+ {
+ Packet A0i = ploadu<Packet>(a0It); a0It += PacketSize;
+ Packet A1i = ploadu<Packet>(a1It); a1It += PacketSize;
+ Packet Bi = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases
+ Packet Xi = pload <Packet>(resIt);
+
+ Xi = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi));
+ ptmp2 = pcj1.pmadd(A0i, Bi, ptmp2);
+ ptmp3 = pcj1.pmadd(A1i, Bi, ptmp3);
+ pstore(resIt,Xi); resIt += PacketSize;
+ }
+ for (size_t i=alignedEnd; i<endi; i++)
+ {
+ res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
+ t2 += cj1.pmul(A0[i], rhs[i]);
+ t3 += cj1.pmul(A1[i], rhs[i]);
+ }
+
+ res[j] += alpha * (t2 + predux(ptmp2));
+ res[j+1] += alpha * (t3 + predux(ptmp3));
+ }
+ for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
+ {
+ const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+
+ Scalar t1 = cjAlpha * rhs[j];
+ Scalar t2(0);
+ // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
+ res[j] += cjd.pmul(numext::real(A0[j]), t1);
+ for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
+ {
+ res[i] += cj0.pmul(A0[i], t1);
+ t2 += cj1.pmul(A0[i], rhs[i]);
+ }
+ res[j] += alpha * t2;
+ }
+}
+
+} // end namespace internal
+
+/***************************************************************************
+* Wrapper to product_selfadjoint_vector
+***************************************************************************/
+
+namespace internal {
+template<typename Lhs, int LhsMode, typename Rhs>
+struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true> >
+ : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs> >
+{};
+}
+
+template<typename Lhs, int LhsMode, typename Rhs>
+struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>
+ : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
+
+ enum {
+ LhsUpLo = LhsMode&(Upper|Lower)
+ };
+
+ SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ typedef typename Dest::Scalar ResScalar;
+ typedef typename Base::RhsScalar RhsScalar;
+ typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
+
+ eigen_assert(dest.rows()==m_lhs.rows() && dest.cols()==m_rhs.cols());
+
+ typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
+ typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+ * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+ enum {
+ EvalToDest = (Dest::InnerStrideAtCompileTime==1),
+ UseRhs = (_ActualRhsType::InnerStrideAtCompileTime==1)
+ };
+
+ internal::gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,!EvalToDest> static_dest;
+ internal::gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!UseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ EvalToDest ? dest.data() : static_dest.data());
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(),
+ UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data());
+
+ if(!EvalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ int size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ if(!UseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ int size = rhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, rhs.size()) = rhs;
+ }
+
+
+ internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run
+ (
+ lhs.rows(), // size
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ actualRhsPtr, 1, // rhs info
+ actualDestPtr, // result info
+ actualAlpha // scale factor
+ );
+
+ if(!EvalToDest)
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+};
+
+namespace internal {
+template<typename Lhs, typename Rhs, int RhsMode>
+struct traits<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false> >
+ : traits<ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs> >
+{};
+}
+
+template<typename Lhs, typename Rhs, int RhsMode>
+struct SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>
+ : public ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
+
+ enum {
+ RhsUpLo = RhsMode&(Upper|Lower)
+ };
+
+ SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ // let's simply transpose the product
+ Transpose<Dest> destT(dest);
+ SelfadjointProductMatrix<Transpose<const Rhs>, int(RhsUpLo)==Upper ? Lower : Upper, false,
+ Transpose<const Lhs>, 0, true>(m_rhs.transpose(), m_lhs.transpose()).scaleAndAddTo(destT, alpha);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector_MKL.h b/Eigen/src/Core/products/SelfadjointMatrixVector_MKL.h
new file mode 100644
index 0000000..86684b6
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector_MKL.h
@@ -0,0 +1,114 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Selfadjoint matrix-vector product functionality based on ?SYMV/HEMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements selfadjoint matrix-vector multiplication using BLAS
+**********************************************************************/
+
+// symv/hemv specialization
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs>
+struct selfadjoint_matrix_vector_product_symv :
+ selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn> {};
+
+#define EIGEN_MKL_SYMV_SPECIALIZE(Scalar) \
+template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
+struct selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Specialized> { \
+static void run( \
+ Index size, const Scalar* lhs, Index lhsStride, \
+ const Scalar* _rhs, Index rhsIncr, Scalar* res, Scalar alpha) { \
+ enum {\
+ IsColMajor = StorageOrder==ColMajor \
+ }; \
+ if (IsColMajor == ConjugateLhs) {\
+ selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn>::run( \
+ size, lhs, lhsStride, _rhs, rhsIncr, res, alpha); \
+ } else {\
+ selfadjoint_matrix_vector_product_symv<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs>::run( \
+ size, lhs, lhsStride, _rhs, rhsIncr, res, alpha); \
+ }\
+ } \
+}; \
+
+EIGEN_MKL_SYMV_SPECIALIZE(double)
+EIGEN_MKL_SYMV_SPECIALIZE(float)
+EIGEN_MKL_SYMV_SPECIALIZE(dcomplex)
+EIGEN_MKL_SYMV_SPECIALIZE(scomplex)
+
+#define EIGEN_MKL_SYMV_SPECIALIZATION(EIGTYPE,MKLTYPE,MKLFUNC) \
+template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
+struct selfadjoint_matrix_vector_product_symv<EIGTYPE,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs> \
+{ \
+typedef Matrix<EIGTYPE,Dynamic,1,ColMajor> SYMVVector;\
+\
+static void run( \
+Index size, const EIGTYPE* lhs, Index lhsStride, \
+const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* res, EIGTYPE alpha) \
+{ \
+ enum {\
+ IsRowMajor = StorageOrder==RowMajor ? 1 : 0, \
+ IsLower = UpLo == Lower ? 1 : 0 \
+ }; \
+ MKL_INT n=size, lda=lhsStride, incx=rhsIncr, incy=1; \
+ MKLTYPE alpha_, beta_; \
+ const EIGTYPE *x_ptr, myone(1); \
+ char uplo=(IsRowMajor) ? (IsLower ? 'U' : 'L') : (IsLower ? 'L' : 'U'); \
+ assign_scalar_eig2mkl(alpha_, alpha); \
+ assign_scalar_eig2mkl(beta_, myone); \
+ SYMVVector x_tmp; \
+ if (ConjugateRhs) { \
+ Map<const SYMVVector, 0, InnerStride<> > map_x(_rhs,size,1,InnerStride<>(incx)); \
+ x_tmp=map_x.conjugate(); \
+ x_ptr=x_tmp.data(); \
+ incx=1; \
+ } else x_ptr=_rhs; \
+ MKLFUNC(&uplo, &n, &alpha_, (const MKLTYPE*)lhs, &lda, (const MKLTYPE*)x_ptr, &incx, &beta_, (MKLTYPE*)res, &incy); \
+}\
+};
+
+EIGEN_MKL_SYMV_SPECIALIZATION(double, double, dsymv)
+EIGEN_MKL_SYMV_SPECIALIZATION(float, float, ssymv)
+EIGEN_MKL_SYMV_SPECIALIZATION(dcomplex, MKL_Complex16, zhemv)
+EIGEN_MKL_SYMV_SPECIALIZATION(scomplex, MKL_Complex8, chemv)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
diff --git a/Eigen/src/Core/products/SelfadjointProduct.h b/Eigen/src/Core/products/SelfadjointProduct.h
new file mode 100644
index 0000000..6ca4ae6
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointProduct.h
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_PRODUCT_H
+#define EIGEN_SELFADJOINT_PRODUCT_H
+
+/**********************************************************************
+* This file implements a self adjoint product: C += A A^T updating only
+* half of the selfadjoint matrix C.
+* It corresponds to the level 3 SYRK and level 2 SYR Blas routines.
+**********************************************************************/
+
+namespace Eigen {
+
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
+{
+ static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)
+ {
+ internal::conj_if<ConjRhs> cj;
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ typedef typename internal::conditional<ConjLhs,typename OtherMap::ConjugateReturnType,const OtherMap&>::type ConjLhsType;
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), (UpLo==Lower ? size-i : (i+1)))
+ += (alpha * cj(vecY[i])) * ConjLhsType(OtherMap(vecX+(UpLo==Lower ? i : 0),UpLo==Lower ? size-i : (i+1)));
+ }
+ }
+};
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
+{
+ static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)
+ {
+ selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,stride,vecY,vecX,alpha);
+ }
+};
+
+template<typename MatrixType, typename OtherType, int UpLo, bool OtherIsVector = OtherType::IsVectorAtCompileTime>
+struct selfadjoint_product_selector;
+
+template<typename MatrixType, typename OtherType, int UpLo>
+struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,true>
+{
+ static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef internal::blas_traits<OtherType> OtherBlasTraits;
+ typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;
+ typedef typename internal::remove_all<ActualOtherType>::type _ActualOtherType;
+ typename internal::add_const_on_value_type<ActualOtherType>::type actualOther = OtherBlasTraits::extract(other.derived());
+
+ Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());
+
+ enum {
+ StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ UseOtherDirectly = _ActualOtherType::InnerStrideAtCompileTime==1
+ };
+ internal::gemv_static_vector_if<Scalar,OtherType::SizeAtCompileTime,OtherType::MaxSizeAtCompileTime,!UseOtherDirectly> static_other;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualOtherPtr, other.size(),
+ (UseOtherDirectly ? const_cast<Scalar*>(actualOther.data()) : static_other.data()));
+
+ if(!UseOtherDirectly)
+ Map<typename _ActualOtherType::PlainObject>(actualOtherPtr, actualOther.size()) = actualOther;
+
+ selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
+ OtherBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex>
+ ::run(other.size(), mat.data(), mat.outerStride(), actualOtherPtr, actualOtherPtr, actualAlpha);
+ }
+};
+
+template<typename MatrixType, typename OtherType, int UpLo>
+struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,false>
+{
+ static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef internal::blas_traits<OtherType> OtherBlasTraits;
+ typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;
+ typedef typename internal::remove_all<ActualOtherType>::type _ActualOtherType;
+ typename internal::add_const_on_value_type<ActualOtherType>::type actualOther = OtherBlasTraits::extract(other.derived());
+
+ Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());
+
+ enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
+
+ internal::general_matrix_matrix_triangular_product<Index,
+ Scalar, _ActualOtherType::Flags&RowMajorBit ? RowMajor : ColMajor, OtherBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ Scalar, _ActualOtherType::Flags&RowMajorBit ? ColMajor : RowMajor, (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex,
+ MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
+ ::run(mat.cols(), actualOther.cols(),
+ &actualOther.coeffRef(0,0), actualOther.outerStride(), &actualOther.coeffRef(0,0), actualOther.outerStride(),
+ mat.data(), mat.outerStride(), actualAlpha);
+ }
+};
+
+// high level API
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename DerivedU>
+SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
+::rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha)
+{
+ selfadjoint_product_selector<MatrixType,DerivedU,UpLo>::run(_expression().const_cast_derived(), u.derived(), alpha);
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_PRODUCT_H
diff --git a/Eigen/src/Core/products/SelfadjointRank2Update.h b/Eigen/src/Core/products/SelfadjointRank2Update.h
new file mode 100644
index 0000000..8594a97
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointRank2Update.h
@@ -0,0 +1,93 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTRANK2UPTADE_H
+#define EIGEN_SELFADJOINTRANK2UPTADE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
+ * It corresponds to the Level2 syr2 BLAS routine
+ */
+
+template<typename Scalar, typename Index, typename UType, typename VType, int UpLo>
+struct selfadjoint_rank2_update_selector;
+
+template<typename Scalar, typename Index, typename UType, typename VType>
+struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>
+{
+ static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
+ {
+ const Index size = u.size();
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
+ (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)
+ + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);
+ }
+ }
+};
+
+template<typename Scalar, typename Index, typename UType, typename VType>
+struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>
+{
+ static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
+ {
+ const Index size = u.size();
+ for (Index i=0; i<size; ++i)
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
+ (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.head(i+1)
+ + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);
+ }
+};
+
+template<bool Cond, typename T> struct conj_expr_if
+ : conditional<!Cond, const T&,
+ CwiseUnaryOp<scalar_conjugate_op<typename traits<T>::Scalar>,T> > {};
+
+} // end namespace internal
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename DerivedU, typename DerivedV>
+SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
+::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha)
+{
+ typedef internal::blas_traits<DerivedU> UBlasTraits;
+ typedef typename UBlasTraits::DirectLinearAccessType ActualUType;
+ typedef typename internal::remove_all<ActualUType>::type _ActualUType;
+ typename internal::add_const_on_value_type<ActualUType>::type actualU = UBlasTraits::extract(u.derived());
+
+ typedef internal::blas_traits<DerivedV> VBlasTraits;
+ typedef typename VBlasTraits::DirectLinearAccessType ActualVType;
+ typedef typename internal::remove_all<ActualVType>::type _ActualVType;
+ typename internal::add_const_on_value_type<ActualVType>::type actualV = VBlasTraits::extract(v.derived());
+
+ // If MatrixType is row major, then we use the routine for lower triangular in the upper triangular case and
+ // vice versa, and take the complex conjugate of all coefficients and vector entries.
+
+ enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
+ Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())
+ * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));
+ if (IsRowMajor)
+ actualAlpha = numext::conj(actualAlpha);
+
+ internal::selfadjoint_rank2_update_selector<Scalar, Index,
+ typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ UBlasTraits::NeedToConjugate,_ActualUType>::type>::type,
+ typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ VBlasTraits::NeedToConjugate,_ActualVType>::type>::type,
+ (IsRowMajor ? int(UpLo==Upper ? Lower : Upper) : UpLo)>
+ ::run(_expression().const_cast_derived().data(),_expression().outerStride(),actualU,actualV,actualAlpha);
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTRANK2UPTADE_H
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix.h b/Eigen/src/Core/products/TriangularMatrixMatrix.h
new file mode 100644
index 0000000..8110507
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix.h
@@ -0,0 +1,427 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
+// struct gemm_pack_lhs_triangular
+// {
+// Matrix<Scalar,mr,mr,
+// void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)
+// {
+// conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+// const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride);
+// int count = 0;
+// const int peeled_mc = (rows/mr)*mr;
+// for(int i=0; i<peeled_mc; i+=mr)
+// {
+// for(int k=0; k<depth; k++)
+// for(int w=0; w<mr; w++)
+// blockA[count++] = cj(lhs(i+w, k));
+// }
+// for(int i=peeled_mc; i<rows; i++)
+// {
+// for(int k=0; k<depth; k++)
+// blockA[count++] = cj(lhs(i, k));
+// }
+// }
+// };
+
+/* Optimized triangular matrix * matrix (_TRMM++) product built on top of
+ * the general matrix matrix product.
+ */
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder, int Version = Specialized>
+struct product_triangular_matrix_matrix;
+
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,RowMajor,Version>
+{
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols, Index depth,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ product_triangular_matrix_matrix<Scalar, Index,
+ (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),
+ (!LhsIsTriangular),
+ RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+ ConjugateRhs,
+ LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+ ConjugateLhs,
+ ColMajor>
+ ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha, blocking);
+ }
+};
+
+// implements col-major += alpha * op(triangular) * op(general)
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,Version>
+{
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ SmallPanelWidth = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
+ IsLower = (Mode&Lower) == Lower,
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
+ };
+
+ static EIGEN_DONT_INLINE void run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ // strip zeros
+ Index diagSize = (std::min)(_rows,_depth);
+ Index rows = IsLower ? _rows : diagSize;
+ Index depth = IsLower ? diagSize : _depth;
+ Index cols = _cols;
+
+ const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
+
+ Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
+ triangularBuffer.setZero();
+ if((Mode&ZeroDiag)==ZeroDiag)
+ triangularBuffer.diagonal().setZero();
+ else
+ triangularBuffer.diagonal().setOnes();
+
+ gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+
+ for(Index k2=IsLower ? depth : 0;
+ IsLower ? k2>0 : k2<depth;
+ IsLower ? k2-=kc : k2+=kc)
+ {
+ Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
+ Index actual_k2 = IsLower ? k2-actual_kc : k2;
+
+ // align blocks with the end of the triangular part for trapezoidal lhs
+ if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
+ {
+ actual_kc = rows-k2;
+ k2 = k2+actual_kc-kc;
+ }
+
+ pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
+
+ // the selected lhs's panel has to be split in three different parts:
+ // 1 - the part which is zero => skip it
+ // 2 - the diagonal block => special kernel
+ // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
+
+ // the block diagonal, if any:
+ if(IsLower || actual_k2<rows)
+ {
+ // for each small vertical panels of lhs
+ for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
+ Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
+ Index startBlock = actual_k2+k1;
+ Index blockBOffset = k1;
+
+ // => GEBP with the micro triangular block
+ // The trick is to pack this micro block while filling the opposite triangular part with zeros.
+ // To this end we do an extra triangular copy to a small temporary buffer
+ for (Index k=0;k<actualPanelWidth;++k)
+ {
+ if (SetDiag)
+ triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
+ for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
+ triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
+ }
+ pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
+
+ gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
+ actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
+
+ // GEBP with remaining micro panel
+ if (lengthTarget>0)
+ {
+ Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
+
+ pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
+
+ gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
+ actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
+ }
+ }
+ }
+ // the part below (lower case) or above (upper case) the diagonal => GEPP
+ {
+ Index start = IsLower ? k2 : 0;
+ Index end = IsLower ? rows : (std::min)(actual_k2,rows);
+ for(Index i2=start; i2<end; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,end)-i2;
+ gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
+ (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
+ }
+ }
+ }
+ }
+
+// implements col-major += alpha * op(general) * op(triangular)
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,Version>
+{
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
+ IsLower = (Mode&Lower) == Lower,
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
+ };
+
+ static EIGEN_DONT_INLINE void run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ // strip zeros
+ Index diagSize = (std::min)(_cols,_depth);
+ Index rows = _rows;
+ Index depth = IsLower ? _depth : diagSize;
+ Index cols = IsLower ? diagSize : _cols;
+
+ const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
+
+ Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
+ triangularBuffer.setZero();
+ if((Mode&ZeroDiag)==ZeroDiag)
+ triangularBuffer.diagonal().setZero();
+ else
+ triangularBuffer.diagonal().setOnes();
+
+ gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
+
+ for(Index k2=IsLower ? 0 : depth;
+ IsLower ? k2<depth : k2>0;
+ IsLower ? k2+=kc : k2-=kc)
+ {
+ Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
+ Index actual_k2 = IsLower ? k2 : k2-actual_kc;
+
+ // align blocks with the end of the triangular part for trapezoidal rhs
+ if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
+ {
+ actual_kc = cols-k2;
+ k2 = actual_k2 + actual_kc - kc;
+ }
+
+ // remaining size
+ Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
+ // size of the triangular part
+ Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
+
+ Scalar* geb = blockB+ts*ts;
+
+ pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
+
+ // pack the triangular part of the rhs padding the unrolled blocks with zeros
+ if(ts>0)
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index actual_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
+ // general part
+ pack_rhs_panel(blockB+j2*actual_kc,
+ &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
+ panelLength, actualPanelWidth,
+ actual_kc, panelOffset);
+
+ // append the triangular part via a temporary buffer
+ for (Index j=0;j<actualPanelWidth;++j)
+ {
+ if (SetDiag)
+ triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
+ for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
+ triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
+ }
+
+ pack_rhs_panel(blockB+j2*actual_kc,
+ triangularBuffer.data(), triangularBuffer.outerStride(),
+ actualPanelWidth, actualPanelWidth,
+ actual_kc, j2);
+ }
+ }
+
+ for (Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,rows-i2);
+ pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
+
+ // triangular kernel
+ if(ts>0)
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
+ Index blockOffset = IsLower ? j2 : 0;
+
+ gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
+ blockA, blockB+j2*actual_kc,
+ actual_mc, panelLength, actualPanelWidth,
+ alpha,
+ actual_kc, actual_kc, // strides
+ blockOffset, blockOffset,// offsets
+ blockW); // workspace
+ }
+ }
+ gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
+ blockA, geb, actual_mc, actual_kc, rs,
+ alpha,
+ -1, -1, 0, 0, blockW);
+ }
+ }
+ }
+
+/***************************************************************************
+* Wrapper to product_triangular_matrix_matrix
+***************************************************************************/
+
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
+ : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
+{};
+
+} // end namespace internal
+
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
+ : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
+
+ TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
+ typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+ * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
+
+ enum { IsLower = (Mode&Lower) == Lower };
+ Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
+ Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
+ Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
+ : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
+
+ BlockingType blocking(stripedRows, stripedCols, stripedDepth);
+
+ internal::product_triangular_matrix_matrix<Scalar, Index,
+ Mode, LhsIsTriangular,
+ (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+ (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+ (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
+ ::run(
+ stripedRows, stripedCols, stripedDepth, // sizes
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
+ &dst.coeffRef(0,0), dst.outerStride(), // result info
+ actualAlpha, blocking
+ );
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix_MKL.h b/Eigen/src/Core/products/TriangularMatrixMatrix_MKL.h
new file mode 100644
index 0000000..ba41a1c
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix_MKL.h
@@ -0,0 +1,309 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Triangular matrix * matrix product functionality based on ?TRMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder>
+struct product_triangular_matrix_matrix_trmm :
+ product_triangular_matrix_matrix<Scalar,Index,Mode,
+ LhsIsTriangular,LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder, ConjugateRhs, ResStorageOrder, BuiltIn> {};
+
+
+// try to go to BLAS specialization
+#define EIGEN_MKL_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,Specialized> { \
+ static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\
+ const Scalar* _rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha, level3_blocking<Scalar,Scalar>& blocking) { \
+ product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \
+ LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \
+ RhsStorageOrder, ConjugateRhs, ColMajor>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
+ } \
+};
+
+EIGEN_MKL_TRMM_SPECIALIZE(double, true)
+EIGEN_MKL_TRMM_SPECIALIZE(double, false)
+EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, true)
+EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, false)
+EIGEN_MKL_TRMM_SPECIALIZE(float, true)
+EIGEN_MKL_TRMM_SPECIALIZE(float, false)
+EIGEN_MKL_TRMM_SPECIALIZE(scomplex, true)
+EIGEN_MKL_TRMM_SPECIALIZE(scomplex, false)
+
+// implements col-major += alpha * op(triangular) * op(general)
+#define EIGEN_MKL_TRMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
+ LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \
+ }; \
+\
+ static void run( \
+ Index _rows, Index _cols, Index _depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
+ { \
+ Index diagSize = (std::min)(_rows,_depth); \
+ Index rows = IsLower ? _rows : diagSize; \
+ Index depth = IsLower ? diagSize : _depth; \
+ Index cols = _cols; \
+\
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
+\
+/* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
+ if (rows != depth) { \
+\
+ int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+\
+ if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
+ /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
+ product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
+ /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \
+ } else { \
+ /* Make sense to call GEMM */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
+ MKL_INT aStride = aa_tmp.outerStride(); \
+ gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth); \
+ general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
+ rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, resStride, alpha, gemm_blocking, 0); \
+\
+ /*std::cout << "TRMM_L: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
+ } \
+ return; \
+ } \
+ char side = 'L', transa, uplo, diag = 'N'; \
+ EIGTYPE *b; \
+ const EIGTYPE *a; \
+ MKL_INT m, n, lda, ldb; \
+ MKLTYPE alpha_; \
+\
+/* Set alpha_*/ \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
+\
+/* Set m, n */ \
+ m = (MKL_INT)diagSize; \
+ n = (MKL_INT)cols; \
+\
+/* Set trans */ \
+ transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set b, ldb */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+ if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+\
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixLhs a_tmp; \
+\
+ if ((conjA!=0) || (SetDiag==0)) { \
+ if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \
+ if (IsZeroDiag) \
+ a_tmp.diagonal().setZero(); \
+ else if (IsUnitDiag) \
+ a_tmp.diagonal().setOnes();\
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else { \
+ a = _lhs; \
+ lda = lhsStride; \
+ } \
+ /*std::cout << "TRMM_L: A is square! Go to MKL TRMM implementation! \n";*/ \
+/* call ?trmm*/ \
+ MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
+\
+/* Add op(a_triangular)*b into res*/ \
+ Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
+ res_tmp=res_tmp+b_tmp; \
+ } \
+};
+
+EIGEN_MKL_TRMM_L(double, double, d, d)
+EIGEN_MKL_TRMM_L(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_TRMM_L(float, float, f, s)
+EIGEN_MKL_TRMM_L(scomplex, MKL_Complex8, cf, c)
+
+// implements col-major += alpha * op(general) * op(triangular)
+#define EIGEN_MKL_TRMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
+ LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \
+ }; \
+\
+ static void run( \
+ Index _rows, Index _cols, Index _depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
+ { \
+ Index diagSize = (std::min)(_cols,_depth); \
+ Index rows = _rows; \
+ Index depth = IsLower ? _depth : diagSize; \
+ Index cols = IsLower ? diagSize : _cols; \
+\
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
+\
+/* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
+ if (cols != depth) { \
+\
+ int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+\
+ if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
+ /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
+ product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
+ /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \
+ } else { \
+ /* Make sense to call GEMM */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
+ MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
+ MKL_INT aStride = aa_tmp.outerStride(); \
+ gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth); \
+ general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
+ rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, resStride, alpha, gemm_blocking, 0); \
+\
+ /*std::cout << "TRMM_R: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
+ } \
+ return; \
+ } \
+ char side = 'R', transa, uplo, diag = 'N'; \
+ EIGTYPE *b; \
+ const EIGTYPE *a; \
+ MKL_INT m, n, lda, ldb; \
+ MKLTYPE alpha_; \
+\
+/* Set alpha_*/ \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
+\
+/* Set m, n */ \
+ m = (MKL_INT)rows; \
+ n = (MKL_INT)diagSize; \
+\
+/* Set trans */ \
+ transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set b, ldb */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+ if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
+ b = b_tmp.data(); \
+ ldb = b_tmp.outerStride(); \
+\
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \
+ MatrixRhs a_tmp; \
+\
+ if ((conjA!=0) || (SetDiag==0)) { \
+ if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \
+ if (IsZeroDiag) \
+ a_tmp.diagonal().setZero(); \
+ else if (IsUnitDiag) \
+ a_tmp.diagonal().setOnes();\
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else { \
+ a = _rhs; \
+ lda = rhsStride; \
+ } \
+ /*std::cout << "TRMM_R: A is square! Go to MKL TRMM implementation! \n";*/ \
+/* call ?trmm*/ \
+ MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
+\
+/* Add op(a_triangular)*b into res*/ \
+ Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
+ res_tmp=res_tmp+b_tmp; \
+ } \
+};
+
+EIGEN_MKL_TRMM_R(double, double, d, d)
+EIGEN_MKL_TRMM_R(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_TRMM_R(float, float, f, s)
+EIGEN_MKL_TRMM_R(scomplex, MKL_Complex8, cf, c)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
new file mode 100644
index 0000000..6117d5a
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -0,0 +1,348 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULARMATRIXVECTOR_H
+#define EIGEN_TRIANGULARMATRIXVECTOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder, int Version=Specialized>
+struct triangular_matrix_vector_product;
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>
+struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha);
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>
+EIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>
+ ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha)
+ {
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ Index size = (std::min)(_rows,_cols);
+ Index rows = IsLower ? _rows : (std::min)(_rows,_cols);
+ Index cols = IsLower ? (std::min)(_rows,_cols) : _cols;
+
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
+ typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
+
+ typedef Map<const Matrix<RhsScalar,Dynamic,1>, 0, InnerStride<> > RhsMap;
+ const RhsMap rhs(_rhs,cols,InnerStride<>(rhsIncr));
+ typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
+
+ typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;
+ ResMap res(_res,rows);
+
+ for (Index pi=0; pi<size; pi+=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(PanelWidth, size-pi);
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = pi + k;
+ Index s = IsLower ? ((HasUnitDiag||HasZeroDiag) ? i+1 : i ) : pi;
+ Index r = IsLower ? actualPanelWidth-k : k+1;
+ if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)
+ res.segment(s,r) += (alpha * cjRhs.coeff(i)) * cjLhs.col(i).segment(s,r);
+ if (HasUnitDiag)
+ res.coeffRef(i) += alpha * cjRhs.coeff(i);
+ }
+ Index r = IsLower ? rows - pi - actualPanelWidth : pi;
+ if (r>0)
+ {
+ Index s = IsLower ? pi+actualPanelWidth : 0;
+ general_matrix_vector_product<Index,LhsScalar,ColMajor,ConjLhs,RhsScalar,ConjRhs,BuiltIn>::run(
+ r, actualPanelWidth,
+ &lhs.coeffRef(s,pi), lhsStride,
+ &rhs.coeffRef(pi), rhsIncr,
+ &res.coeffRef(s), resIncr, alpha);
+ }
+ }
+ if((!IsLower) && cols>size)
+ {
+ general_matrix_vector_product<Index,LhsScalar,ColMajor,ConjLhs,RhsScalar,ConjRhs>::run(
+ rows, cols-size,
+ &lhs.coeffRef(0,size), lhsStride,
+ &rhs.coeffRef(size), rhsIncr,
+ _res, resIncr, alpha);
+ }
+ }
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>
+struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha);
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>
+EIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>
+ ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha)
+ {
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ Index diagSize = (std::min)(_rows,_cols);
+ Index rows = IsLower ? _rows : diagSize;
+ Index cols = IsLower ? diagSize : _cols;
+
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
+ typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
+
+ typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;
+ const RhsMap rhs(_rhs,cols);
+ typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
+
+ typedef Map<Matrix<ResScalar,Dynamic,1>, 0, InnerStride<> > ResMap;
+ ResMap res(_res,rows,InnerStride<>(resIncr));
+
+ for (Index pi=0; pi<diagSize; pi+=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(PanelWidth, diagSize-pi);
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = pi + k;
+ Index s = IsLower ? pi : ((HasUnitDiag||HasZeroDiag) ? i+1 : i);
+ Index r = IsLower ? k+1 : actualPanelWidth-k;
+ if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)
+ res.coeffRef(i) += alpha * (cjLhs.row(i).segment(s,r).cwiseProduct(cjRhs.segment(s,r).transpose())).sum();
+ if (HasUnitDiag)
+ res.coeffRef(i) += alpha * cjRhs.coeff(i);
+ }
+ Index r = IsLower ? pi : cols - pi - actualPanelWidth;
+ if (r>0)
+ {
+ Index s = IsLower ? 0 : pi + actualPanelWidth;
+ general_matrix_vector_product<Index,LhsScalar,RowMajor,ConjLhs,RhsScalar,ConjRhs,BuiltIn>::run(
+ actualPanelWidth, r,
+ &lhs.coeffRef(pi,s), lhsStride,
+ &rhs.coeffRef(s), rhsIncr,
+ &res.coeffRef(pi), resIncr, alpha);
+ }
+ }
+ if(IsLower && rows>diagSize)
+ {
+ general_matrix_vector_product<Index,LhsScalar,RowMajor,ConjLhs,RhsScalar,ConjRhs>::run(
+ rows-diagSize, cols,
+ &lhs.coeffRef(diagSize,0), lhsStride,
+ &rhs.coeffRef(0), rhsIncr,
+ &res.coeffRef(diagSize), resIncr, alpha);
+ }
+ }
+
+/***************************************************************************
+* Wrapper to product_triangular_vector
+***************************************************************************/
+
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,true> >
+ : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,true>, Lhs, Rhs> >
+{};
+
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,true,Rhs,false> >
+ : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,true,Rhs,false>, Lhs, Rhs> >
+{};
+
+
+template<int StorageOrder>
+struct trmv_selector;
+
+} // end namespace internal
+
+template<int Mode, typename Lhs, typename Rhs>
+struct TriangularProduct<Mode,true,Lhs,false,Rhs,true>
+ : public ProductBase<TriangularProduct<Mode,true,Lhs,false,Rhs,true>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
+
+ TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
+
+ internal::trmv_selector<(int(internal::traits<Lhs>::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(*this, dst, alpha);
+ }
+};
+
+template<int Mode, typename Lhs, typename Rhs>
+struct TriangularProduct<Mode,false,Lhs,true,Rhs,false>
+ : public ProductBase<TriangularProduct<Mode,false,Lhs,true,Rhs,false>, Lhs, Rhs >
+{
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
+
+ TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
+ {
+ eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
+
+ typedef TriangularProduct<(Mode & (UnitDiag|ZeroDiag)) | ((Mode & Lower) ? Upper : Lower),true,Transpose<const Rhs>,false,Transpose<const Lhs>,true> TriangularProductTranspose;
+ Transpose<Dest> dstT(dst);
+ internal::trmv_selector<(int(internal::traits<Rhs>::Flags)&RowMajorBit) ? ColMajor : RowMajor>::run(
+ TriangularProductTranspose(m_rhs.transpose(),m_lhs.transpose()), dstT, alpha);
+ }
+};
+
+namespace internal {
+
+// TODO: find a way to factorize this piece of code with gemv_selector since the logic is exactly the same.
+
+template<> struct trmv_selector<ColMajor>
+{
+ template<int Mode, typename Lhs, typename Rhs, typename Dest>
+ static void run(const TriangularProduct<Mode,true,Lhs,false,Rhs,true>& prod, Dest& dest, const typename TriangularProduct<Mode,true,Lhs,false,Rhs,true>::Scalar& alpha)
+ {
+ typedef TriangularProduct<Mode,true,Lhs,false,Rhs,true> ProductType;
+ typedef typename ProductType::Index Index;
+ typedef typename ProductType::LhsScalar LhsScalar;
+ typedef typename ProductType::RhsScalar RhsScalar;
+ typedef typename ProductType::Scalar ResScalar;
+ typedef typename ProductType::RealScalar RealScalar;
+ typedef typename ProductType::ActualLhsType ActualLhsType;
+ typedef typename ProductType::ActualRhsType ActualRhsType;
+ typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+ typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+ typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
+
+ typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+ typename internal::add_const_on_value_type<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+ * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
+ ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
+ MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
+ };
+
+ gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+
+ bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
+ bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
+
+ RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ evalToDest ? dest.data() : static_dest.data());
+
+ if(!evalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ if(!alphaIsCompatible)
+ {
+ MappedDest(actualDestPtr, dest.size()).setZero();
+ compatibleAlpha = RhsScalar(1);
+ }
+ else
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ internal::triangular_matrix_vector_product
+ <Index,Mode,
+ LhsScalar, LhsBlasTraits::NeedToConjugate,
+ RhsScalar, RhsBlasTraits::NeedToConjugate,
+ ColMajor>
+ ::run(actualLhs.rows(),actualLhs.cols(),
+ actualLhs.data(),actualLhs.outerStride(),
+ actualRhs.data(),actualRhs.innerStride(),
+ actualDestPtr,1,compatibleAlpha);
+
+ if (!evalToDest)
+ {
+ if(!alphaIsCompatible)
+ dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
+ else
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+ }
+};
+
+template<> struct trmv_selector<RowMajor>
+{
+ template<int Mode, typename Lhs, typename Rhs, typename Dest>
+ static void run(const TriangularProduct<Mode,true,Lhs,false,Rhs,true>& prod, Dest& dest, const typename TriangularProduct<Mode,true,Lhs,false,Rhs,true>::Scalar& alpha)
+ {
+ typedef TriangularProduct<Mode,true,Lhs,false,Rhs,true> ProductType;
+ typedef typename ProductType::LhsScalar LhsScalar;
+ typedef typename ProductType::RhsScalar RhsScalar;
+ typedef typename ProductType::Scalar ResScalar;
+ typedef typename ProductType::Index Index;
+ typedef typename ProductType::ActualLhsType ActualLhsType;
+ typedef typename ProductType::ActualRhsType ActualRhsType;
+ typedef typename ProductType::_ActualRhsType _ActualRhsType;
+ typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+ typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+
+ typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+ typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+ * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+ enum {
+ DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
+ };
+
+ gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
+ DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
+
+ if(!DirectlyUseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ int size = actualRhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+ }
+
+ internal::triangular_matrix_vector_product
+ <Index,Mode,
+ LhsScalar, LhsBlasTraits::NeedToConjugate,
+ RhsScalar, RhsBlasTraits::NeedToConjugate,
+ RowMajor>
+ ::run(actualLhs.rows(),actualLhs.cols(),
+ actualLhs.data(),actualLhs.outerStride(),
+ actualRhsPtr,1,
+ dest.data(),dest.innerStride(),
+ actualAlpha);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULARMATRIXVECTOR_H
diff --git a/Eigen/src/Core/products/TriangularMatrixVector_MKL.h b/Eigen/src/Core/products/TriangularMatrixVector_MKL.h
new file mode 100644
index 0000000..09f110d
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixVector_MKL.h
@@ -0,0 +1,247 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Triangular matrix-vector product functionality based on ?TRMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
+#define EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements triangular matrix-vector multiplication using BLAS
+**********************************************************************/
+
+// trmv/hemv specialization
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>
+struct triangular_matrix_vector_product_trmv :
+ triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {};
+
+#define EIGEN_MKL_TRMV_SPECIALIZE(Scalar) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \
+ static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
+ const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
+ triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ } \
+}; \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor,Specialized> { \
+ static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
+ const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
+ triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ } \
+};
+
+EIGEN_MKL_TRMV_SPECIALIZE(double)
+EIGEN_MKL_TRMV_SPECIALIZE(float)
+EIGEN_MKL_TRMV_SPECIALIZE(dcomplex)
+EIGEN_MKL_TRMV_SPECIALIZE(scomplex)
+
+// implements col-major: res += alpha * op(triangular) * vector
+#define EIGEN_MKL_TRMV_CM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor> { \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper \
+ }; \
+ static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \
+ { \
+ if (ConjLhs || IsZeroDiag) { \
+ triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor,BuiltIn>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ return; \
+ }\
+ Index size = (std::min)(_rows,_cols); \
+ Index rows = IsLower ? _rows : size; \
+ Index cols = IsLower ? size : _cols; \
+\
+ typedef VectorX##EIGPREFIX VectorRhs; \
+ EIGTYPE *x, *y;\
+\
+/* Set x*/ \
+ Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
+ VectorRhs x_tmp; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+\
+/* Square part handling */\
+\
+ char trans, uplo, diag; \
+ MKL_INT m, n, lda, incx, incy; \
+ EIGTYPE const *a; \
+ MKLTYPE alpha_, beta_; \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
+\
+/* Set m, n */ \
+ n = (MKL_INT)size; \
+ lda = lhsStride; \
+ incx = 1; \
+ incy = resIncr; \
+\
+/* Set uplo, trans and diag*/ \
+ trans = 'N'; \
+ uplo = IsLower ? 'L' : 'U'; \
+ diag = IsUnitDiag ? 'U' : 'N'; \
+\
+/* call ?TRMV*/ \
+ MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
+\
+/* Add op(a_tr)rhs into res*/ \
+ MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
+/* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
+ if (size<(std::max)(rows,cols)) { \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic> MatrixLhs; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+ if (size<rows) { \
+ y = _res + size*resIncr; \
+ a = _lhs + size; \
+ m = rows-size; \
+ n = size; \
+ } \
+ else { \
+ x += size; \
+ y = _res; \
+ a = _lhs + size*lda; \
+ m = size; \
+ n = cols-size; \
+ } \
+ MKLPREFIX##gemv(&trans, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
+ } \
+ } \
+};
+
+EIGEN_MKL_TRMV_CM(double, double, d, d)
+EIGEN_MKL_TRMV_CM(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_TRMV_CM(float, float, f, s)
+EIGEN_MKL_TRMV_CM(scomplex, MKL_Complex8, cf, c)
+
+// implements row-major: res += alpha * op(triangular) * vector
+#define EIGEN_MKL_TRMV_RM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper \
+ }; \
+ static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \
+ { \
+ if (IsZeroDiag) { \
+ triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor,BuiltIn>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ return; \
+ }\
+ Index size = (std::min)(_rows,_cols); \
+ Index rows = IsLower ? _rows : size; \
+ Index cols = IsLower ? size : _cols; \
+\
+ typedef VectorX##EIGPREFIX VectorRhs; \
+ EIGTYPE *x, *y;\
+\
+/* Set x*/ \
+ Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
+ VectorRhs x_tmp; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+\
+/* Square part handling */\
+\
+ char trans, uplo, diag; \
+ MKL_INT m, n, lda, incx, incy; \
+ EIGTYPE const *a; \
+ MKLTYPE alpha_, beta_; \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
+ assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
+\
+/* Set m, n */ \
+ n = (MKL_INT)size; \
+ lda = lhsStride; \
+ incx = 1; \
+ incy = resIncr; \
+\
+/* Set uplo, trans and diag*/ \
+ trans = ConjLhs ? 'C' : 'T'; \
+ uplo = IsLower ? 'U' : 'L'; \
+ diag = IsUnitDiag ? 'U' : 'N'; \
+\
+/* call ?TRMV*/ \
+ MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
+\
+/* Add op(a_tr)rhs into res*/ \
+ MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
+/* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
+ if (size<(std::max)(rows,cols)) { \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic> MatrixLhs; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+ if (size<rows) { \
+ y = _res + size*resIncr; \
+ a = _lhs + size*lda; \
+ m = rows-size; \
+ n = size; \
+ } \
+ else { \
+ x += size; \
+ y = _res; \
+ a = _lhs + size; \
+ m = size; \
+ n = cols-size; \
+ } \
+ MKLPREFIX##gemv(&trans, &n, &m, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
+ } \
+ } \
+};
+
+EIGEN_MKL_TRMV_RM(double, double, d, d)
+EIGEN_MKL_TRMV_RM(dcomplex, MKL_Complex16, cd, z)
+EIGEN_MKL_TRMV_RM(float, float, f, s)
+EIGEN_MKL_TRMV_RM(scomplex, MKL_Complex8, cf, c)
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix.h b/Eigen/src/Core/products/TriangularSolverMatrix.h
new file mode 100644
index 0000000..f103eae
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverMatrix.h
@@ -0,0 +1,329 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_H
+#define EIGEN_TRIANGULAR_SOLVER_MATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+// if the rhs is row major, let's transpose the product
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder>
+struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor>
+{
+ static void run(
+ Index size, Index cols,
+ const Scalar* tri, Index triStride,
+ Scalar* _other, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ triangular_solve_matrix<
+ Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,
+ (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
+ NumTraits<Scalar>::IsComplex && Conjugate,
+ TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor>
+ ::run(size, cols, tri, triStride, _other, otherStride, blocking);
+ }
+};
+
+/* Optimized triangular solver with multiple right hand side and the triangular matrix on the left
+ */
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
+struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>
+{
+ static EIGEN_DONT_INLINE void run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking);
+};
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
+EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index cols = otherSize;
+ const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride);
+ blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
+ IsLower = (Mode&Lower) == Lower
+ };
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(size,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
+
+ conj_if<Conjugate> conj;
+ gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs;
+
+ // the goal here is to subdivise the Rhs panels such that we keep some cache
+ // coherence when accessing the rhs elements
+ std::ptrdiff_t l1, l2;
+ manage_caching_sizes(GetAction, &l1, &l2);
+ Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * otherStride) : 0;
+ subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr);
+
+ for(Index k2=IsLower ? 0 : size;
+ IsLower ? k2<size : k2>0;
+ IsLower ? k2+=kc : k2-=kc)
+ {
+ const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc);
+
+ // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel,
+ // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into
+ // A11 (the triangular part) and A21 the remaining rectangular part.
+ // Then the high level algorithm is:
+ // - B = R1 => general block copy (done during the next step)
+ // - R1 = A11^-1 B => tricky part
+ // - update B from the new R1 => actually this has to be performed continuously during the above step
+ // - R2 -= A21 * B => GEPP
+
+ // The tricky part: compute R1 = A11^-1 B while updating B from R1
+ // The idea is to split A11 into multiple small vertical panels.
+ // Each panel can be split into a small triangular part T1k which is processed without optimization,
+ // and the remaining small part T2k which is processed using gebp with appropriate block strides
+ for(Index j2=0; j2<cols; j2+=subcols)
+ {
+ Index actual_cols = (std::min)(cols-j2,subcols);
+ // for each small vertical panels [T1k^T, T2k^T]^T of lhs
+ for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
+ // tr solve
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ // TODO write a small kernel handling this (can be shared with trsv)
+ Index i = IsLower ? k2+k1+k : k2-k1-k-1;
+ Index s = IsLower ? k2+k1 : i+1;
+ Index rs = actualPanelWidth - k - 1; // remaining size
+
+ Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i));
+ for (Index j=j2; j<j2+actual_cols; ++j)
+ {
+ if (TriStorageOrder==RowMajor)
+ {
+ Scalar b(0);
+ const Scalar* l = &tri(i,s);
+ Scalar* r = &other(s,j);
+ for (Index i3=0; i3<k; ++i3)
+ b += conj(l[i3]) * r[i3];
+
+ other(i,j) = (other(i,j) - b)*a;
+ }
+ else
+ {
+ Index s = IsLower ? i+1 : i-rs;
+ Scalar b = (other(i,j) *= a);
+ Scalar* r = &other(s,j);
+ const Scalar* l = &tri(s,i);
+ for (Index i3=0;i3<rs;++i3)
+ r[i3] -= b * conj(l[i3]);
+ }
+ }
+ }
+
+ Index lengthTarget = actual_kc-k1-actualPanelWidth;
+ Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth;
+ Index blockBOffset = IsLower ? k1 : lengthTarget;
+
+ // update the respective rows of B from other
+ pack_rhs(blockB+actual_kc*j2, &other(startBlock,j2), otherStride, actualPanelWidth, actual_cols, actual_kc, blockBOffset);
+
+ // GEBP
+ if (lengthTarget>0)
+ {
+ Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc;
+
+ pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget);
+
+ gebp_kernel(&other(startTarget,j2), otherStride, blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1),
+ actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
+ }
+ }
+ }
+
+ // R2 -= A21 * B => GEPP
+ {
+ Index start = IsLower ? k2+kc : 0;
+ Index end = IsLower ? size : k2-kc;
+ for(Index i2=start; i2<end; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,end-i2);
+ if (actual_mc>0)
+ {
+ pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc);
+
+ gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0, blockW);
+ }
+ }
+ }
+ }
+ }
+
+/* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right
+ */
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
+struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>
+{
+ static EIGEN_DONT_INLINE void run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking);
+};
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
+EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index rows = otherSize;
+ const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride);
+ blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ RhsStorageOrder = TriStorageOrder,
+ SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
+ IsLower = (Mode&Lower) == Lower
+ };
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*size;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
+
+ conj_if<Conjugate> conj;
+ gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+ gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
+ gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel;
+
+ for(Index k2=IsLower ? size : 0;
+ IsLower ? k2>0 : k2<size;
+ IsLower ? k2-=kc : k2+=kc)
+ {
+ const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc);
+ Index actual_k2 = IsLower ? k2-actual_kc : k2 ;
+
+ Index startPanel = IsLower ? 0 : k2+actual_kc;
+ Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc;
+ Scalar* geb = blockB+actual_kc*actual_kc;
+
+ if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs);
+
+ // triangular packing (we only pack the panels off the diagonal,
+ // neglecting the blocks overlapping the diagonal
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index actual_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
+
+ if (panelLength>0)
+ pack_rhs_panel(blockB+j2*actual_kc,
+ &rhs(actual_k2+panelOffset, actual_j2), triStride,
+ panelLength, actualPanelWidth,
+ actual_kc, panelOffset);
+ }
+ }
+
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,rows-i2);
+
+ // triangular solver kernel
+ {
+ // for each small block of the diagonal (=> vertical panels of rhs)
+ for (Index j2 = IsLower
+ ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth)
+ : Index(SmallPanelWidth)))
+ : 0;
+ IsLower ? j2>=0 : j2<actual_kc;
+ IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index absolute_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;
+
+ // GEBP
+ if(panelLength>0)
+ {
+ gebp_kernel(&lhs(i2,absolute_j2), otherStride,
+ blockA, blockB+j2*actual_kc,
+ actual_mc, panelLength, actualPanelWidth,
+ Scalar(-1),
+ actual_kc, actual_kc, // strides
+ panelOffset, panelOffset, // offsets
+ blockW); // workspace
+ }
+
+ // unblocked triangular solve
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k;
+
+ Scalar* r = &lhs(i2,j);
+ for (Index k3=0; k3<k; ++k3)
+ {
+ Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j));
+ Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3);
+ for (Index i=0; i<actual_mc; ++i)
+ r[i] -= a[i] * b;
+ }
+ Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j));
+ for (Index i=0; i<actual_mc; ++i)
+ r[i] *= b;
+ }
+
+ // pack the just computed part of lhs to A
+ pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride,
+ actualPanelWidth, actual_mc,
+ actual_kc, j2);
+ }
+ }
+
+ if (rs>0)
+ gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb,
+ actual_mc, actual_kc, rs, Scalar(-1),
+ -1, -1, 0, 0, blockW);
+ }
+ }
+ }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix_MKL.h b/Eigen/src/Core/products/TriangularSolverMatrix_MKL.h
new file mode 100644
index 0000000..6a0bb83
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverMatrix_MKL.h
@@ -0,0 +1,155 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Triangular matrix * matrix product functionality based on ?TRMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
+#define EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
+
+namespace Eigen {
+
+namespace internal {
+
+// implements LeftSide op(triangular)^-1 * general
+#define EIGEN_MKL_TRSM_L(EIGTYPE, MKLTYPE, MKLPREFIX) \
+template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
+struct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \
+ }; \
+ static void run( \
+ Index size, Index otherSize, \
+ const EIGTYPE* _tri, Index triStride, \
+ EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
+ { \
+ MKL_INT m = size, n = otherSize, lda, ldb; \
+ char side = 'L', uplo, diag='N', transa; \
+ /* Set alpha_ */ \
+ MKLTYPE alpha; \
+ EIGTYPE myone(1); \
+ assign_scalar_eig2mkl(alpha, myone); \
+ ldb = otherStride;\
+\
+ const EIGTYPE *a; \
+/* Set trans */ \
+ transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \
+ Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \
+ MatrixTri a_tmp; \
+\
+ if (conjA) { \
+ a_tmp = tri.conjugate(); \
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else { \
+ a = _tri; \
+ lda = triStride; \
+ } \
+ if (IsUnitDiag) diag='U'; \
+/* call ?trsm*/ \
+ MKLPREFIX##trsm(&side, &uplo, &transa, &diag, &m, &n, &alpha, (const MKLTYPE*)a, &lda, (MKLTYPE*)_other, &ldb); \
+ } \
+};
+
+EIGEN_MKL_TRSM_L(double, double, d)
+EIGEN_MKL_TRSM_L(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_TRSM_L(float, float, s)
+EIGEN_MKL_TRSM_L(scomplex, MKL_Complex8, c)
+
+
+// implements RightSide general * op(triangular)^-1
+#define EIGEN_MKL_TRSM_R(EIGTYPE, MKLTYPE, MKLPREFIX) \
+template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
+struct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \
+ }; \
+ static void run( \
+ Index size, Index otherSize, \
+ const EIGTYPE* _tri, Index triStride, \
+ EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
+ { \
+ MKL_INT m = otherSize, n = size, lda, ldb; \
+ char side = 'R', uplo, diag='N', transa; \
+ /* Set alpha_ */ \
+ MKLTYPE alpha; \
+ EIGTYPE myone(1); \
+ assign_scalar_eig2mkl(alpha, myone); \
+ ldb = otherStride;\
+\
+ const EIGTYPE *a; \
+/* Set trans */ \
+ transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \
+ Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \
+ MatrixTri a_tmp; \
+\
+ if (conjA) { \
+ a_tmp = tri.conjugate(); \
+ a = a_tmp.data(); \
+ lda = a_tmp.outerStride(); \
+ } else { \
+ a = _tri; \
+ lda = triStride; \
+ } \
+ if (IsUnitDiag) diag='U'; \
+/* call ?trsm*/ \
+ MKLPREFIX##trsm(&side, &uplo, &transa, &diag, &m, &n, &alpha, (const MKLTYPE*)a, &lda, (MKLTYPE*)_other, &ldb); \
+ /*std::cout << "TRMS_L specialization!\n";*/ \
+ } \
+};
+
+EIGEN_MKL_TRSM_R(double, double, d)
+EIGEN_MKL_TRSM_R(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_TRSM_R(float, float, s)
+EIGEN_MKL_TRSM_R(scomplex, MKL_Complex8, c)
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
diff --git a/Eigen/src/Core/products/TriangularSolverVector.h b/Eigen/src/Core/products/TriangularSolverVector.h
new file mode 100644
index 0000000..ce4d100
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverVector.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_VECTOR_H
+#define EIGEN_TRIANGULAR_SOLVER_VECTOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>
+{
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ Conjugate,StorageOrder==RowMajor?ColMajor:RowMajor
+ >::run(size, _lhs, lhsStride, rhs);
+ }
+};
+
+// forward and backward substitution, row-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>
+{
+ enum {
+ IsLower = ((Mode&Lower)==Lower)
+ };
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
+ typename internal::conditional<
+ Conjugate,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&>
+ ::type cjLhs(lhs);
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ for(Index pi=IsLower ? 0 : size;
+ IsLower ? pi<size : pi>0;
+ IsLower ? pi+=PanelWidth : pi-=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);
+
+ Index r = IsLower ? pi : size - pi; // remaining size
+ if (r > 0)
+ {
+ // let's directly call the low level product function because:
+ // 1 - it is faster to compile
+ // 2 - it is slighlty faster at runtime
+ Index startRow = IsLower ? pi : pi-actualPanelWidth;
+ Index startCol = IsLower ? 0 : pi;
+
+ general_matrix_vector_product<Index,LhsScalar,RowMajor,Conjugate,RhsScalar,false>::run(
+ actualPanelWidth, r,
+ &lhs.coeffRef(startRow,startCol), lhsStride,
+ rhs + startCol, 1,
+ rhs + startRow, 1,
+ RhsScalar(-1));
+ }
+
+ for(Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = IsLower ? pi+k : pi-k-1;
+ Index s = IsLower ? pi : i+1;
+ if (k>0)
+ rhs[i] -= (cjLhs.row(i).segment(s,k).transpose().cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+s,k))).sum();
+
+ if(!(Mode & UnitDiag))
+ rhs[i] /= cjLhs(i,i);
+ }
+ }
+ }
+};
+
+// forward and backward substitution, column-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>
+{
+ enum {
+ IsLower = ((Mode&Lower)==Lower)
+ };
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
+ typename internal::conditional<Conjugate,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&
+ >::type cjLhs(lhs);
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+
+ for(Index pi=IsLower ? 0 : size;
+ IsLower ? pi<size : pi>0;
+ IsLower ? pi+=PanelWidth : pi-=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);
+ Index startBlock = IsLower ? pi : pi-actualPanelWidth;
+ Index endBlock = IsLower ? pi + actualPanelWidth : 0;
+
+ for(Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = IsLower ? pi+k : pi-k-1;
+ if(!(Mode & UnitDiag))
+ rhs[i] /= cjLhs.coeff(i,i);
+
+ Index r = actualPanelWidth - k - 1; // remaining size
+ Index s = IsLower ? i+1 : i-r;
+ if (r>0)
+ Map<Matrix<RhsScalar,Dynamic,1> >(rhs+s,r) -= rhs[i] * cjLhs.col(i).segment(s,r);
+ }
+ Index r = IsLower ? size - endBlock : startBlock; // remaining size
+ if (r > 0)
+ {
+ // let's directly call the low level product function because:
+ // 1 - it is faster to compile
+ // 2 - it is slighlty faster at runtime
+ general_matrix_vector_product<Index,LhsScalar,ColMajor,Conjugate,RhsScalar,false>::run(
+ r, actualPanelWidth,
+ &lhs.coeffRef(endBlock,startBlock), lhsStride,
+ rhs+startBlock, 1,
+ rhs+endBlock, 1, RhsScalar(-1));
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_VECTOR_H
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
new file mode 100644
index 0000000..a28f16f
--- /dev/null
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLASUTIL_H
+#define EIGEN_BLASUTIL_H
+
+// This file contains many lightweight helper classes used to
+// implement and control fast level 2 and level 3 BLAS-like routines.
+
+namespace Eigen {
+
+namespace internal {
+
+// forward declarations
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>
+struct gebp_kernel;
+
+template<typename Scalar, typename Index, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>
+struct gemm_pack_rhs;
+
+template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate = false, bool PanelMode = false>
+struct gemm_pack_lhs;
+
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder>
+struct general_matrix_matrix_product;
+
+template<typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version=Specialized>
+struct general_matrix_vector_product;
+
+
+template<bool Conjugate> struct conj_if;
+
+template<> struct conj_if<true> {
+ template<typename T>
+ inline T operator()(const T& x) { return numext::conj(x); }
+ template<typename T>
+ inline T pconj(const T& x) { return internal::pconj(x); }
+};
+
+template<> struct conj_if<false> {
+ template<typename T>
+ inline const T& operator()(const T& x) { return x; }
+ template<typename T>
+ inline const T& pconj(const T& x) { return x; }
+};
+
+template<typename Scalar> struct conj_helper<Scalar,Scalar,false,false>
+{
+ EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const { return internal::pmadd(x,y,c); }
+ EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const { return internal::pmul(x,y); }
+};
+
+template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, false,true>
+{
+ typedef std::complex<RealScalar> Scalar;
+ EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const
+ { return c + pmul(x,y); }
+
+ EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
+ { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::imag(x)*numext::real(y) - numext::real(x)*numext::imag(y)); }
+};
+
+template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,false>
+{
+ typedef std::complex<RealScalar> Scalar;
+ EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const
+ { return c + pmul(x,y); }
+
+ EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
+ { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
+};
+
+template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,true>
+{
+ typedef std::complex<RealScalar> Scalar;
+ EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const
+ { return c + pmul(x,y); }
+
+ EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
+ { return Scalar(numext::real(x)*numext::real(y) - numext::imag(x)*numext::imag(y), - numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
+};
+
+template<typename RealScalar,bool Conj> struct conj_helper<std::complex<RealScalar>, RealScalar, Conj,false>
+{
+ typedef std::complex<RealScalar> Scalar;
+ EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const RealScalar& y, const Scalar& c) const
+ { return padd(c, pmul(x,y)); }
+ EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const RealScalar& y) const
+ { return conj_if<Conj>()(x)*y; }
+};
+
+template<typename RealScalar,bool Conj> struct conj_helper<RealScalar, std::complex<RealScalar>, false,Conj>
+{
+ typedef std::complex<RealScalar> Scalar;
+ EIGEN_STRONG_INLINE Scalar pmadd(const RealScalar& x, const Scalar& y, const Scalar& c) const
+ { return padd(c, pmul(x,y)); }
+ EIGEN_STRONG_INLINE Scalar pmul(const RealScalar& x, const Scalar& y) const
+ { return x*conj_if<Conj>()(y); }
+};
+
+template<typename From,typename To> struct get_factor {
+ static EIGEN_STRONG_INLINE To run(const From& x) { return x; }
+};
+
+template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
+ static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
+};
+
+// Lightweight helper class to access matrix coefficients.
+// Yes, this is somehow redundant with Map<>, but this version is much much lighter,
+// and so I hope better compilation performance (time and code quality).
+template<typename Scalar, typename Index, int StorageOrder>
+class blas_data_mapper
+{
+ public:
+ blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
+ EIGEN_STRONG_INLINE Scalar& operator()(Index i, Index j)
+ { return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride]; }
+ protected:
+ Scalar* EIGEN_RESTRICT m_data;
+ Index m_stride;
+};
+
+// lightweight helper class to access matrix coefficients (const version)
+template<typename Scalar, typename Index, int StorageOrder>
+class const_blas_data_mapper
+{
+ public:
+ const_blas_data_mapper(const Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
+ EIGEN_STRONG_INLINE const Scalar& operator()(Index i, Index j) const
+ { return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride]; }
+ protected:
+ const Scalar* EIGEN_RESTRICT m_data;
+ Index m_stride;
+};
+
+
+/* Helper class to analyze the factors of a Product expression.
+ * In particular it allows to pop out operator-, scalar multiples,
+ * and conjugate */
+template<typename XprType> struct blas_traits
+{
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef const XprType& ExtractType;
+ typedef XprType _ExtractType;
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ IsTransposed = false,
+ NeedToConjugate = false,
+ HasUsableDirectAccess = ( (int(XprType::Flags)&DirectAccessBit)
+ && ( bool(XprType::IsVectorAtCompileTime)
+ || int(inner_stride_at_compile_time<XprType>::ret) == 1)
+ ) ? 1 : 0
+ };
+ typedef typename conditional<bool(HasUsableDirectAccess),
+ ExtractType,
+ typename _ExtractType::PlainObject
+ >::type DirectLinearAccessType;
+ static inline ExtractType extract(const XprType& x) { return x; }
+ static inline const Scalar extractScalarFactor(const XprType&) { return Scalar(1); }
+};
+
+// pop conjugate
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ NeedToConjugate = Base::NeedToConjugate ? 0 : IsComplex
+ };
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x) { return conj(Base::extractScalarFactor(x.nestedExpression())); }
+};
+
+// pop scalar multiple
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_multiple_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseUnaryOp<scalar_multiple_op<Scalar>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x)
+ { return x.functor().m_other * Base::extractScalarFactor(x.nestedExpression()); }
+};
+
+// pop opposite
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x)
+ { return - Base::extractScalarFactor(x.nestedExpression()); }
+};
+
+// pop/push transpose
+template<typename NestedXpr>
+struct blas_traits<Transpose<NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef typename NestedXpr::Scalar Scalar;
+ typedef blas_traits<NestedXpr> Base;
+ typedef Transpose<NestedXpr> XprType;
+ typedef Transpose<const typename Base::_ExtractType> ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS
+ typedef Transpose<const typename Base::_ExtractType> _ExtractType;
+ typedef typename conditional<bool(Base::HasUsableDirectAccess),
+ ExtractType,
+ typename ExtractType::PlainObject
+ >::type DirectLinearAccessType;
+ enum {
+ IsTransposed = Base::IsTransposed ? 0 : 1
+ };
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }
+};
+
+template<typename T>
+struct blas_traits<const T>
+ : blas_traits<T>
+{};
+
+template<typename T, bool HasUsableDirectAccess=blas_traits<T>::HasUsableDirectAccess>
+struct extract_data_selector {
+ static const typename T::Scalar* run(const T& m)
+ {
+ return blas_traits<T>::extract(m).data();
+ }
+};
+
+template<typename T>
+struct extract_data_selector<T,false> {
+ static typename T::Scalar* run(const T&) { return 0; }
+};
+
+template<typename T> const typename T::Scalar* extract_data(const T& m)
+{
+ return extract_data_selector<T>::run(m);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLASUTIL_H
diff --git a/Eigen/src/Core/util/CMakeLists.txt b/Eigen/src/Core/util/CMakeLists.txt
new file mode 100644
index 0000000..a1e2e52
--- /dev/null
+++ b/Eigen/src/Core/util/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_util_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Core_util_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/util COMPONENT Devel
+ )
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
new file mode 100644
index 0000000..1e6277c
--- /dev/null
+++ b/Eigen/src/Core/util/Constants.h
@@ -0,0 +1,451 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONSTANTS_H
+#define EIGEN_CONSTANTS_H
+
+namespace Eigen {
+
+/** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is
+ * stored in some runtime variable.
+ *
+ * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
+ */
+const int Dynamic = -1;
+
+/** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value
+ * has to be specified at runtime.
+ */
+const int DynamicIndex = 0xffffff;
+
+/** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
+ * The value Infinity there means the L-infinity norm.
+ */
+const int Infinity = -1;
+
+/** \defgroup flags Flags
+ * \ingroup Core_Module
+ *
+ * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
+ * expression.
+ *
+ * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
+ * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
+ * runtime overhead.
+ *
+ * \sa MatrixBase::Flags
+ */
+
+/** \ingroup flags
+ *
+ * for a matrix, this means that the storage order is row-major.
+ * If this bit is not set, the storage order is column-major.
+ * For an expression, this determines the storage order of
+ * the matrix created by evaluation of that expression.
+ * \sa \ref TopicStorageOrders */
+const unsigned int RowMajorBit = 0x1;
+
+/** \ingroup flags
+ *
+ * means the expression should be evaluated by the calling expression */
+const unsigned int EvalBeforeNestingBit = 0x2;
+
+/** \ingroup flags
+ *
+ * means the expression should be evaluated before any assignment */
+const unsigned int EvalBeforeAssigningBit = 0x4;
+
+/** \ingroup flags
+ *
+ * Short version: means the expression might be vectorized
+ *
+ * Long version: means that the coefficients can be handled by packets
+ * and start at a memory location whose alignment meets the requirements
+ * of the present CPU architecture for optimized packet access. In the fixed-size
+ * case, there is the additional condition that it be possible to access all the
+ * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,
+ * and that any nontrivial strides don't break the alignment). In the dynamic-size case,
+ * there is no such condition on the total size and strides, so it might not be possible to access
+ * all coeffs by packets.
+ *
+ * \note This bit can be set regardless of whether vectorization is actually enabled.
+ * To check for actual vectorizability, see \a ActualPacketAccessBit.
+ */
+const unsigned int PacketAccessBit = 0x8;
+
+#ifdef EIGEN_VECTORIZE
+/** \ingroup flags
+ *
+ * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
+ * is set to the value \a PacketAccessBit.
+ *
+ * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
+ * is set to the value 0.
+ */
+const unsigned int ActualPacketAccessBit = PacketAccessBit;
+#else
+const unsigned int ActualPacketAccessBit = 0x0;
+#endif
+
+/** \ingroup flags
+ *
+ * Short version: means the expression can be seen as 1D vector.
+ *
+ * Long version: means that one can access the coefficients
+ * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
+ * index-based access methods are guaranteed
+ * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
+ * is guaranteed that whenever it is available, index-based access is at least as fast as
+ * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
+ *
+ * If both PacketAccessBit and LinearAccessBit are set, then the
+ * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
+ * lvalue expression.
+ *
+ * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
+ * Product expressions don't have it, because it would be troublesome for vectorization, even when the
+ * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
+ * not index-based packet access, so they don't have the LinearAccessBit.
+ */
+const unsigned int LinearAccessBit = 0x10;
+
+/** \ingroup flags
+ *
+ * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.
+ * This rules out read-only expressions.
+ *
+ * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note
+ * the other:
+ * \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit
+ * \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit
+ *
+ * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.
+ */
+const unsigned int LvalueBit = 0x20;
+
+/** \ingroup flags
+ *
+ * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
+ * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
+ * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
+ * though referencable, do not have such a regular memory layout.
+ *
+ * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
+ */
+const unsigned int DirectAccessBit = 0x40;
+
+/** \ingroup flags
+ *
+ * means the first coefficient packet is guaranteed to be aligned */
+const unsigned int AlignedBit = 0x80;
+
+const unsigned int NestByRefBit = 0x100;
+
+// list of flags that are inherited by default
+const unsigned int HereditaryBits = RowMajorBit
+ | EvalBeforeNestingBit
+ | EvalBeforeAssigningBit;
+
+/** \defgroup enums Enumerations
+ * \ingroup Core_Module
+ *
+ * Various enumerations used in %Eigen. Many of these are used as template parameters.
+ */
+
+/** \ingroup enums
+ * Enum containing possible values for the \p Mode parameter of
+ * MatrixBase::selfadjointView() and MatrixBase::triangularView(). */
+enum {
+ /** View matrix as a lower triangular matrix. */
+ Lower=0x1,
+ /** View matrix as an upper triangular matrix. */
+ Upper=0x2,
+ /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */
+ UnitDiag=0x4,
+ /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */
+ ZeroDiag=0x8,
+ /** View matrix as a lower triangular matrix with ones on the diagonal. */
+ UnitLower=UnitDiag|Lower,
+ /** View matrix as an upper triangular matrix with ones on the diagonal. */
+ UnitUpper=UnitDiag|Upper,
+ /** View matrix as a lower triangular matrix with zeros on the diagonal. */
+ StrictlyLower=ZeroDiag|Lower,
+ /** View matrix as an upper triangular matrix with zeros on the diagonal. */
+ StrictlyUpper=ZeroDiag|Upper,
+ /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */
+ SelfAdjoint=0x10,
+ /** Used to support symmetric, non-selfadjoint, complex matrices. */
+ Symmetric=0x20
+};
+
+/** \ingroup enums
+ * Enum for indicating whether an object is aligned or not. */
+enum {
+ /** Object is not correctly aligned for vectorization. */
+ Unaligned=0,
+ /** Object is aligned for vectorization. */
+ Aligned=1
+};
+
+/** \ingroup enums
+ * Enum used by DenseBase::corner() in Eigen2 compatibility mode. */
+// FIXME after the corner() API change, this was not needed anymore, except by AlignedBox
+// TODO: find out what to do with that. Adapt the AlignedBox API ?
+enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
+
+/** \ingroup enums
+ * Enum containing possible values for the \p Direction parameter of
+ * Reverse, PartialReduxExpr and VectorwiseOp. */
+enum DirectionType {
+ /** For Reverse, all columns are reversed;
+ * for PartialReduxExpr and VectorwiseOp, act on columns. */
+ Vertical,
+ /** For Reverse, all rows are reversed;
+ * for PartialReduxExpr and VectorwiseOp, act on rows. */
+ Horizontal,
+ /** For Reverse, both rows and columns are reversed;
+ * not used for PartialReduxExpr and VectorwiseOp. */
+ BothDirections
+};
+
+/** \internal \ingroup enums
+ * Enum to specify how to traverse the entries of a matrix. */
+enum {
+ /** \internal Default traversal, no vectorization, no index-based access */
+ DefaultTraversal,
+ /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */
+ LinearTraversal,
+ /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
+ * and good size */
+ InnerVectorizedTraversal,
+ /** \internal Vectorization path using a single loop plus scalar loops for the
+ * unaligned boundaries */
+ LinearVectorizedTraversal,
+ /** \internal Generic vectorization path using one vectorized loop per row/column with some
+ * scalar loops to handle the unaligned boundaries */
+ SliceVectorizedTraversal,
+ /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/
+ InvalidTraversal,
+ /** \internal Evaluate all entries at once */
+ AllAtOnceTraversal
+};
+
+/** \internal \ingroup enums
+ * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */
+enum {
+ /** \internal Do not unroll loops. */
+ NoUnrolling,
+ /** \internal Unroll only the inner loop, but not the outer loop. */
+ InnerUnrolling,
+ /** \internal Unroll both the inner and the outer loop. If there is only one loop,
+ * because linear traversal is used, then unroll that loop. */
+ CompleteUnrolling
+};
+
+/** \internal \ingroup enums
+ * Enum to specify whether to use the default (built-in) implementation or the specialization. */
+enum {
+ Specialized,
+ BuiltIn
+};
+
+/** \ingroup enums
+ * Enum containing possible values for the \p _Options template parameter of
+ * Matrix, Array and BandMatrix. */
+enum {
+ /** Storage order is column major (see \ref TopicStorageOrders). */
+ ColMajor = 0,
+ /** Storage order is row major (see \ref TopicStorageOrders). */
+ RowMajor = 0x1, // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
+ /** Align the matrix itself if it is vectorizable fixed-size */
+ AutoAlign = 0,
+ /** Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be requested to be aligned) */ // FIXME --- clarify the situation
+ DontAlign = 0x2
+};
+
+/** \ingroup enums
+ * Enum for specifying whether to apply or solve on the left or right. */
+enum {
+ /** Apply transformation on the left. */
+ OnTheLeft = 1,
+ /** Apply transformation on the right. */
+ OnTheRight = 2
+};
+
+/* the following used to be written as:
+ *
+ * struct NoChange_t {};
+ * namespace {
+ * EIGEN_UNUSED NoChange_t NoChange;
+ * }
+ *
+ * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.
+ * However, this leads to "variable declared but never referenced" warnings on Intel Composer XE,
+ * and we do not know how to get rid of them (bug 450).
+ */
+
+enum NoChange_t { NoChange };
+enum Sequential_t { Sequential };
+enum Default_t { Default };
+
+/** \internal \ingroup enums
+ * Used in AmbiVector. */
+enum {
+ IsDense = 0,
+ IsSparse
+};
+
+/** \ingroup enums
+ * Used as template parameter in DenseCoeffBase and MapBase to indicate
+ * which accessors should be provided. */
+enum AccessorLevels {
+ /** Read-only access via a member function. */
+ ReadOnlyAccessors,
+ /** Read/write access via member functions. */
+ WriteAccessors,
+ /** Direct read-only access to the coefficients. */
+ DirectAccessors,
+ /** Direct read/write access to the coefficients. */
+ DirectWriteAccessors
+};
+
+/** \ingroup enums
+ * Enum with options to give to various decompositions. */
+enum DecompositionOptions {
+ /** \internal Not used (meant for LDLT?). */
+ Pivoting = 0x01,
+ /** \internal Not used (meant for LDLT?). */
+ NoPivoting = 0x02,
+ /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */
+ ComputeFullU = 0x04,
+ /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */
+ ComputeThinU = 0x08,
+ /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */
+ ComputeFullV = 0x10,
+ /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */
+ ComputeThinV = 0x20,
+ /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
+ * that only the eigenvalues are to be computed and not the eigenvectors. */
+ EigenvaluesOnly = 0x40,
+ /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
+ * that both the eigenvalues and the eigenvectors are to be computed. */
+ ComputeEigenvectors = 0x80,
+ /** \internal */
+ EigVecMask = EigenvaluesOnly | ComputeEigenvectors,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */
+ Ax_lBx = 0x100,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */
+ ABx_lx = 0x200,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */
+ BAx_lx = 0x400,
+ /** \internal */
+ GenEigMask = Ax_lBx | ABx_lx | BAx_lx
+};
+
+/** \ingroup enums
+ * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */
+enum QRPreconditioners {
+ /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
+ NoQRPreconditioner,
+ /** Use a QR decomposition without pivoting as the first step. */
+ HouseholderQRPreconditioner,
+ /** Use a QR decomposition with column pivoting as the first step. */
+ ColPivHouseholderQRPreconditioner,
+ /** Use a QR decomposition with full pivoting as the first step. */
+ FullPivHouseholderQRPreconditioner
+};
+
+#ifdef Success
+#error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h
+#endif
+
+/** \ingroup enums
+ * Enum for reporting the status of a computation. */
+enum ComputationInfo {
+ /** Computation was successful. */
+ Success = 0,
+ /** The provided data did not satisfy the prerequisites. */
+ NumericalIssue = 1,
+ /** Iterative procedure did not converge. */
+ NoConvergence = 2,
+ /** The inputs are invalid, or the algorithm has been improperly called.
+ * When assertions are enabled, such errors trigger an assert. */
+ InvalidInput = 3
+};
+
+/** \ingroup enums
+ * Enum used to specify how a particular transformation is stored in a matrix.
+ * \sa Transform, Hyperplane::transform(). */
+enum TransformTraits {
+ /** Transformation is an isometry. */
+ Isometry = 0x1,
+ /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is
+ * assumed to be [0 ... 0 1]. */
+ Affine = 0x2,
+ /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */
+ AffineCompact = 0x10 | Affine,
+ /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */
+ Projective = 0x20
+};
+
+/** \internal \ingroup enums
+ * Enum used to choose between implementation depending on the computer architecture. */
+namespace Architecture
+{
+ enum Type {
+ Generic = 0x0,
+ SSE = 0x1,
+ AltiVec = 0x2,
+#if defined EIGEN_VECTORIZE_SSE
+ Target = SSE
+#elif defined EIGEN_VECTORIZE_ALTIVEC
+ Target = AltiVec
+#else
+ Target = Generic
+#endif
+ };
+}
+
+/** \internal \ingroup enums
+ * Enum used as template parameter in GeneralProduct. */
+enum { CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
+
+/** \internal \ingroup enums
+ * Enum used in experimental parallel implementation. */
+enum Action {GetAction, SetAction};
+
+/** The type used to identify a dense storage. */
+struct Dense {};
+
+/** The type used to identify a matrix expression */
+struct MatrixXpr {};
+
+/** The type used to identify an array expression */
+struct ArrayXpr {};
+
+namespace internal {
+ /** \internal
+ * Constants for comparison functors
+ */
+ enum ComparisonName {
+ cmp_EQ = 0,
+ cmp_LT = 1,
+ cmp_LE = 2,
+ cmp_UNORD = 3,
+ cmp_NEQ = 4
+ };
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONSTANTS_H
diff --git a/Eigen/src/Core/util/DisableStupidWarnings.h b/Eigen/src/Core/util/DisableStupidWarnings.h
new file mode 100644
index 0000000..6a0bf06
--- /dev/null
+++ b/Eigen/src/Core/util/DisableStupidWarnings.h
@@ -0,0 +1,40 @@
+#ifndef EIGEN_WARNINGS_DISABLED
+#define EIGEN_WARNINGS_DISABLED
+
+#ifdef _MSC_VER
+ // 4100 - unreferenced formal parameter (occurred e.g. in aligned_allocator::destroy(pointer p))
+ // 4101 - unreferenced local variable
+ // 4127 - conditional expression is constant
+ // 4181 - qualifier applied to reference type ignored
+ // 4211 - nonstandard extension used : redefined extern to static
+ // 4244 - 'argument' : conversion from 'type1' to 'type2', possible loss of data
+ // 4273 - QtAlignedMalloc, inconsistent DLL linkage
+ // 4324 - structure was padded due to declspec(align())
+ // 4512 - assignment operator could not be generated
+ // 4522 - 'class' : multiple assignment operators specified
+ // 4700 - uninitialized local variable 'xyz' used
+ // 4717 - 'function' : recursive on all control paths, function will cause runtime stack overflow
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma warning( push )
+ #endif
+ #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4512 4522 4700 4717 )
+#elif defined __INTEL_COMPILER
+ // 2196 - routine is both "inline" and "noinline" ("noinline" assumed)
+ // ICC 12 generates this warning even without any inline keyword, when defining class methods 'inline' i.e. inside of class body
+ // typedef that may be a reference type.
+ // 279 - controlling expression is constant
+ // ICC 12 generates this warning on assert(constant_expression_depending_on_template_params) and frankly this is a legitimate use case.
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma warning push
+ #endif
+ #pragma warning disable 2196 279
+#elif defined __clang__
+ // -Wconstant-logical-operand - warning: use of logical && with constant operand; switch to bitwise & or remove constant
+ // this is really a stupid warning as it warns on compile-time expressions involving enums
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma clang diagnostic push
+ #endif
+ #pragma clang diagnostic ignored "-Wconstant-logical-operand"
+#endif
+
+#endif // not EIGEN_WARNINGS_DISABLED
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
new file mode 100644
index 0000000..d6a8145
--- /dev/null
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -0,0 +1,299 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FORWARDDECLARATIONS_H
+#define EIGEN_FORWARDDECLARATIONS_H
+
+namespace Eigen {
+namespace internal {
+
+template<typename T> struct traits;
+
+// here we say once and for all that traits<const T> == traits<T>
+// When constness must affect traits, it has to be constness on template parameters on which T itself depends.
+// For example, traits<Map<const T> > != traits<Map<T> >, but
+// traits<const Map<T> > == traits<Map<T> >
+template<typename T> struct traits<const T> : traits<T> {};
+
+template<typename Derived> struct has_direct_access
+{
+ enum { ret = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0 };
+};
+
+template<typename Derived> struct accessors_level
+{
+ enum { has_direct_access = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0,
+ has_write_access = (traits<Derived>::Flags & LvalueBit) ? 1 : 0,
+ value = has_direct_access ? (has_write_access ? DirectWriteAccessors : DirectAccessors)
+ : (has_write_access ? WriteAccessors : ReadOnlyAccessors)
+ };
+};
+
+} // end namespace internal
+
+template<typename T> struct NumTraits;
+
+template<typename Derived> struct EigenBase;
+template<typename Derived> class DenseBase;
+template<typename Derived> class PlainObjectBase;
+
+
+template<typename Derived,
+ int Level = internal::accessors_level<Derived>::value >
+class DenseCoeffsBase;
+
+template<typename _Scalar, int _Rows, int _Cols,
+ int _Options = AutoAlign |
+#if defined(__GNUC__) && __GNUC__==3 && __GNUC_MINOR__==4
+ // workaround a bug in at least gcc 3.4.6
+ // the innermost ?: ternary operator is misparsed. We write it slightly
+ // differently and this makes gcc 3.4.6 happy, but it's ugly.
+ // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined
+ // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)
+ ( (_Rows==1 && _Cols!=1) ? RowMajor
+ : !(_Cols==1 && _Rows!=1) ? EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION
+ : ColMajor ),
+#else
+ ( (_Rows==1 && _Cols!=1) ? RowMajor
+ : (_Cols==1 && _Rows!=1) ? ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+#endif
+ int _MaxRows = _Rows,
+ int _MaxCols = _Cols
+> class Matrix;
+
+template<typename Derived> class MatrixBase;
+template<typename Derived> class ArrayBase;
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged;
+template<typename ExpressionType, template <typename> class StorageBase > class NoAlias;
+template<typename ExpressionType> class NestByValue;
+template<typename ExpressionType> class ForceAlignedAccess;
+template<typename ExpressionType> class SwapWrapper;
+
+template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false> class Block;
+
+template<typename MatrixType, int Size=Dynamic> class VectorBlock;
+template<typename MatrixType> class Transpose;
+template<typename MatrixType> class Conjugate;
+template<typename NullaryOp, typename MatrixType> class CwiseNullaryOp;
+template<typename UnaryOp, typename MatrixType> class CwiseUnaryOp;
+template<typename ViewOp, typename MatrixType> class CwiseUnaryView;
+template<typename BinaryOp, typename Lhs, typename Rhs> class CwiseBinaryOp;
+template<typename BinOp, typename Lhs, typename Rhs> class SelfCwiseBinaryOp;
+template<typename Derived, typename Lhs, typename Rhs> class ProductBase;
+template<typename Lhs, typename Rhs, int Mode> class GeneralProduct;
+template<typename Lhs, typename Rhs, int NestingFlags> class CoeffBasedProduct;
+
+template<typename Derived> class DiagonalBase;
+template<typename _DiagonalVectorType> class DiagonalWrapper;
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime=SizeAtCompileTime> class DiagonalMatrix;
+template<typename MatrixType, typename DiagonalType, int ProductOrder> class DiagonalProduct;
+template<typename MatrixType, int Index = 0> class Diagonal;
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class PermutationMatrix;
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class Transpositions;
+template<typename Derived> class PermutationBase;
+template<typename Derived> class TranspositionsBase;
+template<typename _IndicesType> class PermutationWrapper;
+template<typename _IndicesType> class TranspositionsWrapper;
+
+template<typename Derived,
+ int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors
+> class MapBase;
+template<int InnerStrideAtCompileTime, int OuterStrideAtCompileTime> class Stride;
+template<typename MatrixType, int MapOptions=Unaligned, typename StrideType = Stride<0,0> > class Map;
+
+template<typename Derived> class TriangularBase;
+template<typename MatrixType, unsigned int Mode> class TriangularView;
+template<typename MatrixType, unsigned int Mode> class SelfAdjointView;
+template<typename MatrixType> class SparseView;
+template<typename ExpressionType> class WithFormat;
+template<typename MatrixType> struct CommaInitializer;
+template<typename Derived> class ReturnByValue;
+template<typename ExpressionType> class ArrayWrapper;
+template<typename ExpressionType> class MatrixWrapper;
+
+namespace internal {
+template<typename DecompositionType, typename Rhs> struct solve_retval_base;
+template<typename DecompositionType, typename Rhs> struct solve_retval;
+template<typename DecompositionType> struct kernel_retval_base;
+template<typename DecompositionType> struct kernel_retval;
+template<typename DecompositionType> struct image_retval_base;
+template<typename DecompositionType> struct image_retval;
+} // end namespace internal
+
+namespace internal {
+template<typename _Scalar, int Rows=Dynamic, int Cols=Dynamic, int Supers=Dynamic, int Subs=Dynamic, int Options=0> class BandMatrix;
+}
+
+namespace internal {
+template<typename Lhs, typename Rhs> struct product_type;
+}
+
+template<typename Lhs, typename Rhs,
+ int ProductType = internal::product_type<Lhs,Rhs>::value>
+struct ProductReturnType;
+
+// this is a workaround for sun CC
+template<typename Lhs, typename Rhs> struct LazyProductReturnType;
+
+namespace internal {
+
+// Provides scalar/packet-wise product and product with accumulation
+// with optional conjugation of the arguments.
+template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;
+
+template<typename Scalar> struct scalar_sum_op;
+template<typename Scalar> struct scalar_difference_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op;
+template<typename Scalar> struct scalar_opposite_op;
+template<typename Scalar> struct scalar_conjugate_op;
+template<typename Scalar> struct scalar_real_op;
+template<typename Scalar> struct scalar_imag_op;
+template<typename Scalar> struct scalar_abs_op;
+template<typename Scalar> struct scalar_abs2_op;
+template<typename Scalar> struct scalar_sqrt_op;
+template<typename Scalar> struct scalar_exp_op;
+template<typename Scalar> struct scalar_log_op;
+template<typename Scalar> struct scalar_cos_op;
+template<typename Scalar> struct scalar_sin_op;
+template<typename Scalar> struct scalar_acos_op;
+template<typename Scalar> struct scalar_asin_op;
+template<typename Scalar> struct scalar_tan_op;
+template<typename Scalar> struct scalar_pow_op;
+template<typename Scalar> struct scalar_inverse_op;
+template<typename Scalar> struct scalar_square_op;
+template<typename Scalar> struct scalar_cube_op;
+template<typename Scalar, typename NewType> struct scalar_cast_op;
+template<typename Scalar> struct scalar_multiple_op;
+template<typename Scalar> struct scalar_quotient1_op;
+template<typename Scalar> struct scalar_min_op;
+template<typename Scalar> struct scalar_max_op;
+template<typename Scalar> struct scalar_random_op;
+template<typename Scalar> struct scalar_add_op;
+template<typename Scalar> struct scalar_constant_op;
+template<typename Scalar> struct scalar_identity_op;
+
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
+
+} // end namespace internal
+
+struct IOFormat;
+
+// Array module
+template<typename _Scalar, int _Rows, int _Cols,
+ int _Options = AutoAlign |
+#if defined(__GNUC__) && __GNUC__==3 && __GNUC_MINOR__==4
+ // workaround a bug in at least gcc 3.4.6
+ // the innermost ?: ternary operator is misparsed. We write it slightly
+ // differently and this makes gcc 3.4.6 happy, but it's ugly.
+ // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined
+ // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)
+ ( (_Rows==1 && _Cols!=1) ? RowMajor
+ : !(_Cols==1 && _Rows!=1) ? EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION
+ : ColMajor ),
+#else
+ ( (_Rows==1 && _Cols!=1) ? RowMajor
+ : (_Cols==1 && _Rows!=1) ? ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+#endif
+ int _MaxRows = _Rows, int _MaxCols = _Cols> class Array;
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType> class Select;
+template<typename MatrixType, typename BinaryOp, int Direction> class PartialReduxExpr;
+template<typename ExpressionType, int Direction> class VectorwiseOp;
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate;
+template<typename MatrixType, int Direction = BothDirections> class Reverse;
+
+template<typename MatrixType> class FullPivLU;
+template<typename MatrixType> class PartialPivLU;
+namespace internal {
+template<typename MatrixType> struct inverse_impl;
+}
+template<typename MatrixType> class HouseholderQR;
+template<typename MatrixType> class ColPivHouseholderQR;
+template<typename MatrixType> class FullPivHouseholderQR;
+template<typename MatrixType, int QRPreconditioner = ColPivHouseholderQRPreconditioner> class JacobiSVD;
+template<typename MatrixType, int UpLo = Lower> class LLT;
+template<typename MatrixType, int UpLo = Lower> class LDLT;
+template<typename VectorsType, typename CoeffsType, int Side=OnTheLeft> class HouseholderSequence;
+template<typename Scalar> class JacobiRotation;
+
+// Geometry module:
+template<typename Derived, int _Dim> class RotationBase;
+template<typename Lhs, typename Rhs> class Cross;
+template<typename Derived> class QuaternionBase;
+template<typename Scalar> class Rotation2D;
+template<typename Scalar> class AngleAxis;
+template<typename Scalar,int Dim> class Translation;
+
+#ifdef EIGEN2_SUPPORT
+template<typename Derived, int _Dim> class eigen2_RotationBase;
+template<typename Lhs, typename Rhs> class eigen2_Cross;
+template<typename Scalar> class eigen2_Quaternion;
+template<typename Scalar> class eigen2_Rotation2D;
+template<typename Scalar> class eigen2_AngleAxis;
+template<typename Scalar,int Dim> class eigen2_Transform;
+template <typename _Scalar, int _AmbientDim> class eigen2_ParametrizedLine;
+template <typename _Scalar, int _AmbientDim> class eigen2_Hyperplane;
+template<typename Scalar,int Dim> class eigen2_Translation;
+template<typename Scalar,int Dim> class eigen2_Scaling;
+#endif
+
+#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+template<typename Scalar> class Quaternion;
+template<typename Scalar,int Dim> class Transform;
+template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
+template <typename _Scalar, int _AmbientDim> class Hyperplane;
+template<typename Scalar,int Dim> class Scaling;
+#endif
+
+#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+template<typename Scalar, int Options = AutoAlign> class Quaternion;
+template<typename Scalar,int Dim,int Mode,int _Options=AutoAlign> class Transform;
+template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class ParametrizedLine;
+template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class Hyperplane;
+template<typename Scalar> class UniformScaling;
+template<typename MatrixType,int Direction> class Homogeneous;
+#endif
+
+// MatrixFunctions module
+template<typename Derived> struct MatrixExponentialReturnValue;
+template<typename Derived> class MatrixFunctionReturnValue;
+template<typename Derived> class MatrixSquareRootReturnValue;
+template<typename Derived> class MatrixLogarithmReturnValue;
+template<typename Derived> class MatrixPowerReturnValue;
+template<typename Derived, typename Lhs, typename Rhs> class MatrixPowerProduct;
+
+namespace internal {
+template <typename Scalar>
+struct stem_function
+{
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef ComplexScalar type(ComplexScalar, int);
+};
+}
+
+
+#ifdef EIGEN2_SUPPORT
+template<typename ExpressionType> class Cwise;
+template<typename MatrixType> class Minor;
+template<typename MatrixType> class LU;
+template<typename MatrixType> class QR;
+template<typename MatrixType> class SVD;
+namespace internal {
+template<typename MatrixType, unsigned int Mode> struct eigen2_part_return_type;
+}
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_FORWARDDECLARATIONS_H
diff --git a/Eigen/src/Core/util/MKL_support.h b/Eigen/src/Core/util/MKL_support.h
new file mode 100644
index 0000000..8acca9c
--- /dev/null
+++ b/Eigen/src/Core/util/MKL_support.h
@@ -0,0 +1,126 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Include file with common MKL declarations
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_MKL_SUPPORT_H
+#define EIGEN_MKL_SUPPORT_H
+
+#ifdef EIGEN_USE_MKL_ALL
+ #ifndef EIGEN_USE_BLAS
+ #define EIGEN_USE_BLAS
+ #endif
+ #ifndef EIGEN_USE_LAPACKE
+ #define EIGEN_USE_LAPACKE
+ #endif
+ #ifndef EIGEN_USE_MKL_VML
+ #define EIGEN_USE_MKL_VML
+ #endif
+#endif
+
+#ifdef EIGEN_USE_LAPACKE_STRICT
+ #define EIGEN_USE_LAPACKE
+#endif
+
+#if defined(EIGEN_USE_BLAS) || defined(EIGEN_USE_LAPACKE) || defined(EIGEN_USE_MKL_VML)
+ #define EIGEN_USE_MKL
+#endif
+
+#if defined EIGEN_USE_MKL
+# include <mkl.h>
+/*Check IMKL version for compatibility: < 10.3 is not usable with Eigen*/
+# ifndef INTEL_MKL_VERSION
+# undef EIGEN_USE_MKL /* INTEL_MKL_VERSION is not even defined on older versions */
+# elif INTEL_MKL_VERSION < 100305 /* the intel-mkl-103-release-notes say this was when the lapacke.h interface was added*/
+# undef EIGEN_USE_MKL
+# endif
+# ifndef EIGEN_USE_MKL
+ /*If the MKL version is too old, undef everything*/
+# undef EIGEN_USE_MKL_ALL
+# undef EIGEN_USE_BLAS
+# undef EIGEN_USE_LAPACKE
+# undef EIGEN_USE_MKL_VML
+# undef EIGEN_USE_LAPACKE_STRICT
+# undef EIGEN_USE_LAPACKE
+# endif
+#endif
+
+#if defined EIGEN_USE_MKL
+#include <mkl_lapacke.h>
+#define EIGEN_MKL_VML_THRESHOLD 128
+
+namespace Eigen {
+
+typedef std::complex<double> dcomplex;
+typedef std::complex<float> scomplex;
+
+namespace internal {
+
+template<typename MKLType, typename EigenType>
+static inline void assign_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
+ mklScalar=eigenScalar;
+}
+
+template<typename MKLType, typename EigenType>
+static inline void assign_conj_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
+ mklScalar=eigenScalar;
+}
+
+template <>
+inline void assign_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
+ mklScalar.real=eigenScalar.real();
+ mklScalar.imag=eigenScalar.imag();
+}
+
+template <>
+inline void assign_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
+ mklScalar.real=eigenScalar.real();
+ mklScalar.imag=eigenScalar.imag();
+}
+
+template <>
+inline void assign_conj_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
+ mklScalar.real=eigenScalar.real();
+ mklScalar.imag=-eigenScalar.imag();
+}
+
+template <>
+inline void assign_conj_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
+ mklScalar.real=eigenScalar.real();
+ mklScalar.imag=-eigenScalar.imag();
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
+
+#endif // EIGEN_MKL_SUPPORT_H
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
new file mode 100644
index 0000000..f69970f
--- /dev/null
+++ b/Eigen/src/Core/util/Macros.h
@@ -0,0 +1,435 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MACROS_H
+#define EIGEN_MACROS_H
+
+#define EIGEN_WORLD_VERSION 3
+#define EIGEN_MAJOR_VERSION 2
+#define EIGEN_MINOR_VERSION 5
+
+#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
+ (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
+ EIGEN_MINOR_VERSION>=z))))
+#ifdef __GNUC__
+ #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
+#else
+ #define EIGEN_GNUC_AT_LEAST(x,y) 0
+#endif
+
+#ifdef __GNUC__
+ #define EIGEN_GNUC_AT_MOST(x,y) ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
+#else
+ #define EIGEN_GNUC_AT_MOST(x,y) 0
+#endif
+
+#if EIGEN_GNUC_AT_MOST(4,3) && !defined(__clang__)
+ // see bug 89
+ #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
+#else
+ #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
+#endif
+
+#if defined(__GNUC__) && (__GNUC__ <= 3)
+#define EIGEN_GCC3_OR_OLDER 1
+#else
+#define EIGEN_GCC3_OR_OLDER 0
+#endif
+
+// 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
+// 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
+// enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
+// certain common platform (compiler+architecture combinations) to avoid these problems.
+// Only static alignment is really problematic (relies on nonstandard compiler extensions that don't
+// work everywhere, for example don't work on GCC/ARM), try to keep heap alignment even
+// when we have to disable static alignment.
+#if defined(__GNUC__) && !(defined(__i386__) || defined(__x86_64__) || defined(__powerpc__) || defined(__ppc__) || defined(__ia64__))
+#define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+#else
+#define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
+#endif
+
+// static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
+#if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
+ && !EIGEN_GCC3_OR_OLDER \
+ && !defined(__SUNPRO_CC) \
+ && !defined(__QNXNTO__)
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
+#else
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
+#endif
+
+#ifdef EIGEN_DONT_ALIGN
+ #ifndef EIGEN_DONT_ALIGN_STATICALLY
+ #define EIGEN_DONT_ALIGN_STATICALLY
+ #endif
+ #define EIGEN_ALIGN 0
+#else
+ #define EIGEN_ALIGN 1
+#endif
+
+// EIGEN_ALIGN_STATICALLY is the true test whether we want to align arrays on the stack or not. It takes into account both the user choice to explicitly disable
+// alignment (EIGEN_DONT_ALIGN_STATICALLY) and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT). Henceforth, only EIGEN_ALIGN_STATICALLY should be used.
+#if EIGEN_ARCH_WANTS_STACK_ALIGNMENT && !defined(EIGEN_DONT_ALIGN_STATICALLY)
+ #define EIGEN_ALIGN_STATICALLY 1
+#else
+ #define EIGEN_ALIGN_STATICALLY 0
+ #ifndef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+ #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+ #endif
+#endif
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION RowMajor
+#else
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ColMajor
+#endif
+
+#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
+#endif
+
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+# define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+#else
+# define EIGEN_HAS_BUILTIN(x) 0
+#endif
+
+/** Allows to disable some optimizations which might affect the accuracy of the result.
+ * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
+ * They currently include:
+ * - single precision Cwise::sin() and Cwise::cos() when SSE vectorization is enabled.
+ */
+#ifndef EIGEN_FAST_MATH
+#define EIGEN_FAST_MATH 1
+#endif
+
+#define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
+
+// concatenate two tokens
+#define EIGEN_CAT2(a,b) a ## b
+#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
+
+// convert a token to a string
+#define EIGEN_MAKESTRING2(a) #a
+#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
+
+// EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
+// but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
+// but GCC is still doing fine with just inline.
+#if (defined _MSC_VER) || (defined __INTEL_COMPILER)
+#define EIGEN_STRONG_INLINE __forceinline
+#else
+#define EIGEN_STRONG_INLINE inline
+#endif
+
+// EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
+// attribute to maximize inlining. This should only be used when really necessary: in particular,
+// it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
+// FIXME with the always_inline attribute,
+// gcc 3.4.x reports the following compilation error:
+// Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
+// : function body not available
+#if EIGEN_GNUC_AT_LEAST(4,0)
+#define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
+#else
+#define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_DONT_INLINE __attribute__((noinline))
+#elif (defined _MSC_VER)
+#define EIGEN_DONT_INLINE __declspec(noinline)
+#else
+#define EIGEN_DONT_INLINE
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_PERMISSIVE_EXPR __extension__
+#else
+#define EIGEN_PERMISSIVE_EXPR
+#endif
+
+// this macro allows to get rid of linking errors about multiply defined functions.
+// - static is not very good because it prevents definitions from different object files to be merged.
+// So static causes the resulting linked executable to be bloated with multiple copies of the same function.
+// - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
+#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline
+
+#ifdef NDEBUG
+# ifndef EIGEN_NO_DEBUG
+# define EIGEN_NO_DEBUG
+# endif
+#endif
+
+// eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
+#ifdef EIGEN_NO_DEBUG
+ #define eigen_plain_assert(x)
+#else
+ #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
+ namespace Eigen {
+ namespace internal {
+ inline bool copy_bool(bool b) { return b; }
+ }
+ }
+ #define eigen_plain_assert(x) assert(x)
+ #else
+ // work around bug 89
+ #include <cstdlib> // for abort
+ #include <iostream> // for std::cerr
+
+ namespace Eigen {
+ namespace internal {
+ // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
+ // see bug 89.
+ namespace {
+ EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
+ }
+ inline void assert_fail(const char *condition, const char *function, const char *file, int line)
+ {
+ std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
+ abort();
+ }
+ }
+ }
+ #define eigen_plain_assert(x) \
+ do { \
+ if(!Eigen::internal::copy_bool(x)) \
+ Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
+ } while(false)
+ #endif
+#endif
+
+// eigen_assert can be overridden
+#ifndef eigen_assert
+#define eigen_assert(x) eigen_plain_assert(x)
+#endif
+
+#ifdef EIGEN_INTERNAL_DEBUGGING
+#define eigen_internal_assert(x) eigen_assert(x)
+#else
+#define eigen_internal_assert(x)
+#endif
+
+#ifdef EIGEN_NO_DEBUG
+#define EIGEN_ONLY_USED_FOR_DEBUG(x) (void)x
+#else
+#define EIGEN_ONLY_USED_FOR_DEBUG(x)
+#endif
+
+#ifndef EIGEN_NO_DEPRECATED_WARNING
+ #if (defined __GNUC__)
+ #define EIGEN_DEPRECATED __attribute__((deprecated))
+ #elif (defined _MSC_VER)
+ #define EIGEN_DEPRECATED __declspec(deprecated)
+ #else
+ #define EIGEN_DEPRECATED
+ #endif
+#else
+ #define EIGEN_DEPRECATED
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_UNUSED __attribute__((unused))
+#else
+#define EIGEN_UNUSED
+#endif
+
+// Suppresses 'unused variable' warnings.
+namespace Eigen {
+ namespace internal {
+ template<typename T> void ignore_unused_variable(const T&) {}
+ }
+}
+#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
+
+#if !defined(EIGEN_ASM_COMMENT)
+ #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
+ #define EIGEN_ASM_COMMENT(X) __asm__("#" X)
+ #else
+ #define EIGEN_ASM_COMMENT(X)
+ #endif
+#endif
+
+/* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
+ * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
+ * so that vectorization doesn't affect binary compatibility.
+ *
+ * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
+ * vectorized and non-vectorized code.
+ */
+#if (defined __GNUC__) || (defined __PGI) || (defined __IBMCPP__) || (defined __ARMCC_VERSION)
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
+#elif (defined _MSC_VER)
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
+#elif (defined __SUNPRO_CC)
+ // FIXME not sure about this one:
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
+#else
+ #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
+#endif
+
+#define EIGEN_ALIGN8 EIGEN_ALIGN_TO_BOUNDARY(8)
+#define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
+
+#if EIGEN_ALIGN_STATICALLY
+#define EIGEN_USER_ALIGN_TO_BOUNDARY(n) EIGEN_ALIGN_TO_BOUNDARY(n)
+#define EIGEN_USER_ALIGN16 EIGEN_ALIGN16
+#else
+#define EIGEN_USER_ALIGN_TO_BOUNDARY(n)
+#define EIGEN_USER_ALIGN16
+#endif
+
+#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
+ #define EIGEN_RESTRICT
+#endif
+#ifndef EIGEN_RESTRICT
+ #define EIGEN_RESTRICT __restrict
+#endif
+
+#ifndef EIGEN_STACK_ALLOCATION_LIMIT
+// 131072 == 128 KB
+#define EIGEN_STACK_ALLOCATION_LIMIT 131072
+#endif
+
+#ifndef EIGEN_DEFAULT_IO_FORMAT
+#ifdef EIGEN_MAKING_DOCS
+// format used in Eigen's documentation
+// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
+#else
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
+#endif
+#endif
+
+// just an empty macro !
+#define EIGEN_EMPTY
+
+#if defined(_MSC_VER) && (_MSC_VER < 1800) && (!defined(__INTEL_COMPILER))
+#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =;
+#elif defined(__clang__) // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
+#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
+ template <typename OtherDerived> \
+ EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
+#else
+#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
+ { \
+ Base::operator=(other); \
+ return *this; \
+ }
+#endif
+
+/** \internal
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+
+/**
+* Just a side note. Commenting within defines works only by documenting
+* behind the object (via '!<'). Comments cannot be multi-line and thus
+* we have these extra long lines. What is confusing doxygen over here is
+* that we use '\' and basically have a bunch of typedefs with their
+* documentation in a single line.
+**/
+
+#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+ typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
+ typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
+ typedef typename Eigen::internal::nested<Derived>::type Nested; \
+ typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
+ typedef typename Eigen::internal::traits<Derived>::Index Index; \
+ enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
+ ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
+ Flags = Eigen::internal::traits<Derived>::Flags, \
+ CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
+ SizeAtCompileTime = Base::SizeAtCompileTime, \
+ MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
+ IsVectorAtCompileTime = Base::IsVectorAtCompileTime };
+
+
+#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+ typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
+ typedef typename Base::PacketScalar PacketScalar; \
+ typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
+ typedef typename Eigen::internal::nested<Derived>::type Nested; \
+ typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
+ typedef typename Eigen::internal::traits<Derived>::Index Index; \
+ enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
+ ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
+ MaxRowsAtCompileTime = Eigen::internal::traits<Derived>::MaxRowsAtCompileTime, \
+ MaxColsAtCompileTime = Eigen::internal::traits<Derived>::MaxColsAtCompileTime, \
+ Flags = Eigen::internal::traits<Derived>::Flags, \
+ CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
+ SizeAtCompileTime = Base::SizeAtCompileTime, \
+ MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
+ IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
+ using Base::derived; \
+ using Base::const_cast_derived;
+
+
+#define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
+#define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
+
+// EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
+// followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
+// finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
+#define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
+ : ((int)a == 1 || (int)b == 1) ? 1 \
+ : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
+ : ((int)a <= (int)b) ? (int)a : (int)b)
+
+// EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
+// now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
+// (between 0 and 3), it is not more than 3.
+#define EIGEN_SIZE_MIN_PREFER_FIXED(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
+ : ((int)a == 1 || (int)b == 1) ? 1 \
+ : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
+ : ((int)a == Dynamic) ? (int)b \
+ : ((int)b == Dynamic) ? (int)a \
+ : ((int)a <= (int)b) ? (int)a : (int)b)
+
+// see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
+#define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
+ : ((int)a >= (int)b) ? (int)a : (int)b)
+
+#define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
+
+#define EIGEN_IMPLIES(a,b) (!(a) || (b))
+
+#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR) \
+ template<typename OtherDerived> \
+ EIGEN_STRONG_INLINE const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> \
+ (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+ { \
+ return CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived>(derived(), other.derived()); \
+ }
+
+// the expression type of a cwise product
+#define EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS) \
+ CwiseBinaryOp< \
+ internal::scalar_product_op< \
+ typename internal::traits<LHS>::Scalar, \
+ typename internal::traits<RHS>::Scalar \
+ >, \
+ const LHS, \
+ const RHS \
+ >
+
+#endif // EIGEN_MACROS_H
diff --git a/Eigen/src/Core/util/Memory.h b/Eigen/src/Core/util/Memory.h
new file mode 100644
index 0000000..b9af5cf
--- /dev/null
+++ b/Eigen/src/Core/util/Memory.h
@@ -0,0 +1,977 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/*****************************************************************************
+*** Platform checks for aligned malloc functions ***
+*****************************************************************************/
+
+#ifndef EIGEN_MEMORY_H
+#define EIGEN_MEMORY_H
+
+#ifndef EIGEN_MALLOC_ALREADY_ALIGNED
+
+// Try to determine automatically if malloc is already aligned.
+
+// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:
+// http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html
+// This is true at least since glibc 2.8.
+// This leaves the question how to detect 64-bit. According to this document,
+// http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf
+// page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
+// quite safe, at least within the context of glibc, to equate 64-bit with LP64.
+#if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 8) || __GLIBC__>2) \
+ && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ )
+ #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+// FreeBSD 6 seems to have 16-byte aligned malloc
+// See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
+// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
+// See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
+#if defined(__FreeBSD__) && !defined(__arm__) && !defined(__mips__)
+ #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+#if defined(__APPLE__) \
+ || defined(_WIN64) \
+ || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED \
+ || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
+ #define EIGEN_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+#endif
+
+// See bug 554 (http://eigen.tuxfamily.org/bz/show_bug.cgi?id=554)
+// It seems to be unsafe to check _POSIX_ADVISORY_INFO without including unistd.h first.
+// Currently, let's include it only on unix systems:
+#if defined(__unix__) || defined(__unix)
+ #include <unistd.h>
+ #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || (defined __PGI) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+ #define EIGEN_HAS_POSIX_MEMALIGN 1
+ #endif
+#endif
+
+#ifndef EIGEN_HAS_POSIX_MEMALIGN
+ #define EIGEN_HAS_POSIX_MEMALIGN 0
+#endif
+
+#ifdef EIGEN_VECTORIZE_SSE
+ #define EIGEN_HAS_MM_MALLOC 1
+#else
+ #define EIGEN_HAS_MM_MALLOC 0
+#endif
+
+namespace Eigen {
+
+namespace internal {
+
+inline void throw_std_bad_alloc()
+{
+ #ifdef EIGEN_EXCEPTIONS
+ throw std::bad_alloc();
+ #else
+ std::size_t huge = -1;
+ new int[huge];
+ #endif
+}
+
+/*****************************************************************************
+*** Implementation of handmade aligned functions ***
+*****************************************************************************/
+
+/* ----- Hand made implementations of aligned malloc/free and realloc ----- */
+
+/** \internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
+ * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.
+ */
+inline void* handmade_aligned_malloc(std::size_t size)
+{
+ void *original = std::malloc(size+16);
+ if (original == 0) return 0;
+ void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+ *(reinterpret_cast<void**>(aligned) - 1) = original;
+ return aligned;
+}
+
+/** \internal Frees memory allocated with handmade_aligned_malloc */
+inline void handmade_aligned_free(void *ptr)
+{
+ if (ptr) std::free(*(reinterpret_cast<void**>(ptr) - 1));
+}
+
+/** \internal
+ * \brief Reallocates aligned memory.
+ * Since we know that our handmade version is based on std::realloc
+ * we can use std::realloc to implement efficient reallocation.
+ */
+inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
+{
+ if (ptr == 0) return handmade_aligned_malloc(size);
+ void *original = *(reinterpret_cast<void**>(ptr) - 1);
+ std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);
+ original = std::realloc(original,size+16);
+ if (original == 0) return 0;
+ void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+ void *previous_aligned = static_cast<char *>(original)+previous_offset;
+ if(aligned!=previous_aligned)
+ std::memmove(aligned, previous_aligned, size);
+
+ *(reinterpret_cast<void**>(aligned) - 1) = original;
+ return aligned;
+}
+
+/*****************************************************************************
+*** Implementation of generic aligned realloc (when no realloc can be used)***
+*****************************************************************************/
+
+void* aligned_malloc(std::size_t size);
+void aligned_free(void *ptr);
+
+/** \internal
+ * \brief Reallocates aligned memory.
+ * Allows reallocation with aligned ptr types. This implementation will
+ * always create a new memory chunk and copy the old data.
+ */
+inline void* generic_aligned_realloc(void* ptr, size_t size, size_t old_size)
+{
+ if (ptr==0)
+ return aligned_malloc(size);
+
+ if (size==0)
+ {
+ aligned_free(ptr);
+ return 0;
+ }
+
+ void* newptr = aligned_malloc(size);
+ if (newptr == 0)
+ {
+ #ifdef EIGEN_HAS_ERRNO
+ errno = ENOMEM; // according to the standard
+ #endif
+ return 0;
+ }
+
+ if (ptr != 0)
+ {
+ std::memcpy(newptr, ptr, (std::min)(size,old_size));
+ aligned_free(ptr);
+ }
+
+ return newptr;
+}
+
+/*****************************************************************************
+*** Implementation of portable aligned versions of malloc/free/realloc ***
+*****************************************************************************/
+
+#ifdef EIGEN_NO_MALLOC
+inline void check_that_malloc_is_allowed()
+{
+ eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
+}
+#elif defined EIGEN_RUNTIME_NO_MALLOC
+inline bool is_malloc_allowed_impl(bool update, bool new_value = false)
+{
+ static bool value = true;
+ if (update == 1)
+ value = new_value;
+ return value;
+}
+inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
+inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
+inline void check_that_malloc_is_allowed()
+{
+ eigen_assert(is_malloc_allowed() && "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)");
+}
+#else
+inline void check_that_malloc_is_allowed()
+{}
+#endif
+
+/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 bytes alignment.
+ * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
+ */
+inline void* aligned_malloc(size_t size)
+{
+ check_that_malloc_is_allowed();
+
+ void *result;
+ #if !EIGEN_ALIGN
+ result = std::malloc(size);
+ #elif EIGEN_MALLOC_ALREADY_ALIGNED
+ result = std::malloc(size);
+ #elif EIGEN_HAS_POSIX_MEMALIGN
+ if(posix_memalign(&result, 16, size)) result = 0;
+ #elif EIGEN_HAS_MM_MALLOC
+ result = _mm_malloc(size, 16);
+ #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
+ result = _aligned_malloc(size, 16);
+ #else
+ result = handmade_aligned_malloc(size);
+ #endif
+
+ if(!result && size)
+ throw_std_bad_alloc();
+
+ return result;
+}
+
+/** \internal Frees memory allocated with aligned_malloc. */
+inline void aligned_free(void *ptr)
+{
+ #if !EIGEN_ALIGN
+ std::free(ptr);
+ #elif EIGEN_MALLOC_ALREADY_ALIGNED
+ std::free(ptr);
+ #elif EIGEN_HAS_POSIX_MEMALIGN
+ std::free(ptr);
+ #elif EIGEN_HAS_MM_MALLOC
+ _mm_free(ptr);
+ #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
+ _aligned_free(ptr);
+ #else
+ handmade_aligned_free(ptr);
+ #endif
+}
+
+/**
+* \internal
+* \brief Reallocates an aligned block of memory.
+* \throws std::bad_alloc on allocation failure
+**/
+inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
+{
+ EIGEN_UNUSED_VARIABLE(old_size);
+
+ void *result;
+#if !EIGEN_ALIGN
+ result = std::realloc(ptr,new_size);
+#elif EIGEN_MALLOC_ALREADY_ALIGNED
+ result = std::realloc(ptr,new_size);
+#elif EIGEN_HAS_POSIX_MEMALIGN
+ result = generic_aligned_realloc(ptr,new_size,old_size);
+#elif EIGEN_HAS_MM_MALLOC
+ // The defined(_mm_free) is just here to verify that this MSVC version
+ // implements _mm_malloc/_mm_free based on the corresponding _aligned_
+ // functions. This may not always be the case and we just try to be safe.
+ #if defined(_MSC_VER) && (!defined(_WIN32_WCE)) && defined(_mm_free)
+ result = _aligned_realloc(ptr,new_size,16);
+ #else
+ result = generic_aligned_realloc(ptr,new_size,old_size);
+ #endif
+#elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
+ result = _aligned_realloc(ptr,new_size,16);
+#else
+ result = handmade_aligned_realloc(ptr,new_size,old_size);
+#endif
+
+ if (!result && new_size)
+ throw_std_bad_alloc();
+
+ return result;
+}
+
+/*****************************************************************************
+*** Implementation of conditionally aligned functions ***
+*****************************************************************************/
+
+/** \internal Allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
+ * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.
+ */
+template<bool Align> inline void* conditional_aligned_malloc(size_t size)
+{
+ return aligned_malloc(size);
+}
+
+template<> inline void* conditional_aligned_malloc<false>(size_t size)
+{
+ check_that_malloc_is_allowed();
+
+ void *result = std::malloc(size);
+ if(!result && size)
+ throw_std_bad_alloc();
+ return result;
+}
+
+/** \internal Frees memory allocated with conditional_aligned_malloc */
+template<bool Align> inline void conditional_aligned_free(void *ptr)
+{
+ aligned_free(ptr);
+}
+
+template<> inline void conditional_aligned_free<false>(void *ptr)
+{
+ std::free(ptr);
+}
+
+template<bool Align> inline void* conditional_aligned_realloc(void* ptr, size_t new_size, size_t old_size)
+{
+ return aligned_realloc(ptr, new_size, old_size);
+}
+
+template<> inline void* conditional_aligned_realloc<false>(void* ptr, size_t new_size, size_t)
+{
+ return std::realloc(ptr, new_size);
+}
+
+/*****************************************************************************
+*** Construction/destruction of array elements ***
+*****************************************************************************/
+
+/** \internal Constructs the elements of an array.
+ * The \a size parameter tells on how many objects to call the constructor of T.
+ */
+template<typename T> inline T* construct_elements_of_array(T *ptr, size_t size)
+{
+ for (size_t i=0; i < size; ++i) ::new (ptr + i) T;
+ return ptr;
+}
+
+/** \internal Destructs the elements of an array.
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T> inline void destruct_elements_of_array(T *ptr, size_t size)
+{
+ // always destruct an array starting from the end.
+ if(ptr)
+ while(size) ptr[--size].~T();
+}
+
+/*****************************************************************************
+*** Implementation of aligned new/delete-like functions ***
+*****************************************************************************/
+
+template<typename T>
+EIGEN_ALWAYS_INLINE void check_size_for_overflow(size_t size)
+{
+ if(size > size_t(-1) / sizeof(T))
+ throw_std_bad_alloc();
+}
+
+/** \internal Allocates \a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.
+ * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.
+ * The default constructor of T is called.
+ */
+template<typename T> inline T* aligned_new(size_t size)
+{
+ check_size_for_overflow<T>(size);
+ T *result = reinterpret_cast<T*>(aligned_malloc(sizeof(T)*size));
+ return construct_elements_of_array(result, size);
+}
+
+template<typename T, bool Align> inline T* conditional_aligned_new(size_t size)
+{
+ check_size_for_overflow<T>(size);
+ T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
+ return construct_elements_of_array(result, size);
+}
+
+/** \internal Deletes objects constructed with aligned_new
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T> inline void aligned_delete(T *ptr, size_t size)
+{
+ destruct_elements_of_array<T>(ptr, size);
+ aligned_free(ptr);
+}
+
+/** \internal Deletes objects constructed with conditional_aligned_new
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T, bool Align> inline void conditional_aligned_delete(T *ptr, size_t size)
+{
+ destruct_elements_of_array<T>(ptr, size);
+ conditional_aligned_free<Align>(ptr);
+}
+
+template<typename T, bool Align> inline T* conditional_aligned_realloc_new(T* pts, size_t new_size, size_t old_size)
+{
+ check_size_for_overflow<T>(new_size);
+ check_size_for_overflow<T>(old_size);
+ if(new_size < old_size)
+ destruct_elements_of_array(pts+new_size, old_size-new_size);
+ T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));
+ if(new_size > old_size)
+ construct_elements_of_array(result+old_size, new_size-old_size);
+ return result;
+}
+
+
+template<typename T, bool Align> inline T* conditional_aligned_new_auto(size_t size)
+{
+ if(size==0)
+ return 0; // short-cut. Also fixes Bug 884
+ check_size_for_overflow<T>(size);
+ T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
+ if(NumTraits<T>::RequireInitialization)
+ construct_elements_of_array(result, size);
+ return result;
+}
+
+template<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, size_t new_size, size_t old_size)
+{
+ check_size_for_overflow<T>(new_size);
+ check_size_for_overflow<T>(old_size);
+ if(NumTraits<T>::RequireInitialization && (new_size < old_size))
+ destruct_elements_of_array(pts+new_size, old_size-new_size);
+ T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));
+ if(NumTraits<T>::RequireInitialization && (new_size > old_size))
+ construct_elements_of_array(result+old_size, new_size-old_size);
+ return result;
+}
+
+template<typename T, bool Align> inline void conditional_aligned_delete_auto(T *ptr, size_t size)
+{
+ if(NumTraits<T>::RequireInitialization)
+ destruct_elements_of_array<T>(ptr, size);
+ conditional_aligned_free<Align>(ptr);
+}
+
+/****************************************************************************/
+
+/** \internal Returns the index of the first element of the array that is well aligned for vectorization.
+ *
+ * \param array the address of the start of the array
+ * \param size the size of the array
+ *
+ * \note If no element of the array is well aligned, the size of the array is returned. Typically,
+ * for example with SSE, "well aligned" means 16-byte-aligned. If vectorization is disabled or if the
+ * packet size for the given scalar type is 1, then everything is considered well-aligned.
+ *
+ * \note If the scalar type is vectorizable, we rely on the following assumptions: sizeof(Scalar) is a
+ * power of 2, the packet size in bytes is also a power of 2, and is a multiple of sizeof(Scalar). On the
+ * other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
+ * example with Scalar=double on certain 32-bit platforms, see bug #79.
+ *
+ * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
+ */
+template<typename Scalar, typename Index>
+static inline Index first_aligned(const Scalar* array, Index size)
+{
+ static const Index PacketSize = packet_traits<Scalar>::size;
+ static const Index PacketAlignedMask = PacketSize-1;
+
+ if(PacketSize==1)
+ {
+ // Either there is no vectorization, or a packet consists of exactly 1 scalar so that all elements
+ // of the array have the same alignment.
+ return 0;
+ }
+ else if(size_t(array) & (sizeof(Scalar)-1))
+ {
+ // There is vectorization for this scalar type, but the array is not aligned to the size of a single scalar.
+ // Consequently, no element of the array is well aligned.
+ return size;
+ }
+ else
+ {
+ return std::min<Index>( (PacketSize - (Index((size_t(array)/sizeof(Scalar))) & PacketAlignedMask))
+ & PacketAlignedMask, size);
+ }
+}
+
+/** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
+ */
+template<typename Index>
+inline static Index first_multiple(Index size, Index base)
+{
+ return ((size+base-1)/base)*base;
+}
+
+// std::copy is much slower than memcpy, so let's introduce a smart_copy which
+// use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
+template<typename T, bool UseMemcpy> struct smart_copy_helper;
+
+template<typename T> void smart_copy(const T* start, const T* end, T* target)
+{
+ smart_copy_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);
+}
+
+template<typename T> struct smart_copy_helper<T,true> {
+ static inline void run(const T* start, const T* end, T* target)
+ { memcpy(target, start, std::ptrdiff_t(end)-std::ptrdiff_t(start)); }
+};
+
+template<typename T> struct smart_copy_helper<T,false> {
+ static inline void run(const T* start, const T* end, T* target)
+ { std::copy(start, end, target); }
+};
+
+
+/*****************************************************************************
+*** Implementation of runtime stack allocation (falling back to malloc) ***
+*****************************************************************************/
+
+// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
+// to the appropriate stack allocation function
+#ifndef EIGEN_ALLOCA
+ #if (defined __linux__) || (defined __APPLE__) || (defined alloca)
+ #define EIGEN_ALLOCA alloca
+ #elif defined(_MSC_VER)
+ #define EIGEN_ALLOCA _alloca
+ #endif
+#endif
+
+// This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
+// at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
+template<typename T> class aligned_stack_memory_handler
+{
+ public:
+ /* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
+ * Note that \a ptr can be 0 regardless of the other parameters.
+ * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar type T (see NumTraits<T>::RequireInitialization).
+ * In this case, the buffer elements will also be destructed when this handler will be destructed.
+ * Finally, if \a dealloc is true, then the pointer \a ptr is freed.
+ **/
+ aligned_stack_memory_handler(T* ptr, size_t size, bool dealloc)
+ : m_ptr(ptr), m_size(size), m_deallocate(dealloc)
+ {
+ if(NumTraits<T>::RequireInitialization && m_ptr)
+ Eigen::internal::construct_elements_of_array(m_ptr, size);
+ }
+ ~aligned_stack_memory_handler()
+ {
+ if(NumTraits<T>::RequireInitialization && m_ptr)
+ Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);
+ if(m_deallocate)
+ Eigen::internal::aligned_free(m_ptr);
+ }
+ protected:
+ T* m_ptr;
+ size_t m_size;
+ bool m_deallocate;
+};
+
+} // end namespace internal
+
+/** \internal
+ * Declares, allocates and construct an aligned buffer named NAME of SIZE elements of type TYPE on the stack
+ * if SIZE is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and if stack allocation is supported by the platform
+ * (currently, this is Linux and Visual Studio only). Otherwise the memory is allocated on the heap.
+ * The allocated buffer is automatically deleted when exiting the scope of this declaration.
+ * If BUFFER is non null, then the declared variable is simply an alias for BUFFER, and no allocation/deletion occurs.
+ * Here is an example:
+ * \code
+ * {
+ * ei_declare_aligned_stack_constructed_variable(float,data,size,0);
+ * // use data[0] to data[size-1]
+ * }
+ * \endcode
+ * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.
+ */
+#ifdef EIGEN_ALLOCA
+
+ #if defined(__arm__) || defined(_WIN32)
+ #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((reinterpret_cast<size_t>(EIGEN_ALLOCA(SIZE+16)) & ~(size_t(15))) + 16)
+ #else
+ #define EIGEN_ALIGNED_ALLOCA EIGEN_ALLOCA
+ #endif
+
+ #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \
+ Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \
+ TYPE* NAME = (BUFFER)!=0 ? (BUFFER) \
+ : reinterpret_cast<TYPE*>( \
+ (sizeof(TYPE)*SIZE<=EIGEN_STACK_ALLOCATION_LIMIT) ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE)*SIZE) \
+ : Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE) ); \
+ Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,sizeof(TYPE)*SIZE>EIGEN_STACK_ALLOCATION_LIMIT)
+
+#else
+
+ #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \
+ Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \
+ TYPE* NAME = (BUFFER)!=0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE)); \
+ Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,true)
+
+#endif
+
+
+/*****************************************************************************
+*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF] ***
+*****************************************************************************/
+
+#if EIGEN_ALIGN
+ #ifdef EIGEN_EXCEPTIONS
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+ void* operator new(size_t size, const std::nothrow_t&) throw() { \
+ try { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
+ catch (...) { return 0; } \
+ }
+ #else
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+ void* operator new(size_t size, const std::nothrow_t&) throw() { \
+ return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
+ }
+ #endif
+
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) \
+ void *operator new(size_t size) { \
+ return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
+ } \
+ void *operator new[](size_t size) { \
+ return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
+ } \
+ void operator delete(void * ptr) throw() { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ void operator delete[](void * ptr) throw() { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ /* in-place new and delete. since (at least afaik) there is no actual */ \
+ /* memory allocated we can safely let the default implementation handle */ \
+ /* this particular case. */ \
+ static void *operator new(size_t size, void *ptr) { return ::operator new(size,ptr); } \
+ static void *operator new[](size_t size, void* ptr) { return ::operator new[](size,ptr); } \
+ void operator delete(void * memory, void *ptr) throw() { return ::operator delete(memory,ptr); } \
+ void operator delete[](void * memory, void *ptr) throw() { return ::operator delete[](memory,ptr); } \
+ /* nothrow-new (returns zero instead of std::bad_alloc) */ \
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+ void operator delete(void *ptr, const std::nothrow_t&) throw() { \
+ Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); \
+ } \
+ typedef void eigen_aligned_operator_new_marker_type;
+#else
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+#endif
+
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%16==0)))
+
+/****************************************************************************/
+
+/** \class aligned_allocator
+* \ingroup Core_Module
+*
+* \brief STL compatible allocator to use with with 16 byte aligned types
+*
+* Example:
+* \code
+* // Matrix4f requires 16 bytes alignment:
+* std::map< int, Matrix4f, std::less<int>,
+* aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
+* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
+* std::map< int, Vector3f > my_map_vec3;
+* \endcode
+*
+* \sa \ref TopicStlContainers.
+*/
+template<class T>
+class aligned_allocator
+{
+public:
+ typedef size_t size_type;
+ typedef std::ptrdiff_t difference_type;
+ typedef T* pointer;
+ typedef const T* const_pointer;
+ typedef T& reference;
+ typedef const T& const_reference;
+ typedef T value_type;
+
+ template<class U>
+ struct rebind
+ {
+ typedef aligned_allocator<U> other;
+ };
+
+ pointer address( reference value ) const
+ {
+ return &value;
+ }
+
+ const_pointer address( const_reference value ) const
+ {
+ return &value;
+ }
+
+ aligned_allocator()
+ {
+ }
+
+ aligned_allocator( const aligned_allocator& )
+ {
+ }
+
+ template<class U>
+ aligned_allocator( const aligned_allocator<U>& )
+ {
+ }
+
+ ~aligned_allocator()
+ {
+ }
+
+ size_type max_size() const
+ {
+ return (std::numeric_limits<size_type>::max)();
+ }
+
+ pointer allocate( size_type num, const void* hint = 0 )
+ {
+ EIGEN_UNUSED_VARIABLE(hint);
+ internal::check_size_for_overflow<T>(num);
+ return static_cast<pointer>( internal::aligned_malloc( num * sizeof(T) ) );
+ }
+
+ void construct( pointer p, const T& value )
+ {
+ ::new( p ) T( value );
+ }
+
+ void destroy( pointer p )
+ {
+ p->~T();
+ }
+
+ void deallocate( pointer p, size_type /*num*/ )
+ {
+ internal::aligned_free( p );
+ }
+
+ bool operator!=(const aligned_allocator<T>& ) const
+ { return false; }
+
+ bool operator==(const aligned_allocator<T>& ) const
+ { return true; }
+};
+
+//---------- Cache sizes ----------
+
+#if !defined(EIGEN_NO_CPUID)
+# if defined(__GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
+# if defined(__PIC__) && defined(__i386__)
+ // Case for x86 with PIC
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id));
+# elif defined(__PIC__) && defined(__x86_64__)
+ // Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.
+ // However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id));
+# else
+ // Case for x86_64 or x86 w/o PIC
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("cpuid": "=a" (abcd[0]), "=b" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id) );
+# endif
+# elif defined(_MSC_VER)
+# if (_MSC_VER > 1500) && ( defined(_M_IX86) || defined(_M_X64) )
+# define EIGEN_CPUID(abcd,func,id) __cpuidex((int*)abcd,func,id)
+# endif
+# endif
+#endif
+
+namespace internal {
+
+#ifdef EIGEN_CPUID
+
+inline bool cpuid_is_vendor(int abcd[4], const int vendor[3])
+{
+ return abcd[1]==vendor[0] && abcd[3]==vendor[1] && abcd[2]==vendor[2];
+}
+
+inline void queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ l1 = l2 = l3 = 0;
+ int cache_id = 0;
+ int cache_type = 0;
+ do {
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x4,cache_id);
+ cache_type = (abcd[0] & 0x0F) >> 0;
+ if(cache_type==1||cache_type==3) // data or unified cache
+ {
+ int cache_level = (abcd[0] & 0xE0) >> 5; // A[7:5]
+ int ways = (abcd[1] & 0xFFC00000) >> 22; // B[31:22]
+ int partitions = (abcd[1] & 0x003FF000) >> 12; // B[21:12]
+ int line_size = (abcd[1] & 0x00000FFF) >> 0; // B[11:0]
+ int sets = (abcd[2]); // C[31:0]
+
+ int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1);
+
+ switch(cache_level)
+ {
+ case 1: l1 = cache_size; break;
+ case 2: l2 = cache_size; break;
+ case 3: l3 = cache_size; break;
+ default: break;
+ }
+ }
+ cache_id++;
+ } while(cache_type>0 && cache_id<16);
+}
+
+inline void queryCacheSizes_intel_codes(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ l1 = l2 = l3 = 0;
+ EIGEN_CPUID(abcd,0x00000002,0);
+ unsigned char * bytes = reinterpret_cast<unsigned char *>(abcd)+2;
+ bool check_for_p2_core2 = false;
+ for(int i=0; i<14; ++i)
+ {
+ switch(bytes[i])
+ {
+ case 0x0A: l1 = 8; break; // 0Ah data L1 cache, 8 KB, 2 ways, 32 byte lines
+ case 0x0C: l1 = 16; break; // 0Ch data L1 cache, 16 KB, 4 ways, 32 byte lines
+ case 0x0E: l1 = 24; break; // 0Eh data L1 cache, 24 KB, 6 ways, 64 byte lines
+ case 0x10: l1 = 16; break; // 10h data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
+ case 0x15: l1 = 16; break; // 15h code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
+ case 0x2C: l1 = 32; break; // 2Ch data L1 cache, 32 KB, 8 ways, 64 byte lines
+ case 0x30: l1 = 32; break; // 30h code L1 cache, 32 KB, 8 ways, 64 byte lines
+ case 0x60: l1 = 16; break; // 60h data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored
+ case 0x66: l1 = 8; break; // 66h data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored
+ case 0x67: l1 = 16; break; // 67h data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored
+ case 0x68: l1 = 32; break; // 68h data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored
+ case 0x1A: l2 = 96; break; // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)
+ case 0x22: l3 = 512; break; // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored
+ case 0x23: l3 = 1024; break; // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x25: l3 = 2048; break; // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x29: l3 = 4096; break; // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x39: l2 = 128; break; // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored
+ case 0x3A: l2 = 192; break; // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored
+ case 0x3B: l2 = 128; break; // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored
+ case 0x3C: l2 = 256; break; // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored
+ case 0x3D: l2 = 384; break; // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored
+ case 0x3E: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored
+ case 0x40: l2 = 0; break; // no integrated L2 cache (P6 core) or L3 cache (P4 core)
+ case 0x41: l2 = 128; break; // code and data L2 cache, 128 KB, 4 ways, 32 byte lines
+ case 0x42: l2 = 256; break; // code and data L2 cache, 256 KB, 4 ways, 32 byte lines
+ case 0x43: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 32 byte lines
+ case 0x44: l2 = 1024; break; // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines
+ case 0x45: l2 = 2048; break; // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines
+ case 0x46: l3 = 4096; break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines
+ case 0x47: l3 = 8192; break; // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines
+ case 0x48: l2 = 3072; break; // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines
+ case 0x49: if(l2!=0) l3 = 4096; else {check_for_p2_core2=true; l3 = l2 = 4096;} break;// code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2
+ case 0x4A: l3 = 6144; break; // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines
+ case 0x4B: l3 = 8192; break; // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines
+ case 0x4C: l3 = 12288; break; // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines
+ case 0x4D: l3 = 16384; break; // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines
+ case 0x4E: l2 = 6144; break; // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines
+ case 0x78: l2 = 1024; break; // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines
+ case 0x79: l2 = 128; break; // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7A: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7B: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7C: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7D: l2 = 2048; break; // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines
+ case 0x7E: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)
+ case 0x7F: l2 = 512; break; // code and data L2 cache, 512 KB, 2 ways, 64 byte lines
+ case 0x80: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines
+ case 0x81: l2 = 128; break; // code and data L2 cache, 128 KB, 8 ways, 32 byte lines
+ case 0x82: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 32 byte lines
+ case 0x83: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 32 byte lines
+ case 0x84: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines
+ case 0x85: l2 = 2048; break; // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines
+ case 0x86: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines
+ case 0x87: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines
+ case 0x88: l3 = 2048; break; // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x89: l3 = 4096; break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x8A: l3 = 8192; break; // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x8D: l3 = 3072; break; // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)
+
+ default: break;
+ }
+ }
+ if(check_for_p2_core2 && l2 == l3)
+ l3 = 0;
+ l1 *= 1024;
+ l2 *= 1024;
+ l3 *= 1024;
+}
+
+inline void queryCacheSizes_intel(int& l1, int& l2, int& l3, int max_std_funcs)
+{
+ if(max_std_funcs>=4)
+ queryCacheSizes_intel_direct(l1,l2,l3);
+ else
+ queryCacheSizes_intel_codes(l1,l2,l3);
+}
+
+inline void queryCacheSizes_amd(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x80000005,0);
+ l1 = (abcd[2] >> 24) * 1024; // C[31:24] = L1 size in KB
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x80000006,0);
+ l2 = (abcd[2] >> 16) * 1024; // C[31;16] = l2 cache size in KB
+ l3 = ((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024; // D[31;18] = l3 cache size in 512KB
+}
+#endif
+
+/** \internal
+ * Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively */
+inline void queryCacheSizes(int& l1, int& l2, int& l3)
+{
+ #ifdef EIGEN_CPUID
+ int abcd[4];
+ const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};
+ const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};
+ const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574}; // "AMDisbetter!"
+
+ // identify the CPU vendor
+ EIGEN_CPUID(abcd,0x0,0);
+ int max_std_funcs = abcd[1];
+ if(cpuid_is_vendor(abcd,GenuineIntel))
+ queryCacheSizes_intel(l1,l2,l3,max_std_funcs);
+ else if(cpuid_is_vendor(abcd,AuthenticAMD) || cpuid_is_vendor(abcd,AMDisbetter_))
+ queryCacheSizes_amd(l1,l2,l3);
+ else
+ // by default let's use Intel's API
+ queryCacheSizes_intel(l1,l2,l3,max_std_funcs);
+
+ // here is the list of other vendors:
+// ||cpuid_is_vendor(abcd,"VIA VIA VIA ")
+// ||cpuid_is_vendor(abcd,"CyrixInstead")
+// ||cpuid_is_vendor(abcd,"CentaurHauls")
+// ||cpuid_is_vendor(abcd,"GenuineTMx86")
+// ||cpuid_is_vendor(abcd,"TransmetaCPU")
+// ||cpuid_is_vendor(abcd,"RiseRiseRise")
+// ||cpuid_is_vendor(abcd,"Geode by NSC")
+// ||cpuid_is_vendor(abcd,"SiS SiS SiS ")
+// ||cpuid_is_vendor(abcd,"UMC UMC UMC ")
+// ||cpuid_is_vendor(abcd,"NexGenDriven")
+ #else
+ l1 = l2 = l3 = -1;
+ #endif
+}
+
+/** \internal
+ * \returns the size in Bytes of the L1 data cache */
+inline int queryL1CacheSize()
+{
+ int l1(-1), l2, l3;
+ queryCacheSizes(l1,l2,l3);
+ return l1;
+}
+
+/** \internal
+ * \returns the size in Bytes of the L2 or L3 cache if this later is present */
+inline int queryTopLevelCacheSize()
+{
+ int l1, l2(-1), l3(-1);
+ queryCacheSizes(l1,l2,l3);
+ return (std::max)(l2,l3);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MEMORY_H
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
new file mode 100644
index 0000000..71d5871
--- /dev/null
+++ b/Eigen/src/Core/util/Meta.h
@@ -0,0 +1,243 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_META_H
+#define EIGEN_META_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \file Meta.h
+ * This file contains generic metaprogramming classes which are not specifically related to Eigen.
+ * \note In case you wonder, yes we're aware that Boost already provides all these features,
+ * we however don't want to add a dependency to Boost.
+ */
+
+struct true_type { enum { value = 1 }; };
+struct false_type { enum { value = 0 }; };
+
+template<bool Condition, typename Then, typename Else>
+struct conditional { typedef Then type; };
+
+template<typename Then, typename Else>
+struct conditional <false, Then, Else> { typedef Else type; };
+
+template<typename T, typename U> struct is_same { enum { value = 0 }; };
+template<typename T> struct is_same<T,T> { enum { value = 1 }; };
+
+template<typename T> struct remove_reference { typedef T type; };
+template<typename T> struct remove_reference<T&> { typedef T type; };
+
+template<typename T> struct remove_pointer { typedef T type; };
+template<typename T> struct remove_pointer<T*> { typedef T type; };
+template<typename T> struct remove_pointer<T*const> { typedef T type; };
+
+template <class T> struct remove_const { typedef T type; };
+template <class T> struct remove_const<const T> { typedef T type; };
+template <class T> struct remove_const<const T[]> { typedef T type[]; };
+template <class T, unsigned int Size> struct remove_const<const T[Size]> { typedef T type[Size]; };
+
+template<typename T> struct remove_all { typedef T type; };
+template<typename T> struct remove_all<const T> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const*> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T*> { typedef typename remove_all<T>::type type; };
+
+template<typename T> struct is_arithmetic { enum { value = false }; };
+template<> struct is_arithmetic<float> { enum { value = true }; };
+template<> struct is_arithmetic<double> { enum { value = true }; };
+template<> struct is_arithmetic<long double> { enum { value = true }; };
+template<> struct is_arithmetic<bool> { enum { value = true }; };
+template<> struct is_arithmetic<char> { enum { value = true }; };
+template<> struct is_arithmetic<signed char> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned char> { enum { value = true }; };
+template<> struct is_arithmetic<signed short> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned short>{ enum { value = true }; };
+template<> struct is_arithmetic<signed int> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned int> { enum { value = true }; };
+template<> struct is_arithmetic<signed long> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
+
+template <typename T> struct add_const { typedef const T type; };
+template <typename T> struct add_const<T&> { typedef T& type; };
+
+template <typename T> struct is_const { enum { value = 0 }; };
+template <typename T> struct is_const<T const> { enum { value = 1 }; };
+
+template<typename T> struct add_const_on_value_type { typedef const T type; };
+template<typename T> struct add_const_on_value_type<T&> { typedef T const& type; };
+template<typename T> struct add_const_on_value_type<T*> { typedef T const* type; };
+template<typename T> struct add_const_on_value_type<T* const> { typedef T const* const type; };
+template<typename T> struct add_const_on_value_type<T const* const> { typedef T const* const type; };
+
+/** \internal Allows to enable/disable an overload
+ * according to a compile time condition.
+ */
+template<bool Condition, typename T> struct enable_if;
+
+template<typename T> struct enable_if<true,T>
+{ typedef T type; };
+
+
+
+/** \internal
+ * A base class do disable default copy ctor and copy assignement operator.
+ */
+class noncopyable
+{
+ noncopyable(const noncopyable&);
+ const noncopyable& operator=(const noncopyable&);
+protected:
+ noncopyable() {}
+ ~noncopyable() {}
+};
+
+
+/** \internal
+ * Convenient struct to get the result type of a unary or binary functor.
+ *
+ * It supports both the current STL mechanism (using the result_type member) as well as
+ * upcoming next STL generation (using a templated result member).
+ * If none of these members is provided, then the type of the first argument is returned. FIXME, that behavior is a pretty bad hack.
+ */
+template<typename T> struct result_of {};
+
+struct has_none {int a[1];};
+struct has_std_result_type {int a[2];};
+struct has_tr1_result {int a[3];};
+
+template<typename Func, typename ArgType, int SizeOf=sizeof(has_none)>
+struct unary_result_of_select {typedef ArgType type;};
+
+template<typename Func, typename ArgType>
+struct unary_result_of_select<Func, ArgType, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType>
+struct unary_result_of_select<Func, ArgType, sizeof(has_tr1_result)> {typedef typename Func::template result<Func(ArgType)>::type type;};
+
+template<typename Func, typename ArgType>
+struct result_of<Func(ArgType)> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename unary_result_of_select<Func, ArgType, FunctorType>::type type;
+};
+
+template<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(has_none)>
+struct binary_result_of_select {typedef ArgType0 type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct result_of<Func(ArgType0,ArgType1)> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
+};
+
+/** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
+ * Usage example: \code meta_sqrt<1023>::ret \endcode
+ */
+template<int Y,
+ int InfX = 0,
+ int SupX = ((Y==1) ? 1 : Y/2),
+ bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >
+ // use ?: instead of || just to shut up a stupid gcc 4.3 warning
+class meta_sqrt
+{
+ enum {
+ MidX = (InfX+SupX)/2,
+ TakeInf = MidX*MidX > Y ? 1 : 0,
+ NewInf = int(TakeInf) ? InfX : int(MidX),
+ NewSup = int(TakeInf) ? int(MidX) : SupX
+ };
+ public:
+ enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };
+};
+
+template<int Y, int InfX, int SupX>
+class meta_sqrt<Y, InfX, SupX, true> { public: enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
+
+/** \internal determines whether the product of two numeric types is allowed and what the return type is */
+template<typename T, typename U> struct scalar_product_traits
+{
+ enum { Defined = 0 };
+};
+
+template<typename T> struct scalar_product_traits<T,T>
+{
+ enum {
+ // Cost = NumTraits<T>::MulCost,
+ Defined = 1
+ };
+ typedef T ReturnType;
+};
+
+template<typename T> struct scalar_product_traits<T,std::complex<T> >
+{
+ enum {
+ // Cost = 2*NumTraits<T>::MulCost,
+ Defined = 1
+ };
+ typedef std::complex<T> ReturnType;
+};
+
+template<typename T> struct scalar_product_traits<std::complex<T>, T>
+{
+ enum {
+ // Cost = 2*NumTraits<T>::MulCost,
+ Defined = 1
+ };
+ typedef std::complex<T> ReturnType;
+};
+
+// FIXME quick workaround around current limitation of result_of
+// template<typename Scalar, typename ArgType0, typename ArgType1>
+// struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
+// typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
+// };
+
+template<typename T> struct is_diagonal
+{ enum { ret = false }; };
+
+template<typename T> struct is_diagonal<DiagonalBase<T> >
+{ enum { ret = true }; };
+
+template<typename T> struct is_diagonal<DiagonalWrapper<T> >
+{ enum { ret = true }; };
+
+template<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >
+{ enum { ret = true }; };
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_META_H
diff --git a/Eigen/src/Core/util/NonMPL2.h b/Eigen/src/Core/util/NonMPL2.h
new file mode 100644
index 0000000..1af67cf
--- /dev/null
+++ b/Eigen/src/Core/util/NonMPL2.h
@@ -0,0 +1,3 @@
+#ifdef EIGEN_MPL2_ONLY
+#error Including non-MPL2 code in EIGEN_MPL2_ONLY mode
+#endif
diff --git a/Eigen/src/Core/util/ReenableStupidWarnings.h b/Eigen/src/Core/util/ReenableStupidWarnings.h
new file mode 100644
index 0000000..5ddfbd4
--- /dev/null
+++ b/Eigen/src/Core/util/ReenableStupidWarnings.h
@@ -0,0 +1,14 @@
+#ifdef EIGEN_WARNINGS_DISABLED
+#undef EIGEN_WARNINGS_DISABLED
+
+#ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #ifdef _MSC_VER
+ #pragma warning( pop )
+ #elif defined __INTEL_COMPILER
+ #pragma warning pop
+ #elif defined __clang__
+ #pragma clang diagnostic pop
+ #endif
+#endif
+
+#endif // EIGEN_WARNINGS_DISABLED
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
new file mode 100644
index 0000000..bac5d9f
--- /dev/null
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -0,0 +1,208 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STATIC_ASSERT_H
+#define EIGEN_STATIC_ASSERT_H
+
+/* Some notes on Eigen's static assertion mechanism:
+ *
+ * - in EIGEN_STATIC_ASSERT(CONDITION,MSG) the parameter CONDITION must be a compile time boolean
+ * expression, and MSG an enum listed in struct internal::static_assertion<true>
+ *
+ * - define EIGEN_NO_STATIC_ASSERT to disable them (and save compilation time)
+ * in that case, the static assertion is converted to the following runtime assert:
+ * eigen_assert(CONDITION && "MSG")
+ *
+ * - currently EIGEN_STATIC_ASSERT can only be used in function scope
+ *
+ */
+
+#ifndef EIGEN_NO_STATIC_ASSERT
+
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || (defined(_MSC_VER) && (_MSC_VER >= 1600))
+
+ // if native static_assert is enabled, let's use it
+ #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);
+
+ #else // not CXX0X
+
+ namespace Eigen {
+
+ namespace internal {
+
+ template<bool condition>
+ struct static_assertion {};
+
+ template<>
+ struct static_assertion<true>
+ {
+ enum {
+ YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX,
+ YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES,
+ YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES,
+ THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE,
+ THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE,
+ THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE,
+ YOU_MADE_A_PROGRAMMING_MISTAKE,
+ EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT,
+ EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE,
+ YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR,
+ YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR,
+ UNALIGNED_LOAD_AND_STORE_OPERATIONS_UNIMPLEMENTED_ON_ALTIVEC,
+ THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES,
+ FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED,
+ NUMERIC_TYPE_MUST_BE_REAL,
+ COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED,
+ WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED,
+ THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE,
+ INVALID_MATRIX_PRODUCT,
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS,
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION,
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES,
+ THIS_METHOD_IS_ONLY_FOR_ROW_MAJOR_MATRICES,
+ INVALID_MATRIX_TEMPLATE_PARAMETERS,
+ INVALID_MATRIXBASE_TEMPLATE_PARAMETERS,
+ BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
+ THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX,
+ THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE,
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES,
+ YOU_ALREADY_SPECIFIED_THIS_STRIDE,
+ INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION,
+ THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD,
+ PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1,
+ THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS,
+ YOU_CANNOT_MIX_ARRAYS_AND_MATRICES,
+ YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION,
+ THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY,
+ YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT,
+ THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS,
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL,
+ THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES,
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED,
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED,
+ THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE,
+ THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH,
+ OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG,
+ IMPLICIT_CONVERSION_TO_SCALAR_IS_FOR_INNER_PRODUCT_ONLY,
+ STORAGE_LAYOUT_DOES_NOT_MATCH
+ };
+ };
+
+ } // end namespace internal
+
+ } // end namespace Eigen
+
+ // Specialized implementation for MSVC to avoid "conditional
+ // expression is constant" warnings. This implementation doesn't
+ // appear to work under GCC, hence the multiple implementations.
+ #ifdef _MSC_VER
+
+ #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
+ {Eigen::internal::static_assertion<bool(CONDITION)>::MSG;}
+
+ #else
+
+ #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
+ if (Eigen::internal::static_assertion<bool(CONDITION)>::MSG) {}
+
+ #endif
+
+ #endif // not CXX0X
+
+#else // EIGEN_NO_STATIC_ASSERT
+
+ #define EIGEN_STATIC_ASSERT(CONDITION,MSG) eigen_assert((CONDITION) && #MSG);
+
+#endif // EIGEN_NO_STATIC_ASSERT
+
+
+// static assertion failing if the type \a TYPE is not a vector type
+#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime, \
+ YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX)
+
+// static assertion failing if the type \a TYPE is not fixed-size
+#define EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime!=Eigen::Dynamic, \
+ YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR)
+
+// static assertion failing if the type \a TYPE is not dynamic-size
+#define EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime==Eigen::Dynamic, \
+ YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE) \
+ EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime && TYPE::SizeAtCompileTime==SIZE, \
+ THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS) \
+ EIGEN_STATIC_ASSERT(TYPE::RowsAtCompileTime==ROWS && TYPE::ColsAtCompileTime==COLS, \
+ THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the two vector expression types are not compatible (same fixed-size or dynamic size)
+#define EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) \
+ EIGEN_STATIC_ASSERT( \
+ (int(TYPE0::SizeAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::SizeAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::SizeAtCompileTime)==int(TYPE1::SizeAtCompileTime)),\
+ YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES)
+
+#define EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+ ( \
+ (int(TYPE0::SizeAtCompileTime)==0 && int(TYPE1::SizeAtCompileTime)==0) \
+ || (\
+ (int(TYPE0::RowsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::RowsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::RowsAtCompileTime)==int(TYPE1::RowsAtCompileTime)) \
+ && (int(TYPE0::ColsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::ColsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::ColsAtCompileTime)==int(TYPE1::ColsAtCompileTime))\
+ ) \
+ )
+
+#ifdef EIGEN2_SUPPORT
+ #define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
+ eigen_assert(!NumTraits<Scalar>::IsInteger);
+#else
+ #define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
+ EIGEN_STATIC_ASSERT(!NumTraits<TYPE>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
+#endif
+
+
+// static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes
+#define EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+ EIGEN_STATIC_ASSERT( \
+ EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1),\
+ YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)
+
+#define EIGEN_STATIC_ASSERT_SIZE_1x1(TYPE) \
+ EIGEN_STATIC_ASSERT((TYPE::RowsAtCompileTime == 1 || TYPE::RowsAtCompileTime == Dynamic) && \
+ (TYPE::ColsAtCompileTime == 1 || TYPE::ColsAtCompileTime == Dynamic), \
+ THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS)
+
+#define EIGEN_STATIC_ASSERT_LVALUE(Derived) \
+ EIGEN_STATIC_ASSERT(internal::is_lvalue<Derived>::value, \
+ THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY)
+
+#define EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) \
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Derived>::XprKind, ArrayXpr>::value), \
+ THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES)
+
+#define EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2) \
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Derived1>::XprKind, \
+ typename internal::traits<Derived2>::XprKind \
+ >::value), \
+ YOU_CANNOT_MIX_ARRAYS_AND_MATRICES)
+
+
+#endif // EIGEN_STATIC_ASSERT_H
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
new file mode 100644
index 0000000..781965d
--- /dev/null
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -0,0 +1,469 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_XPRHELPER_H
+#define EIGEN_XPRHELPER_H
+
+// just a workaround because GCC seems to not really like empty structs
+// FIXME: gcc 4.3 generates bad code when strict-aliasing is enabled
+// so currently we simply disable this optimization for gcc 4.3
+#if (defined __GNUG__) && !((__GNUC__==4) && (__GNUC_MINOR__==3))
+ #define EIGEN_EMPTY_STRUCT_CTOR(X) \
+ EIGEN_STRONG_INLINE X() {} \
+ EIGEN_STRONG_INLINE X(const X& ) {}
+#else
+ #define EIGEN_EMPTY_STRUCT_CTOR(X)
+#endif
+
+namespace Eigen {
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
+
+namespace internal {
+
+//classes inheriting no_assignment_operator don't generate a default operator=.
+class no_assignment_operator
+{
+ private:
+ no_assignment_operator& operator=(const no_assignment_operator&);
+};
+
+/** \internal return the index type with the largest number of bits */
+template<typename I1, typename I2>
+struct promote_index_type
+{
+ typedef typename conditional<(sizeof(I1)<sizeof(I2)), I2, I1>::type type;
+};
+
+/** \internal If the template parameter Value is Dynamic, this class is just a wrapper around a T variable that
+ * can be accessed using value() and setValue().
+ * Otherwise, this class is an empty structure and value() just returns the template parameter Value.
+ */
+template<typename T, int Value> class variable_if_dynamic
+{
+ public:
+ EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic)
+ explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
+ static T value() { return T(Value); }
+ void setValue(T) {}
+};
+
+template<typename T> class variable_if_dynamic<T, Dynamic>
+{
+ T m_value;
+ variable_if_dynamic() { assert(false); }
+ public:
+ explicit variable_if_dynamic(T value) : m_value(value) {}
+ T value() const { return m_value; }
+ void setValue(T value) { m_value = value; }
+};
+
+/** \internal like variable_if_dynamic but for DynamicIndex
+ */
+template<typename T, int Value> class variable_if_dynamicindex
+{
+ public:
+ EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)
+ explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
+ static T value() { return T(Value); }
+ void setValue(T) {}
+};
+
+template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
+{
+ T m_value;
+ variable_if_dynamicindex() { assert(false); }
+ public:
+ explicit variable_if_dynamicindex(T value) : m_value(value) {}
+ T value() const { return m_value; }
+ void setValue(T value) { m_value = value; }
+};
+
+template<typename T> struct functor_traits
+{
+ enum
+ {
+ Cost = 10,
+ PacketAccess = false,
+ IsRepeatable = false
+ };
+};
+
+template<typename T> struct packet_traits;
+
+template<typename T> struct unpacket_traits
+{
+ typedef T type;
+ enum {size=1};
+};
+
+template<typename _Scalar, int _Rows, int _Cols,
+ int _Options = AutoAlign |
+ ( (_Rows==1 && _Cols!=1) ? RowMajor
+ : (_Cols==1 && _Rows!=1) ? ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+ int _MaxRows = _Rows,
+ int _MaxCols = _Cols
+> class make_proper_matrix_type
+{
+ enum {
+ IsColVector = _Cols==1 && _Rows!=1,
+ IsRowVector = _Rows==1 && _Cols!=1,
+ Options = IsColVector ? (_Options | ColMajor) & ~RowMajor
+ : IsRowVector ? (_Options | RowMajor) & ~ColMajor
+ : _Options
+ };
+ public:
+ typedef Matrix<_Scalar, _Rows, _Cols, Options, _MaxRows, _MaxCols> type;
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+class compute_matrix_flags
+{
+ enum {
+ row_major_bit = Options&RowMajor ? RowMajorBit : 0,
+ is_dynamic_size_storage = MaxRows==Dynamic || MaxCols==Dynamic,
+
+ aligned_bit =
+ (
+ ((Options&DontAlign)==0)
+ && (
+#if EIGEN_ALIGN_STATICALLY
+ ((!is_dynamic_size_storage) && (((MaxCols*MaxRows*int(sizeof(Scalar))) % 16) == 0))
+#else
+ 0
+#endif
+
+ ||
+
+#if EIGEN_ALIGN
+ is_dynamic_size_storage
+#else
+ 0
+#endif
+
+ )
+ ) ? AlignedBit : 0,
+ packet_access_bit = packet_traits<Scalar>::Vectorizable && aligned_bit ? PacketAccessBit : 0
+ };
+
+ public:
+ enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
+};
+
+template<int _Rows, int _Cols> struct size_at_compile_time
+{
+ enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };
+};
+
+/* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,
+ * whereas eval is a const reference in the case of a matrix
+ */
+
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
+template<typename T, typename BaseClassType> struct plain_matrix_type_dense;
+template<typename T> struct plain_matrix_type<T,Dense>
+{
+ typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind>::type type;
+};
+
+template<typename T> struct plain_matrix_type_dense<T,MatrixXpr>
+{
+ typedef Matrix<typename traits<T>::Scalar,
+ traits<T>::RowsAtCompileTime,
+ traits<T>::ColsAtCompileTime,
+ AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ traits<T>::MaxRowsAtCompileTime,
+ traits<T>::MaxColsAtCompileTime
+ > type;
+};
+
+template<typename T> struct plain_matrix_type_dense<T,ArrayXpr>
+{
+ typedef Array<typename traits<T>::Scalar,
+ traits<T>::RowsAtCompileTime,
+ traits<T>::ColsAtCompileTime,
+ AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ traits<T>::MaxRowsAtCompileTime,
+ traits<T>::MaxColsAtCompileTime
+ > type;
+};
+
+/* eval : the return type of eval(). For matrices, this is just a const reference
+ * in order to avoid a useless copy
+ */
+
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;
+
+template<typename T> struct eval<T,Dense>
+{
+ typedef typename plain_matrix_type<T>::type type;
+// typedef typename T::PlainObject type;
+// typedef T::Matrix<typename traits<T>::Scalar,
+// traits<T>::RowsAtCompileTime,
+// traits<T>::ColsAtCompileTime,
+// AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+// traits<T>::MaxRowsAtCompileTime,
+// traits<T>::MaxColsAtCompileTime
+// > type;
+};
+
+// for matrices, no need to evaluate, just use a const reference to avoid a useless copy
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
+{
+ typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
+};
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
+{
+ typedef const Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
+};
+
+
+
+/* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major
+ */
+template<typename T> struct plain_matrix_type_column_major
+{
+ enum { Rows = traits<T>::RowsAtCompileTime,
+ Cols = traits<T>::ColsAtCompileTime,
+ MaxRows = traits<T>::MaxRowsAtCompileTime,
+ MaxCols = traits<T>::MaxColsAtCompileTime
+ };
+ typedef Matrix<typename traits<T>::Scalar,
+ Rows,
+ Cols,
+ (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor,
+ MaxRows,
+ MaxCols
+ > type;
+};
+
+/* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major
+ */
+template<typename T> struct plain_matrix_type_row_major
+{
+ enum { Rows = traits<T>::RowsAtCompileTime,
+ Cols = traits<T>::ColsAtCompileTime,
+ MaxRows = traits<T>::MaxRowsAtCompileTime,
+ MaxCols = traits<T>::MaxColsAtCompileTime
+ };
+ typedef Matrix<typename traits<T>::Scalar,
+ Rows,
+ Cols,
+ (MaxCols==1&&MaxRows!=1) ? RowMajor : ColMajor,
+ MaxRows,
+ MaxCols
+ > type;
+};
+
+// we should be able to get rid of this one too
+template<typename T> struct must_nest_by_value { enum { ret = false }; };
+
+/** \internal The reference selector for template expressions. The idea is that we don't
+ * need to use references for expressions since they are light weight proxy
+ * objects which should generate no copying overhead. */
+template <typename T>
+struct ref_selector
+{
+ typedef typename conditional<
+ bool(traits<T>::Flags & NestByRefBit),
+ T const&,
+ const T
+ >::type type;
+};
+
+/** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */
+template<typename T1, typename T2>
+struct transfer_constness
+{
+ typedef typename conditional<
+ bool(internal::is_const<T1>::value),
+ typename internal::add_const_on_value_type<T2>::type,
+ T2
+ >::type type;
+};
+
+/** \internal Determines how a given expression should be nested into another one.
+ * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
+ * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or
+ * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
+ * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
+ * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
+ *
+ * \param T the type of the expression being nested
+ * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
+ *
+ * Note that if no evaluation occur, then the constness of T is preserved.
+ *
+ * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c).
+ * b+c is an expression "sum of matrices", which we will denote by S. In order to determine how to nest it,
+ * the Product expression uses: nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of
+ * nested determined that in this case it was better to evaluate the expression b+c into a temporary. On the other hand,
+ * since a is of type Matrix3d, the Product expression nests it as nested<Matrix3d, 3>::ret, which turns out to be
+ * const Matrix3d&, because the internal logic of nested determined that since a was already a matrix, there was no point
+ * in copying it into another matrix.
+ */
+template<typename T, int n=1, typename PlainObject = typename eval<T>::type> struct nested
+{
+ enum {
+ // for the purpose of this test, to keep it reasonably simple, we arbitrarily choose a value of Dynamic values.
+ // the choice of 10000 makes it larger than any practical fixed value and even most dynamic values.
+ // in extreme cases where these assumptions would be wrong, we would still at worst suffer performance issues
+ // (poor choice of temporaries).
+ // it's important that this value can still be squared without integer overflowing.
+ DynamicAsInteger = 10000,
+ ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
+ ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost),
+ CoeffReadCost = traits<T>::CoeffReadCost,
+ CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost),
+ NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n,
+ CostEvalAsInteger = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger,
+ CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger
+ };
+
+ typedef typename conditional<
+ ( (int(traits<T>::Flags) & EvalBeforeNestingBit) ||
+ int(CostEvalAsInteger) < int(CostNoEvalAsInteger)
+ ),
+ PlainObject,
+ typename ref_selector<T>::type
+ >::type type;
+};
+
+template<typename T>
+inline T* const_cast_ptr(const T* ptr)
+{
+ return const_cast<T*>(ptr);
+}
+
+template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
+struct dense_xpr_base
+{
+ /* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */
+};
+
+template<typename Derived>
+struct dense_xpr_base<Derived, MatrixXpr>
+{
+ typedef MatrixBase<Derived> type;
+};
+
+template<typename Derived>
+struct dense_xpr_base<Derived, ArrayXpr>
+{
+ typedef ArrayBase<Derived> type;
+};
+
+/** \internal Helper base class to add a scalar multiple operator
+ * overloads for complex types */
+template<typename Derived,typename Scalar,typename OtherScalar,
+ bool EnableIt = !is_same<Scalar,OtherScalar>::value >
+struct special_scalar_op_base : public DenseCoeffsBase<Derived>
+{
+ // dummy operator* so that the
+ // "using special_scalar_op_base::operator*" compiles
+ void operator*() const;
+};
+
+template<typename Derived,typename Scalar,typename OtherScalar>
+struct special_scalar_op_base<Derived,Scalar,OtherScalar,true> : public DenseCoeffsBase<Derived>
+{
+ const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
+ operator*(const OtherScalar& scalar) const
+ {
+ return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
+ (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar));
+ }
+
+ inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
+ operator*(const OtherScalar& scalar, const Derived& matrix)
+ { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); }
+};
+
+template<typename XprType, typename CastType> struct cast_return_type
+{
+ typedef typename XprType::Scalar CurrentScalarType;
+ typedef typename remove_all<CastType>::type _CastType;
+ typedef typename _CastType::Scalar NewScalarType;
+ typedef typename conditional<is_same<CurrentScalarType,NewScalarType>::value,
+ const XprType&,CastType>::type type;
+};
+
+template <typename A, typename B> struct promote_storage_type;
+
+template <typename A> struct promote_storage_type<A,A>
+{
+ typedef A ret;
+};
+
+/** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.
+ * \param Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
+ */
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_row_type
+{
+ typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime,
+ ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType;
+ typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime,
+ ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType;
+
+ typedef typename conditional<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixRowType,
+ ArrayRowType
+ >::type type;
+};
+
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_col_type
+{
+ typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1,
+ ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType;
+ typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1,
+ ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType;
+
+ typedef typename conditional<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixColType,
+ ArrayColType
+ >::type type;
+};
+
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_diag_type
+{
+ enum { diag_size = EIGEN_SIZE_MIN_PREFER_DYNAMIC(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),
+ max_diag_size = EIGEN_SIZE_MIN_PREFER_FIXED(ExpressionType::MaxRowsAtCompileTime, ExpressionType::MaxColsAtCompileTime)
+ };
+ typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType;
+ typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType;
+
+ typedef typename conditional<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixDiagType,
+ ArrayDiagType
+ >::type type;
+};
+
+template<typename ExpressionType>
+struct is_lvalue
+{
+ enum { value = !bool(is_const<ExpressionType>::value) &&
+ bool(traits<ExpressionType>::Flags & LvalueBit) };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_XPRHELPER_H
diff --git a/Eigen/src/Eigen2Support/Block.h b/Eigen/src/Eigen2Support/Block.h
new file mode 100644
index 0000000..604456f
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Block.h
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLOCK2_H
+#define EIGEN_BLOCK2_H
+
+namespace Eigen {
+
+/** \returns a dynamic-size expression of a corner of *this.
+ *
+ * \param type the type of corner. Can be \a Eigen::TopLeft, \a Eigen::TopRight,
+ * \a Eigen::BottomLeft, \a Eigen::BottomRight.
+ * \param cRows the number of rows in the corner
+ * \param cCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_corner_enum_int_int.cpp
+ * Output: \verbinclude MatrixBase_corner_enum_int_int.out
+ *
+ * \note Even though the returned expression has dynamic size, in the case
+ * when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
+ * which means that evaluating it does not cause a dynamic memory allocation.
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<typename Derived>
+inline Block<Derived> DenseBase<Derived>
+ ::corner(CornerType type, Index cRows, Index cCols)
+{
+ switch(type)
+ {
+ default:
+ eigen_assert(false && "Bad corner type.");
+ case TopLeft:
+ return Block<Derived>(derived(), 0, 0, cRows, cCols);
+ case TopRight:
+ return Block<Derived>(derived(), 0, cols() - cCols, cRows, cCols);
+ case BottomLeft:
+ return Block<Derived>(derived(), rows() - cRows, 0, cRows, cCols);
+ case BottomRight:
+ return Block<Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+ }
+}
+
+/** This is the const version of corner(CornerType, Index, Index).*/
+template<typename Derived>
+inline const Block<Derived>
+DenseBase<Derived>::corner(CornerType type, Index cRows, Index cCols) const
+{
+ switch(type)
+ {
+ default:
+ eigen_assert(false && "Bad corner type.");
+ case TopLeft:
+ return Block<Derived>(derived(), 0, 0, cRows, cCols);
+ case TopRight:
+ return Block<Derived>(derived(), 0, cols() - cCols, cRows, cCols);
+ case BottomLeft:
+ return Block<Derived>(derived(), rows() - cRows, 0, cRows, cCols);
+ case BottomRight:
+ return Block<Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+ }
+}
+
+/** \returns a fixed-size expression of a corner of *this.
+ *
+ * \param type the type of corner. Can be \a Eigen::TopLeft, \a Eigen::TopRight,
+ * \a Eigen::BottomLeft, \a Eigen::BottomRight.
+ *
+ * The template parameters CRows and CCols arethe number of rows and columns in the corner.
+ *
+ * Example: \include MatrixBase_template_int_int_corner_enum.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_corner_enum.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<typename Derived>
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols>
+DenseBase<Derived>::corner(CornerType type)
+{
+ switch(type)
+ {
+ default:
+ eigen_assert(false && "Bad corner type.");
+ case TopLeft:
+ return Block<Derived, CRows, CCols>(derived(), 0, 0);
+ case TopRight:
+ return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+ case BottomLeft:
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+ case BottomRight:
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+ }
+}
+
+/** This is the const version of corner<int, int>(CornerType).*/
+template<typename Derived>
+template<int CRows, int CCols>
+inline const Block<Derived, CRows, CCols>
+DenseBase<Derived>::corner(CornerType type) const
+{
+ switch(type)
+ {
+ default:
+ eigen_assert(false && "Bad corner type.");
+ case TopLeft:
+ return Block<Derived, CRows, CCols>(derived(), 0, 0);
+ case TopRight:
+ return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+ case BottomLeft:
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+ case BottomRight:
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLOCK2_H
diff --git a/Eigen/src/Eigen2Support/CMakeLists.txt b/Eigen/src/Eigen2Support/CMakeLists.txt
new file mode 100644
index 0000000..7ae41b3
--- /dev/null
+++ b/Eigen/src/Eigen2Support/CMakeLists.txt
@@ -0,0 +1,8 @@
+FILE(GLOB Eigen_Eigen2Support_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Eigen2Support_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigen2Support COMPONENT Devel
+ )
+
+ADD_SUBDIRECTORY(Geometry)
\ No newline at end of file
diff --git a/Eigen/src/Eigen2Support/Cwise.h b/Eigen/src/Eigen2Support/Cwise.h
new file mode 100644
index 0000000..d95009b
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Cwise.h
@@ -0,0 +1,192 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_H
+#define EIGEN_CWISE_H
+
+namespace Eigen {
+
+/** \internal
+ * convenient macro to defined the return type of a cwise binary operation */
+#define EIGEN_CWISE_BINOP_RETURN_TYPE(OP) \
+ CwiseBinaryOp<OP<typename internal::traits<ExpressionType>::Scalar>, ExpressionType, OtherDerived>
+
+/** \internal
+ * convenient macro to defined the return type of a cwise unary operation */
+#define EIGEN_CWISE_UNOP_RETURN_TYPE(OP) \
+ CwiseUnaryOp<OP<typename internal::traits<ExpressionType>::Scalar>, ExpressionType>
+
+/** \internal
+ * convenient macro to defined the return type of a cwise comparison to a scalar */
+#define EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(OP) \
+ CwiseBinaryOp<OP<typename internal::traits<ExpressionType>::Scalar>, ExpressionType, \
+ typename ExpressionType::ConstantReturnType >
+
+/** \class Cwise
+ *
+ * \brief Pseudo expression providing additional coefficient-wise operations
+ *
+ * \param ExpressionType the type of the object on which to do coefficient-wise operations
+ *
+ * This class represents an expression with additional coefficient-wise features.
+ * It is the return type of MatrixBase::cwise()
+ * and most of the time this is the only way it is used.
+ *
+ * Example: \include MatrixBase_cwise_const.cpp
+ * Output: \verbinclude MatrixBase_cwise_const.out
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_CWISE_PLUGIN.
+ *
+ * \sa MatrixBase::cwise() const, MatrixBase::cwise()
+ */
+template<typename ExpressionType> class Cwise
+{
+ public:
+
+ typedef typename internal::traits<ExpressionType>::Scalar Scalar;
+ typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+ ExpressionType, const ExpressionType&>::type ExpressionTypeNested;
+ typedef CwiseUnaryOp<internal::scalar_add_op<Scalar>, ExpressionType> ScalarAddReturnType;
+
+ inline Cwise(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+ /** \internal */
+ inline const ExpressionType& _expression() const { return m_matrix; }
+
+ template<typename OtherDerived>
+ const EIGEN_CWISE_PRODUCT_RETURN_TYPE(ExpressionType,OtherDerived)
+ operator*(const MatrixBase<OtherDerived> &other) const;
+
+ template<typename OtherDerived>
+ const EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_quotient_op)
+ operator/(const MatrixBase<OtherDerived> &other) const;
+
+ /** \deprecated ArrayBase::min() */
+ template<typename OtherDerived>
+ const EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_min_op)
+ (min)(const MatrixBase<OtherDerived> &other) const
+ { return EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_min_op)(_expression(), other.derived()); }
+
+ /** \deprecated ArrayBase::max() */
+ template<typename OtherDerived>
+ const EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_max_op)
+ (max)(const MatrixBase<OtherDerived> &other) const
+ { return EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_max_op)(_expression(), other.derived()); }
+
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_abs_op) abs() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_abs2_op) abs2() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_square_op) square() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_cube_op) cube() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_inverse_op) inverse() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_sqrt_op) sqrt() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_exp_op) exp() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_log_op) log() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_cos_op) cos() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_sin_op) sin() const;
+ const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_pow_op) pow(const Scalar& exponent) const;
+
+ const ScalarAddReturnType
+ operator+(const Scalar& scalar) const;
+
+ /** \relates Cwise */
+ friend const ScalarAddReturnType
+ operator+(const Scalar& scalar, const Cwise& mat)
+ { return mat + scalar; }
+
+ ExpressionType& operator+=(const Scalar& scalar);
+
+ const ScalarAddReturnType
+ operator-(const Scalar& scalar) const;
+
+ ExpressionType& operator-=(const Scalar& scalar);
+
+ template<typename OtherDerived>
+ inline ExpressionType& operator*=(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline ExpressionType& operator/=(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)
+ operator<(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)
+ operator<=(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)
+ operator>(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)
+ operator>=(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)
+ operator==(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)
+ operator!=(const MatrixBase<OtherDerived>& other) const;
+
+ // comparisons to a scalar value
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)
+ operator<(Scalar s) const;
+
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)
+ operator<=(Scalar s) const;
+
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)
+ operator>(Scalar s) const;
+
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)
+ operator>=(Scalar s) const;
+
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)
+ operator==(Scalar s) const;
+
+ const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)
+ operator!=(Scalar s) const;
+
+ // allow to extend Cwise outside Eigen
+ #ifdef EIGEN_CWISE_PLUGIN
+ #include EIGEN_CWISE_PLUGIN
+ #endif
+
+ protected:
+ ExpressionTypeNested m_matrix;
+};
+
+
+/** \returns a Cwise wrapper of *this providing additional coefficient-wise operations
+ *
+ * Example: \include MatrixBase_cwise_const.cpp
+ * Output: \verbinclude MatrixBase_cwise_const.out
+ *
+ * \sa class Cwise, cwise()
+ */
+template<typename Derived>
+inline const Cwise<Derived> MatrixBase<Derived>::cwise() const
+{
+ return derived();
+}
+
+/** \returns a Cwise wrapper of *this providing additional coefficient-wise operations
+ *
+ * Example: \include MatrixBase_cwise.cpp
+ * Output: \verbinclude MatrixBase_cwise.out
+ *
+ * \sa class Cwise, cwise() const
+ */
+template<typename Derived>
+inline Cwise<Derived> MatrixBase<Derived>::cwise()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_H
diff --git a/Eigen/src/Eigen2Support/CwiseOperators.h b/Eigen/src/Eigen2Support/CwiseOperators.h
new file mode 100644
index 0000000..482f306
--- /dev/null
+++ b/Eigen/src/Eigen2Support/CwiseOperators.h
@@ -0,0 +1,298 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAY_CWISE_OPERATORS_H
+#define EIGEN_ARRAY_CWISE_OPERATORS_H
+
+namespace Eigen {
+
+/***************************************************************************
+* The following functions were defined in Core
+***************************************************************************/
+
+
+/** \deprecated ArrayBase::abs() */
+template<typename ExpressionType>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_abs_op)
+Cwise<ExpressionType>::abs() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::abs2() */
+template<typename ExpressionType>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_abs2_op)
+Cwise<ExpressionType>::abs2() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::exp() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_exp_op)
+Cwise<ExpressionType>::exp() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::log() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_log_op)
+Cwise<ExpressionType>::log() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::operator*() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE(ExpressionType,OtherDerived)
+Cwise<ExpressionType>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_PRODUCT_RETURN_TYPE(ExpressionType,OtherDerived)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator/() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_quotient_op)
+Cwise<ExpressionType>::operator/(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(internal::scalar_quotient_op)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator*=() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline ExpressionType& Cwise<ExpressionType>::operator*=(const MatrixBase<OtherDerived> &other)
+{
+ return m_matrix.const_cast_derived() = *this * other;
+}
+
+/** \deprecated ArrayBase::operator/=() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline ExpressionType& Cwise<ExpressionType>::operator/=(const MatrixBase<OtherDerived> &other)
+{
+ return m_matrix.const_cast_derived() = *this / other;
+}
+
+/***************************************************************************
+* The following functions were defined in Array
+***************************************************************************/
+
+// -- unary operators --
+
+/** \deprecated ArrayBase::sqrt() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_sqrt_op)
+Cwise<ExpressionType>::sqrt() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::cos() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_cos_op)
+Cwise<ExpressionType>::cos() const
+{
+ return _expression();
+}
+
+
+/** \deprecated ArrayBase::sin() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_sin_op)
+Cwise<ExpressionType>::sin() const
+{
+ return _expression();
+}
+
+
+/** \deprecated ArrayBase::log() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_pow_op)
+Cwise<ExpressionType>::pow(const Scalar& exponent) const
+{
+ return EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_pow_op)(_expression(), internal::scalar_pow_op<Scalar>(exponent));
+}
+
+
+/** \deprecated ArrayBase::inverse() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_inverse_op)
+Cwise<ExpressionType>::inverse() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::square() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_square_op)
+Cwise<ExpressionType>::square() const
+{
+ return _expression();
+}
+
+/** \deprecated ArrayBase::cube() */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(internal::scalar_cube_op)
+Cwise<ExpressionType>::cube() const
+{
+ return _expression();
+}
+
+
+// -- binary operators --
+
+/** \deprecated ArrayBase::operator<() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)
+Cwise<ExpressionType>::operator<(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::<=() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)
+Cwise<ExpressionType>::operator<=(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator>() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)
+Cwise<ExpressionType>::operator>(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator>=() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)
+Cwise<ExpressionType>::operator>=(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator==() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)
+Cwise<ExpressionType>::operator==(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)(_expression(), other.derived());
+}
+
+/** \deprecated ArrayBase::operator!=() */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)
+Cwise<ExpressionType>::operator!=(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)(_expression(), other.derived());
+}
+
+// comparisons to scalar value
+
+/** \deprecated ArrayBase::operator<(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)
+Cwise<ExpressionType>::operator<(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \deprecated ArrayBase::operator<=(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)
+Cwise<ExpressionType>::operator<=(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \deprecated ArrayBase::operator>(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)
+Cwise<ExpressionType>::operator>(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \deprecated ArrayBase::operator>=(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)
+Cwise<ExpressionType>::operator>=(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \deprecated ArrayBase::operator==(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)
+Cwise<ExpressionType>::operator==(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \deprecated ArrayBase::operator!=(Scalar) */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)
+Cwise<ExpressionType>::operator!=(Scalar s) const
+{
+ return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)(_expression(),
+ typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+// scalar addition
+
+/** \deprecated ArrayBase::operator+(Scalar) */
+template<typename ExpressionType>
+inline const typename Cwise<ExpressionType>::ScalarAddReturnType
+Cwise<ExpressionType>::operator+(const Scalar& scalar) const
+{
+ return typename Cwise<ExpressionType>::ScalarAddReturnType(m_matrix, internal::scalar_add_op<Scalar>(scalar));
+}
+
+/** \deprecated ArrayBase::operator+=(Scalar) */
+template<typename ExpressionType>
+inline ExpressionType& Cwise<ExpressionType>::operator+=(const Scalar& scalar)
+{
+ return m_matrix.const_cast_derived() = *this + scalar;
+}
+
+/** \deprecated ArrayBase::operator-(Scalar) */
+template<typename ExpressionType>
+inline const typename Cwise<ExpressionType>::ScalarAddReturnType
+Cwise<ExpressionType>::operator-(const Scalar& scalar) const
+{
+ return *this + (-scalar);
+}
+
+/** \deprecated ArrayBase::operator-=(Scalar) */
+template<typename ExpressionType>
+inline ExpressionType& Cwise<ExpressionType>::operator-=(const Scalar& scalar)
+{
+ return m_matrix.const_cast_derived() = *this - scalar;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAY_CWISE_OPERATORS_H
diff --git a/Eigen/src/Eigen2Support/Geometry/AlignedBox.h b/Eigen/src/Eigen2Support/Geometry/AlignedBox.h
new file mode 100644
index 0000000..2e4309d
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/AlignedBox.h
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ * \nonstableyet
+ *
+ * \class AlignedBox
+ *
+ * \brief An axis aligned box
+ *
+ * \param _Scalar the type of the scalar coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ *
+ * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+ */
+template <typename _Scalar, int _AmbientDim>
+class AlignedBox
+{
+public:
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+ /** Default constructor initializing a null box. */
+ inline AlignedBox()
+ { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
+
+ /** Constructs a null box with \a _dim the dimension of the ambient space. */
+ inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim)
+ { setNull(); }
+
+ /** Constructs a box with extremities \a _min and \a _max. */
+ inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {}
+
+ /** Constructs a box containing a single point \a p. */
+ inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {}
+
+ ~AlignedBox() {}
+
+ /** \returns the dimension in which the box holds */
+ inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
+
+ /** \returns true if the box is null, i.e, empty. */
+ inline bool isNull() const { return (m_min.cwise() > m_max).any(); }
+
+ /** Makes \c *this a null/empty box. */
+ inline void setNull()
+ {
+ m_min.setConstant( (std::numeric_limits<Scalar>::max)());
+ m_max.setConstant(-(std::numeric_limits<Scalar>::max)());
+ }
+
+ /** \returns the minimal corner */
+ inline const VectorType& (min)() const { return m_min; }
+ /** \returns a non const reference to the minimal corner */
+ inline VectorType& (min)() { return m_min; }
+ /** \returns the maximal corner */
+ inline const VectorType& (max)() const { return m_max; }
+ /** \returns a non const reference to the maximal corner */
+ inline VectorType& (max)() { return m_max; }
+
+ /** \returns true if the point \a p is inside the box \c *this. */
+ inline bool contains(const VectorType& p) const
+ { return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).all(); }
+
+ /** \returns true if the box \a b is entirely inside the box \c *this. */
+ inline bool contains(const AlignedBox& b) const
+ { return (m_min.cwise()<=(b.min)()).all() && ((b.max)().cwise()<=m_max).all(); }
+
+ /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
+ inline AlignedBox& extend(const VectorType& p)
+ { m_min = (m_min.cwise().min)(p); m_max = (m_max.cwise().max)(p); return *this; }
+
+ /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
+ inline AlignedBox& extend(const AlignedBox& b)
+ { m_min = (m_min.cwise().min)(b.m_min); m_max = (m_max.cwise().max)(b.m_max); return *this; }
+
+ /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
+ inline AlignedBox& clamp(const AlignedBox& b)
+ { m_min = (m_min.cwise().max)(b.m_min); m_max = (m_max.cwise().min)(b.m_max); return *this; }
+
+ /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
+ inline AlignedBox& translate(const VectorType& t)
+ { m_min += t; m_max += t; return *this; }
+
+ /** \returns the squared distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa exteriorDistance()
+ */
+ inline Scalar squaredExteriorDistance(const VectorType& p) const;
+
+ /** \returns the distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa squaredExteriorDistance()
+ */
+ inline Scalar exteriorDistance(const VectorType& p) const
+ { return ei_sqrt(squaredExteriorDistance(p)); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_min = (other.min)().template cast<Scalar>();
+ m_max = (other.max)().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+ VectorType m_min, m_max;
+};
+
+template<typename Scalar,int AmbiantDim>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
+{
+ Scalar dist2(0);
+ Scalar aux;
+ for (int k=0; k<dim(); ++k)
+ {
+ if ((aux = (p[k]-m_min[k]))<Scalar(0))
+ dist2 += aux*aux;
+ else if ( (aux = (m_max[k]-p[k]))<Scalar(0))
+ dist2 += aux*aux;
+ }
+ return dist2;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/All.h b/Eigen/src/Eigen2Support/Geometry/All.h
new file mode 100644
index 0000000..e0b00fc
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/All.h
@@ -0,0 +1,115 @@
+#ifndef EIGEN2_GEOMETRY_MODULE_H
+#define EIGEN2_GEOMETRY_MODULE_H
+
+#include <limits>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+#include "RotationBase.h"
+#include "Rotation2D.h"
+#include "Quaternion.h"
+#include "AngleAxis.h"
+#include "Transform.h"
+#include "Translation.h"
+#include "Scaling.h"
+#include "AlignedBox.h"
+#include "Hyperplane.h"
+#include "ParametrizedLine.h"
+#endif
+
+
+#define RotationBase eigen2_RotationBase
+#define Rotation2D eigen2_Rotation2D
+#define Rotation2Df eigen2_Rotation2Df
+#define Rotation2Dd eigen2_Rotation2Dd
+
+#define Quaternion eigen2_Quaternion
+#define Quaternionf eigen2_Quaternionf
+#define Quaterniond eigen2_Quaterniond
+
+#define AngleAxis eigen2_AngleAxis
+#define AngleAxisf eigen2_AngleAxisf
+#define AngleAxisd eigen2_AngleAxisd
+
+#define Transform eigen2_Transform
+#define Transform2f eigen2_Transform2f
+#define Transform2d eigen2_Transform2d
+#define Transform3f eigen2_Transform3f
+#define Transform3d eigen2_Transform3d
+
+#define Translation eigen2_Translation
+#define Translation2f eigen2_Translation2f
+#define Translation2d eigen2_Translation2d
+#define Translation3f eigen2_Translation3f
+#define Translation3d eigen2_Translation3d
+
+#define Scaling eigen2_Scaling
+#define Scaling2f eigen2_Scaling2f
+#define Scaling2d eigen2_Scaling2d
+#define Scaling3f eigen2_Scaling3f
+#define Scaling3d eigen2_Scaling3d
+
+#define AlignedBox eigen2_AlignedBox
+
+#define Hyperplane eigen2_Hyperplane
+#define ParametrizedLine eigen2_ParametrizedLine
+
+#define ei_toRotationMatrix eigen2_ei_toRotationMatrix
+#define ei_quaternion_assign_impl eigen2_ei_quaternion_assign_impl
+#define ei_transform_product_impl eigen2_ei_transform_product_impl
+
+#include "RotationBase.h"
+#include "Rotation2D.h"
+#include "Quaternion.h"
+#include "AngleAxis.h"
+#include "Transform.h"
+#include "Translation.h"
+#include "Scaling.h"
+#include "AlignedBox.h"
+#include "Hyperplane.h"
+#include "ParametrizedLine.h"
+
+#undef ei_toRotationMatrix
+#undef ei_quaternion_assign_impl
+#undef ei_transform_product_impl
+
+#undef RotationBase
+#undef Rotation2D
+#undef Rotation2Df
+#undef Rotation2Dd
+
+#undef Quaternion
+#undef Quaternionf
+#undef Quaterniond
+
+#undef AngleAxis
+#undef AngleAxisf
+#undef AngleAxisd
+
+#undef Transform
+#undef Transform2f
+#undef Transform2d
+#undef Transform3f
+#undef Transform3d
+
+#undef Translation
+#undef Translation2f
+#undef Translation2d
+#undef Translation3f
+#undef Translation3d
+
+#undef Scaling
+#undef Scaling2f
+#undef Scaling2d
+#undef Scaling3f
+#undef Scaling3d
+
+#undef AlignedBox
+
+#undef Hyperplane
+#undef ParametrizedLine
+
+#endif // EIGEN2_GEOMETRY_MODULE_H
diff --git a/Eigen/src/Eigen2Support/Geometry/AngleAxis.h b/Eigen/src/Eigen2Support/Geometry/AngleAxis.h
new file mode 100644
index 0000000..af598a4
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/AngleAxis.h
@@ -0,0 +1,214 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class AngleAxis
+ *
+ * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c AngleAxisf for \c float
+ * \li \c AngleAxisd for \c double
+ *
+ * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles
+ *
+ * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+ * mimic Euler-angles. Here is an example:
+ * \include AngleAxis_mimic_euler.cpp
+ * Output: \verbinclude AngleAxis_mimic_euler.out
+ *
+ * \note This class is not aimed to be used to store a rotation transformation,
+ * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
+ * and transformation objects.
+ *
+ * \sa class Quaternion, class Transform, MatrixBase::UnitX()
+ */
+
+template<typename _Scalar> struct ei_traits<AngleAxis<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
+{
+ typedef RotationBase<AngleAxis<_Scalar>,3> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 3 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+ Vector3 m_axis;
+ Scalar m_angle;
+
+public:
+
+ /** Default constructor without initialization. */
+ AngleAxis() {}
+ /** Constructs and initialize the angle-axis rotation from an \a angle in radian
+ * and an \a axis which must be normalized. */
+ template<typename Derived>
+ inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+ /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
+ inline AngleAxis(const QuaternionType& q) { *this = q; }
+ /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
+ template<typename Derived>
+ inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
+
+ Scalar angle() const { return m_angle; }
+ Scalar& angle() { return m_angle; }
+
+ const Vector3& axis() const { return m_axis; }
+ Vector3& axis() { return m_axis; }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const AngleAxis& other) const
+ { return QuaternionType(*this) * QuaternionType(other); }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const QuaternionType& other) const
+ { return QuaternionType(*this) * other; }
+
+ /** Concatenates two rotations */
+ friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+ { return a * QuaternionType(b); }
+
+ /** Concatenates two rotations */
+ inline Matrix3 operator* (const Matrix3& other) const
+ { return toRotationMatrix() * other; }
+
+ /** Concatenates two rotations */
+ inline friend Matrix3 operator* (const Matrix3& a, const AngleAxis& b)
+ { return a * b.toRotationMatrix(); }
+
+ /** Applies rotation to vector */
+ inline Vector3 operator* (const Vector3& other) const
+ { return toRotationMatrix() * other; }
+
+ /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+ AngleAxis inverse() const
+ { return AngleAxis(-m_angle, m_axis); }
+
+ AngleAxis& operator=(const QuaternionType& q);
+ template<typename Derived>
+ AngleAxis& operator=(const MatrixBase<Derived>& m);
+
+ template<typename Derived>
+ AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix3 toRotationMatrix(void) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
+ {
+ m_axis = other.axis().template cast<Scalar>();
+ m_angle = Scalar(other.angle());
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision angle-axis type */
+typedef AngleAxis<float> AngleAxisf;
+/** \ingroup Geometry_Module
+ * double precision angle-axis type */
+typedef AngleAxis<double> AngleAxisd;
+
+/** Set \c *this from a quaternion.
+ * The axis is normalized.
+ */
+template<typename Scalar>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q)
+{
+ Scalar n2 = q.vec().squaredNorm();
+ if (n2 < precision<Scalar>()*precision<Scalar>())
+ {
+ m_angle = 0;
+ m_axis << 1, 0, 0;
+ }
+ else
+ {
+ m_angle = 2*std::acos(q.w());
+ m_axis = q.vec() / ei_sqrt(n2);
+ }
+ return *this;
+}
+
+/** Set \c *this from a 3x3 rotation matrix \a mat.
+ */
+template<typename Scalar>
+template<typename Derived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
+{
+ // Since a direct conversion would not be really faster,
+ // let's use the robust Quaternion implementation:
+ return *this = QuaternionType(mat);
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+ */
+template<typename Scalar>
+typename AngleAxis<Scalar>::Matrix3
+AngleAxis<Scalar>::toRotationMatrix(void) const
+{
+ Matrix3 res;
+ Vector3 sin_axis = ei_sin(m_angle) * m_axis;
+ Scalar c = ei_cos(m_angle);
+ Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
+
+ Scalar tmp;
+ tmp = cos1_axis.x() * m_axis.y();
+ res.coeffRef(0,1) = tmp - sin_axis.z();
+ res.coeffRef(1,0) = tmp + sin_axis.z();
+
+ tmp = cos1_axis.x() * m_axis.z();
+ res.coeffRef(0,2) = tmp + sin_axis.y();
+ res.coeffRef(2,0) = tmp - sin_axis.y();
+
+ tmp = cos1_axis.y() * m_axis.z();
+ res.coeffRef(1,2) = tmp - sin_axis.x();
+ res.coeffRef(2,1) = tmp + sin_axis.x();
+
+ res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c;
+
+ return res;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt b/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
new file mode 100644
index 0000000..c347a8f
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Eigen2Support_Geometry_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Eigen2Support_Geometry_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigen2Support/Geometry
+ )
diff --git a/Eigen/src/Eigen2Support/Geometry/Hyperplane.h b/Eigen/src/Eigen2Support/Geometry/Hyperplane.h
new file mode 100644
index 0000000..b95bf00
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Hyperplane.h
@@ -0,0 +1,254 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Hyperplane
+ *
+ * \brief A hyperplane
+ *
+ * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
+ * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ * Notice that the dimension of the hyperplane is _AmbientDim-1.
+ *
+ * This class represents an hyperplane as the zero set of the implicit equation
+ * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
+ * and \f$ d \f$ is the distance (offset) to the origin.
+ */
+template <typename _Scalar, int _AmbientDim>
+class Hyperplane
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+ typedef Matrix<Scalar,int(AmbientDimAtCompileTime)==Dynamic
+ ? Dynamic
+ : int(AmbientDimAtCompileTime)+1,1> Coefficients;
+ typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
+
+ /** Default constructor without initialization */
+ inline Hyperplane() {}
+
+ /** Constructs a dynamic-size hyperplane with \a _dim the dimension
+ * of the ambient space */
+ inline explicit Hyperplane(int _dim) : m_coeffs(_dim+1) {}
+
+ /** Construct a plane from its normal \a n and a point \a e onto the plane.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, const VectorType& e)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = -e.eigen2_dot(n);
+ }
+
+ /** Constructs a plane from its normal \a n and distance to the origin \a d
+ * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, Scalar d)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = d;
+ }
+
+ /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
+ * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
+ {
+ Hyperplane result(p0.size());
+ result.normal() = (p1 - p0).unitOrthogonal();
+ result.offset() = -result.normal().eigen2_dot(p0);
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
+ * is required to be exactly 3.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
+ Hyperplane result(p0.size());
+ result.normal() = (p2 - p0).cross(p1 - p0).normalized();
+ result.offset() = -result.normal().eigen2_dot(p0);
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the parametrized line \a parametrized.
+ * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
+ * so an arbitrary choice is made.
+ */
+ // FIXME to be consitent with the rest this could be implemented as a static Through function ??
+ explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
+ {
+ normal() = parametrized.direction().unitOrthogonal();
+ offset() = -normal().eigen2_dot(parametrized.origin());
+ }
+
+ ~Hyperplane() {}
+
+ /** \returns the dimension in which the plane holds */
+ inline int dim() const { return int(AmbientDimAtCompileTime)==Dynamic ? m_coeffs.size()-1 : int(AmbientDimAtCompileTime); }
+
+ /** normalizes \c *this */
+ void normalize(void)
+ {
+ m_coeffs /= normal().norm();
+ }
+
+ /** \returns the signed distance between the plane \c *this and a point \a p.
+ * \sa absDistance()
+ */
+ inline Scalar signedDistance(const VectorType& p) const { return p.eigen2_dot(normal()) + offset(); }
+
+ /** \returns the absolute distance between the plane \c *this and a point \a p.
+ * \sa signedDistance()
+ */
+ inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the plane \c *this.
+ */
+ inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
+
+ /** \returns a constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline const NormalReturnType normal() const { return NormalReturnType(*const_cast<Coefficients*>(&m_coeffs),0,0,dim(),1); }
+
+ /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
+
+ /** \returns a non-constant reference to the distance to the origin, which is also the constant part
+ * of the implicit equation */
+ inline Scalar& offset() { return m_coeffs(dim()); }
+
+ /** \returns a constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a non-constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** \returns the intersection of *this with \a other.
+ *
+ * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
+ *
+ * \note If \a other is approximately parallel to *this, this method will return any point on *this.
+ */
+ VectorType intersection(const Hyperplane& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
+ // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
+ // whether the two lines are approximately parallel.
+ if(ei_isMuchSmallerThan(det, Scalar(1)))
+ { // special case where the two lines are approximately parallel. Pick any point on the first line.
+ if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0)))
+ return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
+ else
+ return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
+ }
+ else
+ { // general case
+ Scalar invdet = Scalar(1) / det;
+ return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
+ invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
+ }
+ }
+
+ /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+ *
+ * \param mat the Dim x Dim transformation matrix
+ * \param traits specifies whether the matrix \a mat represents an Isometry
+ * or a more generic Affine transformation. The default is Affine.
+ */
+ template<typename XprType>
+ inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+ {
+ if (traits==Affine)
+ normal() = mat.inverse().transpose() * normal();
+ else if (traits==Isometry)
+ normal() = mat * normal();
+ else
+ {
+ ei_assert("invalid traits value in Hyperplane::transform()");
+ }
+ return *this;
+ }
+
+ /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+ *
+ * \param t the transformation of dimension Dim
+ * \param traits specifies whether the transformation \a t represents an Isometry
+ * or a more generic Affine transformation. The default is Affine.
+ * Other kind of transformations are not supported.
+ */
+ inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime>& t,
+ TransformTraits traits = Affine)
+ {
+ transform(t.linear(), traits);
+ offset() -= t.translation().eigen2_dot(normal());
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+
+ Coefficients m_coeffs;
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h b/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
new file mode 100644
index 0000000..9b57b7e
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
@@ -0,0 +1,141 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class ParametrizedLine
+ *
+ * \brief A parametrized line
+ *
+ * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
+ * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
+ * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ l \in \mathbf{R} \f$.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ */
+template <typename _Scalar, int _AmbientDim>
+class ParametrizedLine
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+ /** Default constructor without initialization */
+ inline ParametrizedLine() {}
+
+ /** Constructs a dynamic-size line with \a _dim the dimension
+ * of the ambient space */
+ inline explicit ParametrizedLine(int _dim) : m_origin(_dim), m_direction(_dim) {}
+
+ /** Initializes a parametrized line of direction \a direction and origin \a origin.
+ * \warning the vector direction is assumed to be normalized.
+ */
+ ParametrizedLine(const VectorType& origin, const VectorType& direction)
+ : m_origin(origin), m_direction(direction) {}
+
+ explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+ /** Constructs a parametrized line going from \a p0 to \a p1. */
+ static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+ { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+ ~ParametrizedLine() {}
+
+ /** \returns the dimension in which the line holds */
+ inline int dim() const { return m_direction.size(); }
+
+ const VectorType& origin() const { return m_origin; }
+ VectorType& origin() { return m_origin; }
+
+ const VectorType& direction() const { return m_direction; }
+ VectorType& direction() { return m_direction; }
+
+ /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+ * \sa distance()
+ */
+ RealScalar squaredDistance(const VectorType& p) const
+ {
+ VectorType diff = p-origin();
+ return (diff - diff.eigen2_dot(direction())* direction()).squaredNorm();
+ }
+ /** \returns the distance of a point \a p to its projection onto the line \c *this.
+ * \sa squaredDistance()
+ */
+ RealScalar distance(const VectorType& p) const { return ei_sqrt(squaredDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the line \c *this. */
+ VectorType projection(const VectorType& p) const
+ { return origin() + (p-origin()).eigen2_dot(direction()) * direction(); }
+
+ Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_origin = other.origin().template cast<Scalar>();
+ m_direction = other.direction().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
+
+protected:
+
+ VectorType m_origin, m_direction;
+};
+
+/** Constructs a parametrized line from a 2D hyperplane
+ *
+ * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
+ */
+template <typename _Scalar, int _AmbientDim>
+inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ direction() = hyperplane.normal().unitOrthogonal();
+ origin() = -hyperplane.normal()*hyperplane.offset();
+}
+
+/** \returns the parameter value of the intersection between \c *this and the given hyperplane
+ */
+template <typename _Scalar, int _AmbientDim>
+inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+ return -(hyperplane.offset()+origin().eigen2_dot(hyperplane.normal()))
+ /(direction().eigen2_dot(hyperplane.normal()));
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Quaternion.h b/Eigen/src/Eigen2Support/Geometry/Quaternion.h
new file mode 100644
index 0000000..4b6390c
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Quaternion.h
@@ -0,0 +1,495 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+template<typename Other,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternion_assign_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Quaternion
+ *
+ * \brief The quaternion class used to represent 3D orientations and rotations
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ *
+ * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
+ * orientations and rotations of objects in three dimensions. Compared to other representations
+ * like Euler angles or 3x3 matrices, quatertions offer the following advantages:
+ * \li \b compact storage (4 scalars)
+ * \li \b efficient to compose (28 flops),
+ * \li \b stable spherical interpolation
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c Quaternionf for \c float
+ * \li \c Quaterniond for \c double
+ *
+ * \sa class AngleAxis, class Transform
+ */
+
+template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Quaternion : public RotationBase<Quaternion<_Scalar>,3>
+{
+ typedef RotationBase<Quaternion<_Scalar>,3> Base;
+
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4)
+
+ using Base::operator*;
+
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+
+ /** the type of the Coefficients 4-vector */
+ typedef Matrix<Scalar, 4, 1> Coefficients;
+ /** the type of a 3D vector */
+ typedef Matrix<Scalar,3,1> Vector3;
+ /** the equivalent rotation matrix type */
+ typedef Matrix<Scalar,3,3> Matrix3;
+ /** the equivalent angle-axis type */
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+ /** \returns the \c x coefficient */
+ inline Scalar x() const { return m_coeffs.coeff(0); }
+ /** \returns the \c y coefficient */
+ inline Scalar y() const { return m_coeffs.coeff(1); }
+ /** \returns the \c z coefficient */
+ inline Scalar z() const { return m_coeffs.coeff(2); }
+ /** \returns the \c w coefficient */
+ inline Scalar w() const { return m_coeffs.coeff(3); }
+
+ /** \returns a reference to the \c x coefficient */
+ inline Scalar& x() { return m_coeffs.coeffRef(0); }
+ /** \returns a reference to the \c y coefficient */
+ inline Scalar& y() { return m_coeffs.coeffRef(1); }
+ /** \returns a reference to the \c z coefficient */
+ inline Scalar& z() { return m_coeffs.coeffRef(2); }
+ /** \returns a reference to the \c w coefficient */
+ inline Scalar& w() { return m_coeffs.coeffRef(3); }
+
+ /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+ inline const Block<const Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); }
+
+ /** \returns a vector expression of the imaginary part (x,y,z) */
+ inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); }
+
+ /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a vector expression of the coefficients (x,y,z,w) */
+ inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** Default constructor leaving the quaternion uninitialized. */
+ inline Quaternion() {}
+
+ /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+ * its four coefficients \a w, \a x, \a y and \a z.
+ *
+ * \warning Note the order of the arguments: the real \a w coefficient first,
+ * while internally the coefficients are stored in the following order:
+ * [\c x, \c y, \c z, \c w]
+ */
+ inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
+ { m_coeffs << x, y, z, w; }
+
+ /** Copy constructor */
+ inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
+
+ /** Constructs and initializes a quaternion from the angle-axis \a aa */
+ explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+ /** Constructs and initializes a quaternion from either:
+ * - a rotation matrix expression,
+ * - a 4D vector expression representing quaternion coefficients.
+ * \sa operator=(MatrixBase<Derived>)
+ */
+ template<typename Derived>
+ explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+ Quaternion& operator=(const Quaternion& other);
+ Quaternion& operator=(const AngleAxisType& aa);
+ template<typename Derived>
+ Quaternion& operator=(const MatrixBase<Derived>& m);
+
+ /** \returns a quaternion representing an identity rotation
+ * \sa MatrixBase::Identity()
+ */
+ static inline Quaternion Identity() { return Quaternion(1, 0, 0, 0); }
+
+ /** \sa Quaternion::Identity(), MatrixBase::setIdentity()
+ */
+ inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; }
+
+ /** \returns the squared norm of the quaternion's coefficients
+ * \sa Quaternion::norm(), MatrixBase::squaredNorm()
+ */
+ inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); }
+
+ /** \returns the norm of the quaternion's coefficients
+ * \sa Quaternion::squaredNorm(), MatrixBase::norm()
+ */
+ inline Scalar norm() const { return m_coeffs.norm(); }
+
+ /** Normalizes the quaternion \c *this
+ * \sa normalized(), MatrixBase::normalize() */
+ inline void normalize() { m_coeffs.normalize(); }
+ /** \returns a normalized version of \c *this
+ * \sa normalize(), MatrixBase::normalized() */
+ inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); }
+
+ /** \returns the dot product of \c *this and \a other
+ * Geometrically speaking, the dot product of two unit quaternions
+ * corresponds to the cosine of half the angle between the two rotations.
+ * \sa angularDistance()
+ */
+ inline Scalar eigen2_dot(const Quaternion& other) const { return m_coeffs.eigen2_dot(other.m_coeffs); }
+
+ inline Scalar angularDistance(const Quaternion& other) const;
+
+ Matrix3 toRotationMatrix(void) const;
+
+ template<typename Derived1, typename Derived2>
+ Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ inline Quaternion operator* (const Quaternion& q) const;
+ inline Quaternion& operator*= (const Quaternion& q);
+
+ Quaternion inverse(void) const;
+ Quaternion conjugate(void) const;
+
+ Quaternion slerp(Scalar t, const Quaternion& other) const;
+
+ template<typename Derived>
+ Vector3 operator* (const MatrixBase<Derived>& vec) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Quaternion(const Quaternion<OtherScalarType>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+ Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+ * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+// Generic Quaternion * Quaternion product
+template<typename Scalar> inline Quaternion<Scalar>
+ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b)
+{
+ return Quaternion<Scalar>
+ (
+ a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+ a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+ a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+ a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+ );
+}
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
+{
+ return ei_quaternion_product(*this,other);
+}
+
+/** \sa operator*(Quaternion) */
+template <typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other)
+{
+ return (*this = *this * other);
+}
+
+/** Rotation of a vector by a quaternion.
+ * \remarks If the quaternion is used to rotate several points (>1)
+ * then it is much more efficient to first convert it to a 3x3 Matrix.
+ * Comparison of the operation cost for n transformations:
+ * - Quaternion: 30n
+ * - Via a Matrix3: 24 + 15n
+ */
+template <typename Scalar>
+template<typename Derived>
+inline typename Quaternion<Scalar>::Vector3
+Quaternion<Scalar>::operator* (const MatrixBase<Derived>& v) const
+{
+ // Note that this algorithm comes from the optimization by hand
+ // of the conversion to a Matrix followed by a Matrix/Vector product.
+ // It appears to be much faster than the common algorithm found
+ // in the litterature (30 versus 39 flops). It also requires two
+ // Vector3 as temporaries.
+ Vector3 uv;
+ uv = 2 * this->vec().cross(v);
+ return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other)
+{
+ m_coeffs = other.m_coeffs;
+ return *this;
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+ */
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa)
+{
+ Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+ this->w() = ei_cos(ha);
+ this->vec() = ei_sin(ha) * aa.axis();
+ return *this;
+}
+
+/** Set \c *this from the expression \a xpr:
+ * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+ * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+ * and \a xpr is converted to a quaternion
+ */
+template<typename Scalar>
+template<typename Derived>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr)
+{
+ ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived());
+ return *this;
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix */
+template<typename Scalar>
+inline typename Quaternion<Scalar>::Matrix3
+Quaternion<Scalar>::toRotationMatrix(void) const
+{
+ // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+ // if not inlined then the cost of the return by value is huge ~ +35%,
+ // however, not inlining this function is an order of magnitude slower, so
+ // it has to be inlined, and so the return by value is not an issue
+ Matrix3 res;
+
+ const Scalar tx = Scalar(2)*this->x();
+ const Scalar ty = Scalar(2)*this->y();
+ const Scalar tz = Scalar(2)*this->z();
+ const Scalar twx = tx*this->w();
+ const Scalar twy = ty*this->w();
+ const Scalar twz = tz*this->w();
+ const Scalar txx = tx*this->x();
+ const Scalar txy = ty*this->x();
+ const Scalar txz = tz*this->x();
+ const Scalar tyy = ty*this->y();
+ const Scalar tyz = tz*this->y();
+ const Scalar tzz = tz*this->z();
+
+ res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
+ res.coeffRef(0,1) = txy-twz;
+ res.coeffRef(0,2) = txz+twy;
+ res.coeffRef(1,0) = txy+twz;
+ res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
+ res.coeffRef(1,2) = tyz-twx;
+ res.coeffRef(2,0) = txz-twy;
+ res.coeffRef(2,1) = tyz+twx;
+ res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
+
+ return res;
+}
+
+/** Sets *this to be a quaternion representing a rotation sending the vector \a a to the vector \a b.
+ *
+ * \returns a reference to *this.
+ *
+ * Note that the two input vectors do \b not have to be normalized.
+ */
+template<typename Scalar>
+template<typename Derived1, typename Derived2>
+inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ Vector3 v0 = a.normalized();
+ Vector3 v1 = b.normalized();
+ Scalar c = v0.eigen2_dot(v1);
+
+ // if dot == 1, vectors are the same
+ if (ei_isApprox(c,Scalar(1)))
+ {
+ // set to identity
+ this->w() = 1; this->vec().setZero();
+ return *this;
+ }
+ // if dot == -1, vectors are opposites
+ if (ei_isApprox(c,Scalar(-1)))
+ {
+ this->vec() = v0.unitOrthogonal();
+ this->w() = 0;
+ return *this;
+ }
+
+ Vector3 axis = v0.cross(v1);
+ Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2));
+ Scalar invs = Scalar(1)/s;
+ this->vec() = axis * invs;
+ this->w() = s * Scalar(0.5);
+
+ return *this;
+}
+
+/** \returns the multiplicative inverse of \c *this
+ * Note that in most cases, i.e., if you simply want the opposite rotation,
+ * and/or the quaternion is normalized, then it is enough to use the conjugate.
+ *
+ * \sa Quaternion::conjugate()
+ */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
+{
+ // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
+ Scalar n2 = this->squaredNorm();
+ if (n2 > 0)
+ return Quaternion(conjugate().coeffs() / n2);
+ else
+ {
+ // return an invalid result to flag the error
+ return Quaternion(Coefficients::Zero());
+ }
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+ * if the quaternion is normalized.
+ * The conjugate of a quaternion represents the opposite rotation.
+ *
+ * \sa Quaternion::inverse()
+ */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
+{
+ return Quaternion(this->w(),-this->x(),-this->y(),-this->z());
+}
+
+/** \returns the angle (in radian) between two rotations
+ * \sa eigen2_dot()
+ */
+template <typename Scalar>
+inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
+{
+ double d = ei_abs(this->eigen2_dot(other));
+ if (d>=1.0)
+ return 0;
+ return Scalar(2) * std::acos(d);
+}
+
+/** \returns the spherical linear interpolation between the two quaternions
+ * \c *this and \a other at the parameter \a t
+ */
+template <typename Scalar>
+Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
+{
+ static const Scalar one = Scalar(1) - machine_epsilon<Scalar>();
+ Scalar d = this->eigen2_dot(other);
+ Scalar absD = ei_abs(d);
+
+ Scalar scale0;
+ Scalar scale1;
+
+ if (absD>=one)
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ // theta is the angle between the 2 quaternions
+ Scalar theta = std::acos(absD);
+ Scalar sinTheta = ei_sin(theta);
+
+ scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = ei_sin( ( t * theta) ) / sinTheta;
+ if (d<0)
+ scale1 = -scale1;
+ }
+
+ return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
+}
+
+// set from a rotation matrix
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,3,3>
+{
+ typedef typename Other::Scalar Scalar;
+ static inline void run(Quaternion<Scalar>& q, const Other& mat)
+ {
+ // This algorithm comes from "Quaternion Calculus and Fast Animation",
+ // Ken Shoemake, 1987 SIGGRAPH course notes
+ Scalar t = mat.trace();
+ if (t > 0)
+ {
+ t = ei_sqrt(t + Scalar(1.0));
+ q.w() = Scalar(0.5)*t;
+ t = Scalar(0.5)/t;
+ q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+ q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+ q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+ }
+ else
+ {
+ int i = 0;
+ if (mat.coeff(1,1) > mat.coeff(0,0))
+ i = 1;
+ if (mat.coeff(2,2) > mat.coeff(i,i))
+ i = 2;
+ int j = (i+1)%3;
+ int k = (j+1)%3;
+
+ t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+ q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+ t = Scalar(0.5)/t;
+ q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+ q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+ q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+ }
+ }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,4,1>
+{
+ typedef typename Other::Scalar Scalar;
+ static inline void run(Quaternion<Scalar>& q, const Other& vec)
+ {
+ q.coeffs() = vec;
+ }
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Rotation2D.h b/Eigen/src/Eigen2Support/Geometry/Rotation2D.h
new file mode 100644
index 0000000..19b8582
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Rotation2D.h
@@ -0,0 +1,145 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Rotation2D
+ *
+ * \brief Represents a rotation/orientation in a 2 dimensional space.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ *
+ * This class is equivalent to a single scalar representing a counter clock wise rotation
+ * as a single angle in radian. It provides some additional features such as the automatic
+ * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
+ * interface to Quaternion in order to facilitate the writing of generic algorithms
+ * dealing with rotations.
+ *
+ * \sa class Quaternion, class Transform
+ */
+template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
+{
+ typedef RotationBase<Rotation2D<_Scalar>,2> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 2 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,2,2> Matrix2;
+
+protected:
+
+ Scalar m_angle;
+
+public:
+
+ /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+ inline Rotation2D(Scalar a) : m_angle(a) {}
+
+ /** \returns the rotation angle */
+ inline Scalar angle() const { return m_angle; }
+
+ /** \returns a read-write reference to the rotation angle */
+ inline Scalar& angle() { return m_angle; }
+
+ /** \returns the inverse rotation */
+ inline Rotation2D inverse() const { return -m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D operator*(const Rotation2D& other) const
+ { return m_angle + other.m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D& operator*=(const Rotation2D& other)
+ { return m_angle += other.m_angle; return *this; }
+
+ /** Applies the rotation to a 2D vector */
+ Vector2 operator* (const Vector2& vec) const
+ { return toRotationMatrix() * vec; }
+
+ template<typename Derived>
+ Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix2 toRotationMatrix(void) const;
+
+ /** \returns the spherical interpolation between \c *this and \a other using
+ * parameter \a t. It is in fact equivalent to a linear interpolation.
+ */
+ inline Rotation2D slerp(Scalar t, const Rotation2D& other) const
+ { return m_angle * (1-t) + other.angle() * t; }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
+ {
+ m_angle = Scalar(other.angle());
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision 2D rotation type */
+typedef Rotation2D<float> Rotation2Df;
+/** \ingroup Geometry_Module
+ * double precision 2D rotation type */
+typedef Rotation2D<double> Rotation2Dd;
+
+/** Set \c *this from a 2x2 rotation matrix \a mat.
+ * In other words, this function extract the rotation angle
+ * from the rotation matrix.
+ */
+template<typename Scalar>
+template<typename Derived>
+Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0));
+ return *this;
+}
+
+/** Constructs and \returns an equivalent 2x2 rotation matrix.
+ */
+template<typename Scalar>
+typename Rotation2D<Scalar>::Matrix2
+Rotation2D<Scalar>::toRotationMatrix(void) const
+{
+ Scalar sinA = ei_sin(m_angle);
+ Scalar cosA = ei_cos(m_angle);
+ return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/RotationBase.h b/Eigen/src/Eigen2Support/Geometry/RotationBase.h
new file mode 100644
index 0000000..b1c8f38
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/RotationBase.h
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+// this file aims to contains the various representations of rotation/orientation
+// in 2D and 3D space excepted Matrix and Quaternion.
+
+/** \class RotationBase
+ *
+ * \brief Common base class for compact rotation representations
+ *
+ * \param Derived is the derived type, i.e., a rotation type
+ * \param _Dim the dimension of the space
+ */
+template<typename Derived, int _Dim>
+class RotationBase
+{
+ public:
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef typename ei_traits<Derived>::Scalar Scalar;
+
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
+
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /** \returns an equivalent rotation matrix */
+ inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns the inverse rotation */
+ inline Derived inverse() const { return derived().inverse(); }
+
+ /** \returns the concatenation of the rotation \c *this with a translation \a t */
+ inline Transform<Scalar,Dim> operator*(const Translation<Scalar,Dim>& t) const
+ { return toRotationMatrix() * t; }
+
+ /** \returns the concatenation of the rotation \c *this with a scaling \a s */
+ inline RotationMatrixType operator*(const Scaling<Scalar,Dim>& s) const
+ { return toRotationMatrix() * s; }
+
+ /** \returns the concatenation of the rotation \c *this with an affine transformation \a t */
+ inline Transform<Scalar,Dim> operator*(const Transform<Scalar,Dim>& t) const
+ { return toRotationMatrix() * t; }
+};
+
+/** \geometry_module
+ *
+ * Constructs a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ *this = r.toRotationMatrix();
+}
+
+/** \geometry_module
+ *
+ * Set a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ return *this = r.toRotationMatrix();
+}
+
+/** \internal
+ *
+ * Helper function to return an arbitrary rotation object to a rotation matrix.
+ *
+ * \param Scalar the numeric type of the matrix coefficients
+ * \param Dim the dimension of the current space
+ *
+ * It returns a Dim x Dim fixed size matrix.
+ *
+ * Default specializations are provided for:
+ * - any scalar type (2D),
+ * - any matrix expression,
+ * - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
+ *
+ * Currently ei_toRotationMatrix is only used by Transform.
+ *
+ * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
+ */
+template<typename Scalar, int Dim>
+static inline Matrix<Scalar,2,2> ei_toRotationMatrix(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return Rotation2D<Scalar>(s).toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline Matrix<Scalar,Dim,Dim> ei_toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
+{
+ return r.toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline const MatrixBase<OtherDerived>& ei_toRotationMatrix(const MatrixBase<OtherDerived>& mat)
+{
+ EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
+ YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return mat;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Scaling.h b/Eigen/src/Eigen2Support/Geometry/Scaling.h
new file mode 100644
index 0000000..b8fa6cd
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Scaling.h
@@ -0,0 +1,167 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Scaling
+ *
+ * \brief Represents a possibly non uniform scaling transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ * \param _Dim the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a scaling transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Translation, class Transform
+ */
+template<typename _Scalar, int _Dim>
+class Scaling
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
+ /** dimension of the space */
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim> TransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ Scaling() {}
+ /** Constructs and initialize a uniform scaling transformation */
+ explicit inline Scaling(const Scalar& s) { m_coeffs.setConstant(s); }
+ /** 2D only */
+ inline Scaling(const Scalar& sx, const Scalar& sy)
+ {
+ ei_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** 3D only */
+ inline Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ ei_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+ explicit inline Scaling(const VectorType& coeffs) : m_coeffs(coeffs) {}
+
+ const VectorType& coeffs() const { return m_coeffs; }
+ VectorType& coeffs() { return m_coeffs; }
+
+ /** Concatenates two scaling */
+ inline Scaling operator* (const Scaling& other) const
+ { return Scaling(coeffs().cwise() * other.coeffs()); }
+
+ /** Concatenates a scaling and a translation */
+ inline TransformType operator* (const TranslationType& t) const;
+
+ /** Concatenates a scaling and an affine transformation */
+ inline TransformType operator* (const TransformType& t) const;
+
+ /** Concatenates a scaling and a linear transformation matrix */
+ // TODO returns an expression
+ inline LinearMatrixType operator* (const LinearMatrixType& other) const
+ { return coeffs().asDiagonal() * other; }
+
+ /** Concatenates a linear transformation matrix and a scaling */
+ // TODO returns an expression
+ friend inline LinearMatrixType operator* (const LinearMatrixType& other, const Scaling& s)
+ { return other * s.coeffs().asDiagonal(); }
+
+ template<typename Derived>
+ inline LinearMatrixType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * r.toRotationMatrix(); }
+
+ /** Applies scaling to vector */
+ inline VectorType operator* (const VectorType& other) const
+ { return coeffs().asDiagonal() * other; }
+
+ /** \returns the inverse scaling */
+ inline Scaling inverse() const
+ { return Scaling(coeffs().cwise().inverse()); }
+
+ inline Scaling& operator=(const Scaling& other)
+ {
+ m_coeffs = other.m_coeffs;
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Scaling(const Scaling<OtherScalarType,Dim>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Scaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Scaling<float, 2> Scaling2f;
+typedef Scaling<double,2> Scaling2d;
+typedef Scaling<float, 3> Scaling3f;
+typedef Scaling<double,3> Scaling3d;
+//@}
+
+template<typename Scalar, int Dim>
+inline typename Scaling<Scalar,Dim>::TransformType
+Scaling<Scalar,Dim>::operator* (const TranslationType& t) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal() = coeffs();
+ res.translation() = m_coeffs.cwise() * t.vector();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Scaling<Scalar,Dim>::TransformType
+Scaling<Scalar,Dim>::operator* (const TransformType& t) const
+{
+ TransformType res = t;
+ res.prescale(m_coeffs);
+ return res;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Transform.h b/Eigen/src/Eigen2Support/Geometry/Transform.h
new file mode 100644
index 0000000..fab60b2
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Transform.h
@@ -0,0 +1,786 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+// Note that we have to pass Dim and HDim because it is not allowed to use a template
+// parameter to define a template specialization. To be more precise, in the following
+// specializations, it is not allowed to use Dim+1 instead of HDim.
+template< typename Other,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct ei_transform_product_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Transform
+ *
+ * \brief Represents an homogeneous transformation in a N dimensional space
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _Dim the dimension of the space
+ *
+ * The homography is internally represented and stored as a (Dim+1)^2 matrix which
+ * is available through the matrix() method.
+ *
+ * Conversion methods from/to Qt's QMatrix and QTransform are available if the
+ * preprocessor token EIGEN_QT_SUPPORT is defined.
+ *
+ * \sa class Matrix, class Quaternion
+ */
+template<typename _Scalar, int _Dim>
+class Transform
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
+ enum {
+ Dim = _Dim, ///< space dimension in which the transformation holds
+ HDim = _Dim+1 ///< size of a respective homogeneous vector
+ };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** type of the matrix used to represent the transformation */
+ typedef Matrix<Scalar,HDim,HDim> MatrixType;
+ /** type of the matrix used to represent the linear part of the transformation */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef Block<MatrixType,Dim,Dim> LinearPart;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
+ /** type of a vector */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef Block<MatrixType,Dim,1> TranslationPart;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+ /** corresponding scaling transformation type */
+ typedef Scaling<Scalar,Dim> ScalingType;
+
+protected:
+
+ MatrixType m_matrix;
+
+public:
+
+ /** Default constructor without initialization of the coefficients. */
+ inline Transform() { }
+
+ inline Transform(const Transform& other)
+ {
+ m_matrix = other.m_matrix;
+ }
+
+ inline explicit Transform(const TranslationType& t) { *this = t; }
+ inline explicit Transform(const ScalingType& s) { *this = s; }
+ template<typename Derived>
+ inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
+
+ inline Transform& operator=(const Transform& other)
+ { m_matrix = other.m_matrix; return *this; }
+
+ template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
+ struct construct_from_matrix
+ {
+ static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+ {
+ transform->matrix() = other;
+ }
+ };
+
+ template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
+ {
+ static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+ {
+ transform->linear() = other;
+ transform->translation().setZero();
+ transform->matrix()(Dim,Dim) = Scalar(1);
+ transform->matrix().template block<1,Dim>(Dim,0).setZero();
+ }
+ };
+
+ /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline explicit Transform(const MatrixBase<OtherDerived>& other)
+ {
+ construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
+ }
+
+ /** Set \c *this from a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline Transform& operator=(const MatrixBase<OtherDerived>& other)
+ { m_matrix = other; return *this; }
+
+ #ifdef EIGEN_QT_SUPPORT
+ inline Transform(const QMatrix& other);
+ inline Transform& operator=(const QMatrix& other);
+ inline QMatrix toQMatrix(void) const;
+ inline Transform(const QTransform& other);
+ inline Transform& operator=(const QTransform& other);
+ inline QTransform toQTransform(void) const;
+ #endif
+
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operaror(int,int) const */
+ inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operaror(int,int) */
+ inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
+
+ /** \returns a read-only expression of the transformation matrix */
+ inline const MatrixType& matrix() const { return m_matrix; }
+ /** \returns a writable expression of the transformation matrix */
+ inline MatrixType& matrix() { return m_matrix; }
+
+ /** \returns a read-only expression of the linear (linear) part of the transformation */
+ inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
+ /** \returns a writable expression of the linear (linear) part of the transformation */
+ inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
+
+ /** \returns a read-only expression of the translation vector of the transformation */
+ inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
+ /** \returns a writable expression of the translation vector of the transformation */
+ inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
+
+ /** \returns an expression of the product between the transform \c *this and a matrix expression \a other
+ *
+ * The right hand side \a other might be either:
+ * \li a vector of size Dim,
+ * \li an homogeneous vector of size Dim+1,
+ * \li a transformation matrix of size Dim+1 x Dim+1.
+ */
+ // note: this function is defined here because some compilers cannot find the respective declaration
+ template<typename OtherDerived>
+ inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
+ operator * (const MatrixBase<OtherDerived> &other) const
+ { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
+
+ /** \returns the product expression of a transformation matrix \a a times a transform \a b
+ * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
+ template<typename OtherDerived>
+ friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
+ operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
+ { return a.derived() * b.matrix(); }
+
+ /** Contatenates two transformations */
+ inline const Transform
+ operator * (const Transform& other) const
+ { return Transform(m_matrix * other.matrix()); }
+
+ /** \sa MatrixBase::setIdentity() */
+ void setIdentity() { m_matrix.setIdentity(); }
+ static const typename MatrixType::IdentityReturnType Identity()
+ {
+ return MatrixType::Identity();
+ }
+
+ template<typename OtherDerived>
+ inline Transform& scale(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& prescale(const MatrixBase<OtherDerived> &other);
+
+ inline Transform& scale(Scalar s);
+ inline Transform& prescale(Scalar s);
+
+ template<typename OtherDerived>
+ inline Transform& translate(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
+
+ template<typename RotationType>
+ inline Transform& rotate(const RotationType& rotation);
+
+ template<typename RotationType>
+ inline Transform& prerotate(const RotationType& rotation);
+
+ Transform& shear(Scalar sx, Scalar sy);
+ Transform& preshear(Scalar sx, Scalar sy);
+
+ inline Transform& operator=(const TranslationType& t);
+ inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
+ inline Transform operator*(const TranslationType& t) const;
+
+ inline Transform& operator=(const ScalingType& t);
+ inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
+ inline Transform operator*(const ScalingType& s) const;
+ friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
+ {
+ Transform res = t;
+ res.matrix().row(Dim) = t.matrix().row(Dim);
+ res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
+ return res;
+ }
+
+ template<typename Derived>
+ inline Transform& operator=(const RotationBase<Derived,Dim>& r);
+ template<typename Derived>
+ inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
+ template<typename Derived>
+ inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
+
+ LinearMatrixType rotation() const;
+ template<typename RotationMatrixType, typename ScalingMatrixType>
+ void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
+ template<typename ScalingMatrixType, typename RotationMatrixType>
+ void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
+
+ template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+ Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
+
+ inline const MatrixType inverse(TransformTraits traits = Affine) const;
+
+ /** \returns a const pointer to the column major internal matrix */
+ const Scalar* data() const { return m_matrix.data(); }
+ /** \returns a non-const pointer to the column major internal matrix */
+ Scalar* data() { return m_matrix.data(); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
+ { m_matrix = other.matrix().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_matrix.isApprox(other.m_matrix, prec); }
+
+ #ifdef EIGEN_TRANSFORM_PLUGIN
+ #include EIGEN_TRANSFORM_PLUGIN
+ #endif
+
+protected:
+
+};
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2> Transform2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3> Transform3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2> Transform2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3> Transform3d;
+
+/**************************
+*** Optional QT support ***
+**************************/
+
+#ifdef EIGEN_QT_SUPPORT
+/** Initialises \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>::Transform(const QMatrix& other)
+{
+ *this = other;
+}
+
+/** Set \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ 0, 0, 1;
+ return *this;
+}
+
+/** \returns a QMatrix from \c *this assuming the dimension is 2.
+ *
+ * \warning this convertion might loss data if \c *this is not affine
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+}
+
+/** Initialises \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>::Transform(const QTransform& other)
+{
+ *this = other;
+}
+
+/** Set \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ other.m13(), other.m23(), other.m33();
+ return *this;
+}
+
+/** \returns a QTransform from \c *this assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+QTransform Transform<Scalar,Dim>::toQTransform(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
+}
+#endif
+
+/*********************
+*** Procedural API ***
+*********************/
+
+/** Applies on the right the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa prescale()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ linear() = (linear() * other.asDiagonal()).lazy();
+ return *this;
+}
+
+/** Applies on the right a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa prescale(Scalar)
+ */
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
+{
+ linear() *= s;
+ return *this;
+}
+
+/** Applies on the left the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa scale()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
+ return *this;
+}
+
+/** Applies on the left a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa scale(Scalar)
+ */
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
+{
+ m_matrix.template corner<Dim,HDim>(TopLeft) *= s;
+ return *this;
+}
+
+/** Applies on the right the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa pretranslate()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translation() += linear() * other;
+ return *this;
+}
+
+/** Applies on the left the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa translate()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translation() += other;
+ return *this;
+}
+
+/** Applies on the right the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * The template parameter \a RotationType is the type of the rotation which
+ * must be known by ei_toRotationMatrix<>.
+ *
+ * Natively supported types includes:
+ * - any scalar (2D),
+ * - a Dim x Dim matrix expression,
+ * - a Quaternion (3D),
+ * - a AngleAxis (3D)
+ *
+ * This mechanism is easily extendable to support user types such as Euler angles,
+ * or a pair of Quaternion for 4D rotations.
+ *
+ * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
+ */
+template<typename Scalar, int Dim>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::rotate(const RotationType& rotation)
+{
+ linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation);
+ return *this;
+}
+
+/** Applies on the left the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * See rotate() for further details.
+ *
+ * \sa rotate()
+ */
+template<typename Scalar, int Dim>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
+{
+ m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation)
+ * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/** Applies on the right the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa preshear()
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ VectorType tmp = linear().col(0)*sy + linear().col(1);
+ linear() << linear().col(0) + linear().col(1)*sx, tmp;
+ return *this;
+}
+
+/** Applies on the left the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa shear()
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/******************************************************
+*** Scaling, Translation and Rotation compatibility ***
+******************************************************/
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
+{
+ linear().setIdentity();
+ translation() = t.vector();
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
+{
+ Transform res = *this;
+ res.translate(t.vector());
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
+{
+ m_matrix.setZero();
+ linear().diagonal() = s.coeffs();
+ m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
+{
+ Transform res = *this;
+ res.scale(s.coeffs());
+ return res;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
+{
+ linear() = ei_toRotationMatrix<Scalar,Dim>(r);
+ translation().setZero();
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const
+{
+ Transform res = *this;
+ res.rotate(r.derived());
+ return res;
+}
+
+/************************
+*** Special functions ***
+************************/
+
+/** \returns the rotation part of the transformation
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), computeScalingRotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+typename Transform<Scalar,Dim>::LinearMatrixType
+Transform<Scalar,Dim>::rotation() const
+{
+ LinearMatrixType result;
+ computeRotationScaling(&result, (LinearMatrixType*)0);
+ return result;
+}
+
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeScalingRotation(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+template<typename RotationMatrixType, typename ScalingMatrixType>
+void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling)
+ {
+ scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
+ }
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->noalias() = m * svd.matrixV().adjoint();
+ }
+}
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+template<typename ScalingMatrixType, typename RotationMatrixType>
+void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling)
+ {
+ scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
+ }
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->noalias() = m * svd.matrixV().adjoint();
+ }
+}
+
+/** Convenient method to set \c *this from a position, orientation and scale
+ * of a 3D object.
+ */
+template<typename Scalar, int Dim>
+template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
+{
+ linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
+ linear() *= scale.asDiagonal();
+ translation() = position;
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+/** \nonstableyet
+ *
+ * \returns the inverse transformation matrix according to some given knowledge
+ * on \c *this.
+ *
+ * \param traits allows to optimize the inversion process when the transformion
+ * is known to be not a general transformation. The possible values are:
+ * - Projective if the transformation is not necessarily affine, i.e., if the
+ * last row is not guaranteed to be [0 ... 0 1]
+ * - Affine is the default, the last row is assumed to be [0 ... 0 1]
+ * - Isometry if the transformation is only a concatenations of translations
+ * and rotations.
+ *
+ * \warning unless \a traits is always set to NoShear or NoScaling, this function
+ * requires the generic inverse method of MatrixBase defined in the LU module. If
+ * you forget to include this module, then you will get hard to debug linking errors.
+ *
+ * \sa MatrixBase::inverse()
+ */
+template<typename Scalar, int Dim>
+inline const typename Transform<Scalar,Dim>::MatrixType
+Transform<Scalar,Dim>::inverse(TransformTraits traits) const
+{
+ if (traits == Projective)
+ {
+ return m_matrix.inverse();
+ }
+ else
+ {
+ MatrixType res;
+ if (traits == Affine)
+ {
+ res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
+ }
+ else if (traits == Isometry)
+ {
+ res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
+ }
+ else
+ {
+ ei_assert("invalid traits value in Transform::inverse()");
+ }
+ // translation and remaining parts
+ res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
+ res.template corner<1,Dim>(BottomLeft).setZero();
+ res.coeffRef(Dim,Dim) = Scalar(1);
+ return res;
+ }
+}
+
+/*****************************************************
+*** Specializations of operator* with a MatrixBase ***
+*****************************************************/
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ {
+ TransformType res;
+ res.translation() = tr.translation();
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ res.linear() = (tr.linear() * other).lazy();
+ return res;
+ }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
+{
+ typedef typename Other::Scalar Scalar;
+ typedef Transform<Scalar,Dim> TransformType;
+ typedef Matrix<Scalar,Dim,1> ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return ((tr.linear() * other) + tr.translation())
+ * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Translation.h b/Eigen/src/Eigen2Support/Geometry/Translation.h
new file mode 100644
index 0000000..2b9859f
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Translation.h
@@ -0,0 +1,184 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Translation
+ *
+ * \brief Represents a translation transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ * \param _Dim the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a translation transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Scaling, class Transform
+ */
+template<typename _Scalar, int _Dim>
+class Translation
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
+ /** dimension of the space */
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding scaling transformation type */
+ typedef Scaling<Scalar,Dim> ScalingType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim> TransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ Translation() {}
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy)
+ {
+ ei_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ ei_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+ explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
+
+ const VectorType& vector() const { return m_coeffs; }
+ VectorType& vector() { return m_coeffs; }
+
+ /** Concatenates two translation */
+ inline Translation operator* (const Translation& other) const
+ { return Translation(m_coeffs + other.m_coeffs); }
+
+ /** Concatenates a translation and a scaling */
+ inline TransformType operator* (const ScalingType& other) const;
+
+ /** Concatenates a translation and a linear transformation */
+ inline TransformType operator* (const LinearMatrixType& linear) const;
+
+ template<typename Derived>
+ inline TransformType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * r.toRotationMatrix(); }
+
+ /** Concatenates a linear transformation and a translation */
+ // its a nightmare to define a templated friend function outside its declaration
+ friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t)
+ {
+ TransformType res;
+ res.matrix().setZero();
+ res.linear() = linear;
+ res.translation() = linear * t.m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+ }
+
+ /** Concatenates a translation and an affine transformation */
+ inline TransformType operator* (const TransformType& t) const;
+
+ /** Applies translation to vector */
+ inline VectorType operator* (const VectorType& other) const
+ { return m_coeffs + other; }
+
+ /** \returns the inverse translation (opposite) */
+ Translation inverse() const { return Translation(-m_coeffs); }
+
+ Translation& operator=(const Translation& other)
+ {
+ m_coeffs = other.m_coeffs;
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
+ { m_coeffs = other.vector().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Translation<float, 2> Translation2f;
+typedef Translation<double,2> Translation2d;
+typedef Translation<float, 3> Translation3f;
+typedef Translation<double,3> Translation3d;
+//@}
+
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const ScalingType& other) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal() = other.coeffs();
+ res.translation() = m_coeffs;
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear() = linear;
+ res.translation() = m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const TransformType& t) const
+{
+ TransformType res = t;
+ res.pretranslate(m_coeffs);
+ return res;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/LU.h b/Eigen/src/Eigen2Support/LU.h
new file mode 100644
index 0000000..49f19ad
--- /dev/null
+++ b/Eigen/src/Eigen2Support/LU.h
@@ -0,0 +1,120 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_LU_H
+#define EIGEN2_LU_H
+
+namespace Eigen {
+
+template<typename MatrixType>
+class LU : public FullPivLU<MatrixType>
+{
+ public:
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime, MatrixType::Options, 1, MatrixType::MaxColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1, MatrixType::Options, MatrixType::MaxRowsAtCompileTime, 1> IntColVectorType;
+ typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime, MatrixType::Options, 1, MatrixType::MaxColsAtCompileTime> RowVectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1, MatrixType::Options, MatrixType::MaxRowsAtCompileTime, 1> ColVectorType;
+
+ typedef Matrix<typename MatrixType::Scalar,
+ MatrixType::ColsAtCompileTime, // the number of rows in the "kernel matrix" is the number of cols of the original matrix
+ // so that the product "matrix * kernel = zero" makes sense
+ Dynamic, // we don't know at compile-time the dimension of the kernel
+ MatrixType::Options,
+ MatrixType::MaxColsAtCompileTime, // see explanation for 2nd template parameter
+ MatrixType::MaxColsAtCompileTime // the kernel is a subspace of the domain space, whose dimension is the number
+ // of columns of the original matrix
+ > KernelResultType;
+
+ typedef Matrix<typename MatrixType::Scalar,
+ MatrixType::RowsAtCompileTime, // the image is a subspace of the destination space, whose dimension is the number
+ // of rows of the original matrix
+ Dynamic, // we don't know at compile time the dimension of the image (the rank)
+ MatrixType::Options,
+ MatrixType::MaxRowsAtCompileTime, // the image matrix will consist of columns from the original matrix,
+ MatrixType::MaxColsAtCompileTime // so it has the same number of rows and at most as many columns.
+ > ImageResultType;
+
+ typedef FullPivLU<MatrixType> Base;
+
+ template<typename T>
+ explicit LU(const T& t) : Base(t), m_originalMatrix(t) {}
+
+ template<typename OtherDerived, typename ResultType>
+ bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+ {
+ *result = static_cast<const Base*>(this)->solve(b);
+ return true;
+ }
+
+ template<typename ResultType>
+ inline void computeInverse(ResultType *result) const
+ {
+ solve(MatrixType::Identity(this->rows(), this->cols()), result);
+ }
+
+ template<typename KernelMatrixType>
+ void computeKernel(KernelMatrixType *result) const
+ {
+ *result = static_cast<const Base*>(this)->kernel();
+ }
+
+ template<typename ImageMatrixType>
+ void computeImage(ImageMatrixType *result) const
+ {
+ *result = static_cast<const Base*>(this)->image(m_originalMatrix);
+ }
+
+ const ImageResultType image() const
+ {
+ return static_cast<const Base*>(this)->image(m_originalMatrix);
+ }
+
+ const MatrixType& m_originalMatrix;
+};
+
+#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+/** \lu_module
+ *
+ * Synonym of partialPivLu().
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const LU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::lu() const
+{
+ return LU<PlainObject>(eval());
+}
+#endif
+
+#ifdef EIGEN2_SUPPORT
+/** \lu_module
+ *
+ * Synonym of partialPivLu().
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const LU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::eigen2_lu() const
+{
+ return LU<PlainObject>(eval());
+}
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN2_LU_H
diff --git a/Eigen/src/Eigen2Support/Lazy.h b/Eigen/src/Eigen2Support/Lazy.h
new file mode 100644
index 0000000..593fc78
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Lazy.h
@@ -0,0 +1,71 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LAZY_H
+#define EIGEN_LAZY_H
+
+namespace Eigen {
+
+/** \deprecated it is only used by lazy() which is deprecated
+ *
+ * \returns an expression of *this with added flags
+ *
+ * Example: \include MatrixBase_marked.cpp
+ * Output: \verbinclude MatrixBase_marked.out
+ *
+ * \sa class Flagged, extract(), part()
+ */
+template<typename Derived>
+template<unsigned int Added>
+inline const Flagged<Derived, Added, 0>
+MatrixBase<Derived>::marked() const
+{
+ return derived();
+}
+
+/** \deprecated use MatrixBase::noalias()
+ *
+ * \returns an expression of *this with the EvalBeforeAssigningBit flag removed.
+ *
+ * Example: \include MatrixBase_lazy.cpp
+ * Output: \verbinclude MatrixBase_lazy.out
+ *
+ * \sa class Flagged, marked()
+ */
+template<typename Derived>
+inline const Flagged<Derived, 0, EvalBeforeAssigningBit>
+MatrixBase<Derived>::lazy() const
+{
+ return derived();
+}
+
+
+/** \internal
+ * Overloaded to perform an efficient C += (A*B).lazy() */
+template<typename Derived>
+template<typename ProductDerived, typename Lhs, typename Rhs>
+Derived& MatrixBase<Derived>::operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+ EvalBeforeAssigningBit>& other)
+{
+ other._expression().derived().addTo(derived()); return derived();
+}
+
+/** \internal
+ * Overloaded to perform an efficient C -= (A*B).lazy() */
+template<typename Derived>
+template<typename ProductDerived, typename Lhs, typename Rhs>
+Derived& MatrixBase<Derived>::operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+ EvalBeforeAssigningBit>& other)
+{
+ other._expression().derived().subTo(derived()); return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LAZY_H
diff --git a/Eigen/src/Eigen2Support/LeastSquares.h b/Eigen/src/Eigen2Support/LeastSquares.h
new file mode 100644
index 0000000..7992d49
--- /dev/null
+++ b/Eigen/src/Eigen2Support/LeastSquares.h
@@ -0,0 +1,169 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_LEASTSQUARES_H
+#define EIGEN2_LEASTSQUARES_H
+
+namespace Eigen {
+
+/** \ingroup LeastSquares_Module
+ *
+ * \leastsquares_module
+ *
+ * For a set of points, this function tries to express
+ * one of the coords as a linear (affine) function of the other coords.
+ *
+ * This is best explained by an example. This function works in full
+ * generality, for points in a space of arbitrary dimension, and also over
+ * the complex numbers, but for this example we will work in dimension 3
+ * over the real numbers (doubles).
+ *
+ * So let us work with the following set of 5 points given by their
+ * \f$(x,y,z)\f$ coordinates:
+ * @code
+ Vector3d points[5];
+ points[0] = Vector3d( 3.02, 6.89, -4.32 );
+ points[1] = Vector3d( 2.01, 5.39, -3.79 );
+ points[2] = Vector3d( 2.41, 6.01, -4.01 );
+ points[3] = Vector3d( 2.09, 5.55, -3.86 );
+ points[4] = Vector3d( 2.58, 6.32, -4.10 );
+ * @endcode
+ * Suppose that we want to express the second coordinate (\f$y\f$) as a linear
+ * expression in \f$x\f$ and \f$z\f$, that is,
+ * \f[ y=ax+bz+c \f]
+ * for some constants \f$a,b,c\f$. Thus, we want to find the best possible
+ * constants \f$a,b,c\f$ so that the plane of equation \f$y=ax+bz+c\f$ fits
+ * best the five above points. To do that, call this function as follows:
+ * @code
+ Vector3d coeffs; // will store the coefficients a, b, c
+ linearRegression(
+ 5,
+ &points,
+ &coeffs,
+ 1 // the coord to express as a function of
+ // the other ones. 0 means x, 1 means y, 2 means z.
+ );
+ * @endcode
+ * Now the vector \a coeffs is approximately
+ * \f$( 0.495 , -1.927 , -2.906 )\f$.
+ * Thus, we get \f$a=0.495, b = -1.927, c = -2.906\f$. Let us check for
+ * instance how near points[0] is from the plane of equation \f$y=ax+bz+c\f$.
+ * Looking at the coords of points[0], we see that:
+ * \f[ax+bz+c = 0.495 * 3.02 + (-1.927) * (-4.32) + (-2.906) = 6.91.\f]
+ * On the other hand, we have \f$y=6.89\f$. We see that the values
+ * \f$6.91\f$ and \f$6.89\f$
+ * are near, so points[0] is very near the plane of equation \f$y=ax+bz+c\f$.
+ *
+ * Let's now describe precisely the parameters:
+ * @param numPoints the number of points
+ * @param points the array of pointers to the points on which to perform the linear regression
+ * @param result pointer to the vector in which to store the result.
+ This vector must be of the same type and size as the
+ data points. The meaning of its coords is as follows.
+ For brevity, let \f$n=Size\f$,
+ \f$r_i=result[i]\f$,
+ and \f$f=funcOfOthers\f$. Denote by
+ \f$x_0,\ldots,x_{n-1}\f$
+ the n coordinates in the n-dimensional space.
+ Then the resulting equation is:
+ \f[ x_f = r_0 x_0 + \cdots + r_{f-1}x_{f-1}
+ + r_{f+1}x_{f+1} + \cdots + r_{n-1}x_{n-1} + r_n. \f]
+ * @param funcOfOthers Determines which coord to express as a function of the
+ others. Coords are numbered starting from 0, so that a
+ value of 0 means \f$x\f$, 1 means \f$y\f$,
+ 2 means \f$z\f$, ...
+ *
+ * \sa fitHyperplane()
+ */
+template<typename VectorType>
+void linearRegression(int numPoints,
+ VectorType **points,
+ VectorType *result,
+ int funcOfOthers )
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef Hyperplane<Scalar, VectorType::SizeAtCompileTime> HyperplaneType;
+ const int size = points[0]->size();
+ result->resize(size);
+ HyperplaneType h(size);
+ fitHyperplane(numPoints, points, &h);
+ for(int i = 0; i < funcOfOthers; i++)
+ result->coeffRef(i) = - h.coeffs()[i] / h.coeffs()[funcOfOthers];
+ for(int i = funcOfOthers; i < size; i++)
+ result->coeffRef(i) = - h.coeffs()[i+1] / h.coeffs()[funcOfOthers];
+}
+
+/** \ingroup LeastSquares_Module
+ *
+ * \leastsquares_module
+ *
+ * This function is quite similar to linearRegression(), so we refer to the
+ * documentation of this function and only list here the differences.
+ *
+ * The main difference from linearRegression() is that this function doesn't
+ * take a \a funcOfOthers argument. Instead, it finds a general equation
+ * of the form
+ * \f[ r_0 x_0 + \cdots + r_{n-1}x_{n-1} + r_n = 0, \f]
+ * where \f$n=Size\f$, \f$r_i=retCoefficients[i]\f$, and we denote by
+ * \f$x_0,\ldots,x_{n-1}\f$ the n coordinates in the n-dimensional space.
+ *
+ * Thus, the vector \a retCoefficients has size \f$n+1\f$, which is another
+ * difference from linearRegression().
+ *
+ * In practice, this function performs an hyper-plane fit in a total least square sense
+ * via the following steps:
+ * 1 - center the data to the mean
+ * 2 - compute the covariance matrix
+ * 3 - pick the eigenvector corresponding to the smallest eigenvalue of the covariance matrix
+ * The ratio of the smallest eigenvalue and the second one gives us a hint about the relevance
+ * of the solution. This value is optionally returned in \a soundness.
+ *
+ * \sa linearRegression()
+ */
+template<typename VectorType, typename HyperplaneType>
+void fitHyperplane(int numPoints,
+ VectorType **points,
+ HyperplaneType *result,
+ typename NumTraits<typename VectorType::Scalar>::Real* soundness = 0)
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef Matrix<Scalar,VectorType::SizeAtCompileTime,VectorType::SizeAtCompileTime> CovMatrixType;
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType)
+ ei_assert(numPoints >= 1);
+ int size = points[0]->size();
+ ei_assert(size+1 == result->coeffs().size());
+
+ // compute the mean of the data
+ VectorType mean = VectorType::Zero(size);
+ for(int i = 0; i < numPoints; ++i)
+ mean += *(points[i]);
+ mean /= numPoints;
+
+ // compute the covariance matrix
+ CovMatrixType covMat = CovMatrixType::Zero(size, size);
+ for(int i = 0; i < numPoints; ++i)
+ {
+ VectorType diff = (*(points[i]) - mean).conjugate();
+ covMat += diff * diff.adjoint();
+ }
+
+ // now we just have to pick the eigen vector with smallest eigen value
+ SelfAdjointEigenSolver<CovMatrixType> eig(covMat);
+ result->normal() = eig.eigenvectors().col(0);
+ if (soundness)
+ *soundness = eig.eigenvalues().coeff(0)/eig.eigenvalues().coeff(1);
+
+ // let's compute the constant coefficient such that the
+ // plane pass trough the mean point:
+ result->offset() = - (result->normal().cwise()* mean).sum();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_LEASTSQUARES_H
diff --git a/Eigen/src/Eigen2Support/Macros.h b/Eigen/src/Eigen2Support/Macros.h
new file mode 100644
index 0000000..351c32a
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Macros.h
@@ -0,0 +1,20 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_MACROS_H
+#define EIGEN2_MACROS_H
+
+#define ei_assert eigen_assert
+#define ei_internal_assert eigen_internal_assert
+
+#define EIGEN_ALIGN_128 EIGEN_ALIGN16
+
+#define EIGEN_ARCH_WANTS_ALIGNMENT EIGEN_ALIGN_STATICALLY
+
+#endif // EIGEN2_MACROS_H
diff --git a/Eigen/src/Eigen2Support/MathFunctions.h b/Eigen/src/Eigen2Support/MathFunctions.h
new file mode 100644
index 0000000..3544af2
--- /dev/null
+++ b/Eigen/src/Eigen2Support/MathFunctions.h
@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_MATH_FUNCTIONS_H
+#define EIGEN2_MATH_FUNCTIONS_H
+
+namespace Eigen {
+
+template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return numext::real(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return numext::imag(x); }
+template<typename T> inline T ei_conj(const T& x) { return numext::conj(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_abs (const T& x) { using std::abs; return abs(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return numext::abs2(x); }
+template<typename T> inline T ei_sqrt(const T& x) { using std::sqrt; return sqrt(x); }
+template<typename T> inline T ei_exp (const T& x) { using std::exp; return exp(x); }
+template<typename T> inline T ei_log (const T& x) { using std::log; return log(x); }
+template<typename T> inline T ei_sin (const T& x) { using std::sin; return sin(x); }
+template<typename T> inline T ei_cos (const T& x) { using std::cos; return cos(x); }
+template<typename T> inline T ei_atan2(const T& x,const T& y) { using std::atan2; return atan2(x,y); }
+template<typename T> inline T ei_pow (const T& x,const T& y) { return numext::pow(x,y); }
+template<typename T> inline T ei_random () { return internal::random<T>(); }
+template<typename T> inline T ei_random (const T& x, const T& y) { return internal::random(x, y); }
+
+template<typename T> inline T precision () { return NumTraits<T>::dummy_precision(); }
+template<typename T> inline T machine_epsilon () { return NumTraits<T>::epsilon(); }
+
+
+template<typename Scalar, typename OtherScalar>
+inline bool ei_isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return internal::isMuchSmallerThan(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool ei_isApprox(const Scalar& x, const Scalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return internal::isApprox(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool ei_isApproxOrLessThan(const Scalar& x, const Scalar& y,
+ typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+ return internal::isApproxOrLessThan(x, y, precision);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_MATH_FUNCTIONS_H
diff --git a/Eigen/src/Eigen2Support/Memory.h b/Eigen/src/Eigen2Support/Memory.h
new file mode 100644
index 0000000..f86372b
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Memory.h
@@ -0,0 +1,45 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_MEMORY_H
+#define EIGEN2_MEMORY_H
+
+namespace Eigen {
+
+inline void* ei_aligned_malloc(size_t size) { return internal::aligned_malloc(size); }
+inline void ei_aligned_free(void *ptr) { internal::aligned_free(ptr); }
+inline void* ei_aligned_realloc(void *ptr, size_t new_size, size_t old_size) { return internal::aligned_realloc(ptr, new_size, old_size); }
+inline void* ei_handmade_aligned_malloc(size_t size) { return internal::handmade_aligned_malloc(size); }
+inline void ei_handmade_aligned_free(void *ptr) { internal::handmade_aligned_free(ptr); }
+
+template<bool Align> inline void* ei_conditional_aligned_malloc(size_t size)
+{
+ return internal::conditional_aligned_malloc<Align>(size);
+}
+template<bool Align> inline void ei_conditional_aligned_free(void *ptr)
+{
+ internal::conditional_aligned_free<Align>(ptr);
+}
+template<bool Align> inline void* ei_conditional_aligned_realloc(void* ptr, size_t new_size, size_t old_size)
+{
+ return internal::conditional_aligned_realloc<Align>(ptr, new_size, old_size);
+}
+
+template<typename T> inline T* ei_aligned_new(size_t size)
+{
+ return internal::aligned_new<T>(size);
+}
+template<typename T> inline void ei_aligned_delete(T *ptr, size_t size)
+{
+ return internal::aligned_delete(ptr, size);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_MACROS_H
diff --git a/Eigen/src/Eigen2Support/Meta.h b/Eigen/src/Eigen2Support/Meta.h
new file mode 100644
index 0000000..fa37cfc
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Meta.h
@@ -0,0 +1,75 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_META_H
+#define EIGEN2_META_H
+
+namespace Eigen {
+
+template<typename T>
+struct ei_traits : internal::traits<T>
+{};
+
+struct ei_meta_true { enum { ret = 1 }; };
+struct ei_meta_false { enum { ret = 0 }; };
+
+template<bool Condition, typename Then, typename Else>
+struct ei_meta_if { typedef Then ret; };
+
+template<typename Then, typename Else>
+struct ei_meta_if <false, Then, Else> { typedef Else ret; };
+
+template<typename T, typename U> struct ei_is_same_type { enum { ret = 0 }; };
+template<typename T> struct ei_is_same_type<T,T> { enum { ret = 1 }; };
+
+template<typename T> struct ei_unref { typedef T type; };
+template<typename T> struct ei_unref<T&> { typedef T type; };
+
+template<typename T> struct ei_unpointer { typedef T type; };
+template<typename T> struct ei_unpointer<T*> { typedef T type; };
+template<typename T> struct ei_unpointer<T*const> { typedef T type; };
+
+template<typename T> struct ei_unconst { typedef T type; };
+template<typename T> struct ei_unconst<const T> { typedef T type; };
+template<typename T> struct ei_unconst<T const &> { typedef T & type; };
+template<typename T> struct ei_unconst<T const *> { typedef T * type; };
+
+template<typename T> struct ei_cleantype { typedef T type; };
+template<typename T> struct ei_cleantype<const T> { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<const T&> { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<T&> { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<const T*> { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<T*> { typedef typename ei_cleantype<T>::type type; };
+
+/** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
+ * Usage example: \code ei_meta_sqrt<1023>::ret \endcode
+ */
+template<int Y,
+ int InfX = 0,
+ int SupX = ((Y==1) ? 1 : Y/2),
+ bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >
+ // use ?: instead of || just to shut up a stupid gcc 4.3 warning
+class ei_meta_sqrt
+{
+ enum {
+ MidX = (InfX+SupX)/2,
+ TakeInf = MidX*MidX > Y ? 1 : 0,
+ NewInf = int(TakeInf) ? InfX : int(MidX),
+ NewSup = int(TakeInf) ? int(MidX) : SupX
+ };
+ public:
+ enum { ret = ei_meta_sqrt<Y,NewInf,NewSup>::ret };
+};
+
+template<int Y, int InfX, int SupX>
+class ei_meta_sqrt<Y, InfX, SupX, true> { public: enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
+
+} // end namespace Eigen
+
+#endif // EIGEN2_META_H
diff --git a/Eigen/src/Eigen2Support/Minor.h b/Eigen/src/Eigen2Support/Minor.h
new file mode 100644
index 0000000..4cded57
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Minor.h
@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MINOR_H
+#define EIGEN_MINOR_H
+
+namespace Eigen {
+
+/**
+ * \class Minor
+ *
+ * \brief Expression of a minor
+ *
+ * \param MatrixType the type of the object in which we are taking a minor
+ *
+ * This class represents an expression of a minor. It is the return
+ * type of MatrixBase::minor() and most of the time this is the only way it
+ * is used.
+ *
+ * \sa MatrixBase::minor()
+ */
+
+namespace internal {
+template<typename MatrixType>
+struct traits<Minor<MatrixType> >
+ : traits<MatrixType>
+{
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+ typedef typename MatrixType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = (MatrixType::RowsAtCompileTime != Dynamic) ?
+ int(MatrixType::RowsAtCompileTime) - 1 : Dynamic,
+ ColsAtCompileTime = (MatrixType::ColsAtCompileTime != Dynamic) ?
+ int(MatrixType::ColsAtCompileTime) - 1 : Dynamic,
+ MaxRowsAtCompileTime = (MatrixType::MaxRowsAtCompileTime != Dynamic) ?
+ int(MatrixType::MaxRowsAtCompileTime) - 1 : Dynamic,
+ MaxColsAtCompileTime = (MatrixType::MaxColsAtCompileTime != Dynamic) ?
+ int(MatrixType::MaxColsAtCompileTime) - 1 : Dynamic,
+ Flags = _MatrixTypeNested::Flags & (HereditaryBits | LvalueBit),
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost // minor is used typically on tiny matrices,
+ // where loops are unrolled and the 'if' evaluates at compile time
+ };
+};
+}
+
+template<typename MatrixType> class Minor
+ : public MatrixBase<Minor<MatrixType> >
+{
+ public:
+
+ typedef MatrixBase<Minor> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Minor)
+
+ inline Minor(const MatrixType& matrix,
+ Index row, Index col)
+ : m_matrix(matrix), m_row(row), m_col(col)
+ {
+ eigen_assert(row >= 0 && row < matrix.rows()
+ && col >= 0 && col < matrix.cols());
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Minor)
+
+ inline Index rows() const { return m_matrix.rows() - 1; }
+ inline Index cols() const { return m_matrix.cols() - 1; }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_matrix.const_cast_derived().coeffRef(row + (row >= m_row), col + (col >= m_col));
+ }
+
+ inline const Scalar coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(row + (row >= m_row), col + (col >= m_col));
+ }
+
+ protected:
+ const typename MatrixType::Nested m_matrix;
+ const Index m_row, m_col;
+};
+
+/**
+ * \return an expression of the (\a row, \a col)-minor of *this,
+ * i.e. an expression constructed from *this by removing the specified
+ * row and column.
+ *
+ * Example: \include MatrixBase_minor.cpp
+ * Output: \verbinclude MatrixBase_minor.out
+ *
+ * \sa class Minor
+ */
+template<typename Derived>
+inline Minor<Derived>
+MatrixBase<Derived>::minor(Index row, Index col)
+{
+ return Minor<Derived>(derived(), row, col);
+}
+
+/**
+ * This is the const version of minor(). */
+template<typename Derived>
+inline const Minor<Derived>
+MatrixBase<Derived>::minor(Index row, Index col) const
+{
+ return Minor<Derived>(derived(), row, col);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MINOR_H
diff --git a/Eigen/src/Eigen2Support/QR.h b/Eigen/src/Eigen2Support/QR.h
new file mode 100644
index 0000000..2042c98
--- /dev/null
+++ b/Eigen/src/Eigen2Support/QR.h
@@ -0,0 +1,67 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_QR_H
+#define EIGEN2_QR_H
+
+namespace Eigen {
+
+template<typename MatrixType>
+class QR : public HouseholderQR<MatrixType>
+{
+ public:
+
+ typedef HouseholderQR<MatrixType> Base;
+ typedef Block<const MatrixType, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixRBlockType;
+
+ QR() : Base() {}
+
+ template<typename T>
+ explicit QR(const T& t) : Base(t) {}
+
+ template<typename OtherDerived, typename ResultType>
+ bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+ {
+ *result = static_cast<const Base*>(this)->solve(b);
+ return true;
+ }
+
+ MatrixType matrixQ(void) const {
+ MatrixType ret = MatrixType::Identity(this->rows(), this->cols());
+ ret = this->householderQ() * ret;
+ return ret;
+ }
+
+ bool isFullRank() const {
+ return true;
+ }
+
+ const TriangularView<MatrixRBlockType, UpperTriangular>
+ matrixR(void) const
+ {
+ int cols = this->cols();
+ return MatrixRBlockType(this->matrixQR(), 0, 0, cols, cols).template triangularView<UpperTriangular>();
+ }
+};
+
+/** \return the QR decomposition of \c *this.
+ *
+ * \sa class QR
+ */
+template<typename Derived>
+const QR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::qr() const
+{
+ return QR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_QR_H
diff --git a/Eigen/src/Eigen2Support/SVD.h b/Eigen/src/Eigen2Support/SVD.h
new file mode 100644
index 0000000..3d03d22
--- /dev/null
+++ b/Eigen/src/Eigen2Support/SVD.h
@@ -0,0 +1,637 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_SVD_H
+#define EIGEN2_SVD_H
+
+namespace Eigen {
+
+/** \ingroup SVD_Module
+ * \nonstableyet
+ *
+ * \class SVD
+ *
+ * \brief Standard SVD decomposition of a matrix and associated features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+ *
+ * This class performs a standard SVD decomposition of a real matrix A of size \c M x \c N
+ * with \c M \>= \c N.
+ *
+ *
+ * \sa MatrixBase::SVD()
+ */
+template<typename MatrixType> class SVD
+{
+ private:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ AlignmentMask = int(PacketSize)-1,
+ MinSize = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime)
+ };
+
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVector;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> RowVector;
+
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MinSize> MatrixUType;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixVType;
+ typedef Matrix<Scalar, MinSize, 1> SingularValuesType;
+
+ public:
+
+ SVD() {} // a user who relied on compiler-generated default compiler reported problems with MSVC in 2.0.7
+
+ SVD(const MatrixType& matrix)
+ : m_matU(matrix.rows(), (std::min)(matrix.rows(), matrix.cols())),
+ m_matV(matrix.cols(),matrix.cols()),
+ m_sigma((std::min)(matrix.rows(),matrix.cols()))
+ {
+ compute(matrix);
+ }
+
+ template<typename OtherDerived, typename ResultType>
+ bool solve(const MatrixBase<OtherDerived> &b, ResultType* result) const;
+
+ const MatrixUType& matrixU() const { return m_matU; }
+ const SingularValuesType& singularValues() const { return m_sigma; }
+ const MatrixVType& matrixV() const { return m_matV; }
+
+ void compute(const MatrixType& matrix);
+ SVD& sort();
+
+ template<typename UnitaryType, typename PositiveType>
+ void computeUnitaryPositive(UnitaryType *unitary, PositiveType *positive) const;
+ template<typename PositiveType, typename UnitaryType>
+ void computePositiveUnitary(PositiveType *positive, UnitaryType *unitary) const;
+ template<typename RotationType, typename ScalingType>
+ void computeRotationScaling(RotationType *unitary, ScalingType *positive) const;
+ template<typename ScalingType, typename RotationType>
+ void computeScalingRotation(ScalingType *positive, RotationType *unitary) const;
+
+ protected:
+ /** \internal */
+ MatrixUType m_matU;
+ /** \internal */
+ MatrixVType m_matV;
+ /** \internal */
+ SingularValuesType m_sigma;
+};
+
+/** Computes / recomputes the SVD decomposition A = U S V^* of \a matrix
+ *
+ * \note this code has been adapted from JAMA (public domain)
+ */
+template<typename MatrixType>
+void SVD<MatrixType>::compute(const MatrixType& matrix)
+{
+ const int m = matrix.rows();
+ const int n = matrix.cols();
+ const int nu = (std::min)(m,n);
+ ei_assert(m>=n && "In Eigen 2.0, SVD only works for MxN matrices with M>=N. Sorry!");
+ ei_assert(m>1 && "In Eigen 2.0, SVD doesn't work on 1x1 matrices");
+
+ m_matU.resize(m, nu);
+ m_matU.setZero();
+ m_sigma.resize((std::min)(m,n));
+ m_matV.resize(n,n);
+
+ RowVector e(n);
+ ColVector work(m);
+ MatrixType matA(matrix);
+ const bool wantu = true;
+ const bool wantv = true;
+ int i=0, j=0, k=0;
+
+ // Reduce A to bidiagonal form, storing the diagonal elements
+ // in s and the super-diagonal elements in e.
+ int nct = (std::min)(m-1,n);
+ int nrt = (std::max)(0,(std::min)(n-2,m));
+ for (k = 0; k < (std::max)(nct,nrt); ++k)
+ {
+ if (k < nct)
+ {
+ // Compute the transformation for the k-th column and
+ // place the k-th diagonal in m_sigma[k].
+ m_sigma[k] = matA.col(k).end(m-k).norm();
+ if (m_sigma[k] != 0.0) // FIXME
+ {
+ if (matA(k,k) < 0.0)
+ m_sigma[k] = -m_sigma[k];
+ matA.col(k).end(m-k) /= m_sigma[k];
+ matA(k,k) += 1.0;
+ }
+ m_sigma[k] = -m_sigma[k];
+ }
+
+ for (j = k+1; j < n; ++j)
+ {
+ if ((k < nct) && (m_sigma[k] != 0.0))
+ {
+ // Apply the transformation.
+ Scalar t = matA.col(k).end(m-k).eigen2_dot(matA.col(j).end(m-k)); // FIXME dot product or cwise prod + .sum() ??
+ t = -t/matA(k,k);
+ matA.col(j).end(m-k) += t * matA.col(k).end(m-k);
+ }
+
+ // Place the k-th row of A into e for the
+ // subsequent calculation of the row transformation.
+ e[j] = matA(k,j);
+ }
+
+ // Place the transformation in U for subsequent back multiplication.
+ if (wantu & (k < nct))
+ m_matU.col(k).end(m-k) = matA.col(k).end(m-k);
+
+ if (k < nrt)
+ {
+ // Compute the k-th row transformation and place the
+ // k-th super-diagonal in e[k].
+ e[k] = e.end(n-k-1).norm();
+ if (e[k] != 0.0)
+ {
+ if (e[k+1] < 0.0)
+ e[k] = -e[k];
+ e.end(n-k-1) /= e[k];
+ e[k+1] += 1.0;
+ }
+ e[k] = -e[k];
+ if ((k+1 < m) & (e[k] != 0.0))
+ {
+ // Apply the transformation.
+ work.end(m-k-1) = matA.corner(BottomRight,m-k-1,n-k-1) * e.end(n-k-1);
+ for (j = k+1; j < n; ++j)
+ matA.col(j).end(m-k-1) += (-e[j]/e[k+1]) * work.end(m-k-1);
+ }
+
+ // Place the transformation in V for subsequent back multiplication.
+ if (wantv)
+ m_matV.col(k).end(n-k-1) = e.end(n-k-1);
+ }
+ }
+
+
+ // Set up the final bidiagonal matrix or order p.
+ int p = (std::min)(n,m+1);
+ if (nct < n)
+ m_sigma[nct] = matA(nct,nct);
+ if (m < p)
+ m_sigma[p-1] = 0.0;
+ if (nrt+1 < p)
+ e[nrt] = matA(nrt,p-1);
+ e[p-1] = 0.0;
+
+ // If required, generate U.
+ if (wantu)
+ {
+ for (j = nct; j < nu; ++j)
+ {
+ m_matU.col(j).setZero();
+ m_matU(j,j) = 1.0;
+ }
+ for (k = nct-1; k >= 0; k--)
+ {
+ if (m_sigma[k] != 0.0)
+ {
+ for (j = k+1; j < nu; ++j)
+ {
+ Scalar t = m_matU.col(k).end(m-k).eigen2_dot(m_matU.col(j).end(m-k)); // FIXME is it really a dot product we want ?
+ t = -t/m_matU(k,k);
+ m_matU.col(j).end(m-k) += t * m_matU.col(k).end(m-k);
+ }
+ m_matU.col(k).end(m-k) = - m_matU.col(k).end(m-k);
+ m_matU(k,k) = Scalar(1) + m_matU(k,k);
+ if (k-1>0)
+ m_matU.col(k).start(k-1).setZero();
+ }
+ else
+ {
+ m_matU.col(k).setZero();
+ m_matU(k,k) = 1.0;
+ }
+ }
+ }
+
+ // If required, generate V.
+ if (wantv)
+ {
+ for (k = n-1; k >= 0; k--)
+ {
+ if ((k < nrt) & (e[k] != 0.0))
+ {
+ for (j = k+1; j < nu; ++j)
+ {
+ Scalar t = m_matV.col(k).end(n-k-1).eigen2_dot(m_matV.col(j).end(n-k-1)); // FIXME is it really a dot product we want ?
+ t = -t/m_matV(k+1,k);
+ m_matV.col(j).end(n-k-1) += t * m_matV.col(k).end(n-k-1);
+ }
+ }
+ m_matV.col(k).setZero();
+ m_matV(k,k) = 1.0;
+ }
+ }
+
+ // Main iteration loop for the singular values.
+ int pp = p-1;
+ int iter = 0;
+ Scalar eps = ei_pow(Scalar(2),ei_is_same_type<Scalar,float>::ret ? Scalar(-23) : Scalar(-52));
+ while (p > 0)
+ {
+ int k=0;
+ int kase=0;
+
+ // Here is where a test for too many iterations would go.
+
+ // This section of the program inspects for
+ // negligible elements in the s and e arrays. On
+ // completion the variables kase and k are set as follows.
+
+ // kase = 1 if s(p) and e[k-1] are negligible and k<p
+ // kase = 2 if s(k) is negligible and k<p
+ // kase = 3 if e[k-1] is negligible, k<p, and
+ // s(k), ..., s(p) are not negligible (qr step).
+ // kase = 4 if e(p-1) is negligible (convergence).
+
+ for (k = p-2; k >= -1; --k)
+ {
+ if (k == -1)
+ break;
+ if (ei_abs(e[k]) <= eps*(ei_abs(m_sigma[k]) + ei_abs(m_sigma[k+1])))
+ {
+ e[k] = 0.0;
+ break;
+ }
+ }
+ if (k == p-2)
+ {
+ kase = 4;
+ }
+ else
+ {
+ int ks;
+ for (ks = p-1; ks >= k; --ks)
+ {
+ if (ks == k)
+ break;
+ Scalar t = (ks != p ? ei_abs(e[ks]) : Scalar(0)) + (ks != k+1 ? ei_abs(e[ks-1]) : Scalar(0));
+ if (ei_abs(m_sigma[ks]) <= eps*t)
+ {
+ m_sigma[ks] = 0.0;
+ break;
+ }
+ }
+ if (ks == k)
+ {
+ kase = 3;
+ }
+ else if (ks == p-1)
+ {
+ kase = 1;
+ }
+ else
+ {
+ kase = 2;
+ k = ks;
+ }
+ }
+ ++k;
+
+ // Perform the task indicated by kase.
+ switch (kase)
+ {
+
+ // Deflate negligible s(p).
+ case 1:
+ {
+ Scalar f(e[p-2]);
+ e[p-2] = 0.0;
+ for (j = p-2; j >= k; --j)
+ {
+ Scalar t(numext::hypot(m_sigma[j],f));
+ Scalar cs(m_sigma[j]/t);
+ Scalar sn(f/t);
+ m_sigma[j] = t;
+ if (j != k)
+ {
+ f = -sn*e[j-1];
+ e[j-1] = cs*e[j-1];
+ }
+ if (wantv)
+ {
+ for (i = 0; i < n; ++i)
+ {
+ t = cs*m_matV(i,j) + sn*m_matV(i,p-1);
+ m_matV(i,p-1) = -sn*m_matV(i,j) + cs*m_matV(i,p-1);
+ m_matV(i,j) = t;
+ }
+ }
+ }
+ }
+ break;
+
+ // Split at negligible s(k).
+ case 2:
+ {
+ Scalar f(e[k-1]);
+ e[k-1] = 0.0;
+ for (j = k; j < p; ++j)
+ {
+ Scalar t(numext::hypot(m_sigma[j],f));
+ Scalar cs( m_sigma[j]/t);
+ Scalar sn(f/t);
+ m_sigma[j] = t;
+ f = -sn*e[j];
+ e[j] = cs*e[j];
+ if (wantu)
+ {
+ for (i = 0; i < m; ++i)
+ {
+ t = cs*m_matU(i,j) + sn*m_matU(i,k-1);
+ m_matU(i,k-1) = -sn*m_matU(i,j) + cs*m_matU(i,k-1);
+ m_matU(i,j) = t;
+ }
+ }
+ }
+ }
+ break;
+
+ // Perform one qr step.
+ case 3:
+ {
+ // Calculate the shift.
+ Scalar scale = (std::max)((std::max)((std::max)((std::max)(
+ ei_abs(m_sigma[p-1]),ei_abs(m_sigma[p-2])),ei_abs(e[p-2])),
+ ei_abs(m_sigma[k])),ei_abs(e[k]));
+ Scalar sp = m_sigma[p-1]/scale;
+ Scalar spm1 = m_sigma[p-2]/scale;
+ Scalar epm1 = e[p-2]/scale;
+ Scalar sk = m_sigma[k]/scale;
+ Scalar ek = e[k]/scale;
+ Scalar b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/Scalar(2);
+ Scalar c = (sp*epm1)*(sp*epm1);
+ Scalar shift(0);
+ if ((b != 0.0) || (c != 0.0))
+ {
+ shift = ei_sqrt(b*b + c);
+ if (b < 0.0)
+ shift = -shift;
+ shift = c/(b + shift);
+ }
+ Scalar f = (sk + sp)*(sk - sp) + shift;
+ Scalar g = sk*ek;
+
+ // Chase zeros.
+
+ for (j = k; j < p-1; ++j)
+ {
+ Scalar t = numext::hypot(f,g);
+ Scalar cs = f/t;
+ Scalar sn = g/t;
+ if (j != k)
+ e[j-1] = t;
+ f = cs*m_sigma[j] + sn*e[j];
+ e[j] = cs*e[j] - sn*m_sigma[j];
+ g = sn*m_sigma[j+1];
+ m_sigma[j+1] = cs*m_sigma[j+1];
+ if (wantv)
+ {
+ for (i = 0; i < n; ++i)
+ {
+ t = cs*m_matV(i,j) + sn*m_matV(i,j+1);
+ m_matV(i,j+1) = -sn*m_matV(i,j) + cs*m_matV(i,j+1);
+ m_matV(i,j) = t;
+ }
+ }
+ t = numext::hypot(f,g);
+ cs = f/t;
+ sn = g/t;
+ m_sigma[j] = t;
+ f = cs*e[j] + sn*m_sigma[j+1];
+ m_sigma[j+1] = -sn*e[j] + cs*m_sigma[j+1];
+ g = sn*e[j+1];
+ e[j+1] = cs*e[j+1];
+ if (wantu && (j < m-1))
+ {
+ for (i = 0; i < m; ++i)
+ {
+ t = cs*m_matU(i,j) + sn*m_matU(i,j+1);
+ m_matU(i,j+1) = -sn*m_matU(i,j) + cs*m_matU(i,j+1);
+ m_matU(i,j) = t;
+ }
+ }
+ }
+ e[p-2] = f;
+ iter = iter + 1;
+ }
+ break;
+
+ // Convergence.
+ case 4:
+ {
+ // Make the singular values positive.
+ if (m_sigma[k] <= 0.0)
+ {
+ m_sigma[k] = m_sigma[k] < Scalar(0) ? -m_sigma[k] : Scalar(0);
+ if (wantv)
+ m_matV.col(k).start(pp+1) = -m_matV.col(k).start(pp+1);
+ }
+
+ // Order the singular values.
+ while (k < pp)
+ {
+ if (m_sigma[k] >= m_sigma[k+1])
+ break;
+ Scalar t = m_sigma[k];
+ m_sigma[k] = m_sigma[k+1];
+ m_sigma[k+1] = t;
+ if (wantv && (k < n-1))
+ m_matV.col(k).swap(m_matV.col(k+1));
+ if (wantu && (k < m-1))
+ m_matU.col(k).swap(m_matU.col(k+1));
+ ++k;
+ }
+ iter = 0;
+ p--;
+ }
+ break;
+ } // end big switch
+ } // end iterations
+}
+
+template<typename MatrixType>
+SVD<MatrixType>& SVD<MatrixType>::sort()
+{
+ int mu = m_matU.rows();
+ int mv = m_matV.rows();
+ int n = m_matU.cols();
+
+ for (int i=0; i<n; ++i)
+ {
+ int k = i;
+ Scalar p = m_sigma.coeff(i);
+
+ for (int j=i+1; j<n; ++j)
+ {
+ if (m_sigma.coeff(j) > p)
+ {
+ k = j;
+ p = m_sigma.coeff(j);
+ }
+ }
+ if (k != i)
+ {
+ m_sigma.coeffRef(k) = m_sigma.coeff(i); // i.e.
+ m_sigma.coeffRef(i) = p; // swaps the i-th and the k-th elements
+
+ int j = mu;
+ for(int s=0; j!=0; ++s, --j)
+ std::swap(m_matU.coeffRef(s,i), m_matU.coeffRef(s,k));
+
+ j = mv;
+ for (int s=0; j!=0; ++s, --j)
+ std::swap(m_matV.coeffRef(s,i), m_matV.coeffRef(s,k));
+ }
+ }
+ return *this;
+}
+
+/** \returns the solution of \f$ A x = b \f$ using the current SVD decomposition of A.
+ * The parts of the solution corresponding to zero singular values are ignored.
+ *
+ * \sa MatrixBase::svd(), LU::solve(), LLT::solve()
+ */
+template<typename MatrixType>
+template<typename OtherDerived, typename ResultType>
+bool SVD<MatrixType>::solve(const MatrixBase<OtherDerived> &b, ResultType* result) const
+{
+ ei_assert(b.rows() == m_matU.rows());
+
+ Scalar maxVal = m_sigma.cwise().abs().maxCoeff();
+ for (int j=0; j<b.cols(); ++j)
+ {
+ Matrix<Scalar,MatrixUType::RowsAtCompileTime,1> aux = m_matU.transpose() * b.col(j);
+
+ for (int i = 0; i <m_matU.cols(); ++i)
+ {
+ Scalar si = m_sigma.coeff(i);
+ if (ei_isMuchSmallerThan(ei_abs(si),maxVal))
+ aux.coeffRef(i) = 0;
+ else
+ aux.coeffRef(i) /= si;
+ }
+
+ result->col(j) = m_matV * aux;
+ }
+ return true;
+}
+
+/** Computes the polar decomposition of the matrix, as a product unitary x positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * Only for square matrices.
+ *
+ * \sa computePositiveUnitary(), computeRotationScaling()
+ */
+template<typename MatrixType>
+template<typename UnitaryType, typename PositiveType>
+void SVD<MatrixType>::computeUnitaryPositive(UnitaryType *unitary,
+ PositiveType *positive) const
+{
+ ei_assert(m_matU.cols() == m_matV.cols() && "Polar decomposition is only for square matrices");
+ if(unitary) *unitary = m_matU * m_matV.adjoint();
+ if(positive) *positive = m_matV * m_sigma.asDiagonal() * m_matV.adjoint();
+}
+
+/** Computes the polar decomposition of the matrix, as a product positive x unitary.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * Only for square matrices.
+ *
+ * \sa computeUnitaryPositive(), computeRotationScaling()
+ */
+template<typename MatrixType>
+template<typename UnitaryType, typename PositiveType>
+void SVD<MatrixType>::computePositiveUnitary(UnitaryType *positive,
+ PositiveType *unitary) const
+{
+ ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
+ if(unitary) *unitary = m_matU * m_matV.adjoint();
+ if(positive) *positive = m_matU * m_sigma.asDiagonal() * m_matU.adjoint();
+}
+
+/** decomposes the matrix as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * This method requires the Geometry module.
+ *
+ * \sa computeScalingRotation(), computeUnitaryPositive()
+ */
+template<typename MatrixType>
+template<typename RotationType, typename ScalingType>
+void SVD<MatrixType>::computeRotationScaling(RotationType *rotation, ScalingType *scaling) const
+{
+ ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
+ Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma);
+ sv.coeffRef(0) *= x;
+ if(scaling) scaling->lazyAssign(m_matV * sv.asDiagonal() * m_matV.adjoint());
+ if(rotation)
+ {
+ MatrixType m(m_matU);
+ m.col(0) /= x;
+ rotation->lazyAssign(m * m_matV.adjoint());
+ }
+}
+
+/** decomposes the matrix as a product scaling x rotation, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * This method requires the Geometry module.
+ *
+ * \sa computeRotationScaling(), computeUnitaryPositive()
+ */
+template<typename MatrixType>
+template<typename ScalingType, typename RotationType>
+void SVD<MatrixType>::computeScalingRotation(ScalingType *scaling, RotationType *rotation) const
+{
+ ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices");
+ Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma);
+ sv.coeffRef(0) *= x;
+ if(scaling) scaling->lazyAssign(m_matU * sv.asDiagonal() * m_matU.adjoint());
+ if(rotation)
+ {
+ MatrixType m(m_matU);
+ m.col(0) /= x;
+ rotation->lazyAssign(m * m_matV.adjoint());
+ }
+}
+
+
+/** \svd_module
+ * \returns the SVD decomposition of \c *this
+ */
+template<typename Derived>
+inline SVD<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::svd() const
+{
+ return SVD<PlainObject>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_SVD_H
diff --git a/Eigen/src/Eigen2Support/TriangularSolver.h b/Eigen/src/Eigen2Support/TriangularSolver.h
new file mode 100644
index 0000000..ebbeb3b
--- /dev/null
+++ b/Eigen/src/Eigen2Support/TriangularSolver.h
@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_SOLVER2_H
+#define EIGEN_TRIANGULAR_SOLVER2_H
+
+namespace Eigen {
+
+const unsigned int UnitDiagBit = UnitDiag;
+const unsigned int SelfAdjointBit = SelfAdjoint;
+const unsigned int UpperTriangularBit = Upper;
+const unsigned int LowerTriangularBit = Lower;
+
+const unsigned int UpperTriangular = Upper;
+const unsigned int LowerTriangular = Lower;
+const unsigned int UnitUpperTriangular = UnitUpper;
+const unsigned int UnitLowerTriangular = UnitLower;
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed>
+template<typename OtherDerived>
+typename ExpressionType::PlainObject
+Flagged<ExpressionType,Added,Removed>::solveTriangular(const MatrixBase<OtherDerived>& other) const
+{
+ return m_matrix.template triangularView<Added>().solve(other.derived());
+}
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed>
+template<typename OtherDerived>
+void Flagged<ExpressionType,Added,Removed>::solveTriangularInPlace(const MatrixBase<OtherDerived>& other) const
+{
+ m_matrix.template triangularView<Added>().solveInPlace(other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER2_H
diff --git a/Eigen/src/Eigen2Support/VectorBlock.h b/Eigen/src/Eigen2Support/VectorBlock.h
new file mode 100644
index 0000000..71a8080
--- /dev/null
+++ b/Eigen/src/Eigen2Support/VectorBlock.h
@@ -0,0 +1,94 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN2_VECTORBLOCK_H
+#define EIGEN2_VECTORBLOCK_H
+
+namespace Eigen {
+
+/** \deprecated use DenseMase::head(Index) */
+template<typename Derived>
+inline VectorBlock<Derived>
+MatrixBase<Derived>::start(Index size)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<Derived>(derived(), 0, size);
+}
+
+/** \deprecated use DenseMase::head(Index) */
+template<typename Derived>
+inline const VectorBlock<const Derived>
+MatrixBase<Derived>::start(Index size) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<const Derived>(derived(), 0, size);
+}
+
+/** \deprecated use DenseMase::tail(Index) */
+template<typename Derived>
+inline VectorBlock<Derived>
+MatrixBase<Derived>::end(Index size)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<Derived>(derived(), this->size() - size, size);
+}
+
+/** \deprecated use DenseMase::tail(Index) */
+template<typename Derived>
+inline const VectorBlock<const Derived>
+MatrixBase<Derived>::end(Index size) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<const Derived>(derived(), this->size() - size, size);
+}
+
+/** \deprecated use DenseMase::head() */
+template<typename Derived>
+template<int Size>
+inline VectorBlock<Derived,Size>
+MatrixBase<Derived>::start()
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<Derived,Size>(derived(), 0);
+}
+
+/** \deprecated use DenseMase::head() */
+template<typename Derived>
+template<int Size>
+inline const VectorBlock<const Derived,Size>
+MatrixBase<Derived>::start() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<const Derived,Size>(derived(), 0);
+}
+
+/** \deprecated use DenseMase::tail() */
+template<typename Derived>
+template<int Size>
+inline VectorBlock<Derived,Size>
+MatrixBase<Derived>::end()
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<Derived, Size>(derived(), size() - Size);
+}
+
+/** \deprecated use DenseMase::tail() */
+template<typename Derived>
+template<int Size>
+inline const VectorBlock<const Derived,Size>
+MatrixBase<Derived>::end() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return VectorBlock<const Derived, Size>(derived(), size() - Size);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN2_VECTORBLOCK_H
diff --git a/Eigen/src/Eigenvalues/CMakeLists.txt b/Eigen/src/Eigenvalues/CMakeLists.txt
new file mode 100644
index 0000000..193e026
--- /dev/null
+++ b/Eigen/src/Eigenvalues/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_EIGENVALUES_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_EIGENVALUES_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigenvalues COMPONENT Devel
+ )
diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
new file mode 100644
index 0000000..417c729
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
@@ -0,0 +1,341 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Claire Maurice
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
+#define EIGEN_COMPLEX_EIGEN_SOLVER_H
+
+#include "./ComplexSchur.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class ComplexEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of general complex matrices
+ *
+ * \tparam _MatrixType the type of the matrix of which we are
+ * computing the eigendecomposition; this is expected to be an
+ * instantiation of the Matrix class template.
+ *
+ * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v
+ * \f$. If \f$ D \f$ is a diagonal matrix with the eigenvalues on
+ * the diagonal, and \f$ V \f$ is a matrix with the eigenvectors as
+ * its columns, then \f$ A V = V D \f$. The matrix \f$ V \f$ is
+ * almost always invertible, in which case we have \f$ A = V D V^{-1}
+ * \f$. This is called the eigendecomposition.
+ *
+ * The main function in this class is compute(), which computes the
+ * eigenvalues and eigenvectors of a given function. The
+ * documentation for that function contains an example showing the
+ * main features of the class.
+ *
+ * \sa class EigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename _MatrixType> class ComplexEigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p _MatrixType. */
+ typedef _MatrixType MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options&(~RowMajor), MaxColsAtCompileTime, 1> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute().
+ */
+ ComplexEigenSolver()
+ : m_eivec(),
+ m_eivalues(),
+ m_schur(),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX()
+ {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa ComplexEigenSolver()
+ */
+ ComplexEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_schur(size),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX(size, size)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ *
+ * This constructor calls compute() to compute the eigendecomposition.
+ */
+ ComplexEigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
+ : m_eivec(matrix.rows(),matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_schur(matrix.rows()),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX(matrix.rows(),matrix.cols())
+ {
+ compute(matrix, computeEigenvectors);
+ }
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns A const reference to the matrix whose columns are the eigenvectors.
+ *
+ * \pre Either the constructor
+ * ComplexEigenSolver(const MatrixType& matrix, bool) or the member
+ * function compute(const MatrixType& matrix, bool) has been called before
+ * to compute the eigendecomposition of a matrix, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * This function returns a matrix whose columns are the eigenvectors. Column
+ * \f$ k \f$ is an eigenvector corresponding to eigenvalue number \f$ k
+ * \f$ as returned by eigenvalues(). The eigenvectors are normalized to
+ * have (Euclidean) norm equal to one. The matrix returned by this
+ * function is the matrix \f$ V \f$ in the eigendecomposition \f$ A = V D
+ * V^{-1} \f$, if it exists.
+ *
+ * Example: \include ComplexEigenSolver_eigenvectors.cpp
+ * Output: \verbinclude ComplexEigenSolver_eigenvectors.out
+ */
+ const EigenvectorType& eigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre Either the constructor
+ * ComplexEigenSolver(const MatrixType& matrix, bool) or the member
+ * function compute(const MatrixType& matrix, bool) has been called before
+ * to compute the eigendecomposition of a matrix.
+ *
+ * This function returns a column vector containing the
+ * eigenvalues. Eigenvalues are repeated according to their
+ * algebraic multiplicity, so there are as many eigenvalues as
+ * rows in the matrix. The eigenvalues are not sorted in any particular
+ * order.
+ *
+ * Example: \include ComplexEigenSolver_eigenvalues.cpp
+ * Output: \verbinclude ComplexEigenSolver_eigenvalues.out
+ */
+ const EigenvalueType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the complex matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to Schur form using the
+ * ComplexSchur class. The Schur decomposition is then used to
+ * compute the eigenvalues and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * Schur decomposition, which is \f$ O(n^3) \f$ where \f$ n \f$
+ * is the size of the matrix.
+ *
+ * Example: \include ComplexEigenSolver_compute.cpp
+ * Output: \verbinclude ComplexEigenSolver_compute.out
+ */
+ ComplexEigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ return m_schur.info();
+ }
+
+ /** \brief Sets the maximum number of iterations allowed. */
+ ComplexEigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_schur.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_schur.getMaxIterations();
+ }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ EigenvectorType m_eivec;
+ EigenvalueType m_eivalues;
+ ComplexSchur<MatrixType> m_schur;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+ EigenvectorType m_matX;
+
+ private:
+ void doComputeEigenvectors(const RealScalar& matrixnorm);
+ void sortEigenvalues(bool computeEigenvectors);
+};
+
+
+template<typename MatrixType>
+ComplexEigenSolver<MatrixType>&
+ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
+{
+ check_template_parameters();
+
+ // this code is inspired from Jampack
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ // Do a complex Schur decomposition, A = U T U^*
+ // The eigenvalues are on the diagonal of T.
+ m_schur.compute(matrix, computeEigenvectors);
+
+ if(m_schur.info() == Success)
+ {
+ m_eivalues = m_schur.matrixT().diagonal();
+ if(computeEigenvectors)
+ doComputeEigenvectors(matrix.norm());
+ sortEigenvalues(computeEigenvectors);
+ }
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+}
+
+
+template<typename MatrixType>
+void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(const RealScalar& matrixnorm)
+{
+ const Index n = m_eivalues.size();
+
+ // Compute X such that T = X D X^(-1), where D is the diagonal of T.
+ // The matrix X is unit triangular.
+ m_matX = EigenvectorType::Zero(n, n);
+ for(Index k=n-1 ; k>=0 ; k--)
+ {
+ m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
+ // Compute X(i,k) using the (i,k) entry of the equation X T = D X
+ for(Index i=k-1 ; i>=0 ; i--)
+ {
+ m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
+ if(k-i-1>0)
+ m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();
+ ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
+ if(z==ComplexScalar(0))
+ {
+ // If the i-th and k-th eigenvalue are equal, then z equals 0.
+ // Use a small value instead, to prevent division by zero.
+ numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
+ }
+ m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
+ }
+ }
+
+ // Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)
+ m_eivec.noalias() = m_schur.matrixU() * m_matX;
+ // .. and normalize the eigenvectors
+ for(Index k=0 ; k<n ; k++)
+ {
+ m_eivec.col(k).normalize();
+ }
+}
+
+
+template<typename MatrixType>
+void ComplexEigenSolver<MatrixType>::sortEigenvalues(bool computeEigenvectors)
+{
+ const Index n = m_eivalues.size();
+ for (Index i=0; i<n; i++)
+ {
+ Index k;
+ m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
+ if (k != 0)
+ {
+ k += i;
+ std::swap(m_eivalues[k],m_eivalues[i]);
+ if(computeEigenvectors)
+ m_eivec.col(i).swap(m_eivec.col(k));
+ }
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H
diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h
new file mode 100644
index 0000000..89e6cad
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexSchur.h
@@ -0,0 +1,456 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Claire Maurice
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_SCHUR_H
+#define EIGEN_COMPLEX_SCHUR_H
+
+#include "./HessenbergDecomposition.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType, bool IsComplex> struct complex_schur_reduce_to_hessenberg;
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class ComplexSchur
+ *
+ * \brief Performs a complex Schur decomposition of a real or complex square matrix
+ *
+ * \tparam _MatrixType the type of the matrix of which we are
+ * computing the Schur decomposition; this is expected to be an
+ * instantiation of the Matrix class template.
+ *
+ * Given a real or complex square matrix A, this class computes the
+ * Schur decomposition: \f$ A = U T U^*\f$ where U is a unitary
+ * complex matrix, and T is a complex upper triangular matrix. The
+ * diagonal of the matrix T corresponds to the eigenvalues of the
+ * matrix A.
+ *
+ * Call the function compute() to compute the Schur decomposition of
+ * a given matrix. Alternatively, you can use the
+ * ComplexSchur(const MatrixType&, bool) constructor which computes
+ * the Schur decomposition at construction time. Once the
+ * decomposition is computed, you can use the matrixU() and matrixT()
+ * functions to retrieve the matrices U and V in the decomposition.
+ *
+ * \note This code is inspired from Jampack
+ *
+ * \sa class RealSchur, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename _MatrixType> class ComplexSchur
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type \p _MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Complex scalar type for \p _MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for the matrices in the Schur decomposition.
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of \p _MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> ComplexMatrixType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a
+ * wrong \p size, but it may impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ ComplexSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
+ : m_matT(size,size),
+ m_matU(size,size),
+ m_hess(size),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {}
+
+ /** \brief Constructor; computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ *
+ * This constructor calls compute() to compute the Schur decomposition.
+ *
+ * \sa matrixT() and matrixU() for examples.
+ */
+ ComplexSchur(const MatrixType& matrix, bool computeU = true)
+ : m_matT(matrix.rows(),matrix.cols()),
+ m_matU(matrix.rows(),matrix.cols()),
+ m_hess(matrix.rows()),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {
+ compute(matrix, computeU);
+ }
+
+ /** \brief Returns the unitary matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix U.
+ *
+ * It is assumed that either the constructor
+ * ComplexSchur(const MatrixType& matrix, bool computeU) or the
+ * member function compute(const MatrixType& matrix, bool computeU)
+ * has been called before to compute the Schur decomposition of a
+ * matrix, and that \p computeU was set to true (the default
+ * value).
+ *
+ * Example: \include ComplexSchur_matrixU.cpp
+ * Output: \verbinclude ComplexSchur_matrixU.out
+ */
+ const ComplexMatrixType& matrixU() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the ComplexSchur decomposition.");
+ return m_matU;
+ }
+
+ /** \brief Returns the triangular matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix T.
+ *
+ * It is assumed that either the constructor
+ * ComplexSchur(const MatrixType& matrix, bool computeU) or the
+ * member function compute(const MatrixType& matrix, bool computeU)
+ * has been called before to compute the Schur decomposition of a
+ * matrix.
+ *
+ * Note that this function returns a plain square matrix. If you want to reference
+ * only the upper triangular part, use:
+ * \code schur.matrixT().triangularView<Upper>() \endcode
+ *
+ * Example: \include ComplexSchur_matrixT.cpp
+ * Output: \verbinclude ComplexSchur_matrixT.out
+ */
+ const ComplexMatrixType& matrixT() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ return m_matT;
+ }
+
+ /** \brief Computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+
+ * \returns Reference to \c *this
+ *
+ * The Schur decomposition is computed by first reducing the
+ * matrix to Hessenberg form using the class
+ * HessenbergDecomposition. The Hessenberg matrix is then reduced
+ * to triangular form by performing QR iterations with a single
+ * shift. The cost of computing the Schur decomposition depends
+ * on the number of iterations; as a rough guide, it may be taken
+ * on the number of iterations; as a rough guide, it may be taken
+ * to be \f$25n^3\f$ complex flops, or \f$10n^3\f$ complex flops
+ * if \a computeU is false.
+ *
+ * Example: \include ComplexSchur_compute.cpp
+ * Output: \verbinclude ComplexSchur_compute.out
+ *
+ * \sa compute(const MatrixType&, bool, Index)
+ */
+ ComplexSchur& compute(const MatrixType& matrix, bool computeU = true);
+
+ /** \brief Compute Schur decomposition from a given Hessenberg matrix
+ * \param[in] matrixH Matrix in Hessenberg form H
+ * \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
+ * \param computeU Computes the matriX U of the Schur vectors
+ * \return Reference to \c *this
+ *
+ * This routine assumes that the matrix is already reduced in Hessenberg form matrixH
+ * using either the class HessenbergDecomposition or another mean.
+ * It computes the upper quasi-triangular matrix T of the Schur decomposition of H
+ * When computeU is true, this routine computes the matrix U such that
+ * A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
+ *
+ * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
+ * is not available, the user should give an identity matrix (Q.setIdentity())
+ *
+ * \sa compute(const MatrixType&, bool)
+ */
+ template<typename HessMatrixType, typename OrthMatrixType>
+ ComplexSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU=true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Sets the maximum number of iterations allowed.
+ *
+ * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size
+ * of the matrix.
+ */
+ ComplexSchur& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_maxIters;
+ }
+
+ /** \brief Maximum number of iterations per row.
+ *
+ * If not otherwise specified, the maximum number of iterations is this number times the size of the
+ * matrix. It is currently set to 30.
+ */
+ static const int m_maxIterationsPerRow = 30;
+
+ protected:
+ ComplexMatrixType m_matT, m_matU;
+ HessenbergDecomposition<MatrixType> m_hess;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_matUisUptodate;
+ Index m_maxIters;
+
+ private:
+ bool subdiagonalEntryIsNeglegible(Index i);
+ ComplexScalar computeShift(Index iu, Index iter);
+ void reduceToTriangularForm(bool computeU);
+ friend struct internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>;
+};
+
+/** If m_matT(i+1,i) is neglegible in floating point arithmetic
+ * compared to m_matT(i,i) and m_matT(j,j), then set it to zero and
+ * return true, else return false. */
+template<typename MatrixType>
+inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
+{
+ RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
+ RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
+ if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
+ {
+ m_matT.coeffRef(i+1,i) = ComplexScalar(0);
+ return true;
+ }
+ return false;
+}
+
+
+/** Compute the shift in the current QR iteration. */
+template<typename MatrixType>
+typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)
+{
+ using std::abs;
+ if (iter == 10 || iter == 20)
+ {
+ // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
+ return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
+ }
+
+ // compute the shift as one of the eigenvalues of t, the 2x2
+ // diagonal block on the bottom of the active submatrix
+ Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);
+ RealScalar normt = t.cwiseAbs().sum();
+ t /= normt; // the normalization by sf is to avoid under/overflow
+
+ ComplexScalar b = t.coeff(0,1) * t.coeff(1,0);
+ ComplexScalar c = t.coeff(0,0) - t.coeff(1,1);
+ ComplexScalar disc = sqrt(c*c + RealScalar(4)*b);
+ ComplexScalar det = t.coeff(0,0) * t.coeff(1,1) - b;
+ ComplexScalar trace = t.coeff(0,0) + t.coeff(1,1);
+ ComplexScalar eival1 = (trace + disc) / RealScalar(2);
+ ComplexScalar eival2 = (trace - disc) / RealScalar(2);
+
+ if(numext::norm1(eival1) > numext::norm1(eival2))
+ eival2 = det / eival1;
+ else
+ eival1 = det / eival2;
+
+ // choose the eigenvalue closest to the bottom entry of the diagonal
+ if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
+ return normt * eival1;
+ else
+ return normt * eival2;
+}
+
+
+template<typename MatrixType>
+ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool computeU)
+{
+ m_matUisUptodate = false;
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ if(matrix.cols() == 1)
+ {
+ m_matT = matrix.template cast<ComplexScalar>();
+ if(computeU) m_matU = ComplexMatrixType::Identity(1,1);
+ m_info = Success;
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+ return *this;
+ }
+
+ internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix, computeU);
+ computeFromHessenberg(m_matT, m_matU, computeU);
+ return *this;
+}
+
+template<typename MatrixType>
+template<typename HessMatrixType, typename OrthMatrixType>
+ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
+{
+ m_matT = matrixH;
+ if(computeU)
+ m_matU = matrixQ;
+ reduceToTriangularForm(computeU);
+ return *this;
+}
+namespace internal {
+
+/* Reduce given matrix to Hessenberg form */
+template<typename MatrixType, bool IsComplex>
+struct complex_schur_reduce_to_hessenberg
+{
+ // this is the implementation for the case IsComplex = true
+ static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
+ {
+ _this.m_hess.compute(matrix);
+ _this.m_matT = _this.m_hess.matrixH();
+ if(computeU) _this.m_matU = _this.m_hess.matrixQ();
+ }
+};
+
+template<typename MatrixType>
+struct complex_schur_reduce_to_hessenberg<MatrixType, false>
+{
+ static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
+ {
+ typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
+
+ // Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar
+ _this.m_hess.compute(matrix);
+ _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();
+ if(computeU)
+ {
+ // This may cause an allocation which seems to be avoidable
+ MatrixType Q = _this.m_hess.matrixQ();
+ _this.m_matU = Q.template cast<ComplexScalar>();
+ }
+ }
+};
+
+} // end namespace internal
+
+// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.
+template<typename MatrixType>
+void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
+{
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * m_matT.rows();
+
+ // The matrix m_matT is divided in three parts.
+ // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
+ // Rows il,...,iu is the part we are working on (the active submatrix).
+ // Rows iu+1,...,end are already brought in triangular form.
+ Index iu = m_matT.cols() - 1;
+ Index il;
+ Index iter = 0; // number of iterations we are working on the (iu,iu) element
+ Index totalIter = 0; // number of iterations for whole matrix
+
+ while(true)
+ {
+ // find iu, the bottom row of the active submatrix
+ while(iu > 0)
+ {
+ if(!subdiagonalEntryIsNeglegible(iu-1)) break;
+ iter = 0;
+ --iu;
+ }
+
+ // if iu is zero then we are done; the whole matrix is triangularized
+ if(iu==0) break;
+
+ // if we spent too many iterations, we give up
+ iter++;
+ totalIter++;
+ if(totalIter > maxIters) break;
+
+ // find il, the top row of the active submatrix
+ il = iu-1;
+ while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))
+ {
+ --il;
+ }
+
+ /* perform the QR step using Givens rotations. The first rotation
+ creates a bulge; the (il+2,il) element becomes nonzero. This
+ bulge is chased down to the bottom of the active submatrix. */
+
+ ComplexScalar shift = computeShift(iu, iter);
+ JacobiRotation<ComplexScalar> rot;
+ rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));
+ m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
+ m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
+ if(computeU) m_matU.applyOnTheRight(il, il+1, rot);
+
+ for(Index i=il+1 ; i<iu ; i++)
+ {
+ rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));
+ m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);
+ m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
+ m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
+ if(computeU) m_matU.applyOnTheRight(i, i+1, rot);
+ }
+ }
+
+ if(totalIter <= maxIters)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SCHUR_H
diff --git a/Eigen/src/Eigenvalues/ComplexSchur_MKL.h b/Eigen/src/Eigenvalues/ComplexSchur_MKL.h
new file mode 100644
index 0000000..91496ae
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexSchur_MKL.h
@@ -0,0 +1,94 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_COMPLEX_SCHUR_MKL_H
+#define EIGEN_COMPLEX_SCHUR_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_SCHUR_COMPLEX(EIGTYPE, MKLTYPE, MKLPREFIX, MKLPREFIX_U, EIGCOLROW, MKLCOLROW) \
+template<> inline \
+ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW>& matrix, bool computeU) \
+{ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \
+ typedef MatrixType::Scalar Scalar; \
+ typedef MatrixType::RealScalar RealScalar; \
+ typedef std::complex<RealScalar> ComplexScalar; \
+\
+ eigen_assert(matrix.cols() == matrix.rows()); \
+\
+ m_matUisUptodate = false; \
+ if(matrix.cols() == 1) \
+ { \
+ m_matT = matrix.cast<ComplexScalar>(); \
+ if(computeU) m_matU = ComplexMatrixType::Identity(1,1); \
+ m_info = Success; \
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+ } \
+ lapack_int n = matrix.cols(), sdim, info; \
+ lapack_int lda = matrix.outerStride(); \
+ lapack_int matrix_order = MKLCOLROW; \
+ char jobvs, sort='N'; \
+ LAPACK_##MKLPREFIX_U##_SELECT1 select = 0; \
+ jobvs = (computeU) ? 'V' : 'N'; \
+ m_matU.resize(n, n); \
+ lapack_int ldvs = m_matU.outerStride(); \
+ m_matT = matrix; \
+ Matrix<EIGTYPE, Dynamic, Dynamic> w; \
+ w.resize(n, 1);\
+ info = LAPACKE_##MKLPREFIX##gees( matrix_order, jobvs, sort, select, n, (MKLTYPE*)m_matT.data(), lda, &sdim, (MKLTYPE*)w.data(), (MKLTYPE*)m_matU.data(), ldvs ); \
+ if(info == 0) \
+ m_info = Success; \
+ else \
+ m_info = NoConvergence; \
+\
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+\
+}
+
+EIGEN_MKL_SCHUR_COMPLEX(dcomplex, MKL_Complex16, z, Z, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SCHUR_COMPLEX(scomplex, MKL_Complex8, c, C, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SCHUR_COMPLEX(dcomplex, MKL_Complex16, z, Z, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_SCHUR_COMPLEX(scomplex, MKL_Complex8, c, C, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SCHUR_MKL_H
diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h
new file mode 100644
index 0000000..20c59a7
--- /dev/null
+++ b/Eigen/src/Eigenvalues/EigenSolver.h
@@ -0,0 +1,607 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EIGENSOLVER_H
+#define EIGEN_EIGENSOLVER_H
+
+#include "./RealSchur.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class EigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of general matrices
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template. Currently, only real matrices are supported.
+ *
+ * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v \f$. If
+ * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
+ * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
+ * V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
+ * have \f$ A = V D V^{-1} \f$. This is called the eigendecomposition.
+ *
+ * The eigenvalues and eigenvectors of a matrix may be complex, even when the
+ * matrix is real. However, we can choose real matrices \f$ V \f$ and \f$ D
+ * \f$ satisfying \f$ A V = V D \f$, just like the eigendecomposition, if the
+ * matrix \f$ D \f$ is not required to be diagonal, but if it is allowed to
+ * have blocks of the form
+ * \f[ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f]
+ * (where \f$ u \f$ and \f$ v \f$ are real numbers) on the diagonal. These
+ * blocks correspond to complex eigenvalue pairs \f$ u \pm iv \f$. We call
+ * this variant of the eigendecomposition the pseudo-eigendecomposition.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * EigenSolver(const MatrixType&, bool) constructor which computes the
+ * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
+ * eigenvectors are computed, they can be retrieved with the eigenvalues() and
+ * eigenvectors() functions. The pseudoEigenvalueMatrix() and
+ * pseudoEigenvectors() methods allow the construction of the
+ * pseudo-eigendecomposition.
+ *
+ * The documentation for EigenSolver(const MatrixType&, bool) contains an
+ * example of the typical use of this class.
+ *
+ * \note The implementation is adapted from
+ * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
+ * Their code is based on EISPACK.
+ *
+ * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename _MatrixType> class EigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p _MatrixType. */
+ typedef _MatrixType MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via EigenSolver::compute(const MatrixType&, bool).
+ *
+ * \sa compute() for an example.
+ */
+ EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_realSchur(), m_matT(), m_tmp() {}
+
+ /** \brief Default constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa EigenSolver()
+ */
+ EigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realSchur(size),
+ m_matT(size, size),
+ m_tmp(size)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ *
+ * This constructor calls compute() to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * Example: \include EigenSolver_EigenSolver_MatrixType.cpp
+ * Output: \verbinclude EigenSolver_EigenSolver_MatrixType.out
+ *
+ * \sa compute()
+ */
+ EigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
+ : m_eivec(matrix.rows(), matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realSchur(matrix.cols()),
+ m_matT(matrix.rows(), matrix.cols()),
+ m_tmp(matrix.cols())
+ {
+ compute(matrix, computeEigenvectors);
+ }
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns %Matrix whose columns are the (possibly complex) eigenvectors.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. The
+ * matrix returned by this function is the matrix \f$ V \f$ in the
+ * eigendecomposition \f$ A = V D V^{-1} \f$, if it exists.
+ *
+ * Example: \include EigenSolver_eigenvectors.cpp
+ * Output: \verbinclude EigenSolver_eigenvectors.out
+ *
+ * \sa eigenvalues(), pseudoEigenvectors()
+ */
+ EigenvectorsType eigenvectors() const;
+
+ /** \brief Returns the pseudo-eigenvectors of given matrix.
+ *
+ * \returns Const reference to matrix whose columns are the pseudo-eigenvectors.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * The real matrix \f$ V \f$ returned by this function and the
+ * block-diagonal matrix \f$ D \f$ returned by pseudoEigenvalueMatrix()
+ * satisfy \f$ AV = VD \f$.
+ *
+ * Example: \include EigenSolver_pseudoEigenvectors.cpp
+ * Output: \verbinclude EigenSolver_pseudoEigenvectors.out
+ *
+ * \sa pseudoEigenvalueMatrix(), eigenvectors()
+ */
+ const MatrixType& pseudoEigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the block-diagonal matrix in the pseudo-eigendecomposition.
+ *
+ * \returns A block-diagonal matrix.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before.
+ *
+ * The matrix \f$ D \f$ returned by this function is real and
+ * block-diagonal. The blocks on the diagonal are either 1-by-1 or 2-by-2
+ * blocks of the form
+ * \f$ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f$.
+ * These blocks are not sorted in any particular order.
+ * The matrix \f$ D \f$ and the matrix \f$ V \f$ returned by
+ * pseudoEigenvectors() satisfy \f$ AV = VD \f$.
+ *
+ * \sa pseudoEigenvectors() for an example, eigenvalues()
+ */
+ MatrixType pseudoEigenvalueMatrix() const;
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are not sorted in any particular order.
+ *
+ * Example: \include EigenSolver_eigenvalues.cpp
+ * Output: \verbinclude EigenSolver_eigenvalues.out
+ *
+ * \sa eigenvectors(), pseudoEigenvalueMatrix(),
+ * MatrixBase::eigenvalues()
+ */
+ const EigenvalueType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the real matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to real Schur form using the RealSchur
+ * class. The Schur decomposition is then used to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * Schur decomposition, which is very approximately \f$ 25n^3 \f$
+ * (where \f$ n \f$ is the size of the matrix) if \p computeEigenvectors
+ * is true, and \f$ 10n^3 \f$ if \p computeEigenvectors is false.
+ *
+ * This method reuses of the allocated data in the EigenSolver object.
+ *
+ * Example: \include EigenSolver_compute.cpp
+ * Output: \verbinclude EigenSolver_compute.out
+ */
+ EigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true);
+
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_realSchur.info();
+ }
+
+ /** \brief Sets the maximum number of iterations allowed. */
+ EigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_realSchur.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_realSchur.getMaxIterations();
+ }
+
+ private:
+ void doComputeEigenvectors();
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+ }
+
+ MatrixType m_eivec;
+ EigenvalueType m_eivalues;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+ RealSchur<MatrixType> m_realSchur;
+ MatrixType m_matT;
+
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+ ColumnVectorType m_tmp;
+};
+
+template<typename MatrixType>
+MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
+{
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ Index n = m_eivalues.rows();
+ MatrixType matD = MatrixType::Zero(n,n);
+ for (Index i=0; i<n; ++i)
+ {
+ if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i))))
+ matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
+ else
+ {
+ matD.template block<2,2>(i,i) << numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
+ -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
+ ++i;
+ }
+ }
+ return matD;
+}
+
+template<typename MatrixType>
+typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eigenvectors() const
+{
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ Index n = m_eivec.cols();
+ EigenvectorsType matV(n,n);
+ for (Index j=0; j<n; ++j)
+ {
+ if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j))) || j+1==n)
+ {
+ // we have a real eigen value
+ matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
+ matV.col(j).normalize();
+ }
+ else
+ {
+ // we have a pair of complex eigen values
+ for (Index i=0; i<n; ++i)
+ {
+ matV.coeffRef(i,j) = ComplexScalar(m_eivec.coeff(i,j), m_eivec.coeff(i,j+1));
+ matV.coeffRef(i,j+1) = ComplexScalar(m_eivec.coeff(i,j), -m_eivec.coeff(i,j+1));
+ }
+ matV.col(j).normalize();
+ matV.col(j+1).normalize();
+ ++j;
+ }
+ }
+ return matV;
+}
+
+template<typename MatrixType>
+EigenSolver<MatrixType>&
+EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
+{
+ check_template_parameters();
+
+ using std::sqrt;
+ using std::abs;
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ // Reduce to real Schur form.
+ m_realSchur.compute(matrix, computeEigenvectors);
+
+ if (m_realSchur.info() == Success)
+ {
+ m_matT = m_realSchur.matrixT();
+ if (computeEigenvectors)
+ m_eivec = m_realSchur.matrixU();
+
+ // Compute eigenvalues from matT
+ m_eivalues.resize(matrix.cols());
+ Index i = 0;
+ while (i < matrix.cols())
+ {
+ if (i == matrix.cols() - 1 || m_matT.coeff(i+1, i) == Scalar(0))
+ {
+ m_eivalues.coeffRef(i) = m_matT.coeff(i, i);
+ ++i;
+ }
+ else
+ {
+ Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));
+ Scalar z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
+ m_eivalues.coeffRef(i) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);
+ m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);
+ i += 2;
+ }
+ }
+
+ // Compute eigenvectors.
+ if (computeEigenvectors)
+ doComputeEigenvectors();
+ }
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+
+ return *this;
+}
+
+// Complex scalar division.
+template<typename Scalar>
+std::complex<Scalar> cdiv(const Scalar& xr, const Scalar& xi, const Scalar& yr, const Scalar& yi)
+{
+ using std::abs;
+ Scalar r,d;
+ if (abs(yr) > abs(yi))
+ {
+ r = yi/yr;
+ d = yr + r*yi;
+ return std::complex<Scalar>((xr + r*xi)/d, (xi - r*xr)/d);
+ }
+ else
+ {
+ r = yr/yi;
+ d = yi + r*yr;
+ return std::complex<Scalar>((r*xr + xi)/d, (r*xi - xr)/d);
+ }
+}
+
+
+template<typename MatrixType>
+void EigenSolver<MatrixType>::doComputeEigenvectors()
+{
+ using std::abs;
+ const Index size = m_eivec.cols();
+ const Scalar eps = NumTraits<Scalar>::epsilon();
+
+ // inefficient! this is already computed in RealSchur
+ Scalar norm(0);
+ for (Index j = 0; j < size; ++j)
+ {
+ norm += m_matT.row(j).segment((std::max)(j-1,Index(0)), size-(std::max)(j-1,Index(0))).cwiseAbs().sum();
+ }
+
+ // Backsubstitute to find vectors of upper triangular form
+ if (norm == 0.0)
+ {
+ return;
+ }
+
+ for (Index n = size-1; n >= 0; n--)
+ {
+ Scalar p = m_eivalues.coeff(n).real();
+ Scalar q = m_eivalues.coeff(n).imag();
+
+ // Scalar vector
+ if (q == Scalar(0))
+ {
+ Scalar lastr(0), lastw(0);
+ Index l = n;
+
+ m_matT.coeffRef(n,n) = 1.0;
+ for (Index i = n-1; i >= 0; i--)
+ {
+ Scalar w = m_matT.coeff(i,i) - p;
+ Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
+
+ if (m_eivalues.coeff(i).imag() < 0.0)
+ {
+ lastw = w;
+ lastr = r;
+ }
+ else
+ {
+ l = i;
+ if (m_eivalues.coeff(i).imag() == 0.0)
+ {
+ if (w != 0.0)
+ m_matT.coeffRef(i,n) = -r / w;
+ else
+ m_matT.coeffRef(i,n) = -r / (eps * norm);
+ }
+ else // Solve real equations
+ {
+ Scalar x = m_matT.coeff(i,i+1);
+ Scalar y = m_matT.coeff(i+1,i);
+ Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
+ Scalar t = (x * lastr - lastw * r) / denom;
+ m_matT.coeffRef(i,n) = t;
+ if (abs(x) > abs(lastw))
+ m_matT.coeffRef(i+1,n) = (-r - w * t) / x;
+ else
+ m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
+ }
+
+ // Overflow control
+ Scalar t = abs(m_matT.coeff(i,n));
+ if ((eps * t) * t > Scalar(1))
+ m_matT.col(n).tail(size-i) /= t;
+ }
+ }
+ }
+ else if (q < Scalar(0) && n > 0) // Complex vector
+ {
+ Scalar lastra(0), lastsa(0), lastw(0);
+ Index l = n-1;
+
+ // Last vector component imaginary so matrix is triangular
+ if (abs(m_matT.coeff(n,n-1)) > abs(m_matT.coeff(n-1,n)))
+ {
+ m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);
+ m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);
+ }
+ else
+ {
+ std::complex<Scalar> cc = cdiv<Scalar>(0.0,-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q);
+ m_matT.coeffRef(n-1,n-1) = numext::real(cc);
+ m_matT.coeffRef(n-1,n) = numext::imag(cc);
+ }
+ m_matT.coeffRef(n,n-1) = 0.0;
+ m_matT.coeffRef(n,n) = 1.0;
+ for (Index i = n-2; i >= 0; i--)
+ {
+ Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));
+ Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
+ Scalar w = m_matT.coeff(i,i) - p;
+
+ if (m_eivalues.coeff(i).imag() < 0.0)
+ {
+ lastw = w;
+ lastra = ra;
+ lastsa = sa;
+ }
+ else
+ {
+ l = i;
+ if (m_eivalues.coeff(i).imag() == RealScalar(0))
+ {
+ std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
+ m_matT.coeffRef(i,n-1) = numext::real(cc);
+ m_matT.coeffRef(i,n) = numext::imag(cc);
+ }
+ else
+ {
+ // Solve complex equations
+ Scalar x = m_matT.coeff(i,i+1);
+ Scalar y = m_matT.coeff(i+1,i);
+ Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
+ Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;
+ if ((vr == 0.0) && (vi == 0.0))
+ vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
+
+ std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
+ m_matT.coeffRef(i,n-1) = numext::real(cc);
+ m_matT.coeffRef(i,n) = numext::imag(cc);
+ if (abs(x) > (abs(lastw) + abs(q)))
+ {
+ m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
+ m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;
+ }
+ else
+ {
+ cc = cdiv(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n),lastw,q);
+ m_matT.coeffRef(i+1,n-1) = numext::real(cc);
+ m_matT.coeffRef(i+1,n) = numext::imag(cc);
+ }
+ }
+
+ // Overflow control
+ using std::max;
+ Scalar t = (max)(abs(m_matT.coeff(i,n-1)),abs(m_matT.coeff(i,n)));
+ if ((eps * t) * t > Scalar(1))
+ m_matT.block(i, n-1, size-i, 2) /= t;
+
+ }
+ }
+
+ // We handled a pair of complex conjugate eigenvalues, so need to skip them both
+ n--;
+ }
+ else
+ {
+ eigen_assert(0 && "Internal bug in EigenSolver"); // this should not happen
+ }
+ }
+
+ // Back transformation to get eigenvectors of original matrix
+ for (Index j = size-1; j >= 0; j--)
+ {
+ m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);
+ m_eivec.col(j) = m_tmp;
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
new file mode 100644
index 0000000..956e80d
--- /dev/null
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -0,0 +1,350 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERALIZEDEIGENSOLVER_H
+#define EIGEN_GENERALIZEDEIGENSOLVER_H
+
+#include "./RealQZ.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class GeneralizedEigenSolver
+ *
+ * \brief Computes the generalized eigenvalues and eigenvectors of a pair of general matrices
+ *
+ * \tparam _MatrixType the type of the matrices of which we are computing the
+ * eigen-decomposition; this is expected to be an instantiation of the Matrix
+ * class template. Currently, only real matrices are supported.
+ *
+ * The generalized eigenvalues and eigenvectors of a matrix pair \f$ A \f$ and \f$ B \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda Bv \f$. If
+ * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
+ * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
+ * B V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
+ * have \f$ A = B V D V^{-1} \f$. This is called the generalized eigen-decomposition.
+ *
+ * The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the
+ * matrices are real. Moreover, the generalized eigenvalue might be infinite if the matrix B is
+ * singular. To workaround this difficulty, the eigenvalues are provided as a pair of complex \f$ \alpha \f$
+ * and real \f$ \beta \f$ such that: \f$ \lambda_i = \alpha_i / \beta_i \f$. If \f$ \beta_i \f$ is (nearly) zero,
+ * then one can consider the well defined left eigenvalue \f$ \mu = \beta_i / \alpha_i\f$ such that:
+ * \f$ \mu_i A v_i = B v_i \f$, or even \f$ \mu_i u_i^T A = u_i^T B \f$ where \f$ u_i \f$ is
+ * called the left eigenvector.
+ *
+ * Call the function compute() to compute the generalized eigenvalues and eigenvectors of
+ * a given matrix pair. Alternatively, you can use the
+ * GeneralizedEigenSolver(const MatrixType&, const MatrixType&, bool) constructor which computes the
+ * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
+ * eigenvectors are computed, they can be retrieved with the eigenvalues() and
+ * eigenvectors() functions.
+ *
+ * Here is an usage example of this class:
+ * Example: \include GeneralizedEigenSolver.cpp
+ * Output: \verbinclude GeneralizedEigenSolver.out
+ *
+ * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename _MatrixType> class GeneralizedEigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p _MatrixType. */
+ typedef _MatrixType MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of real scalar values eigenvalues as returned by betas().
+ *
+ * This is a column vector with entries of type #Scalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> VectorType;
+
+ /** \brief Type for vector of complex scalar values eigenvalues as returned by betas().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ComplexVectorType;
+
+ /** \brief Expression type for the eigenvalues as returned by eigenvalues().
+ */
+ typedef CwiseBinaryOp<internal::scalar_quotient_op<ComplexScalar,Scalar>,ComplexVectorType,VectorType> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via EigenSolver::compute(const MatrixType&, bool).
+ *
+ * \sa compute() for an example.
+ */
+ GeneralizedEigenSolver() : m_eivec(), m_alphas(), m_betas(), m_isInitialized(false), m_realQZ(), m_matS(), m_tmp() {}
+
+ /** \brief Default constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa GeneralizedEigenSolver()
+ */
+ GeneralizedEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_alphas(size),
+ m_betas(size),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realQZ(size),
+ m_matS(size, size),
+ m_tmp(size)
+ {}
+
+ /** \brief Constructor; computes the generalized eigendecomposition of given matrix pair.
+ *
+ * \param[in] A Square matrix whose eigendecomposition is to be computed.
+ * \param[in] B Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are computed.
+ *
+ * This constructor calls compute() to compute the generalized eigenvalues
+ * and eigenvectors.
+ *
+ * \sa compute()
+ */
+ GeneralizedEigenSolver(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true)
+ : m_eivec(A.rows(), A.cols()),
+ m_alphas(A.cols()),
+ m_betas(A.cols()),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realQZ(A.cols()),
+ m_matS(A.rows(), A.cols()),
+ m_tmp(A.cols())
+ {
+ compute(A, B, computeEigenvectors);
+ }
+
+ /* \brief Returns the computed generalized eigenvectors.
+ *
+ * \returns %Matrix whose columns are the (possibly complex) eigenvectors.
+ *
+ * \pre Either the constructor
+ * GeneralizedEigenSolver(const MatrixType&,const MatrixType&, bool) or the member function
+ * compute(const MatrixType&, const MatrixType& bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. The
+ * matrix returned by this function is the matrix \f$ V \f$ in the
+ * generalized eigendecomposition \f$ A = B V D V^{-1} \f$, if it exists.
+ *
+ * \sa eigenvalues()
+ */
+// EigenvectorsType eigenvectors() const;
+
+ /** \brief Returns an expression of the computed generalized eigenvalues.
+ *
+ * \returns An expression of the column vector containing the eigenvalues.
+ *
+ * It is a shortcut for \code this->alphas().cwiseQuotient(this->betas()); \endcode
+ * Not that betas might contain zeros. It is therefore not recommended to use this function,
+ * but rather directly deal with the alphas and betas vectors.
+ *
+ * \pre Either the constructor
+ * GeneralizedEigenSolver(const MatrixType&,const MatrixType&,bool) or the member function
+ * compute(const MatrixType&,const MatrixType&,bool) has been called before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are not sorted in any particular order.
+ *
+ * \sa alphas(), betas(), eigenvectors()
+ */
+ EigenvalueType eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "GeneralizedEigenSolver is not initialized.");
+ return EigenvalueType(m_alphas,m_betas);
+ }
+
+ /** \returns A const reference to the vectors containing the alpha values
+ *
+ * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
+ *
+ * \sa betas(), eigenvalues() */
+ ComplexVectorType alphas() const
+ {
+ eigen_assert(m_isInitialized && "GeneralizedEigenSolver is not initialized.");
+ return m_alphas;
+ }
+
+ /** \returns A const reference to the vectors containing the beta values
+ *
+ * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
+ *
+ * \sa alphas(), eigenvalues() */
+ VectorType betas() const
+ {
+ eigen_assert(m_isInitialized && "GeneralizedEigenSolver is not initialized.");
+ return m_betas;
+ }
+
+ /** \brief Computes generalized eigendecomposition of given matrix.
+ *
+ * \param[in] A Square matrix whose eigendecomposition is to be computed.
+ * \param[in] B Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the real matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to real generalized Schur form using the RealQZ
+ * class. The generalized Schur decomposition is then used to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * generalized Schur decomposition.
+ *
+ * This method reuses of the allocated data in the GeneralizedEigenSolver object.
+ */
+ GeneralizedEigenSolver& compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true);
+
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_realQZ.info();
+ }
+
+ /** Sets the maximal number of iterations allowed.
+ */
+ GeneralizedEigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_realQZ.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+ }
+
+ MatrixType m_eivec;
+ ComplexVectorType m_alphas;
+ VectorType m_betas;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+ RealQZ<MatrixType> m_realQZ;
+ MatrixType m_matS;
+
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+ ColumnVectorType m_tmp;
+};
+
+//template<typename MatrixType>
+//typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType GeneralizedEigenSolver<MatrixType>::eigenvectors() const
+//{
+// eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+// eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+// Index n = m_eivec.cols();
+// EigenvectorsType matV(n,n);
+// // TODO
+// return matV;
+//}
+
+template<typename MatrixType>
+GeneralizedEigenSolver<MatrixType>&
+GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)
+{
+ check_template_parameters();
+
+ using std::sqrt;
+ using std::abs;
+ eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());
+
+ // Reduce to generalized real Schur form:
+ // A = Q S Z and B = Q T Z
+ m_realQZ.compute(A, B, computeEigenvectors);
+
+ if (m_realQZ.info() == Success)
+ {
+ m_matS = m_realQZ.matrixS();
+ if (computeEigenvectors)
+ m_eivec = m_realQZ.matrixZ().transpose();
+
+ // Compute eigenvalues from matS
+ m_alphas.resize(A.cols());
+ m_betas.resize(A.cols());
+ Index i = 0;
+ while (i < A.cols())
+ {
+ if (i == A.cols() - 1 || m_matS.coeff(i+1, i) == Scalar(0))
+ {
+ m_alphas.coeffRef(i) = m_matS.coeff(i, i);
+ m_betas.coeffRef(i) = m_realQZ.matrixT().coeff(i,i);
+ ++i;
+ }
+ else
+ {
+ Scalar p = Scalar(0.5) * (m_matS.coeff(i, i) - m_matS.coeff(i+1, i+1));
+ Scalar z = sqrt(abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));
+ m_alphas.coeffRef(i) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, z);
+ m_alphas.coeffRef(i+1) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, -z);
+
+ m_betas.coeffRef(i) = m_realQZ.matrixT().coeff(i,i);
+ m_betas.coeffRef(i+1) = m_realQZ.matrixT().coeff(i,i);
+ i += 2;
+ }
+ }
+ }
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = false;//computeEigenvectors;
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERALIZEDEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
new file mode 100644
index 0000000..07bf1ea
--- /dev/null
+++ b/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
@@ -0,0 +1,227 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
+#define EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
+
+#include "./Tridiagonalization.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class GeneralizedSelfAdjointEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template.
+ *
+ * This class solves the generalized eigenvalue problem
+ * \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be
+ * selfadjoint and the matrix \f$ B \f$ should be positive definite.
+ *
+ * Only the \b lower \b triangular \b part of the input matrix is referenced.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ * constructor which computes the eigenvalues and eigenvectors at construction time.
+ * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues()
+ * and eigenvectors() functions.
+ *
+ * The documentation for GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ * contains an example of the typical use of this class.
+ *
+ * \sa class SelfAdjointEigenSolver, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename _MatrixType>
+class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixType>
+{
+ typedef SelfAdjointEigenSolver<_MatrixType> Base;
+ public:
+
+ typedef typename Base::Index Index;
+ typedef _MatrixType MatrixType;
+
+ /** \brief Default constructor for fixed-size matrices.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). This constructor
+ * can only be used if \p _MatrixType is a fixed-size matrix; use
+ * GeneralizedSelfAdjointEigenSolver(Index) for dynamic-size matrices.
+ */
+ GeneralizedSelfAdjointEigenSolver() : Base() {}
+
+ /** \brief Constructor, pre-allocates memory for dynamic-size matrices.
+ *
+ * \param [in] size Positive integer, size of the matrix whose
+ * eigenvalues and eigenvectors will be computed.
+ *
+ * This constructor is useful for dynamic-size matrices, when the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a wrong
+ * \p size, but it may impair performance.
+ *
+ * \sa compute() for an example
+ */
+ GeneralizedSelfAdjointEigenSolver(Index size)
+ : Base(size)
+ {}
+
+ /** \brief Constructor; computes generalized eigendecomposition of given matrix pencil.
+ *
+ * \param[in] matA Selfadjoint matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] matB Positive-definite matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.
+ * Default is #ComputeEigenvectors|#Ax_lBx.
+ *
+ * This constructor calls compute(const MatrixType&, const MatrixType&, int)
+ * to compute the eigenvalues and (if requested) the eigenvectors of the
+ * generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA the
+ * selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix
+ * \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property
+ * \f$ x^* B x = 1 \f$. The eigenvectors are computed if
+ * \a options contains ComputeEigenvectors.
+ *
+ * In addition, the two following variants can be solved via \p options:
+ * - \c ABx_lx: \f$ ABx = \lambda x \f$
+ * - \c BAx_lx: \f$ BAx = \lambda x \f$
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out
+ *
+ * \sa compute(const MatrixType&, const MatrixType&, int)
+ */
+ GeneralizedSelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB,
+ int options = ComputeEigenvectors|Ax_lBx)
+ : Base(matA.cols())
+ {
+ compute(matA, matB, options);
+ }
+
+ /** \brief Computes generalized eigendecomposition of given matrix pencil.
+ *
+ * \param[in] matA Selfadjoint matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] matB Positive-definite matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.
+ * Default is #ComputeEigenvectors|#Ax_lBx.
+ *
+ * \returns Reference to \c *this
+ *
+ * Accoring to \p options, this function computes eigenvalues and (if requested)
+ * the eigenvectors of one of the following three generalized eigenproblems:
+ * - \c Ax_lBx: \f$ Ax = \lambda B x \f$
+ * - \c ABx_lx: \f$ ABx = \lambda x \f$
+ * - \c BAx_lx: \f$ BAx = \lambda x \f$
+ * with \a matA the selfadjoint matrix \f$ A \f$ and \a matB the positive definite
+ * matrix \f$ B \f$.
+ * In addition, each eigenvector \f$ x \f$ satisfies the property \f$ x^* B x = 1 \f$.
+ *
+ * The eigenvalues() function can be used to retrieve
+ * the eigenvalues. If \p options contains ComputeEigenvectors, then the
+ * eigenvectors are also computed and can be retrieved by calling
+ * eigenvectors().
+ *
+ * The implementation uses LLT to compute the Cholesky decomposition
+ * \f$ B = LL^* \f$ and computes the classical eigendecomposition
+ * of the selfadjoint matrix \f$ L^{-1} A (L^*)^{-1} \f$ if \p options contains Ax_lBx
+ * and of \f$ L^{*} A L \f$ otherwise. This solves the
+ * generalized eigenproblem, because any solution of the generalized
+ * eigenproblem \f$ Ax = \lambda B x \f$ corresponds to a solution
+ * \f$ L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \f$ of the
+ * eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$. Similar statements
+ * can be made for the two other variants.
+ *
+ * Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out
+ *
+ * \sa GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ */
+ GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB,
+ int options = ComputeEigenvectors|Ax_lBx);
+
+ protected:
+
+};
+
+
+template<typename MatrixType>
+GeneralizedSelfAdjointEigenSolver<MatrixType>& GeneralizedSelfAdjointEigenSolver<MatrixType>::
+compute(const MatrixType& matA, const MatrixType& matB, int options)
+{
+ eigen_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && ((options&GenEigMask)==0 || (options&GenEigMask)==Ax_lBx
+ || (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx)
+ && "invalid option parameter");
+
+ bool computeEigVecs = ((options&EigVecMask)==0) || ((options&EigVecMask)==ComputeEigenvectors);
+
+ // Compute the cholesky decomposition of matB = L L' = U'U
+ LLT<MatrixType> cholB(matB);
+
+ int type = (options&GenEigMask);
+ if(type==0)
+ type = Ax_lBx;
+
+ if(type==Ax_lBx)
+ {
+ // compute C = inv(L) A inv(L')
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ cholB.matrixL().template solveInPlace<OnTheLeft>(matC);
+ cholB.matrixU().template solveInPlace<OnTheRight>(matC);
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly );
+
+ // transform back the eigen vectors: evecs = inv(U) * evecs
+ if(computeEigVecs)
+ cholB.matrixU().solveInPlace(Base::m_eivec);
+ }
+ else if(type==ABx_lx)
+ {
+ // compute C = L' A L
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ matC = matC * cholB.matrixL();
+ matC = cholB.matrixU() * matC;
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
+
+ // transform back the eigen vectors: evecs = inv(U) * evecs
+ if(computeEigVecs)
+ cholB.matrixU().solveInPlace(Base::m_eivec);
+ }
+ else if(type==BAx_lx)
+ {
+ // compute C = L' A L
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ matC = matC * cholB.matrixL();
+ matC = cholB.matrixU() * matC;
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
+
+ // transform back the eigen vectors: evecs = L * evecs
+ if(computeEigVecs)
+ Base::m_eivec = cholB.matrixL() * Base::m_eivec;
+ }
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/HessenbergDecomposition.h b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
new file mode 100644
index 0000000..3db0c01
--- /dev/null
+++ b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
@@ -0,0 +1,373 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HESSENBERGDECOMPOSITION_H
+#define EIGEN_HESSENBERGDECOMPOSITION_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType;
+template<typename MatrixType>
+struct traits<HessenbergDecompositionMatrixHReturnType<MatrixType> >
+{
+ typedef MatrixType ReturnType;
+};
+
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class HessenbergDecomposition
+ *
+ * \brief Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the Hessenberg decomposition
+ *
+ * This class performs an Hessenberg decomposition of a matrix \f$ A \f$. In
+ * the real case, the Hessenberg decomposition consists of an orthogonal
+ * matrix \f$ Q \f$ and a Hessenberg matrix \f$ H \f$ such that \f$ A = Q H
+ * Q^T \f$. An orthogonal matrix is a matrix whose inverse equals its
+ * transpose (\f$ Q^{-1} = Q^T \f$). A Hessenberg matrix has zeros below the
+ * subdiagonal, so it is almost upper triangular. The Hessenberg decomposition
+ * of a complex matrix is \f$ A = Q H Q^* \f$ with \f$ Q \f$ unitary (that is,
+ * \f$ Q^{-1} = Q^* \f$).
+ *
+ * Call the function compute() to compute the Hessenberg decomposition of a
+ * given matrix. Alternatively, you can use the
+ * HessenbergDecomposition(const MatrixType&) constructor which computes the
+ * Hessenberg decomposition at construction time. Once the decomposition is
+ * computed, you can use the matrixH() and matrixQ() functions to construct
+ * the matrices H and Q in the decomposition.
+ *
+ * The documentation for matrixH() contains an example of the typical use of
+ * this class.
+ *
+ * \sa class ComplexSchur, class Tridiagonalization, \ref QR_Module "QR Module"
+ */
+template<typename _MatrixType> class HessenbergDecomposition
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p _MatrixType. */
+ typedef _MatrixType MatrixType;
+
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1,
+ Options = MatrixType::Options,
+ MaxSize = MatrixType::MaxRowsAtCompileTime,
+ MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Type for vector of Householder coefficients.
+ *
+ * This is column vector with entries of type #Scalar. The length of the
+ * vector is one less than the size of #MatrixType, if it is a fixed-side
+ * type.
+ */
+ typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
+
+ /** \brief Return type of matrixQ() */
+ typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
+
+ typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
+
+ /** \brief Default constructor; the decomposition will be computed later.
+ *
+ * \param [in] size The size of the matrix whose Hessenberg decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ HessenbergDecomposition(Index size = Size==Dynamic ? 2 : Size)
+ : m_matrix(size,size),
+ m_temp(size),
+ m_isInitialized(false)
+ {
+ if(size>1)
+ m_hCoeffs.resize(size-1);
+ }
+
+ /** \brief Constructor; computes Hessenberg decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Hessenberg decomposition is to be computed.
+ *
+ * This constructor calls compute() to compute the Hessenberg
+ * decomposition.
+ *
+ * \sa matrixH() for an example.
+ */
+ HessenbergDecomposition(const MatrixType& matrix)
+ : m_matrix(matrix),
+ m_temp(matrix.rows()),
+ m_isInitialized(false)
+ {
+ if(matrix.rows()<2)
+ {
+ m_isInitialized = true;
+ return;
+ }
+ m_hCoeffs.resize(matrix.rows()-1,1);
+ _compute(m_matrix, m_hCoeffs, m_temp);
+ m_isInitialized = true;
+ }
+
+ /** \brief Computes Hessenberg decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Hessenberg decomposition is to be computed.
+ * \returns Reference to \c *this
+ *
+ * The Hessenberg decomposition is computed by bringing the columns of the
+ * matrix successively in the required form using Householder reflections
+ * (see, e.g., Algorithm 7.4.2 in Golub \& Van Loan, <i>%Matrix
+ * Computations</i>). The cost is \f$ 10n^3/3 \f$ flops, where \f$ n \f$
+ * denotes the size of the given matrix.
+ *
+ * This method reuses of the allocated data in the HessenbergDecomposition
+ * object.
+ *
+ * Example: \include HessenbergDecomposition_compute.cpp
+ * Output: \verbinclude HessenbergDecomposition_compute.out
+ */
+ HessenbergDecomposition& compute(const MatrixType& matrix)
+ {
+ m_matrix = matrix;
+ if(matrix.rows()<2)
+ {
+ m_isInitialized = true;
+ return *this;
+ }
+ m_hCoeffs.resize(matrix.rows()-1,1);
+ _compute(m_matrix, m_hCoeffs, m_temp);
+ m_isInitialized = true;
+ return *this;
+ }
+
+ /** \brief Returns the Householder coefficients.
+ *
+ * \returns a const reference to the vector of Householder coefficients
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The Householder coefficients allow the reconstruction of the matrix
+ * \f$ Q \f$ in the Hessenberg decomposition from the packed data.
+ *
+ * \sa packedMatrix(), \ref Householder_Module "Householder module"
+ */
+ const CoeffVectorType& householderCoefficients() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return m_hCoeffs;
+ }
+
+ /** \brief Returns the internal representation of the decomposition
+ *
+ * \returns a const reference to a matrix with the internal representation
+ * of the decomposition.
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The returned matrix contains the following information:
+ * - the upper part and lower sub-diagonal represent the Hessenberg matrix H
+ * - the rest of the lower part contains the Householder vectors that, combined with
+ * Householder coefficients returned by householderCoefficients(),
+ * allows to reconstruct the matrix Q as
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * Here, the matrices \f$ H_i \f$ are the Householder transformations
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
+ * with M the matrix returned by this function.
+ *
+ * See LAPACK for further details on this packed storage.
+ *
+ * Example: \include HessenbergDecomposition_packedMatrix.cpp
+ * Output: \verbinclude HessenbergDecomposition_packedMatrix.out
+ *
+ * \sa householderCoefficients()
+ */
+ const MatrixType& packedMatrix() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return m_matrix;
+ }
+
+ /** \brief Reconstructs the orthogonal matrix Q in the decomposition
+ *
+ * \returns object representing the matrix Q
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * This function returns a light-weight object of template class
+ * HouseholderSequence. You can either apply it directly to a matrix or
+ * you can convert it to a matrix of type #MatrixType.
+ *
+ * \sa matrixH() for an example, class HouseholderSequence
+ */
+ HouseholderSequenceType matrixQ() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
+ .setLength(m_matrix.rows() - 1)
+ .setShift(1);
+ }
+
+ /** \brief Constructs the Hessenberg matrix H in the decomposition
+ *
+ * \returns expression object representing the matrix H
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The object returned by this function constructs the Hessenberg matrix H
+ * when it is assigned to a matrix or otherwise evaluated. The matrix H is
+ * constructed from the packed matrix as returned by packedMatrix(): The
+ * upper part (including the subdiagonal) of the packed matrix contains
+ * the matrix H. It may sometimes be better to directly use the packed
+ * matrix instead of constructing the matrix H.
+ *
+ * Example: \include HessenbergDecomposition_matrixH.cpp
+ * Output: \verbinclude HessenbergDecomposition_matrixH.out
+ *
+ * \sa matrixQ(), packedMatrix()
+ */
+ MatrixHReturnType matrixH() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return MatrixHReturnType(*this);
+ }
+
+ private:
+
+ typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> VectorType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp);
+
+ protected:
+ MatrixType m_matrix;
+ CoeffVectorType m_hCoeffs;
+ VectorType m_temp;
+ bool m_isInitialized;
+};
+
+/** \internal
+ * Performs a tridiagonal decomposition of \a matA in place.
+ *
+ * \param matA the input selfadjoint matrix
+ * \param hCoeffs returned Householder coefficients
+ *
+ * The result is written in the lower triangular part of \a matA.
+ *
+ * Implemented from Golub's "%Matrix Computations", algorithm 8.3.1.
+ *
+ * \sa packedMatrix()
+ */
+template<typename MatrixType>
+void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp)
+{
+ eigen_assert(matA.rows()==matA.cols());
+ Index n = matA.rows();
+ temp.resize(n);
+ for (Index i = 0; i<n-1; ++i)
+ {
+ // let's consider the vector v = i-th column starting at position i+1
+ Index remainingSize = n-i-1;
+ RealScalar beta;
+ Scalar h;
+ matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
+ matA.col(i).coeffRef(i+1) = beta;
+ hCoeffs.coeffRef(i) = h;
+
+ // Apply similarity transformation to remaining columns,
+ // i.e., compute A = H A H'
+
+ // A = H A
+ matA.bottomRightCorner(remainingSize, remainingSize)
+ .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));
+
+ // A = A H'
+ matA.rightCols(remainingSize)
+ .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));
+ }
+}
+
+namespace internal {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \brief Expression type for return value of HessenbergDecomposition::matrixH()
+ *
+ * \tparam MatrixType type of matrix in the Hessenberg decomposition
+ *
+ * Objects of this type represent the Hessenberg matrix in the Hessenberg
+ * decomposition of some matrix. The object holds a reference to the
+ * HessenbergDecomposition class until the it is assigned or evaluated for
+ * some other reason (the reference should remain valid during the life time
+ * of this object). This class is the return type of
+ * HessenbergDecomposition::matrixH(); there is probably no other use for this
+ * class.
+ */
+template<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType
+: public ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> >
+{
+ typedef typename MatrixType::Index Index;
+ public:
+ /** \brief Constructor.
+ *
+ * \param[in] hess Hessenberg decomposition
+ */
+ HessenbergDecompositionMatrixHReturnType(const HessenbergDecomposition<MatrixType>& hess) : m_hess(hess) { }
+
+ /** \brief Hessenberg matrix in decomposition.
+ *
+ * \param[out] result Hessenberg matrix in decomposition \p hess which
+ * was passed to the constructor
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ result = m_hess.packedMatrix();
+ Index n = result.rows();
+ if (n>2)
+ result.bottomLeftCorner(n-2, n-2).template triangularView<Lower>().setZero();
+ }
+
+ Index rows() const { return m_hess.packedMatrix().rows(); }
+ Index cols() const { return m_hess.packedMatrix().cols(); }
+
+ protected:
+ const HessenbergDecomposition<MatrixType>& m_hess;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_HESSENBERGDECOMPOSITION_H
diff --git a/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h b/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
new file mode 100644
index 0000000..4fec8af
--- /dev/null
+++ b/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXBASEEIGENVALUES_H
+#define EIGEN_MATRIXBASEEIGENVALUES_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived, bool IsComplex>
+struct eigenvalues_selector
+{
+ // this is the implementation for the case IsComplex = true
+ static inline typename MatrixBase<Derived>::EigenvaluesReturnType const
+ run(const MatrixBase<Derived>& m)
+ {
+ typedef typename Derived::PlainObject PlainObject;
+ PlainObject m_eval(m);
+ return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues();
+ }
+};
+
+template<typename Derived>
+struct eigenvalues_selector<Derived, false>
+{
+ static inline typename MatrixBase<Derived>::EigenvaluesReturnType const
+ run(const MatrixBase<Derived>& m)
+ {
+ typedef typename Derived::PlainObject PlainObject;
+ PlainObject m_eval(m);
+ return EigenSolver<PlainObject>(m_eval, false).eigenvalues();
+ }
+};
+
+} // end namespace internal
+
+/** \brief Computes the eigenvalues of a matrix
+ * \returns Column vector containing the eigenvalues.
+ *
+ * \eigenvalues_module
+ * This function computes the eigenvalues with the help of the EigenSolver
+ * class (for real matrices) or the ComplexEigenSolver class (for complex
+ * matrices).
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix.
+ *
+ * The SelfAdjointView class provides a better algorithm for selfadjoint
+ * matrices.
+ *
+ * Example: \include MatrixBase_eigenvalues.cpp
+ * Output: \verbinclude MatrixBase_eigenvalues.out
+ *
+ * \sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(),
+ * SelfAdjointView::eigenvalues()
+ */
+template<typename Derived>
+inline typename MatrixBase<Derived>::EigenvaluesReturnType
+MatrixBase<Derived>::eigenvalues() const
+{
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived());
+}
+
+/** \brief Computes the eigenvalues of a matrix
+ * \returns Column vector containing the eigenvalues.
+ *
+ * \eigenvalues_module
+ * This function computes the eigenvalues with the help of the
+ * SelfAdjointEigenSolver class. The eigenvalues are repeated according to
+ * their algebraic multiplicity, so there are as many eigenvalues as rows in
+ * the matrix.
+ *
+ * Example: \include SelfAdjointView_eigenvalues.cpp
+ * Output: \verbinclude SelfAdjointView_eigenvalues.out
+ *
+ * \sa SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline typename SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType
+SelfAdjointView<MatrixType, UpLo>::eigenvalues() const
+{
+ typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject;
+ PlainObject thisAsMatrix(*this);
+ return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues();
+}
+
+
+
+/** \brief Computes the L2 operator norm
+ * \returns Operator norm of the matrix.
+ *
+ * \eigenvalues_module
+ * This function computes the L2 operator norm of a matrix, which is also
+ * known as the spectral norm. The norm of a matrix \f$ A \f$ is defined to be
+ * \f[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \f]
+ * where the maximum is over all vectors and the norm on the right is the
+ * Euclidean vector norm. The norm equals the largest singular value, which is
+ * the square root of the largest eigenvalue of the positive semi-definite
+ * matrix \f$ A^*A \f$.
+ *
+ * The current implementation uses the eigenvalues of \f$ A^*A \f$, as computed
+ * by SelfAdjointView::eigenvalues(), to compute the operator norm of a
+ * matrix. The SelfAdjointView class provides a better algorithm for
+ * selfadjoint matrices.
+ *
+ * Example: \include MatrixBase_operatorNorm.cpp
+ * Output: \verbinclude MatrixBase_operatorNorm.out
+ *
+ * \sa SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()
+ */
+template<typename Derived>
+inline typename MatrixBase<Derived>::RealScalar
+MatrixBase<Derived>::operatorNorm() const
+{
+ using std::sqrt;
+ typename Derived::PlainObject m_eval(derived());
+ // FIXME if it is really guaranteed that the eigenvalues are already sorted,
+ // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.
+ return sqrt((m_eval*m_eval.adjoint())
+ .eval()
+ .template selfadjointView<Lower>()
+ .eigenvalues()
+ .maxCoeff()
+ );
+}
+
+/** \brief Computes the L2 operator norm
+ * \returns Operator norm of the matrix.
+ *
+ * \eigenvalues_module
+ * This function computes the L2 operator norm of a self-adjoint matrix. For a
+ * self-adjoint matrix, the operator norm is the largest eigenvalue.
+ *
+ * The current implementation uses the eigenvalues of the matrix, as computed
+ * by eigenvalues(), to compute the operator norm of the matrix.
+ *
+ * Example: \include SelfAdjointView_operatorNorm.cpp
+ * Output: \verbinclude SelfAdjointView_operatorNorm.out
+ *
+ * \sa eigenvalues(), MatrixBase::operatorNorm()
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline typename SelfAdjointView<MatrixType, UpLo>::RealScalar
+SelfAdjointView<MatrixType, UpLo>::operatorNorm() const
+{
+ return eigenvalues().cwiseAbs().maxCoeff();
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/Eigenvalues/RealQZ.h b/Eigen/src/Eigenvalues/RealQZ.h
new file mode 100644
index 0000000..aa3833e
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealQZ.h
@@ -0,0 +1,624 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REAL_QZ_H
+#define EIGEN_REAL_QZ_H
+
+namespace Eigen {
+
+ /** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class RealQZ
+ *
+ * \brief Performs a real QZ decomposition of a pair of square matrices
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * real QZ decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * Given a real square matrices A and B, this class computes the real QZ
+ * decomposition: \f$ A = Q S Z \f$, \f$ B = Q T Z \f$ where Q and Z are
+ * real orthogonal matrixes, T is upper-triangular matrix, and S is upper
+ * quasi-triangular matrix. An orthogonal matrix is a matrix whose
+ * inverse is equal to its transpose, \f$ U^{-1} = U^T \f$. A quasi-triangular
+ * matrix is a block-triangular matrix whose diagonal consists of 1-by-1
+ * blocks and 2-by-2 blocks where further reduction is impossible due to
+ * complex eigenvalues.
+ *
+ * The eigenvalues of the pencil \f$ A - z B \f$ can be obtained from
+ * 1x1 and 2x2 blocks on the diagonals of S and T.
+ *
+ * Call the function compute() to compute the real QZ decomposition of a
+ * given pair of matrices. Alternatively, you can use the
+ * RealQZ(const MatrixType& B, const MatrixType& B, bool computeQZ)
+ * constructor which computes the real QZ decomposition at construction
+ * time. Once the decomposition is computed, you can use the matrixS(),
+ * matrixT(), matrixQ() and matrixZ() functions to retrieve the matrices
+ * S, T, Q and Z in the decomposition. If computeQZ==false, some time
+ * is saved by not computing matrices Q and Z.
+ *
+ * Example: \include RealQZ_compute.cpp
+ * Output: \include RealQZ_compute.out
+ *
+ * \note The implementation is based on the algorithm in "Matrix Computations"
+ * by Gene H. Golub and Charles F. Van Loan, and a paper "An algorithm for
+ * generalized eigenvalue problems" by C.B.Moler and G.W.Stewart.
+ *
+ * \sa class RealSchur, class ComplexSchur, class EigenSolver, class ComplexEigenSolver
+ */
+
+ template<typename _MatrixType> class RealQZ
+ {
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef typename MatrixType::Index Index;
+
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose QZ decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ RealQZ(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime) :
+ m_S(size, size),
+ m_T(size, size),
+ m_Q(size, size),
+ m_Z(size, size),
+ m_workspace(size*2),
+ m_maxIters(400),
+ m_isInitialized(false)
+ { }
+
+ /** \brief Constructor; computes real QZ decomposition of given matrices
+ *
+ * \param[in] A Matrix A.
+ * \param[in] B Matrix B.
+ * \param[in] computeQZ If false, A and Z are not computed.
+ *
+ * This constructor calls compute() to compute the QZ decomposition.
+ */
+ RealQZ(const MatrixType& A, const MatrixType& B, bool computeQZ = true) :
+ m_S(A.rows(),A.cols()),
+ m_T(A.rows(),A.cols()),
+ m_Q(A.rows(),A.cols()),
+ m_Z(A.rows(),A.cols()),
+ m_workspace(A.rows()*2),
+ m_maxIters(400),
+ m_isInitialized(false) {
+ compute(A, B, computeQZ);
+ }
+
+ /** \brief Returns matrix Q in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix Q.
+ */
+ const MatrixType& matrixQ() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ eigen_assert(m_computeQZ && "The matrices Q and Z have not been computed during the QZ decomposition.");
+ return m_Q;
+ }
+
+ /** \brief Returns matrix Z in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix Z.
+ */
+ const MatrixType& matrixZ() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ eigen_assert(m_computeQZ && "The matrices Q and Z have not been computed during the QZ decomposition.");
+ return m_Z;
+ }
+
+ /** \brief Returns matrix S in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix S.
+ */
+ const MatrixType& matrixS() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_S;
+ }
+
+ /** \brief Returns matrix S in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix S.
+ */
+ const MatrixType& matrixT() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_T;
+ }
+
+ /** \brief Computes QZ decomposition of given matrix.
+ *
+ * \param[in] A Matrix A.
+ * \param[in] B Matrix B.
+ * \param[in] computeQZ If false, A and Z are not computed.
+ * \returns Reference to \c *this
+ */
+ RealQZ& compute(const MatrixType& A, const MatrixType& B, bool computeQZ = true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Returns number of performed QR-like iterations.
+ */
+ Index iterations() const
+ {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_global_iter;
+ }
+
+ /** Sets the maximal number of iterations allowed to converge to one eigenvalue
+ * or decouple the problem.
+ */
+ RealQZ& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ private:
+
+ MatrixType m_S, m_T, m_Q, m_Z;
+ Matrix<Scalar,Dynamic,1> m_workspace;
+ ComputationInfo m_info;
+ Index m_maxIters;
+ bool m_isInitialized;
+ bool m_computeQZ;
+ Scalar m_normOfT, m_normOfS;
+ Index m_global_iter;
+
+ typedef Matrix<Scalar,3,1> Vector3s;
+ typedef Matrix<Scalar,2,1> Vector2s;
+ typedef Matrix<Scalar,2,2> Matrix2s;
+ typedef JacobiRotation<Scalar> JRs;
+
+ void hessenbergTriangular();
+ void computeNorms();
+ Index findSmallSubdiagEntry(Index iu);
+ Index findSmallDiagEntry(Index f, Index l);
+ void splitOffTwoRows(Index i);
+ void pushDownZero(Index z, Index f, Index l);
+ void step(Index f, Index l, Index iter);
+
+ }; // RealQZ
+
+ /** \internal Reduces S and T to upper Hessenberg - triangular form */
+ template<typename MatrixType>
+ void RealQZ<MatrixType>::hessenbergTriangular()
+ {
+
+ const Index dim = m_S.cols();
+
+ // perform QR decomposition of T, overwrite T with R, save Q
+ HouseholderQR<MatrixType> qrT(m_T);
+ m_T = qrT.matrixQR();
+ m_T.template triangularView<StrictlyLower>().setZero();
+ m_Q = qrT.householderQ();
+ // overwrite S with Q* S
+ m_S.applyOnTheLeft(m_Q.adjoint());
+ // init Z as Identity
+ if (m_computeQZ)
+ m_Z = MatrixType::Identity(dim,dim);
+ // reduce S to upper Hessenberg with Givens rotations
+ for (Index j=0; j<=dim-3; j++) {
+ for (Index i=dim-1; i>=j+2; i--) {
+ JRs G;
+ // kill S(i,j)
+ if(m_S.coeff(i,j) != 0)
+ {
+ G.makeGivens(m_S.coeff(i-1,j), m_S.coeff(i,j), &m_S.coeffRef(i-1, j));
+ m_S.coeffRef(i,j) = Scalar(0.0);
+ m_S.rightCols(dim-j-1).applyOnTheLeft(i-1,i,G.adjoint());
+ m_T.rightCols(dim-i+1).applyOnTheLeft(i-1,i,G.adjoint());
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(i-1,i,G);
+ }
+ // kill T(i,i-1)
+ if(m_T.coeff(i,i-1)!=Scalar(0))
+ {
+ G.makeGivens(m_T.coeff(i,i), m_T.coeff(i,i-1), &m_T.coeffRef(i,i));
+ m_T.coeffRef(i,i-1) = Scalar(0.0);
+ m_S.applyOnTheRight(i,i-1,G);
+ m_T.topRows(i).applyOnTheRight(i,i-1,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(i,i-1,G.adjoint());
+ }
+ }
+ }
+ }
+
+ /** \internal Computes vector L1 norms of S and T when in Hessenberg-Triangular form already */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::computeNorms()
+ {
+ const Index size = m_S.cols();
+ m_normOfS = Scalar(0.0);
+ m_normOfT = Scalar(0.0);
+ for (Index j = 0; j < size; ++j)
+ {
+ m_normOfS += m_S.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();
+ m_normOfT += m_T.row(j).segment(j, size - j).cwiseAbs().sum();
+ }
+ }
+
+
+ /** \internal Look for single small sub-diagonal element S(res, res-1) and return res (or 0) */
+ template<typename MatrixType>
+ inline typename MatrixType::Index RealQZ<MatrixType>::findSmallSubdiagEntry(Index iu)
+ {
+ using std::abs;
+ Index res = iu;
+ while (res > 0)
+ {
+ Scalar s = abs(m_S.coeff(res-1,res-1)) + abs(m_S.coeff(res,res));
+ if (s == Scalar(0.0))
+ s = m_normOfS;
+ if (abs(m_S.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
+ break;
+ res--;
+ }
+ return res;
+ }
+
+ /** \internal Look for single small diagonal element T(res, res) for res between f and l, and return res (or f-1) */
+ template<typename MatrixType>
+ inline typename MatrixType::Index RealQZ<MatrixType>::findSmallDiagEntry(Index f, Index l)
+ {
+ using std::abs;
+ Index res = l;
+ while (res >= f) {
+ if (abs(m_T.coeff(res,res)) <= NumTraits<Scalar>::epsilon() * m_normOfT)
+ break;
+ res--;
+ }
+ return res;
+ }
+
+ /** \internal decouple 2x2 diagonal block in rows i, i+1 if eigenvalues are real */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::splitOffTwoRows(Index i)
+ {
+ using std::abs;
+ using std::sqrt;
+ const Index dim=m_S.cols();
+ if (abs(m_S.coeff(i+1,i))==Scalar(0))
+ return;
+ Index z = findSmallDiagEntry(i,i+1);
+ if (z==i-1)
+ {
+ // block of (S T^{-1})
+ Matrix2s STi = m_T.template block<2,2>(i,i).template triangularView<Upper>().
+ template solve<OnTheRight>(m_S.template block<2,2>(i,i));
+ Scalar p = Scalar(0.5)*(STi(0,0)-STi(1,1));
+ Scalar q = p*p + STi(1,0)*STi(0,1);
+ if (q>=0) {
+ Scalar z = sqrt(q);
+ // one QR-like iteration for ABi - lambda I
+ // is enough - when we know exact eigenvalue in advance,
+ // convergence is immediate
+ JRs G;
+ if (p>=0)
+ G.makeGivens(p + z, STi(1,0));
+ else
+ G.makeGivens(p - z, STi(1,0));
+ m_S.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());
+ m_T.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(i,i+1,G);
+
+ G.makeGivens(m_T.coeff(i+1,i+1), m_T.coeff(i+1,i));
+ m_S.topRows(i+2).applyOnTheRight(i+1,i,G);
+ m_T.topRows(i+2).applyOnTheRight(i+1,i,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(i+1,i,G.adjoint());
+
+ m_S.coeffRef(i+1,i) = Scalar(0.0);
+ m_T.coeffRef(i+1,i) = Scalar(0.0);
+ }
+ }
+ else
+ {
+ pushDownZero(z,i,i+1);
+ }
+ }
+
+ /** \internal use zero in T(z,z) to zero S(l,l-1), working in block f..l */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::pushDownZero(Index z, Index f, Index l)
+ {
+ JRs G;
+ const Index dim = m_S.cols();
+ for (Index zz=z; zz<l; zz++)
+ {
+ // push 0 down
+ Index firstColS = zz>f ? (zz-1) : zz;
+ G.makeGivens(m_T.coeff(zz, zz+1), m_T.coeff(zz+1, zz+1));
+ m_S.rightCols(dim-firstColS).applyOnTheLeft(zz,zz+1,G.adjoint());
+ m_T.rightCols(dim-zz).applyOnTheLeft(zz,zz+1,G.adjoint());
+ m_T.coeffRef(zz+1,zz+1) = Scalar(0.0);
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(zz,zz+1,G);
+ // kill S(zz+1, zz-1)
+ if (zz>f)
+ {
+ G.makeGivens(m_S.coeff(zz+1, zz), m_S.coeff(zz+1,zz-1));
+ m_S.topRows(zz+2).applyOnTheRight(zz, zz-1,G);
+ m_T.topRows(zz+1).applyOnTheRight(zz, zz-1,G);
+ m_S.coeffRef(zz+1,zz-1) = Scalar(0.0);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(zz,zz-1,G.adjoint());
+ }
+ }
+ // finally kill S(l,l-1)
+ G.makeGivens(m_S.coeff(l,l), m_S.coeff(l,l-1));
+ m_S.applyOnTheRight(l,l-1,G);
+ m_T.applyOnTheRight(l,l-1,G);
+ m_S.coeffRef(l,l-1)=Scalar(0.0);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(l,l-1,G.adjoint());
+ }
+
+ /** \internal QR-like iterative step for block f..l */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::step(Index f, Index l, Index iter)
+ {
+ using std::abs;
+ const Index dim = m_S.cols();
+
+ // x, y, z
+ Scalar x, y, z;
+ if (iter==10)
+ {
+ // Wilkinson ad hoc shift
+ const Scalar
+ a11=m_S.coeff(f+0,f+0), a12=m_S.coeff(f+0,f+1),
+ a21=m_S.coeff(f+1,f+0), a22=m_S.coeff(f+1,f+1), a32=m_S.coeff(f+2,f+1),
+ b12=m_T.coeff(f+0,f+1),
+ b11i=Scalar(1.0)/m_T.coeff(f+0,f+0),
+ b22i=Scalar(1.0)/m_T.coeff(f+1,f+1),
+ a87=m_S.coeff(l-1,l-2),
+ a98=m_S.coeff(l-0,l-1),
+ b77i=Scalar(1.0)/m_T.coeff(l-2,l-2),
+ b88i=Scalar(1.0)/m_T.coeff(l-1,l-1);
+ Scalar ss = abs(a87*b77i) + abs(a98*b88i),
+ lpl = Scalar(1.5)*ss,
+ ll = ss*ss;
+ x = ll + a11*a11*b11i*b11i - lpl*a11*b11i + a12*a21*b11i*b22i
+ - a11*a21*b12*b11i*b11i*b22i;
+ y = a11*a21*b11i*b11i - lpl*a21*b11i + a21*a22*b11i*b22i
+ - a21*a21*b12*b11i*b11i*b22i;
+ z = a21*a32*b11i*b22i;
+ }
+ else if (iter==16)
+ {
+ // another exceptional shift
+ x = m_S.coeff(f,f)/m_T.coeff(f,f)-m_S.coeff(l,l)/m_T.coeff(l,l) + m_S.coeff(l,l-1)*m_T.coeff(l-1,l) /
+ (m_T.coeff(l-1,l-1)*m_T.coeff(l,l));
+ y = m_S.coeff(f+1,f)/m_T.coeff(f,f);
+ z = 0;
+ }
+ else if (iter>23 && !(iter%8))
+ {
+ // extremely exceptional shift
+ x = internal::random<Scalar>(-1.0,1.0);
+ y = internal::random<Scalar>(-1.0,1.0);
+ z = internal::random<Scalar>(-1.0,1.0);
+ }
+ else
+ {
+ // Compute the shifts: (x,y,z,0...) = (AB^-1 - l1 I) (AB^-1 - l2 I) e1
+ // where l1 and l2 are the eigenvalues of the 2x2 matrix C = U V^-1 where
+ // U and V are 2x2 bottom right sub matrices of A and B. Thus:
+ // = AB^-1AB^-1 + l1 l2 I - (l1+l2)(AB^-1)
+ // = AB^-1AB^-1 + det(M) - tr(M)(AB^-1)
+ // Since we are only interested in having x, y, z with a correct ratio, we have:
+ const Scalar
+ a11 = m_S.coeff(f,f), a12 = m_S.coeff(f,f+1),
+ a21 = m_S.coeff(f+1,f), a22 = m_S.coeff(f+1,f+1),
+ a32 = m_S.coeff(f+2,f+1),
+
+ a88 = m_S.coeff(l-1,l-1), a89 = m_S.coeff(l-1,l),
+ a98 = m_S.coeff(l,l-1), a99 = m_S.coeff(l,l),
+
+ b11 = m_T.coeff(f,f), b12 = m_T.coeff(f,f+1),
+ b22 = m_T.coeff(f+1,f+1),
+
+ b88 = m_T.coeff(l-1,l-1), b89 = m_T.coeff(l-1,l),
+ b99 = m_T.coeff(l,l);
+
+ x = ( (a88/b88 - a11/b11)*(a99/b99 - a11/b11) - (a89/b99)*(a98/b88) + (a98/b88)*(b89/b99)*(a11/b11) ) * (b11/a21)
+ + a12/b22 - (a11/b11)*(b12/b22);
+ y = (a22/b22-a11/b11) - (a21/b11)*(b12/b22) - (a88/b88-a11/b11) - (a99/b99-a11/b11) + (a98/b88)*(b89/b99);
+ z = a32/b22;
+ }
+
+ JRs G;
+
+ for (Index k=f; k<=l-2; k++)
+ {
+ // variables for Householder reflections
+ Vector2s essential2;
+ Scalar tau, beta;
+
+ Vector3s hr(x,y,z);
+
+ // Q_k to annihilate S(k+1,k-1) and S(k+2,k-1)
+ hr.makeHouseholderInPlace(tau, beta);
+ essential2 = hr.template bottomRows<2>();
+ Index fc=(std::max)(k-1,Index(0)); // first col to update
+ m_S.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());
+ m_T.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());
+ if (m_computeQZ)
+ m_Q.template middleCols<3>(k).applyHouseholderOnTheRight(essential2, tau, m_workspace.data());
+ if (k>f)
+ m_S.coeffRef(k+2,k-1) = m_S.coeffRef(k+1,k-1) = Scalar(0.0);
+
+ // Z_{k1} to annihilate T(k+2,k+1) and T(k+2,k)
+ hr << m_T.coeff(k+2,k+2),m_T.coeff(k+2,k),m_T.coeff(k+2,k+1);
+ hr.makeHouseholderInPlace(tau, beta);
+ essential2 = hr.template bottomRows<2>();
+ {
+ Index lr = (std::min)(k+4,dim); // last row to update
+ Map<Matrix<Scalar,Dynamic,1> > tmp(m_workspace.data(),lr);
+ // S
+ tmp = m_S.template middleCols<2>(k).topRows(lr) * essential2;
+ tmp += m_S.col(k+2).head(lr);
+ m_S.col(k+2).head(lr) -= tau*tmp;
+ m_S.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();
+ // T
+ tmp = m_T.template middleCols<2>(k).topRows(lr) * essential2;
+ tmp += m_T.col(k+2).head(lr);
+ m_T.col(k+2).head(lr) -= tau*tmp;
+ m_T.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();
+ }
+ if (m_computeQZ)
+ {
+ // Z
+ Map<Matrix<Scalar,1,Dynamic> > tmp(m_workspace.data(),dim);
+ tmp = essential2.adjoint()*(m_Z.template middleRows<2>(k));
+ tmp += m_Z.row(k+2);
+ m_Z.row(k+2) -= tau*tmp;
+ m_Z.template middleRows<2>(k) -= essential2 * (tau*tmp);
+ }
+ m_T.coeffRef(k+2,k) = m_T.coeffRef(k+2,k+1) = Scalar(0.0);
+
+ // Z_{k2} to annihilate T(k+1,k)
+ G.makeGivens(m_T.coeff(k+1,k+1), m_T.coeff(k+1,k));
+ m_S.applyOnTheRight(k+1,k,G);
+ m_T.applyOnTheRight(k+1,k,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(k+1,k,G.adjoint());
+ m_T.coeffRef(k+1,k) = Scalar(0.0);
+
+ // update x,y,z
+ x = m_S.coeff(k+1,k);
+ y = m_S.coeff(k+2,k);
+ if (k < l-2)
+ z = m_S.coeff(k+3,k);
+ } // loop over k
+
+ // Q_{n-1} to annihilate y = S(l,l-2)
+ G.makeGivens(x,y);
+ m_S.applyOnTheLeft(l-1,l,G.adjoint());
+ m_T.applyOnTheLeft(l-1,l,G.adjoint());
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(l-1,l,G);
+ m_S.coeffRef(l,l-2) = Scalar(0.0);
+
+ // Z_{n-1} to annihilate T(l,l-1)
+ G.makeGivens(m_T.coeff(l,l),m_T.coeff(l,l-1));
+ m_S.applyOnTheRight(l,l-1,G);
+ m_T.applyOnTheRight(l,l-1,G);
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(l,l-1,G.adjoint());
+ m_T.coeffRef(l,l-1) = Scalar(0.0);
+ }
+
+
+ template<typename MatrixType>
+ RealQZ<MatrixType>& RealQZ<MatrixType>::compute(const MatrixType& A_in, const MatrixType& B_in, bool computeQZ)
+ {
+
+ const Index dim = A_in.cols();
+
+ eigen_assert (A_in.rows()==dim && A_in.cols()==dim
+ && B_in.rows()==dim && B_in.cols()==dim
+ && "Need square matrices of the same dimension");
+
+ m_isInitialized = true;
+ m_computeQZ = computeQZ;
+ m_S = A_in; m_T = B_in;
+ m_workspace.resize(dim*2);
+ m_global_iter = 0;
+
+ // entrance point: hessenberg triangular decomposition
+ hessenbergTriangular();
+ // compute L1 vector norms of T, S into m_normOfS, m_normOfT
+ computeNorms();
+
+ Index l = dim-1,
+ f,
+ local_iter = 0;
+
+ while (l>0 && local_iter<m_maxIters)
+ {
+ f = findSmallSubdiagEntry(l);
+ // now rows and columns f..l (including) decouple from the rest of the problem
+ if (f>0) m_S.coeffRef(f,f-1) = Scalar(0.0);
+ if (f == l) // One root found
+ {
+ l--;
+ local_iter = 0;
+ }
+ else if (f == l-1) // Two roots found
+ {
+ splitOffTwoRows(f);
+ l -= 2;
+ local_iter = 0;
+ }
+ else // No convergence yet
+ {
+ // if there's zero on diagonal of T, we can isolate an eigenvalue with Givens rotations
+ Index z = findSmallDiagEntry(f,l);
+ if (z>=f)
+ {
+ // zero found
+ pushDownZero(z,f,l);
+ }
+ else
+ {
+ // We are sure now that S.block(f,f, l-f+1,l-f+1) is underuced upper-Hessenberg
+ // and T.block(f,f, l-f+1,l-f+1) is invertible uper-triangular, which allows to
+ // apply a QR-like iteration to rows and columns f..l.
+ step(f,l, local_iter);
+ local_iter++;
+ m_global_iter++;
+ }
+ }
+ }
+ // check if we converged before reaching iterations limit
+ m_info = (local_iter<m_maxIters) ? Success : NoConvergence;
+ return *this;
+ } // end compute
+
+} // end namespace Eigen
+
+#endif //EIGEN_REAL_QZ
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
new file mode 100644
index 0000000..16d3875
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -0,0 +1,525 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REAL_SCHUR_H
+#define EIGEN_REAL_SCHUR_H
+
+#include "./HessenbergDecomposition.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class RealSchur
+ *
+ * \brief Performs a real Schur decomposition of a square matrix
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * real Schur decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * Given a real square matrix A, this class computes the real Schur
+ * decomposition: \f$ A = U T U^T \f$ where U is a real orthogonal matrix and
+ * T is a real quasi-triangular matrix. An orthogonal matrix is a matrix whose
+ * inverse is equal to its transpose, \f$ U^{-1} = U^T \f$. A quasi-triangular
+ * matrix is a block-triangular matrix whose diagonal consists of 1-by-1
+ * blocks and 2-by-2 blocks with complex eigenvalues. The eigenvalues of the
+ * blocks on the diagonal of T are the same as the eigenvalues of the matrix
+ * A, and thus the real Schur decomposition is used in EigenSolver to compute
+ * the eigendecomposition of a matrix.
+ *
+ * Call the function compute() to compute the real Schur decomposition of a
+ * given matrix. Alternatively, you can use the RealSchur(const MatrixType&, bool)
+ * constructor which computes the real Schur decomposition at construction
+ * time. Once the decomposition is computed, you can use the matrixU() and
+ * matrixT() functions to retrieve the matrices U and T in the decomposition.
+ *
+ * The documentation of RealSchur(const MatrixType&, bool) contains an example
+ * of the typical use of this class.
+ *
+ * \note The implementation is adapted from
+ * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
+ * Their code is based on EISPACK.
+ *
+ * \sa class ComplexSchur, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename _MatrixType> class RealSchur
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef typename MatrixType::Index Index;
+
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ RealSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
+ : m_matT(size, size),
+ m_matU(size, size),
+ m_workspaceVector(size),
+ m_hess(size),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ { }
+
+ /** \brief Constructor; computes real Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ *
+ * This constructor calls compute() to compute the Schur decomposition.
+ *
+ * Example: \include RealSchur_RealSchur_MatrixType.cpp
+ * Output: \verbinclude RealSchur_RealSchur_MatrixType.out
+ */
+ RealSchur(const MatrixType& matrix, bool computeU = true)
+ : m_matT(matrix.rows(),matrix.cols()),
+ m_matU(matrix.rows(),matrix.cols()),
+ m_workspaceVector(matrix.rows()),
+ m_hess(matrix.rows()),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {
+ compute(matrix, computeU);
+ }
+
+ /** \brief Returns the orthogonal matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix U.
+ *
+ * \pre Either the constructor RealSchur(const MatrixType&, bool) or the
+ * member function compute(const MatrixType&, bool) has been called before
+ * to compute the Schur decomposition of a matrix, and \p computeU was set
+ * to true (the default value).
+ *
+ * \sa RealSchur(const MatrixType&, bool) for an example
+ */
+ const MatrixType& matrixU() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the RealSchur decomposition.");
+ return m_matU;
+ }
+
+ /** \brief Returns the quasi-triangular matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix T.
+ *
+ * \pre Either the constructor RealSchur(const MatrixType&, bool) or the
+ * member function compute(const MatrixType&, bool) has been called before
+ * to compute the Schur decomposition of a matrix.
+ *
+ * \sa RealSchur(const MatrixType&, bool) for an example
+ */
+ const MatrixType& matrixT() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ return m_matT;
+ }
+
+ /** \brief Computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ * \returns Reference to \c *this
+ *
+ * The Schur decomposition is computed by first reducing the matrix to
+ * Hessenberg form using the class HessenbergDecomposition. The Hessenberg
+ * matrix is then reduced to triangular form by performing Francis QR
+ * iterations with implicit double shift. The cost of computing the Schur
+ * decomposition depends on the number of iterations; as a rough guide, it
+ * may be taken to be \f$25n^3\f$ flops if \a computeU is true and
+ * \f$10n^3\f$ flops if \a computeU is false.
+ *
+ * Example: \include RealSchur_compute.cpp
+ * Output: \verbinclude RealSchur_compute.out
+ *
+ * \sa compute(const MatrixType&, bool, Index)
+ */
+ RealSchur& compute(const MatrixType& matrix, bool computeU = true);
+
+ /** \brief Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T
+ * \param[in] matrixH Matrix in Hessenberg form H
+ * \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
+ * \param computeU Computes the matriX U of the Schur vectors
+ * \return Reference to \c *this
+ *
+ * This routine assumes that the matrix is already reduced in Hessenberg form matrixH
+ * using either the class HessenbergDecomposition or another mean.
+ * It computes the upper quasi-triangular matrix T of the Schur decomposition of H
+ * When computeU is true, this routine computes the matrix U such that
+ * A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
+ *
+ * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
+ * is not available, the user should give an identity matrix (Q.setIdentity())
+ *
+ * \sa compute(const MatrixType&, bool)
+ */
+ template<typename HessMatrixType, typename OrthMatrixType>
+ RealSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU);
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Sets the maximum number of iterations allowed.
+ *
+ * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size
+ * of the matrix.
+ */
+ RealSchur& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_maxIters;
+ }
+
+ /** \brief Maximum number of iterations per row.
+ *
+ * If not otherwise specified, the maximum number of iterations is this number times the size of the
+ * matrix. It is currently set to 40.
+ */
+ static const int m_maxIterationsPerRow = 40;
+
+ private:
+
+ MatrixType m_matT;
+ MatrixType m_matU;
+ ColumnVectorType m_workspaceVector;
+ HessenbergDecomposition<MatrixType> m_hess;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_matUisUptodate;
+ Index m_maxIters;
+
+ typedef Matrix<Scalar,3,1> Vector3s;
+
+ Scalar computeNormOfT();
+ Index findSmallSubdiagEntry(Index iu);
+ void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift);
+ void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);
+ void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);
+ void performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace);
+};
+
+
+template<typename MatrixType>
+RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix, bool computeU)
+{
+ eigen_assert(matrix.cols() == matrix.rows());
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * matrix.rows();
+
+ // Step 1. Reduce to Hessenberg form
+ m_hess.compute(matrix);
+
+ // Step 2. Reduce to real Schur form
+ computeFromHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU);
+
+ return *this;
+}
+template<typename MatrixType>
+template<typename HessMatrixType, typename OrthMatrixType>
+RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
+{
+ m_matT = matrixH;
+ if(computeU)
+ m_matU = matrixQ;
+
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * matrixH.rows();
+ m_workspaceVector.resize(m_matT.cols());
+ Scalar* workspace = &m_workspaceVector.coeffRef(0);
+
+ // The matrix m_matT is divided in three parts.
+ // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
+ // Rows il,...,iu is the part we are working on (the active window).
+ // Rows iu+1,...,end are already brought in triangular form.
+ Index iu = m_matT.cols() - 1;
+ Index iter = 0; // iteration count for current eigenvalue
+ Index totalIter = 0; // iteration count for whole matrix
+ Scalar exshift(0); // sum of exceptional shifts
+ Scalar norm = computeNormOfT();
+
+ if(norm!=0)
+ {
+ while (iu >= 0)
+ {
+ Index il = findSmallSubdiagEntry(iu);
+
+ // Check for convergence
+ if (il == iu) // One root found
+ {
+ m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift;
+ if (iu > 0)
+ m_matT.coeffRef(iu, iu-1) = Scalar(0);
+ iu--;
+ iter = 0;
+ }
+ else if (il == iu-1) // Two roots found
+ {
+ splitOffTwoRows(iu, computeU, exshift);
+ iu -= 2;
+ iter = 0;
+ }
+ else // No convergence yet
+ {
+ // The firstHouseholderVector vector has to be initialized to something to get rid of a silly GCC warning (-O1 -Wall -DNDEBUG )
+ Vector3s firstHouseholderVector(0,0,0), shiftInfo;
+ computeShift(iu, iter, exshift, shiftInfo);
+ iter = iter + 1;
+ totalIter = totalIter + 1;
+ if (totalIter > maxIters) break;
+ Index im;
+ initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
+ performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
+ }
+ }
+ }
+ if(totalIter <= maxIters)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+ return *this;
+}
+
+/** \internal Computes and returns vector L1 norm of T */
+template<typename MatrixType>
+inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()
+{
+ const Index size = m_matT.cols();
+ // FIXME to be efficient the following would requires a triangular reduxion code
+ // Scalar norm = m_matT.upper().cwiseAbs().sum()
+ // + m_matT.bottomLeftCorner(size-1,size-1).diagonal().cwiseAbs().sum();
+ Scalar norm(0);
+ for (Index j = 0; j < size; ++j)
+ norm += m_matT.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();
+ return norm;
+}
+
+/** \internal Look for single small sub-diagonal element and returns its index */
+template<typename MatrixType>
+inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu)
+{
+ using std::abs;
+ Index res = iu;
+ while (res > 0)
+ {
+ Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));
+ if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s)
+ break;
+ res--;
+ }
+ return res;
+}
+
+/** \internal Update T given that rows iu-1 and iu decouple from the rest. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift)
+{
+ using std::sqrt;
+ using std::abs;
+ const Index size = m_matT.cols();
+
+ // The eigenvalues of the 2x2 matrix [a b; c d] are
+ // trace +/- sqrt(discr/4) where discr = tr^2 - 4*det, tr = a + d, det = ad - bc
+ Scalar p = Scalar(0.5) * (m_matT.coeff(iu-1,iu-1) - m_matT.coeff(iu,iu));
+ Scalar q = p * p + m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu); // q = tr^2 / 4 - det = discr/4
+ m_matT.coeffRef(iu,iu) += exshift;
+ m_matT.coeffRef(iu-1,iu-1) += exshift;
+
+ if (q >= Scalar(0)) // Two real eigenvalues
+ {
+ Scalar z = sqrt(abs(q));
+ JacobiRotation<Scalar> rot;
+ if (p >= Scalar(0))
+ rot.makeGivens(p + z, m_matT.coeff(iu, iu-1));
+ else
+ rot.makeGivens(p - z, m_matT.coeff(iu, iu-1));
+
+ m_matT.rightCols(size-iu+1).applyOnTheLeft(iu-1, iu, rot.adjoint());
+ m_matT.topRows(iu+1).applyOnTheRight(iu-1, iu, rot);
+ m_matT.coeffRef(iu, iu-1) = Scalar(0);
+ if (computeU)
+ m_matU.applyOnTheRight(iu-1, iu, rot);
+ }
+
+ if (iu > 1)
+ m_matT.coeffRef(iu-1, iu-2) = Scalar(0);
+}
+
+/** \internal Form shift in shiftInfo, and update exshift if an exceptional shift is performed. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo)
+{
+ using std::sqrt;
+ using std::abs;
+ shiftInfo.coeffRef(0) = m_matT.coeff(iu,iu);
+ shiftInfo.coeffRef(1) = m_matT.coeff(iu-1,iu-1);
+ shiftInfo.coeffRef(2) = m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);
+
+ // Wilkinson's original ad hoc shift
+ if (iter == 10)
+ {
+ exshift += shiftInfo.coeff(0);
+ for (Index i = 0; i <= iu; ++i)
+ m_matT.coeffRef(i,i) -= shiftInfo.coeff(0);
+ Scalar s = abs(m_matT.coeff(iu,iu-1)) + abs(m_matT.coeff(iu-1,iu-2));
+ shiftInfo.coeffRef(0) = Scalar(0.75) * s;
+ shiftInfo.coeffRef(1) = Scalar(0.75) * s;
+ shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;
+ }
+
+ // MATLAB's new ad hoc shift
+ if (iter == 30)
+ {
+ Scalar s = (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
+ s = s * s + shiftInfo.coeff(2);
+ if (s > Scalar(0))
+ {
+ s = sqrt(s);
+ if (shiftInfo.coeff(1) < shiftInfo.coeff(0))
+ s = -s;
+ s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
+ s = shiftInfo.coeff(0) - shiftInfo.coeff(2) / s;
+ exshift += s;
+ for (Index i = 0; i <= iu; ++i)
+ m_matT.coeffRef(i,i) -= s;
+ shiftInfo.setConstant(Scalar(0.964));
+ }
+ }
+}
+
+/** \internal Compute index im at which Francis QR step starts and the first Householder vector. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector)
+{
+ using std::abs;
+ Vector3s& v = firstHouseholderVector; // alias to save typing
+
+ for (im = iu-2; im >= il; --im)
+ {
+ const Scalar Tmm = m_matT.coeff(im,im);
+ const Scalar r = shiftInfo.coeff(0) - Tmm;
+ const Scalar s = shiftInfo.coeff(1) - Tmm;
+ v.coeffRef(0) = (r * s - shiftInfo.coeff(2)) / m_matT.coeff(im+1,im) + m_matT.coeff(im,im+1);
+ v.coeffRef(1) = m_matT.coeff(im+1,im+1) - Tmm - r - s;
+ v.coeffRef(2) = m_matT.coeff(im+2,im+1);
+ if (im == il) {
+ break;
+ }
+ const Scalar lhs = m_matT.coeff(im,im-1) * (abs(v.coeff(1)) + abs(v.coeff(2)));
+ const Scalar rhs = v.coeff(0) * (abs(m_matT.coeff(im-1,im-1)) + abs(Tmm) + abs(m_matT.coeff(im+1,im+1)));
+ if (abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)
+ break;
+ }
+}
+
+/** \internal Perform a Francis QR step involving rows il:iu and columns im:iu. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace)
+{
+ eigen_assert(im >= il);
+ eigen_assert(im <= iu-2);
+
+ const Index size = m_matT.cols();
+
+ for (Index k = im; k <= iu-2; ++k)
+ {
+ bool firstIteration = (k == im);
+
+ Vector3s v;
+ if (firstIteration)
+ v = firstHouseholderVector;
+ else
+ v = m_matT.template block<3,1>(k,k-1);
+
+ Scalar tau, beta;
+ Matrix<Scalar, 2, 1> ess;
+ v.makeHouseholder(ess, tau, beta);
+
+ if (beta != Scalar(0)) // if v is not zero
+ {
+ if (firstIteration && k > il)
+ m_matT.coeffRef(k,k-1) = -m_matT.coeff(k,k-1);
+ else if (!firstIteration)
+ m_matT.coeffRef(k,k-1) = beta;
+
+ // These Householder transformations form the O(n^3) part of the algorithm
+ m_matT.block(k, k, 3, size-k).applyHouseholderOnTheLeft(ess, tau, workspace);
+ m_matT.block(0, k, (std::min)(iu,k+3) + 1, 3).applyHouseholderOnTheRight(ess, tau, workspace);
+ if (computeU)
+ m_matU.block(0, k, size, 3).applyHouseholderOnTheRight(ess, tau, workspace);
+ }
+ }
+
+ Matrix<Scalar, 2, 1> v = m_matT.template block<2,1>(iu-1, iu-2);
+ Scalar tau, beta;
+ Matrix<Scalar, 1, 1> ess;
+ v.makeHouseholder(ess, tau, beta);
+
+ if (beta != Scalar(0)) // if v is not zero
+ {
+ m_matT.coeffRef(iu-1, iu-2) = beta;
+ m_matT.block(iu-1, iu-1, 2, size-iu+1).applyHouseholderOnTheLeft(ess, tau, workspace);
+ m_matT.block(0, iu-1, iu+1, 2).applyHouseholderOnTheRight(ess, tau, workspace);
+ if (computeU)
+ m_matU.block(0, iu-1, size, 2).applyHouseholderOnTheRight(ess, tau, workspace);
+ }
+
+ // clean up pollution due to round-off errors
+ for (Index i = im+2; i <= iu; ++i)
+ {
+ m_matT.coeffRef(i,i-2) = Scalar(0);
+ if (i > im+2)
+ m_matT.coeffRef(i,i-3) = Scalar(0);
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REAL_SCHUR_H
diff --git a/Eigen/src/Eigenvalues/RealSchur_MKL.h b/Eigen/src/Eigenvalues/RealSchur_MKL.h
new file mode 100644
index 0000000..ad97364
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealSchur_MKL.h
@@ -0,0 +1,83 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Real Schur needed to real unsymmetrical eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_REAL_SCHUR_MKL_H
+#define EIGEN_REAL_SCHUR_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_SCHUR_REAL(EIGTYPE, MKLTYPE, MKLPREFIX, MKLPREFIX_U, EIGCOLROW, MKLCOLROW) \
+template<> inline \
+RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW>& matrix, bool computeU) \
+{ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \
+ typedef MatrixType::Scalar Scalar; \
+ typedef MatrixType::RealScalar RealScalar; \
+\
+ eigen_assert(matrix.cols() == matrix.rows()); \
+\
+ lapack_int n = matrix.cols(), sdim, info; \
+ lapack_int lda = matrix.outerStride(); \
+ lapack_int matrix_order = MKLCOLROW; \
+ char jobvs, sort='N'; \
+ LAPACK_##MKLPREFIX_U##_SELECT2 select = 0; \
+ jobvs = (computeU) ? 'V' : 'N'; \
+ m_matU.resize(n, n); \
+ lapack_int ldvs = m_matU.outerStride(); \
+ m_matT = matrix; \
+ Matrix<EIGTYPE, Dynamic, Dynamic> wr, wi; \
+ wr.resize(n, 1); wi.resize(n, 1); \
+ info = LAPACKE_##MKLPREFIX##gees( matrix_order, jobvs, sort, select, n, (MKLTYPE*)m_matT.data(), lda, &sdim, (MKLTYPE*)wr.data(), (MKLTYPE*)wi.data(), (MKLTYPE*)m_matU.data(), ldvs ); \
+ if(info == 0) \
+ m_info = Success; \
+ else \
+ m_info = NoConvergence; \
+\
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+\
+}
+
+EIGEN_MKL_SCHUR_REAL(double, double, d, D, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SCHUR_REAL(float, float, s, S, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SCHUR_REAL(double, double, d, D, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_SCHUR_REAL(float, float, s, S, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_REAL_SCHUR_MKL_H
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
new file mode 100644
index 0000000..c2e76c8
--- /dev/null
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -0,0 +1,798 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTEIGENSOLVER_H
+#define EIGEN_SELFADJOINTEIGENSOLVER_H
+
+#include "./Tridiagonalization.h"
+
+namespace Eigen {
+
+template<typename _MatrixType>
+class GeneralizedSelfAdjointEigenSolver;
+
+namespace internal {
+template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues;
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class SelfAdjointEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of selfadjoint matrices
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template.
+ *
+ * A matrix \f$ A \f$ is selfadjoint if it equals its adjoint. For real
+ * matrices, this means that the matrix is symmetric: it equals its
+ * transpose. This class computes the eigenvalues and eigenvectors of a
+ * selfadjoint matrix. These are the scalars \f$ \lambda \f$ and vectors
+ * \f$ v \f$ such that \f$ Av = \lambda v \f$. The eigenvalues of a
+ * selfadjoint matrix are always real. If \f$ D \f$ is a diagonal matrix with
+ * the eigenvalues on the diagonal, and \f$ V \f$ is a matrix with the
+ * eigenvectors as its columns, then \f$ A = V D V^{-1} \f$ (for selfadjoint
+ * matrices, the matrix \f$ V \f$ is always invertible). This is called the
+ * eigendecomposition.
+ *
+ * The algorithm exploits the fact that the matrix is selfadjoint, making it
+ * faster and more accurate than the general purpose eigenvalue algorithms
+ * implemented in EigenSolver and ComplexEigenSolver.
+ *
+ * Only the \b lower \b triangular \b part of the input matrix is referenced.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * SelfAdjointEigenSolver(const MatrixType&, int) constructor which computes
+ * the eigenvalues and eigenvectors at construction time. Once the eigenvalue
+ * and eigenvectors are computed, they can be retrieved with the eigenvalues()
+ * and eigenvectors() functions.
+ *
+ * The documentation for SelfAdjointEigenSolver(const MatrixType&, int)
+ * contains an example of the typical use of this class.
+ *
+ * To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and
+ * the likes, see the class GeneralizedSelfAdjointEigenSolver.
+ *
+ * \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver
+ */
+template<typename _MatrixType> class SelfAdjointEigenSolver
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type \p _MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Real scalar type for \p _MatrixType.
+ *
+ * This is just \c Scalar if #Scalar is real (e.g., \c float or
+ * \c double), and the type of the real part of \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ friend struct internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #RealScalar.
+ * The length of the vector is the size of \p _MatrixType.
+ */
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
+ typedef Tridiagonalization<MatrixType> TridiagonalizationType;
+
+ /** \brief Default constructor for fixed-size matrices.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). This constructor
+ * can only be used if \p _MatrixType is a fixed-size matrix; use
+ * SelfAdjointEigenSolver(Index) for dynamic-size matrices.
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver.out
+ */
+ SelfAdjointEigenSolver()
+ : m_eivec(),
+ m_eivalues(),
+ m_subdiag(),
+ m_isInitialized(false)
+ { }
+
+ /** \brief Constructor, pre-allocates memory for dynamic-size matrices.
+ *
+ * \param [in] size Positive integer, size of the matrix whose
+ * eigenvalues and eigenvectors will be computed.
+ *
+ * This constructor is useful for dynamic-size matrices, when the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a wrong
+ * \p size, but it may impair performance.
+ *
+ * \sa compute() for an example
+ */
+ SelfAdjointEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_subdiag(size > 1 ? size - 1 : 1),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
+ * be computed. Only the lower triangular part of the matrix is referenced.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ *
+ * This constructor calls compute(const MatrixType&, int) to compute the
+ * eigenvalues of the matrix \p matrix. The eigenvectors are computed if
+ * \p options equals #ComputeEigenvectors.
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.out
+ *
+ * \sa compute(const MatrixType&, int)
+ */
+ SelfAdjointEigenSolver(const MatrixType& matrix, int options = ComputeEigenvectors)
+ : m_eivec(matrix.rows(), matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),
+ m_isInitialized(false)
+ {
+ compute(matrix, options);
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
+ * be computed. Only the lower triangular part of the matrix is referenced.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of \p matrix. The eigenvalues()
+ * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
+ * then the eigenvectors are also computed and can be retrieved by
+ * calling eigenvectors().
+ *
+ * This implementation uses a symmetric QR algorithm. The matrix is first
+ * reduced to tridiagonal form using the Tridiagonalization class. The
+ * tridiagonal matrix is then brought to diagonal form with implicit
+ * symmetric QR steps with Wilkinson shift. Details can be found in
+ * Section 8.3 of Golub \& Van Loan, <i>%Matrix Computations</i>.
+ *
+ * The cost of the computation is about \f$ 9n^3 \f$ if the eigenvectors
+ * are required and \f$ 4n^3/3 \f$ if they are not required.
+ *
+ * This method reuses the memory in the SelfAdjointEigenSolver object that
+ * was allocated when the object was constructed, if the size of the
+ * matrix does not change.
+ *
+ * Example: \include SelfAdjointEigenSolver_compute_MatrixType.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType.out
+ *
+ * \sa SelfAdjointEigenSolver(const MatrixType&, int)
+ */
+ SelfAdjointEigenSolver& compute(const MatrixType& matrix, int options = ComputeEigenvectors);
+
+ /** \brief Computes eigendecomposition of given matrix using a direct algorithm
+ *
+ * This is a variant of compute(const MatrixType&, int options) which
+ * directly solves the underlying polynomial equation.
+ *
+ * Currently only 3x3 matrices for which the sizes are known at compile time are supported (e.g., Matrix3d).
+ *
+ * This method is usually significantly faster than the QR algorithm
+ * but it might also be less accurate. It is also worth noting that
+ * for 3x3 matrices it involves trigonometric operations which are
+ * not necessarily available for all scalar types.
+ *
+ * \sa compute(const MatrixType&, int options)
+ */
+ SelfAdjointEigenSolver& computeDirect(const MatrixType& matrix, int options = ComputeEigenvectors);
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns A const reference to the matrix whose columns are the eigenvectors.
+ *
+ * \pre The eigenvectors have been computed before.
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. If
+ * this object was used to solve the eigenproblem for the selfadjoint
+ * matrix \f$ A \f$, then the matrix returned by this function is the
+ * matrix \f$ V \f$ in the eigendecomposition \f$ A = V D V^{-1} \f$.
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
+ *
+ * \sa eigenvalues()
+ */
+ const MatrixType& eigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre The eigenvalues have been computed before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are sorted in increasing order.
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
+ *
+ * \sa eigenvectors(), MatrixBase::eigenvalues()
+ */
+ const RealVectorType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes the positive-definite square root of the matrix.
+ *
+ * \returns the positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * The square root of a positive-definite matrix \f$ A \f$ is the
+ * positive-definite matrix whose square equals \f$ A \f$. This function
+ * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
+ * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
+ *
+ * \sa operatorInverseSqrt(),
+ * \ref MatrixFunctions_Module "MatrixFunctions Module"
+ */
+ MatrixType operatorSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Computes the inverse square root of the matrix.
+ *
+ * \returns the inverse positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
+ * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
+ * cheaper than first computing the square root with operatorSqrt() and
+ * then its inverse with MatrixBase::inverse().
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
+ *
+ * \sa operatorSqrt(), MatrixBase::inverse(),
+ * \ref MatrixFunctions_Module "MatrixFunctions Module"
+ */
+ MatrixType operatorInverseSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Maximum number of iterations.
+ *
+ * The algorithm terminates if it does not converge within m_maxIterations * n iterations, where n
+ * denotes the size of the matrix. This value is currently set to 30 (copied from LAPACK).
+ */
+ static const int m_maxIterations = 30;
+
+ #ifdef EIGEN2_SUPPORT
+ SelfAdjointEigenSolver(const MatrixType& matrix, bool computeEigenvectors)
+ : m_eivec(matrix.rows(), matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),
+ m_isInitialized(false)
+ {
+ compute(matrix, computeEigenvectors);
+ }
+
+ SelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true)
+ : m_eivec(matA.cols(), matA.cols()),
+ m_eivalues(matA.cols()),
+ m_subdiag(matA.cols() > 1 ? matA.cols() - 1 : 1),
+ m_isInitialized(false)
+ {
+ static_cast<GeneralizedSelfAdjointEigenSolver<MatrixType>*>(this)->compute(matA, matB, computeEigenvectors ? ComputeEigenvectors : EigenvaluesOnly);
+ }
+
+ void compute(const MatrixType& matrix, bool computeEigenvectors)
+ {
+ compute(matrix, computeEigenvectors ? ComputeEigenvectors : EigenvaluesOnly);
+ }
+
+ void compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true)
+ {
+ compute(matA, matB, computeEigenvectors ? ComputeEigenvectors : EigenvaluesOnly);
+ }
+ #endif // EIGEN2_SUPPORT
+
+ protected:
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_eivec;
+ RealVectorType m_eivalues;
+ typename TridiagonalizationType::SubDiagonalType m_subdiag;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+};
+
+/** \internal
+ *
+ * \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ * Performs a QR step on a tridiagonal symmetric matrix represented as a
+ * pair of two vectors \a diag and \a subdiag.
+ *
+ * \param matA the input selfadjoint matrix
+ * \param hCoeffs returned Householder coefficients
+ *
+ * For compilation efficiency reasons, this procedure does not use eigen expression
+ * for its arguments.
+ *
+ * Implemented from Golub's "Matrix Computations", algorithm 8.3.2:
+ * "implicit symmetric QR step with Wilkinson shift"
+ */
+namespace internal {
+template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n);
+}
+
+template<typename MatrixType>
+SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
+::compute(const MatrixType& matrix, int options)
+{
+ check_template_parameters();
+
+ using std::abs;
+ eigen_assert(matrix.cols() == matrix.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+ Index n = matrix.cols();
+ m_eivalues.resize(n,1);
+
+ if(n==1)
+ {
+ m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0));
+ if(computeEigenvectors)
+ m_eivec.setOnes(n,n);
+ m_info = Success;
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+ }
+
+ // declare some aliases
+ RealVectorType& diag = m_eivalues;
+ MatrixType& mat = m_eivec;
+
+ // map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ mat = matrix.template triangularView<Lower>();
+ RealScalar scale = mat.cwiseAbs().maxCoeff();
+ if(scale==RealScalar(0)) scale = RealScalar(1);
+ mat.template triangularView<Lower>() /= scale;
+ m_subdiag.resize(n-1);
+ internal::tridiagonalization_inplace(mat, diag, m_subdiag, computeEigenvectors);
+
+ Index end = n-1;
+ Index start = 0;
+ Index iter = 0; // total number of iterations
+
+ while (end>0)
+ {
+ for (Index i = start; i<end; ++i)
+ if (internal::isMuchSmallerThan(abs(m_subdiag[i]),(abs(diag[i])+abs(diag[i+1]))))
+ m_subdiag[i] = 0;
+
+ // find the largest unreduced block
+ while (end>0 && m_subdiag[end-1]==0)
+ {
+ end--;
+ }
+ if (end<=0)
+ break;
+
+ // if we spent too many iterations, we give up
+ iter++;
+ if(iter > m_maxIterations * n) break;
+
+ start = end - 1;
+ while (start>0 && m_subdiag[start-1]!=0)
+ start--;
+
+ internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
+ }
+
+ if (iter <= m_maxIterations * n)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ // Sort eigenvalues and corresponding vectors.
+ // TODO make the sort optional ?
+ // TODO use a better sort algorithm !!
+ if (m_info == Success)
+ {
+ for (Index i = 0; i < n-1; ++i)
+ {
+ Index k;
+ m_eivalues.segment(i,n-i).minCoeff(&k);
+ if (k > 0)
+ {
+ std::swap(m_eivalues[i], m_eivalues[k+i]);
+ if(computeEigenvectors)
+ m_eivec.col(i).swap(m_eivec.col(k+i));
+ }
+ }
+ }
+
+ // scale back the eigen values
+ m_eivalues *= scale;
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+}
+
+
+namespace internal {
+
+template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues
+{
+ static inline void run(SolverType& eig, const typename SolverType::MatrixType& A, int options)
+ { eig.compute(A,options); }
+};
+
+template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3,false>
+{
+ typedef typename SolverType::MatrixType MatrixType;
+ typedef typename SolverType::RealVectorType VectorType;
+ typedef typename SolverType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \internal
+ * Computes the roots of the characteristic polynomial of \a m.
+ * For numerical stability m.trace() should be near zero and to avoid over- or underflow m should be normalized.
+ */
+ static inline void computeRoots(const MatrixType& m, VectorType& roots)
+ {
+ using std::sqrt;
+ using std::atan2;
+ using std::cos;
+ using std::sin;
+ const Scalar s_inv3 = Scalar(1.0)/Scalar(3.0);
+ const Scalar s_sqrt3 = sqrt(Scalar(3.0));
+
+ // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
+ // eigenvalues are the roots to this equation, all guaranteed to be
+ // real-valued, because the matrix is symmetric.
+ Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(1,0)*m(2,0)*m(2,1) - m(0,0)*m(2,1)*m(2,1) - m(1,1)*m(2,0)*m(2,0) - m(2,2)*m(1,0)*m(1,0);
+ Scalar c1 = m(0,0)*m(1,1) - m(1,0)*m(1,0) + m(0,0)*m(2,2) - m(2,0)*m(2,0) + m(1,1)*m(2,2) - m(2,1)*m(2,1);
+ Scalar c2 = m(0,0) + m(1,1) + m(2,2);
+
+ // Construct the parameters used in classifying the roots of the equation
+ // and in solving the equation for the roots in closed form.
+ Scalar c2_over_3 = c2*s_inv3;
+ Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;
+ if(a_over_3<Scalar(0))
+ a_over_3 = Scalar(0);
+
+ Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
+
+ Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
+ if(q<Scalar(0))
+ q = Scalar(0);
+
+ // Compute the eigenvalues by solving for the roots of the polynomial.
+ Scalar rho = sqrt(a_over_3);
+ Scalar theta = atan2(sqrt(q),half_b)*s_inv3; // since sqrt(q) > 0, atan2 is in [0, pi] and theta is in [0, pi/3]
+ Scalar cos_theta = cos(theta);
+ Scalar sin_theta = sin(theta);
+ // roots are already sorted, since cos is monotonically decreasing on [0, pi]
+ roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)
+ roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); // == 2*rho*cos(theta+ pi/3)
+ roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;
+ }
+
+ static inline bool extract_kernel(MatrixType& mat, Ref<VectorType> res, Ref<VectorType> representative)
+ {
+ using std::abs;
+ Index i0;
+ // Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):
+ mat.diagonal().cwiseAbs().maxCoeff(&i0);
+ // mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,
+ // so let's save it:
+ representative = mat.col(i0);
+ Scalar n0, n1;
+ VectorType c0, c1;
+ n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();
+ n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();
+ if(n0>n1) res = c0/std::sqrt(n0);
+ else res = c1/std::sqrt(n1);
+
+ return true;
+ }
+
+ static inline void run(SolverType& solver, const MatrixType& mat, int options)
+ {
+ eigen_assert(mat.cols() == 3 && mat.cols() == mat.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+
+ MatrixType& eivecs = solver.m_eivec;
+ VectorType& eivals = solver.m_eivalues;
+
+ // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ Scalar shift = mat.trace() / Scalar(3);
+ // TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later
+ MatrixType scaledMat = mat.template selfadjointView<Lower>();
+ scaledMat.diagonal().array() -= shift;
+ Scalar scale = scaledMat.cwiseAbs().maxCoeff();
+ if(scale > 0) scaledMat /= scale; // TODO for scale==0 we could save the remaining operations
+
+ // compute the eigenvalues
+ computeRoots(scaledMat,eivals);
+
+ // compute the eigenvectors
+ if(computeEigenvectors)
+ {
+ if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
+ {
+ // All three eigenvalues are numerically the same
+ eivecs.setIdentity();
+ }
+ else
+ {
+ MatrixType tmp;
+ tmp = scaledMat;
+
+ // Compute the eigenvector of the most distinct eigenvalue
+ Scalar d0 = eivals(2) - eivals(1);
+ Scalar d1 = eivals(1) - eivals(0);
+ Index k(0), l(2);
+ if(d0 > d1)
+ {
+ std::swap(k,l);
+ d0 = d1;
+ }
+
+ // Compute the eigenvector of index k
+ {
+ tmp.diagonal().array () -= eivals(k);
+ // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.
+ extract_kernel(tmp, eivecs.col(k), eivecs.col(l));
+ }
+
+ // Compute eigenvector of index l
+ if(d0<=2*Eigen::NumTraits<Scalar>::epsilon()*d1)
+ {
+ // If d0 is too small, then the two other eigenvalues are numerically the same,
+ // and thus we only have to ortho-normalize the near orthogonal vector we saved above.
+ eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);
+ eivecs.col(l).normalize();
+ }
+ else
+ {
+ tmp = scaledMat;
+ tmp.diagonal().array () -= eivals(l);
+
+ VectorType dummy;
+ extract_kernel(tmp, eivecs.col(l), dummy);
+ }
+
+ // Compute last eigenvector from the other two
+ eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();
+ }
+ }
+
+ // Rescale back to the original size.
+ eivals *= scale;
+ eivals.array() += shift;
+
+ solver.m_info = Success;
+ solver.m_isInitialized = true;
+ solver.m_eigenvectorsOk = computeEigenvectors;
+ }
+};
+
+// 2x2 direct eigenvalues decomposition, code from Hauke Heibel
+template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2,false>
+{
+ typedef typename SolverType::MatrixType MatrixType;
+ typedef typename SolverType::RealVectorType VectorType;
+ typedef typename SolverType::Scalar Scalar;
+
+ static inline void computeRoots(const MatrixType& m, VectorType& roots)
+ {
+ using std::sqrt;
+ const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*numext::abs2(m(1,0)));
+ const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));
+ roots(0) = t1 - t0;
+ roots(1) = t1 + t0;
+ }
+
+ static inline void run(SolverType& solver, const MatrixType& mat, int options)
+ {
+ using std::sqrt;
+ using std::abs;
+
+ eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+
+ MatrixType& eivecs = solver.m_eivec;
+ VectorType& eivals = solver.m_eivalues;
+
+ // map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ Scalar scale = mat.cwiseAbs().maxCoeff();
+ scale = (std::max)(scale,Scalar(1));
+ MatrixType scaledMat = mat / scale;
+
+ // Compute the eigenvalues
+ computeRoots(scaledMat,eivals);
+
+ // compute the eigen vectors
+ if(computeEigenvectors)
+ {
+ if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())
+ {
+ eivecs.setIdentity();
+ }
+ else
+ {
+ scaledMat.diagonal().array () -= eivals(1);
+ Scalar a2 = numext::abs2(scaledMat(0,0));
+ Scalar c2 = numext::abs2(scaledMat(1,1));
+ Scalar b2 = numext::abs2(scaledMat(1,0));
+ if(a2>c2)
+ {
+ eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+ eivecs.col(1) /= sqrt(a2+b2);
+ }
+ else
+ {
+ eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+ eivecs.col(1) /= sqrt(c2+b2);
+ }
+
+ eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+ }
+ }
+
+ // Rescale back to the original size.
+ eivals *= scale;
+
+ solver.m_info = Success;
+ solver.m_isInitialized = true;
+ solver.m_eigenvectorsOk = computeEigenvectors;
+ }
+};
+
+}
+
+template<typename MatrixType>
+SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
+::computeDirect(const MatrixType& matrix, int options)
+{
+ internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>::run(*this,matrix,options);
+ return *this;
+}
+
+namespace internal {
+template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)
+{
+ using std::abs;
+ RealScalar td = (diag[end-1] - diag[end])*RealScalar(0.5);
+ RealScalar e = subdiag[end-1];
+ // Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
+ // underflow thus leading to inf/NaN values when using the following commented code:
+// RealScalar e2 = numext::abs2(subdiag[end-1]);
+// RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
+ // This explain the following, somewhat more complicated, version:
+ RealScalar mu = diag[end];
+ if(td==0)
+ mu -= abs(e);
+ else
+ {
+ RealScalar e2 = numext::abs2(subdiag[end-1]);
+ RealScalar h = numext::hypot(td,e);
+ if(e2==0) mu -= (e / (td + (td>0 ? 1 : -1))) * (e / h);
+ else mu -= e2 / (td + (td>0 ? h : -h));
+ }
+
+ RealScalar x = diag[start] - mu;
+ RealScalar z = subdiag[start];
+ for (Index k = start; k < end; ++k)
+ {
+ JacobiRotation<RealScalar> rot;
+ rot.makeGivens(x, z);
+
+ // do T = G' T G
+ RealScalar sdk = rot.s() * diag[k] + rot.c() * subdiag[k];
+ RealScalar dkp1 = rot.s() * subdiag[k] + rot.c() * diag[k+1];
+
+ diag[k] = rot.c() * (rot.c() * diag[k] - rot.s() * subdiag[k]) - rot.s() * (rot.c() * subdiag[k] - rot.s() * diag[k+1]);
+ diag[k+1] = rot.s() * sdk + rot.c() * dkp1;
+ subdiag[k] = rot.c() * sdk - rot.s() * dkp1;
+
+
+ if (k > start)
+ subdiag[k - 1] = rot.c() * subdiag[k-1] - rot.s() * z;
+
+ x = subdiag[k];
+
+ if (k < end - 1)
+ {
+ z = -rot.s() * subdiag[k+1];
+ subdiag[k + 1] = rot.c() * subdiag[k+1];
+ }
+
+ // apply the givens rotation to the unit matrix Q = Q * G
+ if (matrixQ)
+ {
+ // FIXME if StorageOrder == RowMajor this operation is not very efficient
+ Map<Matrix<Scalar,Dynamic,Dynamic,StorageOrder> > q(matrixQ,n,n);
+ q.applyOnTheRight(k,k+1,rot);
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
new file mode 100644
index 0000000..17c0dad
--- /dev/null
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
@@ -0,0 +1,92 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Self-adjoint eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SAEIGENSOLVER_MKL_H
+#define EIGEN_SAEIGENSOLVER_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_EIG_SELFADJ(EIGTYPE, MKLTYPE, MKLRTYPE, MKLNAME, EIGCOLROW, MKLCOLROW ) \
+template<> inline \
+SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW>& matrix, int options) \
+{ \
+ eigen_assert(matrix.cols() == matrix.rows()); \
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0 \
+ && (options&EigVecMask)!=EigVecMask \
+ && "invalid option parameter"); \
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors; \
+ lapack_int n = matrix.cols(), lda, matrix_order, info; \
+ m_eivalues.resize(n,1); \
+ m_subdiag.resize(n-1); \
+ m_eivec = matrix; \
+\
+ if(n==1) \
+ { \
+ m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0)); \
+ if(computeEigenvectors) m_eivec.setOnes(n,n); \
+ m_info = Success; \
+ m_isInitialized = true; \
+ m_eigenvectorsOk = computeEigenvectors; \
+ return *this; \
+ } \
+\
+ lda = matrix.outerStride(); \
+ matrix_order=MKLCOLROW; \
+ char jobz, uplo='L'/*, range='A'*/; \
+ jobz = computeEigenvectors ? 'V' : 'N'; \
+\
+ info = LAPACKE_##MKLNAME( matrix_order, jobz, uplo, n, (MKLTYPE*)m_eivec.data(), lda, (MKLRTYPE*)m_eivalues.data() ); \
+ m_info = (info==0) ? Success : NoConvergence; \
+ m_isInitialized = true; \
+ m_eigenvectorsOk = computeEigenvectors; \
+ return *this; \
+}
+
+
+EIGEN_MKL_EIG_SELFADJ(double, double, double, dsyev, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(float, float, float, ssyev, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(dcomplex, MKL_Complex16, double, zheev, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(scomplex, MKL_Complex8, float, cheev, ColMajor, LAPACK_COL_MAJOR)
+
+EIGEN_MKL_EIG_SELFADJ(double, double, double, dsyev, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(float, float, float, ssyev, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(dcomplex, MKL_Complex16, double, zheev, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_EIG_SELFADJ(scomplex, MKL_Complex8, float, cheev, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_SAEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
new file mode 100644
index 0000000..192278d
--- /dev/null
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -0,0 +1,557 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIDIAGONALIZATION_H
+#define EIGEN_TRIDIAGONALIZATION_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType;
+template<typename MatrixType>
+struct traits<TridiagonalizationMatrixTReturnType<MatrixType> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename MatrixType, typename CoeffVectorType>
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class Tridiagonalization
+ *
+ * \brief Tridiagonal decomposition of a selfadjoint matrix
+ *
+ * \tparam _MatrixType the type of the matrix of which we are computing the
+ * tridiagonal decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
+ * \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix.
+ *
+ * A tridiagonal matrix is a matrix which has nonzero elements only on the
+ * main diagonal and the first diagonal below and above it. The Hessenberg
+ * decomposition of a selfadjoint matrix is in fact a tridiagonal
+ * decomposition. This class is used in SelfAdjointEigenSolver to compute the
+ * eigenvalues and eigenvectors of a selfadjoint matrix.
+ *
+ * Call the function compute() to compute the tridiagonal decomposition of a
+ * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)
+ * constructor which computes the tridiagonal Schur decomposition at
+ * construction time. Once the decomposition is computed, you can use the
+ * matrixQ() and matrixT() functions to retrieve the matrices Q and T in the
+ * decomposition.
+ *
+ * The documentation of Tridiagonalization(const MatrixType&) contains an
+ * example of the typical use of this class.
+ *
+ * \sa class HessenbergDecomposition, class SelfAdjointEigenSolver
+ */
+template<typename _MatrixType> class Tridiagonalization
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p _MatrixType. */
+ typedef _MatrixType MatrixType;
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
+ Options = MatrixType::Options,
+ MaxSize = MatrixType::MaxRowsAtCompileTime,
+ MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
+ };
+
+ typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;
+ typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalType;
+ typedef typename internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView;
+ typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;
+
+ typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ typename internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type,
+ const Diagonal<const MatrixType>
+ >::type DiagonalReturnType;
+
+ typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ typename internal::add_const_on_value_type<typename Diagonal<
+ Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType>::type,
+ const Diagonal<
+ Block<const MatrixType,SizeMinusOne,SizeMinusOne> >
+ >::type SubDiagonalReturnType;
+
+ /** \brief Return type of matrixQ() */
+ typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose tridiagonal
+ * decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ Tridiagonalization(Index size = Size==Dynamic ? 2 : Size)
+ : m_matrix(size,size),
+ m_hCoeffs(size > 1 ? size-1 : 1),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Constructor; computes tridiagonal decomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
+ * is to be computed.
+ *
+ * This constructor calls compute() to compute the tridiagonal decomposition.
+ *
+ * Example: \include Tridiagonalization_Tridiagonalization_MatrixType.cpp
+ * Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out
+ */
+ Tridiagonalization(const MatrixType& matrix)
+ : m_matrix(matrix),
+ m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),
+ m_isInitialized(false)
+ {
+ internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+ m_isInitialized = true;
+ }
+
+ /** \brief Computes tridiagonal decomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
+ * is to be computed.
+ * \returns Reference to \c *this
+ *
+ * The tridiagonal decomposition is computed by bringing the columns of
+ * the matrix successively in the required form using Householder
+ * reflections. The cost is \f$ 4n^3/3 \f$ flops, where \f$ n \f$ denotes
+ * the size of the given matrix.
+ *
+ * This method reuses of the allocated data in the Tridiagonalization
+ * object, if the size of the matrix does not change.
+ *
+ * Example: \include Tridiagonalization_compute.cpp
+ * Output: \verbinclude Tridiagonalization_compute.out
+ */
+ Tridiagonalization& compute(const MatrixType& matrix)
+ {
+ m_matrix = matrix;
+ m_hCoeffs.resize(matrix.rows()-1, 1);
+ internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+ m_isInitialized = true;
+ return *this;
+ }
+
+ /** \brief Returns the Householder coefficients.
+ *
+ * \returns a const reference to the vector of Householder coefficients
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * The Householder coefficients allow the reconstruction of the matrix
+ * \f$ Q \f$ in the tridiagonal decomposition from the packed data.
+ *
+ * Example: \include Tridiagonalization_householderCoefficients.cpp
+ * Output: \verbinclude Tridiagonalization_householderCoefficients.out
+ *
+ * \sa packedMatrix(), \ref Householder_Module "Householder module"
+ */
+ inline CoeffVectorType householderCoefficients() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_hCoeffs;
+ }
+
+ /** \brief Returns the internal representation of the decomposition
+ *
+ * \returns a const reference to a matrix with the internal representation
+ * of the decomposition.
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * The returned matrix contains the following information:
+ * - the strict upper triangular part is equal to the input matrix A.
+ * - the diagonal and lower sub-diagonal represent the real tridiagonal
+ * symmetric matrix T.
+ * - the rest of the lower part contains the Householder vectors that,
+ * combined with Householder coefficients returned by
+ * householderCoefficients(), allows to reconstruct the matrix Q as
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * Here, the matrices \f$ H_i \f$ are the Householder transformations
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
+ * with M the matrix returned by this function.
+ *
+ * See LAPACK for further details on this packed storage.
+ *
+ * Example: \include Tridiagonalization_packedMatrix.cpp
+ * Output: \verbinclude Tridiagonalization_packedMatrix.out
+ *
+ * \sa householderCoefficients()
+ */
+ inline const MatrixType& packedMatrix() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_matrix;
+ }
+
+ /** \brief Returns the unitary matrix Q in the decomposition
+ *
+ * \returns object representing the matrix Q
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * This function returns a light-weight object of template class
+ * HouseholderSequence. You can either apply it directly to a matrix or
+ * you can convert it to a matrix of type #MatrixType.
+ *
+ * \sa Tridiagonalization(const MatrixType&) for an example,
+ * matrixT(), class HouseholderSequence
+ */
+ HouseholderSequenceType matrixQ() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
+ .setLength(m_matrix.rows() - 1)
+ .setShift(1);
+ }
+
+ /** \brief Returns an expression of the tridiagonal matrix T in the decomposition
+ *
+ * \returns expression object representing the matrix T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * Currently, this function can be used to extract the matrix T from internal
+ * data and copy it to a dense matrix object. In most cases, it may be
+ * sufficient to directly use the packed matrix or the vector expressions
+ * returned by diagonal() and subDiagonal() instead of creating a new
+ * dense copy matrix with this function.
+ *
+ * \sa Tridiagonalization(const MatrixType&) for an example,
+ * matrixQ(), packedMatrix(), diagonal(), subDiagonal()
+ */
+ MatrixTReturnType matrixT() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return MatrixTReturnType(m_matrix.real());
+ }
+
+ /** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition.
+ *
+ * \returns expression representing the diagonal of T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * Example: \include Tridiagonalization_diagonal.cpp
+ * Output: \verbinclude Tridiagonalization_diagonal.out
+ *
+ * \sa matrixT(), subDiagonal()
+ */
+ DiagonalReturnType diagonal() const;
+
+ /** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
+ *
+ * \returns expression representing the subdiagonal of T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * \sa diagonal() for an example, matrixT()
+ */
+ SubDiagonalReturnType subDiagonal() const;
+
+ protected:
+
+ MatrixType m_matrix;
+ CoeffVectorType m_hCoeffs;
+ bool m_isInitialized;
+};
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::DiagonalReturnType
+Tridiagonalization<MatrixType>::diagonal() const
+{
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_matrix.diagonal();
+}
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::SubDiagonalReturnType
+Tridiagonalization<MatrixType>::subDiagonal() const
+{
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ Index n = m_matrix.rows();
+ return Block<const MatrixType,SizeMinusOne,SizeMinusOne>(m_matrix, 1, 0, n-1,n-1).diagonal();
+}
+
+namespace internal {
+
+/** \internal
+ * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
+ *
+ * \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced.
+ * On output, the strict upper part is left unchanged, and the lower triangular part
+ * represents the T and Q matrices in packed format has detailed below.
+ * \param[out] hCoeffs returned Householder coefficients (see below)
+ *
+ * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
+ * and lower sub-diagonal of the matrix \a matA.
+ * The unitary matrix Q is represented in a compact way as a product of
+ * Householder reflectors \f$ H_i \f$ such that:
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * The Householder reflectors are defined as
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$.
+ *
+ * Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
+ *
+ * \sa Tridiagonalization::packedMatrix()
+ */
+template<typename MatrixType, typename CoeffVectorType>
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
+{
+ using numext::conj;
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index n = matA.rows();
+ eigen_assert(n==matA.cols());
+ eigen_assert(n==hCoeffs.size()+1 || n==1);
+
+ for (Index i = 0; i<n-1; ++i)
+ {
+ Index remainingSize = n-i-1;
+ RealScalar beta;
+ Scalar h;
+ matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
+
+ // Apply similarity transformation to remaining columns,
+ // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)
+ matA.col(i).coeffRef(i+1) = 1;
+
+ hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
+ * (conj(h) * matA.col(i).tail(remainingSize)));
+
+ hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
+
+ matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
+ .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
+
+ matA.col(i).coeffRef(i+1) = beta;
+ hCoeffs.coeffRef(i) = h;
+ }
+}
+
+// forward declaration, implementation at the end of this file
+template<typename MatrixType,
+ int Size=MatrixType::ColsAtCompileTime,
+ bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct tridiagonalization_inplace_selector;
+
+/** \brief Performs a full tridiagonalization in place
+ *
+ * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
+ * decomposition is to be computed. Only the lower triangular part referenced.
+ * The rest is left unchanged. On output, the orthogonal matrix Q
+ * in the decomposition if \p extractQ is true.
+ * \param[out] diag The diagonal of the tridiagonal matrix T in the
+ * decomposition.
+ * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
+ * the decomposition.
+ * \param[in] extractQ If true, the orthogonal matrix Q in the
+ * decomposition is computed and stored in \p mat.
+ *
+ * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
+ * such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real
+ * symmetric tridiagonal matrix.
+ *
+ * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
+ * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
+ * part of the matrix \p mat is destroyed.
+ *
+ * The vectors \p diag and \p subdiag are not resized. The function
+ * assumes that they are already of the correct size. The length of the
+ * vector \p diag should equal the number of rows in \p mat, and the
+ * length of the vector \p subdiag should be one left.
+ *
+ * This implementation contains an optimized path for 3-by-3 matrices
+ * which is especially useful for plane fitting.
+ *
+ * \note Currently, it requires two temporary vectors to hold the intermediate
+ * Householder coefficients, and to reconstruct the matrix Q from the Householder
+ * reflectors.
+ *
+ * Example (this uses the same matrix as the example in
+ * Tridiagonalization::Tridiagonalization(const MatrixType&)):
+ * \include Tridiagonalization_decomposeInPlace.cpp
+ * Output: \verbinclude Tridiagonalization_decomposeInPlace.out
+ *
+ * \sa class Tridiagonalization
+ */
+template<typename MatrixType, typename DiagonalType, typename SubDiagonalType>
+void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+{
+ eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);
+ tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);
+}
+
+/** \internal
+ * General full tridiagonalization
+ */
+template<typename MatrixType, int Size, bool IsComplex>
+struct tridiagonalization_inplace_selector
+{
+ typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType;
+ typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;
+ typedef typename MatrixType::Index Index;
+ template<typename DiagonalType, typename SubDiagonalType>
+ static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+ {
+ CoeffVectorType hCoeffs(mat.cols()-1);
+ tridiagonalization_inplace(mat,hCoeffs);
+ diag = mat.diagonal().real();
+ subdiag = mat.template diagonal<-1>().real();
+ if(extractQ)
+ mat = HouseholderSequenceType(mat, hCoeffs.conjugate())
+ .setLength(mat.rows() - 1)
+ .setShift(1);
+ }
+};
+
+/** \internal
+ * Specialization for 3x3 real matrices.
+ * Especially useful for plane fitting.
+ */
+template<typename MatrixType>
+struct tridiagonalization_inplace_selector<MatrixType,3,false>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ template<typename DiagonalType, typename SubDiagonalType>
+ static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+ {
+ using std::sqrt;
+ diag[0] = mat(0,0);
+ RealScalar v1norm2 = numext::abs2(mat(2,0));
+ if(v1norm2 == RealScalar(0))
+ {
+ diag[1] = mat(1,1);
+ diag[2] = mat(2,2);
+ subdiag[0] = mat(1,0);
+ subdiag[1] = mat(2,1);
+ if (extractQ)
+ mat.setIdentity();
+ }
+ else
+ {
+ RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
+ RealScalar invBeta = RealScalar(1)/beta;
+ Scalar m01 = mat(1,0) * invBeta;
+ Scalar m02 = mat(2,0) * invBeta;
+ Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));
+ diag[1] = mat(1,1) + m02*q;
+ diag[2] = mat(2,2) - m02*q;
+ subdiag[0] = beta;
+ subdiag[1] = mat(2,1) - m01 * q;
+ if (extractQ)
+ {
+ mat << 1, 0, 0,
+ 0, m01, m02,
+ 0, m02, -m01;
+ }
+ }
+ }
+};
+
+/** \internal
+ * Trivial specialization for 1x1 matrices
+ */
+template<typename MatrixType, bool IsComplex>
+struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ template<typename DiagonalType, typename SubDiagonalType>
+ static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
+ {
+ diag(0,0) = numext::real(mat(0,0));
+ if(extractQ)
+ mat(0,0) = Scalar(1);
+ }
+};
+
+/** \internal
+ * \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ * \brief Expression type for return value of Tridiagonalization::matrixT()
+ *
+ * \tparam MatrixType type of underlying dense matrix
+ */
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType
+: public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> >
+{
+ typedef typename MatrixType::Index Index;
+ public:
+ /** \brief Constructor.
+ *
+ * \param[in] mat The underlying dense matrix
+ */
+ TridiagonalizationMatrixTReturnType(const MatrixType& mat) : m_matrix(mat) { }
+
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ result.setZero();
+ result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();
+ result.diagonal() = m_matrix.diagonal();
+ result.template diagonal<-1>() = m_matrix.template diagonal<-1>();
+ }
+
+ Index rows() const { return m_matrix.rows(); }
+ Index cols() const { return m_matrix.cols(); }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIDIAGONALIZATION_H
diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h
new file mode 100644
index 0000000..b226336
--- /dev/null
+++ b/Eigen/src/Geometry/AlignedBox.h
@@ -0,0 +1,392 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ALIGNEDBOX_H
+#define EIGEN_ALIGNEDBOX_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ *
+ * \class AlignedBox
+ *
+ * \brief An axis aligned box
+ *
+ * \tparam _Scalar the type of the scalar coefficients
+ * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ *
+ * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+ * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
+ * \sa alignedboxtypedefs
+ */
+template <typename _Scalar, int _AmbientDim>
+class AlignedBox
+{
+public:
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef NumTraits<Scalar> ScalarTraits;
+ typedef DenseIndex Index;
+ typedef typename ScalarTraits::Real RealScalar;
+ typedef typename ScalarTraits::NonInteger NonInteger;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+ /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
+ enum CornerType
+ {
+ /** 1D names @{ */
+ Min=0, Max=1,
+ /** @} */
+
+ /** Identifier for 2D corner @{ */
+ BottomLeft=0, BottomRight=1,
+ TopLeft=2, TopRight=3,
+ /** @} */
+
+ /** Identifier for 3D corner @{ */
+ BottomLeftFloor=0, BottomRightFloor=1,
+ TopLeftFloor=2, TopRightFloor=3,
+ BottomLeftCeil=4, BottomRightCeil=5,
+ TopLeftCeil=6, TopRightCeil=7
+ /** @} */
+ };
+
+
+ /** Default constructor initializing a null box. */
+ inline AlignedBox()
+ { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
+
+ /** Constructs a null box with \a _dim the dimension of the ambient space. */
+ inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
+ { setEmpty(); }
+
+ /** Constructs a box with extremities \a _min and \a _max.
+ * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
+ template<typename OtherVectorType1, typename OtherVectorType2>
+ inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
+
+ /** Constructs a box containing a single point \a p. */
+ template<typename Derived>
+ inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
+ { }
+
+ ~AlignedBox() {}
+
+ /** \returns the dimension in which the box holds */
+ inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
+
+ /** \deprecated use isEmpty() */
+ inline bool isNull() const { return isEmpty(); }
+
+ /** \deprecated use setEmpty() */
+ inline void setNull() { setEmpty(); }
+
+ /** \returns true if the box is empty.
+ * \sa setEmpty */
+ inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
+
+ /** Makes \c *this an empty box.
+ * \sa isEmpty */
+ inline void setEmpty()
+ {
+ m_min.setConstant( ScalarTraits::highest() );
+ m_max.setConstant( ScalarTraits::lowest() );
+ }
+
+ /** \returns the minimal corner */
+ inline const VectorType& (min)() const { return m_min; }
+ /** \returns a non const reference to the minimal corner */
+ inline VectorType& (min)() { return m_min; }
+ /** \returns the maximal corner */
+ inline const VectorType& (max)() const { return m_max; }
+ /** \returns a non const reference to the maximal corner */
+ inline VectorType& (max)() { return m_max; }
+
+ /** \returns the center of the box */
+ inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
+ const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
+ center() const
+ { return (m_min+m_max)/2; }
+
+ /** \returns the lengths of the sides of the bounding box.
+ * Note that this function does not get the same
+ * result for integral or floating scalar types: see
+ */
+ inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
+ { return m_max - m_min; }
+
+ /** \returns the volume of the bounding box */
+ inline Scalar volume() const
+ { return sizes().prod(); }
+
+ /** \returns an expression for the bounding box diagonal vector
+ * if the length of the diagonal is needed: diagonal().norm()
+ * will provide it.
+ */
+ inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const
+ { return sizes(); }
+
+ /** \returns the vertex of the bounding box at the corner defined by
+ * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
+ * For 1D bounding boxes corners are named by 2 enum constants:
+ * BottomLeft and BottomRight.
+ * For 2D bounding boxes, corners are named by 4 enum constants:
+ * BottomLeft, BottomRight, TopLeft, TopRight.
+ * For 3D bounding boxes, the following names are added:
+ * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
+ */
+ inline VectorType corner(CornerType corner) const
+ {
+ EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
+
+ VectorType res;
+
+ Index mult = 1;
+ for(Index d=0; d<dim(); ++d)
+ {
+ if( mult & corner ) res[d] = m_max[d];
+ else res[d] = m_min[d];
+ mult *= 2;
+ }
+ return res;
+ }
+
+ /** \returns a random point inside the bounding box sampled with
+ * a uniform distribution */
+ inline VectorType sample() const
+ {
+ VectorType r;
+ for(Index d=0; d<dim(); ++d)
+ {
+ if(!ScalarTraits::IsInteger)
+ {
+ r[d] = m_min[d] + (m_max[d]-m_min[d])
+ * internal::random<Scalar>(Scalar(0), Scalar(1));
+ }
+ else
+ r[d] = internal::random(m_min[d], m_max[d]);
+ }
+ return r;
+ }
+
+ /** \returns true if the point \a p is inside the box \c *this. */
+ template<typename Derived>
+ inline bool contains(const MatrixBase<Derived>& p) const
+ {
+ typename internal::nested<Derived,2>::type p_n(p.derived());
+ return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
+ }
+
+ /** \returns true if the box \a b is entirely inside the box \c *this. */
+ inline bool contains(const AlignedBox& b) const
+ { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
+
+ /** \returns true if the box \a b is intersecting the box \c *this.
+ * \sa intersection, clamp */
+ inline bool intersects(const AlignedBox& b) const
+ { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
+
+ /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
+ * \sa extend(const AlignedBox&) */
+ template<typename Derived>
+ inline AlignedBox& extend(const MatrixBase<Derived>& p)
+ {
+ typename internal::nested<Derived,2>::type p_n(p.derived());
+ m_min = m_min.cwiseMin(p_n);
+ m_max = m_max.cwiseMax(p_n);
+ return *this;
+ }
+
+ /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
+ * \sa merged, extend(const MatrixBase&) */
+ inline AlignedBox& extend(const AlignedBox& b)
+ {
+ m_min = m_min.cwiseMin(b.m_min);
+ m_max = m_max.cwiseMax(b.m_max);
+ return *this;
+ }
+
+ /** Clamps \c *this by the box \a b and returns a reference to \c *this.
+ * \note If the boxes don't intersect, the resulting box is empty.
+ * \sa intersection(), intersects() */
+ inline AlignedBox& clamp(const AlignedBox& b)
+ {
+ m_min = m_min.cwiseMax(b.m_min);
+ m_max = m_max.cwiseMin(b.m_max);
+ return *this;
+ }
+
+ /** Returns an AlignedBox that is the intersection of \a b and \c *this
+ * \note If the boxes don't intersect, the resulting box is empty.
+ * \sa intersects(), clamp, contains() */
+ inline AlignedBox intersection(const AlignedBox& b) const
+ {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
+
+ /** Returns an AlignedBox that is the union of \a b and \c *this.
+ * \note Merging with an empty box may result in a box bigger than \c *this.
+ * \sa extend(const AlignedBox&) */
+ inline AlignedBox merged(const AlignedBox& b) const
+ { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
+
+ /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
+ template<typename Derived>
+ inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
+ {
+ const typename internal::nested<Derived,2>::type t(a_t.derived());
+ m_min += t;
+ m_max += t;
+ return *this;
+ }
+
+ /** \returns the squared distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
+ */
+ template<typename Derived>
+ inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
+
+ /** \returns the squared distance between the boxes \a b and \c *this,
+ * and zero if the boxes intersect.
+ * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
+ */
+ inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
+
+ /** \returns the distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
+ */
+ template<typename Derived>
+ inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
+ { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); }
+
+ /** \returns the distance between the boxes \a b and \c *this,
+ * and zero if the boxes intersect.
+ * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
+ */
+ inline NonInteger exteriorDistance(const AlignedBox& b) const
+ { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_min = (other.min)().template cast<Scalar>();
+ m_max = (other.max)().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
+ { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+ VectorType m_min, m_max;
+};
+
+
+
+template<typename Scalar,int AmbientDim>
+template<typename Derived>
+inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
+{
+ typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived());
+ Scalar dist2(0);
+ Scalar aux;
+ for (Index k=0; k<dim(); ++k)
+ {
+ if( m_min[k] > p[k] )
+ {
+ aux = m_min[k] - p[k];
+ dist2 += aux*aux;
+ }
+ else if( p[k] > m_max[k] )
+ {
+ aux = p[k] - m_max[k];
+ dist2 += aux*aux;
+ }
+ }
+ return dist2;
+}
+
+template<typename Scalar,int AmbientDim>
+inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
+{
+ Scalar dist2(0);
+ Scalar aux;
+ for (Index k=0; k<dim(); ++k)
+ {
+ if( m_min[k] > b.m_max[k] )
+ {
+ aux = m_min[k] - b.m_max[k];
+ dist2 += aux*aux;
+ }
+ else if( b.m_min[k] > m_max[k] )
+ {
+ aux = b.m_min[k] - m_max[k];
+ dist2 += aux*aux;
+ }
+ }
+ return dist2;
+}
+
+/** \defgroup alignedboxtypedefs Global aligned box typedefs
+ *
+ * \ingroup Geometry_Module
+ *
+ * Eigen defines several typedef shortcuts for most common aligned box types.
+ *
+ * The general patterns are the following:
+ *
+ * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double.
+ *
+ * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats.
+ *
+ * \sa class AlignedBox
+ */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup alignedboxtypedefs */ \
+typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+
+} // end namespace Eigen
+
+#endif // EIGEN_ALIGNEDBOX_H
diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
new file mode 100644
index 0000000..553d38c
--- /dev/null
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -0,0 +1,233 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ANGLEAXIS_H
+#define EIGEN_ANGLEAXIS_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class AngleAxis
+ *
+ * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ *
+ * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c AngleAxisf for \c float
+ * \li \c AngleAxisd for \c double
+ *
+ * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+ * mimic Euler-angles. Here is an example:
+ * \include AngleAxis_mimic_euler.cpp
+ * Output: \verbinclude AngleAxis_mimic_euler.out
+ *
+ * \note This class is not aimed to be used to store a rotation transformation,
+ * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
+ * and transformation objects.
+ *
+ * \sa class Quaternion, class Transform, MatrixBase::UnitX()
+ */
+
+namespace internal {
+template<typename _Scalar> struct traits<AngleAxis<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+}
+
+template<typename _Scalar>
+class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
+{
+ typedef RotationBase<AngleAxis<_Scalar>,3> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 3 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+ Vector3 m_axis;
+ Scalar m_angle;
+
+public:
+
+ /** Default constructor without initialization. */
+ AngleAxis() {}
+ /** Constructs and initialize the angle-axis rotation from an \a angle in radian
+ * and an \a axis which \b must \b be \b normalized.
+ *
+ * \warning If the \a axis vector is not normalized, then the angle-axis object
+ * represents an invalid rotation. */
+ template<typename Derived>
+ inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+ /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
+ template<typename QuatDerived> inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
+ /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
+ template<typename Derived>
+ inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
+
+ Scalar angle() const { return m_angle; }
+ Scalar& angle() { return m_angle; }
+
+ const Vector3& axis() const { return m_axis; }
+ Vector3& axis() { return m_axis; }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const AngleAxis& other) const
+ { return QuaternionType(*this) * QuaternionType(other); }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const QuaternionType& other) const
+ { return QuaternionType(*this) * other; }
+
+ /** Concatenates two rotations */
+ friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+ { return a * QuaternionType(b); }
+
+ /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+ AngleAxis inverse() const
+ { return AngleAxis(-m_angle, m_axis); }
+
+ template<class QuatDerived>
+ AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
+ template<typename Derived>
+ AngleAxis& operator=(const MatrixBase<Derived>& m);
+
+ template<typename Derived>
+ AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix3 toRotationMatrix(void) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
+ {
+ m_axis = other.axis().template cast<Scalar>();
+ m_angle = Scalar(other.angle());
+ }
+
+ static inline const AngleAxis Identity() { return AngleAxis(0, Vector3::UnitX()); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision angle-axis type */
+typedef AngleAxis<float> AngleAxisf;
+/** \ingroup Geometry_Module
+ * double precision angle-axis type */
+typedef AngleAxis<double> AngleAxisd;
+
+/** Set \c *this from a \b unit quaternion.
+ * The axis is normalized.
+ *
+ * \warning As any other method dealing with quaternion, if the input quaternion
+ * is not normalized then the result is undefined.
+ */
+template<typename Scalar>
+template<typename QuatDerived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
+{
+ using std::acos;
+ using std::min;
+ using std::max;
+ using std::sqrt;
+ Scalar n2 = q.vec().squaredNorm();
+ if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
+ {
+ m_angle = 0;
+ m_axis << 1, 0, 0;
+ }
+ else
+ {
+ m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1)));
+ m_axis = q.vec() / sqrt(n2);
+ }
+ return *this;
+}
+
+/** Set \c *this from a 3x3 rotation matrix \a mat.
+ */
+template<typename Scalar>
+template<typename Derived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
+{
+ // Since a direct conversion would not be really faster,
+ // let's use the robust Quaternion implementation:
+ return *this = QuaternionType(mat);
+}
+
+/**
+* \brief Sets \c *this from a 3x3 rotation matrix.
+**/
+template<typename Scalar>
+template<typename Derived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ return *this = QuaternionType(mat);
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+ */
+template<typename Scalar>
+typename AngleAxis<Scalar>::Matrix3
+AngleAxis<Scalar>::toRotationMatrix(void) const
+{
+ using std::sin;
+ using std::cos;
+ Matrix3 res;
+ Vector3 sin_axis = sin(m_angle) * m_axis;
+ Scalar c = cos(m_angle);
+ Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
+
+ Scalar tmp;
+ tmp = cos1_axis.x() * m_axis.y();
+ res.coeffRef(0,1) = tmp - sin_axis.z();
+ res.coeffRef(1,0) = tmp + sin_axis.z();
+
+ tmp = cos1_axis.x() * m_axis.z();
+ res.coeffRef(0,2) = tmp + sin_axis.y();
+ res.coeffRef(2,0) = tmp - sin_axis.y();
+
+ tmp = cos1_axis.y() * m_axis.z();
+ res.coeffRef(1,2) = tmp - sin_axis.x();
+ res.coeffRef(2,1) = tmp + sin_axis.x();
+
+ res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;
+
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ANGLEAXIS_H
diff --git a/Eigen/src/Geometry/CMakeLists.txt b/Eigen/src/Geometry/CMakeLists.txt
new file mode 100644
index 0000000..f8f728b
--- /dev/null
+++ b/Eigen/src/Geometry/CMakeLists.txt
@@ -0,0 +1,8 @@
+FILE(GLOB Eigen_Geometry_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Geometry_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Geometry COMPONENT Devel
+ )
+
+ADD_SUBDIRECTORY(arch)
diff --git a/Eigen/src/Geometry/EulerAngles.h b/Eigen/src/Geometry/EulerAngles.h
new file mode 100644
index 0000000..82802fb
--- /dev/null
+++ b/Eigen/src/Geometry/EulerAngles.h
@@ -0,0 +1,104 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERANGLES_H
+#define EIGEN_EULERANGLES_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ *
+ * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
+ *
+ * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
+ * For instance, in:
+ * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
+ * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
+ * we have the following equality:
+ * \code
+ * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
+ * * AngleAxisf(ea[1], Vector3f::UnitX())
+ * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
+ * This corresponds to the right-multiply conventions (with right hand side frames).
+ *
+ * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
+ *
+ * \sa class AngleAxis
+ */
+template<typename Derived>
+inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
+MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
+{
+ using std::atan2;
+ using std::sin;
+ using std::cos;
+ /* Implemented from Graphics Gems IV */
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
+
+ Matrix<Scalar,3,1> res;
+ typedef Matrix<typename Derived::Scalar,2,1> Vector2;
+
+ const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
+ const Index i = a0;
+ const Index j = (a0 + 1 + odd)%3;
+ const Index k = (a0 + 2 - odd)%3;
+
+ if (a0==a2)
+ {
+ res[0] = atan2(coeff(j,i), coeff(k,i));
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
+ {
+ res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = -atan2(s2, coeff(i,i));
+ }
+ else
+ {
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = atan2(s2, coeff(i,i));
+ }
+
+ // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
+ // we can compute their respective rotation, and apply its inverse to M. Since the result must
+ // be a rotation around x, we have:
+ //
+ // c2 s1.s2 c1.s2 1 0 0
+ // 0 c1 -s1 * M = 0 c3 s3
+ // -s2 s1.c2 c1.c2 0 -s3 c3
+ //
+ // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
+
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ else
+ {
+ res[0] = atan2(coeff(j,k), coeff(k,k));
+ Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
+ res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
+ res[1] = atan2(-coeff(i,k), -c2);
+ }
+ else
+ res[1] = atan2(-coeff(i,k), c2);
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ if (!odd)
+ res = -res;
+
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EULERANGLES_H
diff --git a/Eigen/src/Geometry/Homogeneous.h b/Eigen/src/Geometry/Homogeneous.h
new file mode 100644
index 0000000..372e422
--- /dev/null
+++ b/Eigen/src/Geometry/Homogeneous.h
@@ -0,0 +1,307 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOMOGENEOUS_H
+#define EIGEN_HOMOGENEOUS_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Homogeneous
+ *
+ * \brief Expression of one (or a set of) homogeneous vector(s)
+ *
+ * \param MatrixType the type of the object in which we are making homogeneous
+ *
+ * This class represents an expression of one (or a set of) homogeneous vector(s).
+ * It is the return type of MatrixBase::homogeneous() and most of the time
+ * this is the only way it is used.
+ *
+ * \sa MatrixBase::homogeneous()
+ */
+
+namespace internal {
+
+template<typename MatrixType,int Direction>
+struct traits<Homogeneous<MatrixType,Direction> >
+ : traits<MatrixType>
+{
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
+ int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
+ ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
+ int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
+ RowsAtCompileTime = Direction==Vertical ? RowsPlusOne : MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
+ Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
+ : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
+ : TmpFlags,
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+ };
+};
+
+template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
+template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
+
+} // end namespace internal
+
+template<typename MatrixType,int _Direction> class Homogeneous
+ : internal::no_assignment_operator, public MatrixBase<Homogeneous<MatrixType,_Direction> >
+{
+ public:
+
+ enum { Direction = _Direction };
+
+ typedef MatrixBase<Homogeneous> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
+
+ inline Homogeneous(const MatrixType& matrix)
+ : m_matrix(matrix)
+ {}
+
+ inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical ? 1 : 0); }
+ inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
+
+ inline Scalar coeff(Index row, Index col) const
+ {
+ if( (int(Direction)==Vertical && row==m_matrix.rows())
+ || (int(Direction)==Horizontal && col==m_matrix.cols()))
+ return Scalar(1);
+ return m_matrix.coeff(row, col);
+ }
+
+ template<typename Rhs>
+ inline const internal::homogeneous_right_product_impl<Homogeneous,Rhs>
+ operator* (const MatrixBase<Rhs>& rhs) const
+ {
+ eigen_assert(int(Direction)==Horizontal);
+ return internal::homogeneous_right_product_impl<Homogeneous,Rhs>(m_matrix,rhs.derived());
+ }
+
+ template<typename Lhs> friend
+ inline const internal::homogeneous_left_product_impl<Homogeneous,Lhs>
+ operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
+ {
+ eigen_assert(int(Direction)==Vertical);
+ return internal::homogeneous_left_product_impl<Homogeneous,Lhs>(lhs.derived(),rhs.m_matrix);
+ }
+
+ template<typename Scalar, int Dim, int Mode, int Options> friend
+ inline const internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >
+ operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
+ {
+ eigen_assert(int(Direction)==Vertical);
+ return internal::homogeneous_left_product_impl<Homogeneous,Transform<Scalar,Dim,Mode,Options> >(lhs,rhs.m_matrix);
+ }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+/** \geometry_module
+ *
+ * \return an expression of the equivalent homogeneous vector
+ *
+ * \only_for_vectors
+ *
+ * Example: \include MatrixBase_homogeneous.cpp
+ * Output: \verbinclude MatrixBase_homogeneous.out
+ *
+ * \sa class Homogeneous
+ */
+template<typename Derived>
+inline typename MatrixBase<Derived>::HomogeneousReturnType
+MatrixBase<Derived>::homogeneous() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return derived();
+}
+
+/** \geometry_module
+ *
+ * \returns a matrix expression of homogeneous column (or row) vectors
+ *
+ * Example: \include VectorwiseOp_homogeneous.cpp
+ * Output: \verbinclude VectorwiseOp_homogeneous.out
+ *
+ * \sa MatrixBase::homogeneous() */
+template<typename ExpressionType, int Direction>
+inline Homogeneous<ExpressionType,Direction>
+VectorwiseOp<ExpressionType,Direction>::homogeneous() const
+{
+ return _expression();
+}
+
+/** \geometry_module
+ *
+ * \returns an expression of the homogeneous normalized vector of \c *this
+ *
+ * Example: \include MatrixBase_hnormalized.cpp
+ * Output: \verbinclude MatrixBase_hnormalized.out
+ *
+ * \sa VectorwiseOp::hnormalized() */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::HNormalizedReturnType
+MatrixBase<Derived>::hnormalized() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return ConstStartMinusOne(derived(),0,0,
+ ColsAtCompileTime==1?size()-1:1,
+ ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
+}
+
+/** \geometry_module
+ *
+ * \returns an expression of the homogeneous normalized vector of \c *this
+ *
+ * Example: \include DirectionWise_hnormalized.cpp
+ * Output: \verbinclude DirectionWise_hnormalized.out
+ *
+ * \sa MatrixBase::hnormalized() */
+template<typename ExpressionType, int Direction>
+inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
+VectorwiseOp<ExpressionType,Direction>::hnormalized() const
+{
+ return HNormalized_Block(_expression(),0,0,
+ Direction==Vertical ? _expression().rows()-1 : _expression().rows(),
+ Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
+ Replicate<HNormalized_Factors,
+ Direction==Vertical ? HNormalized_SizeMinusOne : 1,
+ Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
+ (HNormalized_Factors(_expression(),
+ Direction==Vertical ? _expression().rows()-1:0,
+ Direction==Horizontal ? _expression().cols()-1:0,
+ Direction==Vertical ? 1 : _expression().rows(),
+ Direction==Horizontal ? 1 : _expression().cols()),
+ Direction==Vertical ? _expression().rows()-1 : 1,
+ Direction==Horizontal ? _expression().cols()-1 : 1));
+}
+
+namespace internal {
+
+template<typename MatrixOrTransformType>
+struct take_matrix_for_product
+{
+ typedef MatrixOrTransformType type;
+ static const type& run(const type &x) { return x; }
+};
+
+template<typename Scalar, int Dim, int Mode,int Options>
+struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
+{
+ typedef Transform<Scalar, Dim, Mode, Options> TransformType;
+ typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
+ static type run (const TransformType& x) { return x.affine(); }
+};
+
+template<typename Scalar, int Dim, int Options>
+struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
+{
+ typedef Transform<Scalar, Dim, Projective, Options> TransformType;
+ typedef typename TransformType::MatrixType type;
+ static const type& run (const TransformType& x) { return x.matrix(); }
+};
+
+template<typename MatrixType,typename Lhs>
+struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
+{
+ typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
+ typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
+ typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
+ typedef typename make_proper_matrix_type<
+ typename traits<MatrixTypeCleaned>::Scalar,
+ LhsMatrixTypeCleaned::RowsAtCompileTime,
+ MatrixTypeCleaned::ColsAtCompileTime,
+ MatrixTypeCleaned::PlainObject::Options,
+ LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
+ MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
+};
+
+template<typename MatrixType,typename Lhs>
+struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
+ : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
+{
+ typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
+ typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
+ typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
+ typedef typename MatrixType::Index Index;
+ homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
+ : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
+ m_rhs(rhs)
+ {}
+
+ inline Index rows() const { return m_lhs.rows(); }
+ inline Index cols() const { return m_rhs.cols(); }
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ // FIXME investigate how to allow lazy evaluation of this product when possible
+ dst = Block<const LhsMatrixTypeNested,
+ LhsMatrixTypeNested::RowsAtCompileTime,
+ LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
+ (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
+ dst += m_lhs.col(m_lhs.cols()-1).rowwise()
+ .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
+ }
+
+ typename LhsMatrixTypeCleaned::Nested m_lhs;
+ typename MatrixType::Nested m_rhs;
+};
+
+template<typename MatrixType,typename Rhs>
+struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
+{
+ typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
+ MatrixType::RowsAtCompileTime,
+ Rhs::ColsAtCompileTime,
+ MatrixType::PlainObject::Options,
+ MatrixType::MaxRowsAtCompileTime,
+ Rhs::MaxColsAtCompileTime>::type ReturnType;
+};
+
+template<typename MatrixType,typename Rhs>
+struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
+ : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
+{
+ typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
+ typedef typename MatrixType::Index Index;
+ homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {}
+
+ inline Index rows() const { return m_lhs.rows(); }
+ inline Index cols() const { return m_rhs.cols(); }
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ // FIXME investigate how to allow lazy evaluation of this product when possible
+ dst = m_lhs * Block<const RhsNested,
+ RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
+ RhsNested::ColsAtCompileTime>
+ (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
+ dst += m_rhs.row(m_rhs.rows()-1).colwise()
+ .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
+ }
+
+ typename MatrixType::Nested m_lhs;
+ typename Rhs::Nested m_rhs;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOMOGENEOUS_H
diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h
new file mode 100644
index 0000000..00b7c43
--- /dev/null
+++ b/Eigen/src/Geometry/Hyperplane.h
@@ -0,0 +1,280 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HYPERPLANE_H
+#define EIGEN_HYPERPLANE_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Hyperplane
+ *
+ * \brief A hyperplane
+ *
+ * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
+ * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ * Notice that the dimension of the hyperplane is _AmbientDim-1.
+ *
+ * This class represents an hyperplane as the zero set of the implicit equation
+ * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
+ * and \f$ d \f$ is the distance (offset) to the origin.
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+class Hyperplane
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+ enum {
+ AmbientDimAtCompileTime = _AmbientDim,
+ Options = _Options
+ };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef DenseIndex Index;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+ typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic
+ ? Dynamic
+ : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;
+ typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
+ typedef const Block<const Coefficients,AmbientDimAtCompileTime,1> ConstNormalReturnType;
+
+ /** Default constructor without initialization */
+ inline Hyperplane() {}
+
+ template<int OtherOptions>
+ Hyperplane(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
+ : m_coeffs(other.coeffs())
+ {}
+
+ /** Constructs a dynamic-size hyperplane with \a _dim the dimension
+ * of the ambient space */
+ inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}
+
+ /** Construct a plane from its normal \a n and a point \a e onto the plane.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, const VectorType& e)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = -n.dot(e);
+ }
+
+ /** Constructs a plane from its normal \a n and distance to the origin \a d
+ * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, const Scalar& d)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = d;
+ }
+
+ /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
+ * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
+ {
+ Hyperplane result(p0.size());
+ result.normal() = (p1 - p0).unitOrthogonal();
+ result.offset() = -p0.dot(result.normal());
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
+ * is required to be exactly 3.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
+ Hyperplane result(p0.size());
+ VectorType v0(p2 - p0), v1(p1 - p0);
+ result.normal() = v0.cross(v1);
+ RealScalar norm = result.normal().norm();
+ if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
+ {
+ Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+ JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
+ result.normal() = svd.matrixV().col(2);
+ }
+ else
+ result.normal() /= norm;
+ result.offset() = -p0.dot(result.normal());
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the parametrized line \a parametrized.
+ * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
+ * so an arbitrary choice is made.
+ */
+ // FIXME to be consitent with the rest this could be implemented as a static Through function ??
+ explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
+ {
+ normal() = parametrized.direction().unitOrthogonal();
+ offset() = -parametrized.origin().dot(normal());
+ }
+
+ ~Hyperplane() {}
+
+ /** \returns the dimension in which the plane holds */
+ inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }
+
+ /** normalizes \c *this */
+ void normalize(void)
+ {
+ m_coeffs /= normal().norm();
+ }
+
+ /** \returns the signed distance between the plane \c *this and a point \a p.
+ * \sa absDistance()
+ */
+ inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
+
+ /** \returns the absolute distance between the plane \c *this and a point \a p.
+ * \sa signedDistance()
+ */
+ inline Scalar absDistance(const VectorType& p) const { using std::abs; return abs(signedDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the plane \c *this.
+ */
+ inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
+
+ /** \returns a constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
+
+ /** \returns a non-constant reference to the distance to the origin, which is also the constant part
+ * of the implicit equation */
+ inline Scalar& offset() { return m_coeffs(dim()); }
+
+ /** \returns a constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a non-constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** \returns the intersection of *this with \a other.
+ *
+ * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
+ *
+ * \note If \a other is approximately parallel to *this, this method will return any point on *this.
+ */
+ VectorType intersection(const Hyperplane& other) const
+ {
+ using std::abs;
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
+ // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
+ // whether the two lines are approximately parallel.
+ if(internal::isMuchSmallerThan(det, Scalar(1)))
+ { // special case where the two lines are approximately parallel. Pick any point on the first line.
+ if(abs(coeffs().coeff(1))>abs(coeffs().coeff(0)))
+ return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
+ else
+ return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
+ }
+ else
+ { // general case
+ Scalar invdet = Scalar(1) / det;
+ return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
+ invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
+ }
+ }
+
+ /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+ *
+ * \param mat the Dim x Dim transformation matrix
+ * \param traits specifies whether the matrix \a mat represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ */
+ template<typename XprType>
+ inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+ {
+ if (traits==Affine)
+ normal() = mat.inverse().transpose() * normal();
+ else if (traits==Isometry)
+ normal() = mat * normal();
+ else
+ {
+ eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
+ }
+ return *this;
+ }
+
+ /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+ *
+ * \param t the transformation of dimension Dim
+ * \param traits specifies whether the transformation \a t represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ * Other kind of transformations are not supported.
+ */
+ template<int TrOptions>
+ inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
+ TransformTraits traits = Affine)
+ {
+ transform(t.linear(), traits);
+ offset() -= normal().dot(t.translation());
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
+ {
+ return typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType,int OtherOptions>
+ inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ template<int OtherOptions>
+ bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+
+ Coefficients m_coeffs;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_HYPERPLANE_H
diff --git a/Eigen/src/Geometry/OrthoMethods.h b/Eigen/src/Geometry/OrthoMethods.h
new file mode 100644
index 0000000..556bc81
--- /dev/null
+++ b/Eigen/src/Geometry/OrthoMethods.h
@@ -0,0 +1,218 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ORTHOMETHODS_H
+#define EIGEN_ORTHOMETHODS_H
+
+namespace Eigen {
+
+/** \geometry_module
+ *
+ * \returns the cross product of \c *this and \a other
+ *
+ * Here is a very good explanation of cross-product: http://xkcd.com/199/
+ * \sa MatrixBase::cross3()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
+MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+
+ // Note that there is no need for an expression here since the compiler
+ // optimize such a small temporary very well (even within a complex expression)
+ typename internal::nested<Derived,2>::type lhs(derived());
+ typename internal::nested<OtherDerived,2>::type rhs(other.derived());
+ return typename cross_product_return_type<OtherDerived>::type(
+ numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
+ );
+}
+
+namespace internal {
+
+template< int Arch,typename VectorLhs,typename VectorRhs,
+ typename Scalar = typename VectorLhs::Scalar,
+ bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
+struct cross3_impl {
+ static inline typename internal::plain_matrix_type<VectorLhs>::type
+ run(const VectorLhs& lhs, const VectorRhs& rhs)
+ {
+ return typename internal::plain_matrix_type<VectorLhs>::type(
+ numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
+ 0
+ );
+ }
+};
+
+}
+
+/** \geometry_module
+ *
+ * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
+ *
+ * The size of \c *this and \a other must be four. This function is especially useful
+ * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
+ *
+ * \sa MatrixBase::cross()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
+
+ typedef typename internal::nested<Derived,2>::type DerivedNested;
+ typedef typename internal::nested<OtherDerived,2>::type OtherDerivedNested;
+ DerivedNested lhs(derived());
+ OtherDerivedNested rhs(other.derived());
+
+ return internal::cross3_impl<Architecture::Target,
+ typename internal::remove_all<DerivedNested>::type,
+ typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
+}
+
+/** \returns a matrix expression of the cross product of each column or row
+ * of the referenced expression with the \a other vector.
+ *
+ * The referenced matrix must have one dimension equal to 3.
+ * The result matrix has the same dimensions than the referenced one.
+ *
+ * \geometry_module
+ *
+ * \sa MatrixBase::cross() */
+template<typename ExpressionType, int Direction>
+template<typename OtherDerived>
+const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
+VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ CrossReturnType res(_expression().rows(),_expression().cols());
+ if(Direction==Vertical)
+ {
+ eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
+ res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
+ res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
+ res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
+ }
+ else
+ {
+ eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
+ res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
+ res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
+ res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
+ }
+ return res;
+}
+
+namespace internal {
+
+template<typename Derived, int Size = Derived::SizeAtCompileTime>
+struct unitOrthogonal_selector
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ typedef typename traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename Derived::Index Index;
+ typedef Matrix<Scalar,2,1> Vector2;
+ static inline VectorType run(const Derived& src)
+ {
+ VectorType perp = VectorType::Zero(src.size());
+ Index maxi = 0;
+ Index sndi = 0;
+ src.cwiseAbs().maxCoeff(&maxi);
+ if (maxi==0)
+ sndi = 1;
+ RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
+ perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
+ perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
+
+ return perp;
+ }
+};
+
+template<typename Derived>
+struct unitOrthogonal_selector<Derived,3>
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ typedef typename traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static inline VectorType run(const Derived& src)
+ {
+ VectorType perp;
+ /* Let us compute the crossed product of *this with a vector
+ * that is not too close to being colinear to *this.
+ */
+
+ /* unless the x and y coords are both close to zero, we can
+ * simply take ( -y, x, 0 ) and normalize it.
+ */
+ if((!isMuchSmallerThan(src.x(), src.z()))
+ || (!isMuchSmallerThan(src.y(), src.z())))
+ {
+ RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
+ perp.coeffRef(0) = -numext::conj(src.y())*invnm;
+ perp.coeffRef(1) = numext::conj(src.x())*invnm;
+ perp.coeffRef(2) = 0;
+ }
+ /* if both x and y are close to zero, then the vector is close
+ * to the z-axis, so it's far from colinear to the x-axis for instance.
+ * So we take the crossed product with (1,0,0) and normalize it.
+ */
+ else
+ {
+ RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
+ perp.coeffRef(0) = 0;
+ perp.coeffRef(1) = -numext::conj(src.z())*invnm;
+ perp.coeffRef(2) = numext::conj(src.y())*invnm;
+ }
+
+ return perp;
+ }
+};
+
+template<typename Derived>
+struct unitOrthogonal_selector<Derived,2>
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ static inline VectorType run(const Derived& src)
+ { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
+};
+
+} // end namespace internal
+
+/** \returns a unit vector which is orthogonal to \c *this
+ *
+ * The size of \c *this must be at least 2. If the size is exactly 2,
+ * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
+ *
+ * \sa cross()
+ */
+template<typename Derived>
+typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::unitOrthogonal() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return internal::unitOrthogonal_selector<Derived>::run(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ORTHOMETHODS_H
diff --git a/Eigen/src/Geometry/ParametrizedLine.h b/Eigen/src/Geometry/ParametrizedLine.h
new file mode 100644
index 0000000..77fa228
--- /dev/null
+++ b/Eigen/src/Geometry/ParametrizedLine.h
@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARAMETRIZEDLINE_H
+#define EIGEN_PARAMETRIZEDLINE_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class ParametrizedLine
+ *
+ * \brief A parametrized line
+ *
+ * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
+ * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
+ * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+class ParametrizedLine
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+ enum {
+ AmbientDimAtCompileTime = _AmbientDim,
+ Options = _Options
+ };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef DenseIndex Index;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
+
+ /** Default constructor without initialization */
+ inline ParametrizedLine() {}
+
+ template<int OtherOptions>
+ ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
+ : m_origin(other.origin()), m_direction(other.direction())
+ {}
+
+ /** Constructs a dynamic-size line with \a _dim the dimension
+ * of the ambient space */
+ inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}
+
+ /** Initializes a parametrized line of direction \a direction and origin \a origin.
+ * \warning the vector direction is assumed to be normalized.
+ */
+ ParametrizedLine(const VectorType& origin, const VectorType& direction)
+ : m_origin(origin), m_direction(direction) {}
+
+ template <int OtherOptions>
+ explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
+
+ /** Constructs a parametrized line going from \a p0 to \a p1. */
+ static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+ { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+ ~ParametrizedLine() {}
+
+ /** \returns the dimension in which the line holds */
+ inline Index dim() const { return m_direction.size(); }
+
+ const VectorType& origin() const { return m_origin; }
+ VectorType& origin() { return m_origin; }
+
+ const VectorType& direction() const { return m_direction; }
+ VectorType& direction() { return m_direction; }
+
+ /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+ * \sa distance()
+ */
+ RealScalar squaredDistance(const VectorType& p) const
+ {
+ VectorType diff = p - origin();
+ return (diff - direction().dot(diff) * direction()).squaredNorm();
+ }
+ /** \returns the distance of a point \a p to its projection onto the line \c *this.
+ * \sa squaredDistance()
+ */
+ RealScalar distance(const VectorType& p) const { using std::sqrt; return sqrt(squaredDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the line \c *this. */
+ VectorType projection(const VectorType& p) const
+ { return origin() + direction().dot(p-origin()) * direction(); }
+
+ VectorType pointAt(const Scalar& t) const;
+
+ template <int OtherOptions>
+ Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
+
+ template <int OtherOptions>
+ Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
+
+ template <int OtherOptions>
+ VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
+ {
+ return typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType,int OtherOptions>
+ inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
+ {
+ m_origin = other.origin().template cast<Scalar>();
+ m_direction = other.direction().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
+
+protected:
+
+ VectorType m_origin, m_direction;
+};
+
+/** Constructs a parametrized line from a 2D hyperplane
+ *
+ * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+template <int OtherOptions>
+inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ direction() = hyperplane.normal().unitOrthogonal();
+ origin() = -hyperplane.normal()*hyperplane.offset();
+}
+
+/** \returns the point at \a t along this line
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
+ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const
+{
+ return origin() + (direction()*t);
+}
+
+/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+template <int OtherOptions>
+inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
+{
+ return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
+ / hyperplane.normal().dot(direction());
+}
+
+
+/** \deprecated use intersectionParameter()
+ * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+template <int OtherOptions>
+inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
+{
+ return intersectionParameter(hyperplane);
+}
+
+/** \returns the point of the intersection between \c *this and the given hyperplane
+ */
+template <typename _Scalar, int _AmbientDim, int _Options>
+template <int OtherOptions>
+inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
+ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
+{
+ return pointAt(intersectionParameter(hyperplane));
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARAMETRIZEDLINE_H
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
new file mode 100644
index 0000000..93056f6
--- /dev/null
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -0,0 +1,776 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QUATERNION_H
+#define EIGEN_QUATERNION_H
+namespace Eigen {
+
+
+/***************************************************************************
+* Definition of QuaternionBase<Derived>
+* The implementation is at the end of the file
+***************************************************************************/
+
+namespace internal {
+template<typename Other,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct quaternionbase_assign_impl;
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ * \class QuaternionBase
+ * \brief Base class for quaternion expressions
+ * \tparam Derived derived type (CRTP)
+ * \sa class Quaternion
+ */
+template<class Derived>
+class QuaternionBase : public RotationBase<Derived, 3>
+{
+ typedef RotationBase<Derived, 3> Base;
+public:
+ using Base::operator*;
+ using Base::derived;
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::traits<Derived>::Coefficients Coefficients;
+ enum {
+ Flags = Eigen::internal::traits<Derived>::Flags
+ };
+
+ // typedef typename Matrix<Scalar,4,1> Coefficients;
+ /** the type of a 3D vector */
+ typedef Matrix<Scalar,3,1> Vector3;
+ /** the equivalent rotation matrix type */
+ typedef Matrix<Scalar,3,3> Matrix3;
+ /** the equivalent angle-axis type */
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+
+
+ /** \returns the \c x coefficient */
+ inline Scalar x() const { return this->derived().coeffs().coeff(0); }
+ /** \returns the \c y coefficient */
+ inline Scalar y() const { return this->derived().coeffs().coeff(1); }
+ /** \returns the \c z coefficient */
+ inline Scalar z() const { return this->derived().coeffs().coeff(2); }
+ /** \returns the \c w coefficient */
+ inline Scalar w() const { return this->derived().coeffs().coeff(3); }
+
+ /** \returns a reference to the \c x coefficient */
+ inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
+ /** \returns a reference to the \c y coefficient */
+ inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
+ /** \returns a reference to the \c z coefficient */
+ inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
+ /** \returns a reference to the \c w coefficient */
+ inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
+
+ /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+ inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
+
+ /** \returns a vector expression of the imaginary part (x,y,z) */
+ inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
+
+ /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+ inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
+
+ /** \returns a vector expression of the coefficients (x,y,z,w) */
+ inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
+
+ EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
+ template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
+
+// disabled this copy operator as it is giving very strange compilation errors when compiling
+// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
+// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
+// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
+// Derived& operator=(const QuaternionBase& other)
+// { return operator=<Derived>(other); }
+
+ Derived& operator=(const AngleAxisType& aa);
+ template<class OtherDerived> Derived& operator=(const MatrixBase<OtherDerived>& m);
+
+ /** \returns a quaternion representing an identity rotation
+ * \sa MatrixBase::Identity()
+ */
+ static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
+
+ /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
+ */
+ inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
+
+ /** \returns the squared norm of the quaternion's coefficients
+ * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
+ */
+ inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
+
+ /** \returns the norm of the quaternion's coefficients
+ * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
+ */
+ inline Scalar norm() const { return coeffs().norm(); }
+
+ /** Normalizes the quaternion \c *this
+ * \sa normalized(), MatrixBase::normalize() */
+ inline void normalize() { coeffs().normalize(); }
+ /** \returns a normalized copy of \c *this
+ * \sa normalize(), MatrixBase::normalized() */
+ inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
+
+ /** \returns the dot product of \c *this and \a other
+ * Geometrically speaking, the dot product of two unit quaternions
+ * corresponds to the cosine of half the angle between the two rotations.
+ * \sa angularDistance()
+ */
+ template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
+
+ template<class OtherDerived> Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
+
+ /** \returns an equivalent 3x3 rotation matrix */
+ Matrix3 toRotationMatrix() const;
+
+ /** \returns the quaternion which transform \a a into \a b through a rotation */
+ template<typename Derived1, typename Derived2>
+ Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ template<class OtherDerived> EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
+ template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
+
+ /** \returns the quaternion describing the inverse rotation */
+ Quaternion<Scalar> inverse() const;
+
+ /** \returns the conjugated quaternion */
+ Quaternion<Scalar> conjugate() const;
+
+ template<class OtherDerived> Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ template<class OtherDerived>
+ bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return coeffs().isApprox(other.coeffs(), prec); }
+
+ /** return the result vector of \a v through the rotation*/
+ EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
+ {
+ return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());
+ }
+
+#ifdef EIGEN_QUATERNIONBASE_PLUGIN
+# include EIGEN_QUATERNIONBASE_PLUGIN
+#endif
+};
+
+/***************************************************************************
+* Definition/implementation of Quaternion<Scalar>
+***************************************************************************/
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Quaternion
+ *
+ * \brief The quaternion class used to represent 3D orientations and rotations
+ *
+ * \tparam _Scalar the scalar type, i.e., the type of the coefficients
+ * \tparam _Options controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
+ *
+ * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
+ * orientations and rotations of objects in three dimensions. Compared to other representations
+ * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
+ * \li \b compact storage (4 scalars)
+ * \li \b efficient to compose (28 flops),
+ * \li \b stable spherical interpolation
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c Quaternionf for \c float
+ * \li \c Quaterniond for \c double
+ *
+ * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
+ *
+ * \sa class AngleAxis, class Transform
+ */
+
+namespace internal {
+template<typename _Scalar,int _Options>
+struct traits<Quaternion<_Scalar,_Options> >
+{
+ typedef Quaternion<_Scalar,_Options> PlainObject;
+ typedef _Scalar Scalar;
+ typedef Matrix<_Scalar,4,1,_Options> Coefficients;
+ enum{
+ IsAligned = internal::traits<Coefficients>::Flags & AlignedBit,
+ Flags = IsAligned ? (AlignedBit | LvalueBit) : LvalueBit
+ };
+};
+}
+
+template<typename _Scalar, int _Options>
+class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
+{
+ typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
+ enum { IsAligned = internal::traits<Quaternion>::IsAligned };
+
+public:
+ typedef _Scalar Scalar;
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
+ using Base::operator*=;
+
+ typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
+ typedef typename Base::AngleAxisType AngleAxisType;
+
+ /** Default constructor leaving the quaternion uninitialized. */
+ inline Quaternion() {}
+
+ /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+ * its four coefficients \a w, \a x, \a y and \a z.
+ *
+ * \warning Note the order of the arguments: the real \a w coefficient first,
+ * while internally the coefficients are stored in the following order:
+ * [\c x, \c y, \c z, \c w]
+ */
+ inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
+
+ /** Constructs and initialize a quaternion from the array data */
+ inline Quaternion(const Scalar* data) : m_coeffs(data) {}
+
+ /** Copy constructor */
+ template<class Derived> EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
+
+ /** Constructs and initializes a quaternion from the angle-axis \a aa */
+ explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+ /** Constructs and initializes a quaternion from either:
+ * - a rotation matrix expression,
+ * - a 4D vector expression representing quaternion coefficients.
+ */
+ template<typename Derived>
+ explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+ /** Explicit copy constructor with scalar conversion */
+ template<typename OtherScalar, int OtherOptions>
+ explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ template<typename Derived1, typename Derived2>
+ static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ inline Coefficients& coeffs() { return m_coeffs;}
+ inline const Coefficients& coeffs() const { return m_coeffs;}
+
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(IsAligned)
+
+protected:
+ Coefficients m_coeffs;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ static EIGEN_STRONG_INLINE void _check_template_params()
+ {
+ EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
+ INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ }
+#endif
+};
+
+/** \ingroup Geometry_Module
+ * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+ * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+/***************************************************************************
+* Specialization of Map<Quaternion<Scalar>>
+***************************************************************************/
+
+namespace internal {
+ template<typename _Scalar, int _Options>
+ struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
+ {
+ typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
+ };
+}
+
+namespace internal {
+ template<typename _Scalar, int _Options>
+ struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
+ {
+ typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
+ typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
+ enum {
+ Flags = TraitsBase::Flags & ~LvalueBit
+ };
+ };
+}
+
+/** \ingroup Geometry_Module
+ * \brief Quaternion expression mapping a constant memory buffer
+ *
+ * \tparam _Scalar the type of the Quaternion coefficients
+ * \tparam _Options see class Map
+ *
+ * This is a specialization of class Map for Quaternion. This class allows to view
+ * a 4 scalar memory buffer as an Eigen's Quaternion object.
+ *
+ * \sa class Map, class Quaternion, class QuaternionBase
+ */
+template<typename _Scalar, int _Options>
+class Map<const Quaternion<_Scalar>, _Options >
+ : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
+{
+ typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;
+
+ public:
+ typedef _Scalar Scalar;
+ typedef typename internal::traits<Map>::Coefficients Coefficients;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+ using Base::operator*=;
+
+ /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+ *
+ * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
+ * \code *coeffs == {x, y, z, w} \endcode
+ *
+ * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
+ EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
+
+ inline const Coefficients& coeffs() const { return m_coeffs;}
+
+ protected:
+ const Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * \brief Expression of a quaternion from a memory buffer
+ *
+ * \tparam _Scalar the type of the Quaternion coefficients
+ * \tparam _Options see class Map
+ *
+ * This is a specialization of class Map for Quaternion. This class allows to view
+ * a 4 scalar memory buffer as an Eigen's Quaternion object.
+ *
+ * \sa class Map, class Quaternion, class QuaternionBase
+ */
+template<typename _Scalar, int _Options>
+class Map<Quaternion<_Scalar>, _Options >
+ : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
+{
+ typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
+
+ public:
+ typedef _Scalar Scalar;
+ typedef typename internal::traits<Map>::Coefficients Coefficients;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+ using Base::operator*=;
+
+ /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+ *
+ * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
+ * \code *coeffs == {x, y, z, w} \endcode
+ *
+ * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
+ EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
+
+ inline Coefficients& coeffs() { return m_coeffs; }
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ protected:
+ Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * Map an unaligned array of single precision scalars as a quaternion */
+typedef Map<Quaternion<float>, 0> QuaternionMapf;
+/** \ingroup Geometry_Module
+ * Map an unaligned array of double precision scalars as a quaternion */
+typedef Map<Quaternion<double>, 0> QuaternionMapd;
+/** \ingroup Geometry_Module
+ * Map a 16-byte aligned array of single precision scalars as a quaternion */
+typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
+/** \ingroup Geometry_Module
+ * Map a 16-byte aligned array of double precision scalars as a quaternion */
+typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
+
+/***************************************************************************
+* Implementation of QuaternionBase methods
+***************************************************************************/
+
+// Generic Quaternion * Quaternion product
+// This product can be specialized for a given architecture via the Arch template argument.
+namespace internal {
+template<int Arch, class Derived1, class Derived2, typename Scalar, int _Options> struct quat_product
+{
+ static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
+ return Quaternion<Scalar>
+ (
+ a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+ a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+ a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+ a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+ );
+ }
+};
+}
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ return internal::quat_product<Architecture::Target, Derived, OtherDerived,
+ typename internal::traits<Derived>::Scalar,
+ internal::traits<Derived>::IsAligned && internal::traits<OtherDerived>::IsAligned>::run(*this, other);
+}
+
+/** \sa operator*(Quaternion) */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
+{
+ derived() = derived() * other.derived();
+ return derived();
+}
+
+/** Rotation of a vector by a quaternion.
+ * \remarks If the quaternion is used to rotate several points (>1)
+ * then it is much more efficient to first convert it to a 3x3 Matrix.
+ * Comparison of the operation cost for n transformations:
+ * - Quaternion2: 30n
+ * - Via a Matrix3: 24 + 15n
+ */
+template <class Derived>
+EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
+QuaternionBase<Derived>::_transformVector(const Vector3& v) const
+{
+ // Note that this algorithm comes from the optimization by hand
+ // of the conversion to a Matrix followed by a Matrix/Vector product.
+ // It appears to be much faster than the common algorithm found
+ // in the literature (30 versus 39 flops). It also requires two
+ // Vector3 as temporaries.
+ Vector3 uv = this->vec().cross(v);
+ uv += uv;
+ return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<class Derived>
+EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
+{
+ coeffs() = other.coeffs();
+ return derived();
+}
+
+template<class Derived>
+template<class OtherDerived>
+EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
+{
+ coeffs() = other.coeffs();
+ return derived();
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+ */
+template<class Derived>
+EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
+{
+ using std::cos;
+ using std::sin;
+ Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+ this->w() = cos(ha);
+ this->vec() = sin(ha) * aa.axis();
+ return derived();
+}
+
+/** Set \c *this from the expression \a xpr:
+ * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+ * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+ * and \a xpr is converted to a quaternion
+ */
+
+template<class Derived>
+template<class MatrixDerived>
+inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
+ return derived();
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
+ * be normalized, otherwise the result is undefined.
+ */
+template<class Derived>
+inline typename QuaternionBase<Derived>::Matrix3
+QuaternionBase<Derived>::toRotationMatrix(void) const
+{
+ // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+ // if not inlined then the cost of the return by value is huge ~ +35%,
+ // however, not inlining this function is an order of magnitude slower, so
+ // it has to be inlined, and so the return by value is not an issue
+ Matrix3 res;
+
+ const Scalar tx = Scalar(2)*this->x();
+ const Scalar ty = Scalar(2)*this->y();
+ const Scalar tz = Scalar(2)*this->z();
+ const Scalar twx = tx*this->w();
+ const Scalar twy = ty*this->w();
+ const Scalar twz = tz*this->w();
+ const Scalar txx = tx*this->x();
+ const Scalar txy = ty*this->x();
+ const Scalar txz = tz*this->x();
+ const Scalar tyy = ty*this->y();
+ const Scalar tyz = tz*this->y();
+ const Scalar tzz = tz*this->z();
+
+ res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
+ res.coeffRef(0,1) = txy-twz;
+ res.coeffRef(0,2) = txz+twy;
+ res.coeffRef(1,0) = txy+twz;
+ res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
+ res.coeffRef(1,2) = tyz-twx;
+ res.coeffRef(2,0) = txz-twy;
+ res.coeffRef(2,1) = tyz+twx;
+ res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
+
+ return res;
+}
+
+/** Sets \c *this to be a quaternion representing a rotation between
+ * the two arbitrary vectors \a a and \a b. In other words, the built
+ * rotation represent a rotation sending the line of direction \a a
+ * to the line of direction \a b, both lines passing through the origin.
+ *
+ * \returns a reference to \c *this.
+ *
+ * Note that the two input vectors do \b not have to be normalized, and
+ * do not need to have the same norm.
+ */
+template<class Derived>
+template<typename Derived1, typename Derived2>
+inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ using std::max;
+ using std::sqrt;
+ Vector3 v0 = a.normalized();
+ Vector3 v1 = b.normalized();
+ Scalar c = v1.dot(v0);
+
+ // if dot == -1, vectors are nearly opposites
+ // => accurately compute the rotation axis by computing the
+ // intersection of the two planes. This is done by solving:
+ // x^T v0 = 0
+ // x^T v1 = 0
+ // under the constraint:
+ // ||x|| = 1
+ // which yields a singular value problem
+ if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
+ {
+ c = (max)(c,Scalar(-1));
+ Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+ JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
+ Vector3 axis = svd.matrixV().col(2);
+
+ Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
+ this->w() = sqrt(w2);
+ this->vec() = axis * sqrt(Scalar(1) - w2);
+ return derived();
+ }
+ Vector3 axis = v0.cross(v1);
+ Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
+ Scalar invs = Scalar(1)/s;
+ this->vec() = axis * invs;
+ this->w() = s * Scalar(0.5);
+
+ return derived();
+}
+
+
+/** Returns a quaternion representing a rotation between
+ * the two arbitrary vectors \a a and \a b. In other words, the built
+ * rotation represent a rotation sending the line of direction \a a
+ * to the line of direction \a b, both lines passing through the origin.
+ *
+ * \returns resulting quaternion
+ *
+ * Note that the two input vectors do \b not have to be normalized, and
+ * do not need to have the same norm.
+ */
+template<typename Scalar, int Options>
+template<typename Derived1, typename Derived2>
+Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ Quaternion quat;
+ quat.setFromTwoVectors(a, b);
+ return quat;
+}
+
+
+/** \returns the multiplicative inverse of \c *this
+ * Note that in most cases, i.e., if you simply want the opposite rotation,
+ * and/or the quaternion is normalized, then it is enough to use the conjugate.
+ *
+ * \sa QuaternionBase::conjugate()
+ */
+template <class Derived>
+inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
+{
+ // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
+ Scalar n2 = this->squaredNorm();
+ if (n2 > Scalar(0))
+ return Quaternion<Scalar>(conjugate().coeffs() / n2);
+ else
+ {
+ // return an invalid result to flag the error
+ return Quaternion<Scalar>(Coefficients::Zero());
+ }
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+ * if the quaternion is normalized.
+ * The conjugate of a quaternion represents the opposite rotation.
+ *
+ * \sa Quaternion2::inverse()
+ */
+template <class Derived>
+inline Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::conjugate() const
+{
+ return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
+}
+
+/** \returns the angle (in radian) between two rotations
+ * \sa dot()
+ */
+template <class Derived>
+template <class OtherDerived>
+inline typename internal::traits<Derived>::Scalar
+QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
+{
+ using std::atan2;
+ using std::abs;
+ Quaternion<Scalar> d = (*this) * other.conjugate();
+ return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
+}
+
+
+
+/** \returns the spherical linear interpolation between the two quaternions
+ * \c *this and \a other at the parameter \a t in [0;1].
+ *
+ * This represents an interpolation for a constant motion between \c *this and \a other,
+ * see also http://en.wikipedia.org/wiki/Slerp.
+ */
+template <class Derived>
+template <class OtherDerived>
+Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
+{
+ using std::acos;
+ using std::sin;
+ using std::abs;
+ static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
+ Scalar d = this->dot(other);
+ Scalar absD = abs(d);
+
+ Scalar scale0;
+ Scalar scale1;
+
+ if(absD>=one)
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ // theta is the angle between the 2 quaternions
+ Scalar theta = acos(absD);
+ Scalar sinTheta = sin(theta);
+
+ scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = sin( ( t * theta) ) / sinTheta;
+ }
+ if(d<Scalar(0)) scale1 = -scale1;
+
+ return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
+}
+
+namespace internal {
+
+// set from a rotation matrix
+template<typename Other>
+struct quaternionbase_assign_impl<Other,3,3>
+{
+ typedef typename Other::Scalar Scalar;
+ typedef DenseIndex Index;
+ template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& mat)
+ {
+ using std::sqrt;
+ // This algorithm comes from "Quaternion Calculus and Fast Animation",
+ // Ken Shoemake, 1987 SIGGRAPH course notes
+ Scalar t = mat.trace();
+ if (t > Scalar(0))
+ {
+ t = sqrt(t + Scalar(1.0));
+ q.w() = Scalar(0.5)*t;
+ t = Scalar(0.5)/t;
+ q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+ q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+ q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+ }
+ else
+ {
+ DenseIndex i = 0;
+ if (mat.coeff(1,1) > mat.coeff(0,0))
+ i = 1;
+ if (mat.coeff(2,2) > mat.coeff(i,i))
+ i = 2;
+ DenseIndex j = (i+1)%3;
+ DenseIndex k = (j+1)%3;
+
+ t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+ q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+ t = Scalar(0.5)/t;
+ q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+ q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+ q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+ }
+ }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct quaternionbase_assign_impl<Other,4,1>
+{
+ typedef typename Other::Scalar Scalar;
+ template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& vec)
+ {
+ q.coeffs() = vec;
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_QUATERNION_H
diff --git a/Eigen/src/Geometry/Rotation2D.h b/Eigen/src/Geometry/Rotation2D.h
new file mode 100644
index 0000000..a2d59fc
--- /dev/null
+++ b/Eigen/src/Geometry/Rotation2D.h
@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ROTATION2D_H
+#define EIGEN_ROTATION2D_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Rotation2D
+ *
+ * \brief Represents a rotation/orientation in a 2 dimensional space.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ *
+ * This class is equivalent to a single scalar representing a counter clock wise rotation
+ * as a single angle in radian. It provides some additional features such as the automatic
+ * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
+ * interface to Quaternion in order to facilitate the writing of generic algorithms
+ * dealing with rotations.
+ *
+ * \sa class Quaternion, class Transform
+ */
+
+namespace internal {
+
+template<typename _Scalar> struct traits<Rotation2D<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+} // end namespace internal
+
+template<typename _Scalar>
+class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
+{
+ typedef RotationBase<Rotation2D<_Scalar>,2> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 2 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,2,2> Matrix2;
+
+protected:
+
+ Scalar m_angle;
+
+public:
+
+ /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+ inline Rotation2D(const Scalar& a) : m_angle(a) {}
+
+ /** Default constructor wihtout initialization. The represented rotation is undefined. */
+ Rotation2D() {}
+
+ /** \returns the rotation angle */
+ inline Scalar angle() const { return m_angle; }
+
+ /** \returns a read-write reference to the rotation angle */
+ inline Scalar& angle() { return m_angle; }
+
+ /** \returns the inverse rotation */
+ inline Rotation2D inverse() const { return -m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D operator*(const Rotation2D& other) const
+ { return m_angle + other.m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D& operator*=(const Rotation2D& other)
+ { m_angle += other.m_angle; return *this; }
+
+ /** Applies the rotation to a 2D vector */
+ Vector2 operator* (const Vector2& vec) const
+ { return toRotationMatrix() * vec; }
+
+ template<typename Derived>
+ Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix2 toRotationMatrix() const;
+
+ /** \returns the spherical interpolation between \c *this and \a other using
+ * parameter \a t. It is in fact equivalent to a linear interpolation.
+ */
+ inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
+ { return m_angle * (1-t) + other.angle() * t; }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
+ {
+ m_angle = Scalar(other.angle());
+ }
+
+ static inline Rotation2D Identity() { return Rotation2D(0); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return internal::isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision 2D rotation type */
+typedef Rotation2D<float> Rotation2Df;
+/** \ingroup Geometry_Module
+ * double precision 2D rotation type */
+typedef Rotation2D<double> Rotation2Dd;
+
+/** Set \c *this from a 2x2 rotation matrix \a mat.
+ * In other words, this function extract the rotation angle
+ * from the rotation matrix.
+ */
+template<typename Scalar>
+template<typename Derived>
+Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ using std::atan2;
+ EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
+ return *this;
+}
+
+/** Constructs and \returns an equivalent 2x2 rotation matrix.
+ */
+template<typename Scalar>
+typename Rotation2D<Scalar>::Matrix2
+Rotation2D<Scalar>::toRotationMatrix(void) const
+{
+ using std::sin;
+ using std::cos;
+ Scalar sinA = sin(m_angle);
+ Scalar cosA = cos(m_angle);
+ return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ROTATION2D_H
diff --git a/Eigen/src/Geometry/RotationBase.h b/Eigen/src/Geometry/RotationBase.h
new file mode 100644
index 0000000..b88661d
--- /dev/null
+++ b/Eigen/src/Geometry/RotationBase.h
@@ -0,0 +1,206 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ROTATIONBASE_H
+#define EIGEN_ROTATIONBASE_H
+
+namespace Eigen {
+
+// forward declaration
+namespace internal {
+template<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
+struct rotation_base_generic_product_selector;
+}
+
+/** \class RotationBase
+ *
+ * \brief Common base class for compact rotation representations
+ *
+ * \param Derived is the derived type, i.e., a rotation type
+ * \param _Dim the dimension of the space
+ */
+template<typename Derived, int _Dim>
+class RotationBase
+{
+ public:
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
+ typedef Matrix<Scalar,Dim,1> VectorType;
+
+ public:
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /** \returns an equivalent rotation matrix */
+ inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns an equivalent rotation matrix
+ * This function is added to be conform with the Transform class' naming scheme.
+ */
+ inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns the inverse rotation */
+ inline Derived inverse() const { return derived().inverse(); }
+
+ /** \returns the concatenation of the rotation \c *this with a translation \a t */
+ inline Transform<Scalar,Dim,Isometry> operator*(const Translation<Scalar,Dim>& t) const
+ { return Transform<Scalar,Dim,Isometry>(*this) * t; }
+
+ /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
+ inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
+ { return toRotationMatrix() * s.factor(); }
+
+ /** \returns the concatenation of the rotation \c *this with a generic expression \a e
+ * \a e can be:
+ * - a DimxDim linear transformation matrix
+ * - a DimxDim diagonal matrix (axis aligned scaling)
+ * - a vector of size Dim
+ */
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE typename internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType
+ operator*(const EigenBase<OtherDerived>& e) const
+ { return internal::rotation_base_generic_product_selector<Derived,OtherDerived>::run(derived(), e.derived()); }
+
+ /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
+ template<typename OtherDerived> friend
+ inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r)
+ { return l.derived() * r.toRotationMatrix(); }
+
+ /** \returns the concatenation of a scaling \a l with the rotation \a r */
+ friend inline Transform<Scalar,Dim,Affine> operator*(const DiagonalMatrix<Scalar,Dim>& l, const Derived& r)
+ {
+ Transform<Scalar,Dim,Affine> res(r);
+ res.linear().applyOnTheLeft(l);
+ return res;
+ }
+
+ /** \returns the concatenation of the rotation \c *this with a transformation \a t */
+ template<int Mode, int Options>
+ inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const
+ { return toRotationMatrix() * t; }
+
+ template<typename OtherVectorType>
+ inline VectorType _transformVector(const OtherVectorType& v) const
+ { return toRotationMatrix() * v; }
+};
+
+namespace internal {
+
+// implementation of the generic product rotation * matrix
+template<typename RotationDerived, typename MatrixType>
+struct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>
+{
+ enum { Dim = RotationDerived::Dim };
+ typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;
+ static inline ReturnType run(const RotationDerived& r, const MatrixType& m)
+ { return r.toRotationMatrix() * m; }
+};
+
+template<typename RotationDerived, typename Scalar, int Dim, int MaxDim>
+struct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >
+{
+ typedef Transform<Scalar,Dim,Affine> ReturnType;
+ static inline ReturnType run(const RotationDerived& r, const DiagonalMatrix<Scalar,Dim,MaxDim>& m)
+ {
+ ReturnType res(r);
+ res.linear() *= m;
+ return res;
+ }
+};
+
+template<typename RotationDerived,typename OtherVectorType>
+struct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>
+{
+ enum { Dim = RotationDerived::Dim };
+ typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;
+ static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v)
+ {
+ return r._transformVector(v);
+ }
+};
+
+} // end namespace internal
+
+/** \geometry_module
+ *
+ * \brief Constructs a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ *this = r.toRotationMatrix();
+}
+
+/** \geometry_module
+ *
+ * \brief Set a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ return *this = r.toRotationMatrix();
+}
+
+namespace internal {
+
+/** \internal
+ *
+ * Helper function to return an arbitrary rotation object to a rotation matrix.
+ *
+ * \param Scalar the numeric type of the matrix coefficients
+ * \param Dim the dimension of the current space
+ *
+ * It returns a Dim x Dim fixed size matrix.
+ *
+ * Default specializations are provided for:
+ * - any scalar type (2D),
+ * - any matrix expression,
+ * - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
+ *
+ * Currently toRotationMatrix is only used by Transform.
+ *
+ * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
+ */
+template<typename Scalar, int Dim>
+static inline Matrix<Scalar,2,2> toRotationMatrix(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return Rotation2D<Scalar>(s).toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
+{
+ return r.toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat)
+{
+ EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
+ YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return mat;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ROTATIONBASE_H
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
new file mode 100644
index 0000000..1c25f36
--- /dev/null
+++ b/Eigen/src/Geometry/Scaling.h
@@ -0,0 +1,166 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SCALING_H
+#define EIGEN_SCALING_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Scaling
+ *
+ * \brief Represents a generic uniform scaling transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ *
+ * This class represent a uniform scaling transformation. It is the return
+ * type of Scaling(Scalar), and most of the time this is the only way it
+ * is used. In particular, this class is not aimed to be used to store a scaling transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * To represent an axis aligned scaling, use the DiagonalMatrix class.
+ *
+ * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
+ */
+template<typename _Scalar>
+class UniformScaling
+{
+public:
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+
+protected:
+
+ Scalar m_factor;
+
+public:
+
+ /** Default constructor without initialization. */
+ UniformScaling() {}
+ /** Constructs and initialize a uniform scaling transformation */
+ explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
+
+ inline const Scalar& factor() const { return m_factor; }
+ inline Scalar& factor() { return m_factor; }
+
+ /** Concatenates two uniform scaling */
+ inline UniformScaling operator* (const UniformScaling& other) const
+ { return UniformScaling(m_factor * other.factor()); }
+
+ /** Concatenates a uniform scaling and a translation */
+ template<int Dim>
+ inline Transform<Scalar,Dim,Affine> operator* (const Translation<Scalar,Dim>& t) const;
+
+ /** Concatenates a uniform scaling and an affine transformation */
+ template<int Dim, int Mode, int Options>
+ inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> operator* (const Transform<Scalar,Dim, Mode, Options>& t) const
+ {
+ Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> res = t;
+ res.prescale(factor());
+ return res;
+}
+
+ /** Concatenates a uniform scaling and a linear transformation matrix */
+ // TODO returns an expression
+ template<typename Derived>
+ inline typename internal::plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const
+ { return other * m_factor; }
+
+ template<typename Derived,int Dim>
+ inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
+ { return r.toRotationMatrix() * m_factor; }
+
+ /** \returns the inverse scaling */
+ inline UniformScaling inverse() const
+ { return UniformScaling(Scalar(1)/m_factor); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline UniformScaling<NewScalarType> cast() const
+ { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
+ { m_factor = Scalar(other.factor()); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return internal::isApprox(m_factor, other.factor(), prec); }
+
+};
+
+/** Concatenates a linear transformation matrix and a uniform scaling */
+// NOTE this operator is defiend in MatrixBase and not as a friend function
+// of UniformScaling to fix an internal crash of Intel's ICC
+template<typename Derived> typename MatrixBase<Derived>::ScalarMultipleReturnType
+MatrixBase<Derived>::operator*(const UniformScaling<Scalar>& s) const
+{ return derived() * s.factor(); }
+
+/** Constructs a uniform scaling from scale factor \a s */
+static inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+static inline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+template<typename RealScalar>
+static inline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)
+{ return UniformScaling<std::complex<RealScalar> >(s); }
+
+/** Constructs a 2D axis aligned scaling */
+template<typename Scalar>
+static inline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)
+{ return DiagonalMatrix<Scalar,2>(sx, sy); }
+/** Constructs a 3D axis aligned scaling */
+template<typename Scalar>
+static inline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
+
+/** Constructs an axis aligned scaling expression from vector expression \a coeffs
+ * This is an alias for coeffs.asDiagonal()
+ */
+template<typename Derived>
+static inline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)
+{ return coeffs.asDiagonal(); }
+
+/** \addtogroup Geometry_Module */
+//@{
+/** \deprecated */
+typedef DiagonalMatrix<float, 2> AlignedScaling2f;
+/** \deprecated */
+typedef DiagonalMatrix<double,2> AlignedScaling2d;
+/** \deprecated */
+typedef DiagonalMatrix<float, 3> AlignedScaling3f;
+/** \deprecated */
+typedef DiagonalMatrix<double,3> AlignedScaling3d;
+//@}
+
+template<typename Scalar>
+template<int Dim>
+inline Transform<Scalar,Dim,Affine>
+UniformScaling<Scalar>::operator* (const Translation<Scalar,Dim>& t) const
+{
+ Transform<Scalar,Dim,Affine> res;
+ res.matrix().setZero();
+ res.linear().diagonal().fill(factor());
+ res.translation() = factor() * t.vector();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SCALING_H
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
new file mode 100644
index 0000000..e786e53
--- /dev/null
+++ b/Eigen/src/Geometry/Transform.h
@@ -0,0 +1,1455 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSFORM_H
+#define EIGEN_TRANSFORM_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Transform>
+struct transform_traits
+{
+ enum
+ {
+ Dim = Transform::Dim,
+ HDim = Transform::HDim,
+ Mode = Transform::Mode,
+ IsProjective = (int(Mode)==int(Projective))
+ };
+};
+
+template< typename TransformType,
+ typename MatrixType,
+ int Case = transform_traits<TransformType>::IsProjective ? 0
+ : int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1
+ : 2>
+struct transform_right_product_impl;
+
+template< typename Other,
+ int Mode,
+ int Options,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct transform_left_product_impl;
+
+template< typename Lhs,
+ typename Rhs,
+ bool AnyProjective =
+ transform_traits<Lhs>::IsProjective ||
+ transform_traits<Rhs>::IsProjective>
+struct transform_transform_product_impl;
+
+template< typename Other,
+ int Mode,
+ int Options,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct transform_construct_from_matrix;
+
+template<typename TransformType> struct transform_take_affine_part;
+
+template<int Mode> struct transform_make_affine;
+
+} // end namespace internal
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Transform
+ *
+ * \brief Represents an homogeneous transformation in a N dimensional space
+ *
+ * \tparam _Scalar the scalar type, i.e., the type of the coefficients
+ * \tparam _Dim the dimension of the space
+ * \tparam _Mode the type of the transformation. Can be:
+ * - #Affine: the transformation is stored as a (Dim+1)^2 matrix,
+ * where the last row is assumed to be [0 ... 0 1].
+ * - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
+ * - #Projective: the transformation is stored as a (Dim+1)^2 matrix
+ * without any assumption.
+ * \tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
+ * These Options are passed directly to the underlying matrix type.
+ *
+ * The homography is internally represented and stored by a matrix which
+ * is available through the matrix() method. To understand the behavior of
+ * this class you have to think a Transform object as its internal
+ * matrix representation. The chosen convention is right multiply:
+ *
+ * \code v' = T * v \endcode
+ *
+ * Therefore, an affine transformation matrix M is shaped like this:
+ *
+ * \f$ \left( \begin{array}{cc}
+ * linear & translation\\
+ * 0 ... 0 & 1
+ * \end{array} \right) \f$
+ *
+ * Note that for a projective transformation the last row can be anything,
+ * and then the interpretation of different parts might be sightly different.
+ *
+ * However, unlike a plain matrix, the Transform class provides many features
+ * simplifying both its assembly and usage. In particular, it can be composed
+ * with any other transformations (Transform,Translation,RotationBase,Matrix)
+ * and can be directly used to transform implicit homogeneous vectors. All these
+ * operations are handled via the operator*. For the composition of transformations,
+ * its principle consists to first convert the right/left hand sides of the product
+ * to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.
+ * Of course, internally, operator* tries to perform the minimal number of operations
+ * according to the nature of each terms. Likewise, when applying the transform
+ * to non homogeneous vectors, the latters are automatically promoted to homogeneous
+ * one before doing the matrix product. The convertions to homogeneous representations
+ * are performed as follow:
+ *
+ * \b Translation t (Dim)x(1):
+ * \f$ \left( \begin{array}{cc}
+ * I & t \\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Rotation R (Dim)x(Dim):
+ * \f$ \left( \begin{array}{cc}
+ * R & 0\\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Linear \b Matrix L (Dim)x(Dim):
+ * \f$ \left( \begin{array}{cc}
+ * L & 0\\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Affine \b Matrix A (Dim)x(Dim+1):
+ * \f$ \left( \begin{array}{c}
+ * A\\
+ * 0\,...\,0\,1
+ * \end{array} \right) \f$
+ *
+ * \b Column \b vector v (Dim)x(1):
+ * \f$ \left( \begin{array}{c}
+ * v\\
+ * 1
+ * \end{array} \right) \f$
+ *
+ * \b Set \b of \b column \b vectors V1...Vn (Dim)x(n):
+ * \f$ \left( \begin{array}{ccc}
+ * v_1 & ... & v_n\\
+ * 1 & ... & 1
+ * \end{array} \right) \f$
+ *
+ * The concatenation of a Transform object with any kind of other transformation
+ * always returns a Transform object.
+ *
+ * A little exception to the "as pure matrix product" rule is the case of the
+ * transformation of non homogeneous vectors by an affine transformation. In
+ * that case the last matrix row can be ignored, and the product returns non
+ * homogeneous vectors.
+ *
+ * Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,
+ * it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.
+ * The solution is either to use a Dim x Dynamic matrix or explicitly request a
+ * vector transformation by making the vector homogeneous:
+ * \code
+ * m' = T * m.colwise().homogeneous();
+ * \endcode
+ * Note that there is zero overhead.
+ *
+ * Conversion methods from/to Qt's QMatrix and QTransform are available if the
+ * preprocessor token EIGEN_QT_SUPPORT is defined.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_TRANSFORM_PLUGIN.
+ *
+ * \sa class Matrix, class Quaternion
+ */
+template<typename _Scalar, int _Dim, int _Mode, int _Options>
+class Transform
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
+ enum {
+ Mode = _Mode,
+ Options = _Options,
+ Dim = _Dim, ///< space dimension in which the transformation holds
+ HDim = _Dim+1, ///< size of a respective homogeneous vector
+ Rows = int(Mode)==(AffineCompact) ? Dim : HDim
+ };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef DenseIndex Index;
+ /** type of the matrix used to represent the transformation */
+ typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;
+ /** constified MatrixType */
+ typedef const MatrixType ConstMatrixType;
+ /** type of the matrix used to represent the linear part of the transformation */
+ typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;
+ /** type of read reference to the linear part of the transformation */
+ typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;
+ /** type of read/write reference to the affine part of the transformation */
+ typedef typename internal::conditional<int(Mode)==int(AffineCompact),
+ MatrixType&,
+ Block<MatrixType,Dim,HDim> >::type AffinePart;
+ /** type of read reference to the affine part of the transformation */
+ typedef typename internal::conditional<int(Mode)==int(AffineCompact),
+ const MatrixType&,
+ const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart;
+ /** type of a vector */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef Block<MatrixType,Dim,1,int(Mode)==(AffineCompact)> TranslationPart;
+ /** type of a read reference to the translation part of the rotation */
+ typedef const Block<ConstMatrixType,Dim,1,int(Mode)==(AffineCompact)> ConstTranslationPart;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+
+ // this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0
+ enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };
+ /** The return type of the product between a diagonal matrix and a transform */
+ typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;
+
+protected:
+
+ MatrixType m_matrix;
+
+public:
+
+ /** Default constructor without initialization of the meaningful coefficients.
+ * If Mode==Affine, then the last row is set to [0 ... 0 1] */
+ inline Transform()
+ {
+ check_template_params();
+ internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
+ }
+
+ inline Transform(const Transform& other)
+ {
+ check_template_params();
+ m_matrix = other.m_matrix;
+ }
+
+ inline explicit Transform(const TranslationType& t)
+ {
+ check_template_params();
+ *this = t;
+ }
+ inline explicit Transform(const UniformScaling<Scalar>& s)
+ {
+ check_template_params();
+ *this = s;
+ }
+ template<typename Derived>
+ inline explicit Transform(const RotationBase<Derived, Dim>& r)
+ {
+ check_template_params();
+ *this = r;
+ }
+
+ inline Transform& operator=(const Transform& other)
+ { m_matrix = other.m_matrix; return *this; }
+
+ typedef internal::transform_take_affine_part<Transform> take_affine_part;
+
+ /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline explicit Transform(const EigenBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
+
+ check_template_params();
+ internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
+ }
+
+ /** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline Transform& operator=(const EigenBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
+
+ internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
+ return *this;
+ }
+
+ template<int OtherOptions>
+ inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)
+ {
+ check_template_params();
+ // only the options change, we can directly copy the matrices
+ m_matrix = other.matrix();
+ }
+
+ template<int OtherMode,int OtherOptions>
+ inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)
+ {
+ check_template_params();
+ // prevent conversions as:
+ // Affine | AffineCompact | Isometry = Projective
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Projective), Mode==int(Projective)),
+ YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
+
+ // prevent conversions as:
+ // Isometry = Affine | AffineCompact
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),
+ YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
+
+ enum { ModeIsAffineCompact = Mode == int(AffineCompact),
+ OtherModeIsAffineCompact = OtherMode == int(AffineCompact)
+ };
+
+ if(ModeIsAffineCompact == OtherModeIsAffineCompact)
+ {
+ // We need the block expression because the code is compiled for all
+ // combinations of transformations and will trigger a compile time error
+ // if one tries to assign the matrices directly
+ m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);
+ makeAffine();
+ }
+ else if(OtherModeIsAffineCompact)
+ {
+ typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;
+ internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());
+ }
+ else
+ {
+ // here we know that Mode == AffineCompact and OtherMode != AffineCompact.
+ // if OtherMode were Projective, the static assert above would already have caught it.
+ // So the only possibility is that OtherMode == Affine
+ linear() = other.linear();
+ translation() = other.translation();
+ }
+ }
+
+ template<typename OtherDerived>
+ Transform(const ReturnByValue<OtherDerived>& other)
+ {
+ check_template_params();
+ other.evalTo(*this);
+ }
+
+ template<typename OtherDerived>
+ Transform& operator=(const ReturnByValue<OtherDerived>& other)
+ {
+ other.evalTo(*this);
+ return *this;
+ }
+
+ #ifdef EIGEN_QT_SUPPORT
+ inline Transform(const QMatrix& other);
+ inline Transform& operator=(const QMatrix& other);
+ inline QMatrix toQMatrix(void) const;
+ inline Transform(const QTransform& other);
+ inline Transform& operator=(const QTransform& other);
+ inline QTransform toQTransform(void) const;
+ #endif
+
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operator(Index,Index) const */
+ inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operator(Index,Index) */
+ inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }
+
+ /** \returns a read-only expression of the transformation matrix */
+ inline const MatrixType& matrix() const { return m_matrix; }
+ /** \returns a writable expression of the transformation matrix */
+ inline MatrixType& matrix() { return m_matrix; }
+
+ /** \returns a read-only expression of the linear part of the transformation */
+ inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }
+ /** \returns a writable expression of the linear part of the transformation */
+ inline LinearPart linear() { return LinearPart(m_matrix,0,0); }
+
+ /** \returns a read-only expression of the Dim x HDim affine part of the transformation */
+ inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }
+ /** \returns a writable expression of the Dim x HDim affine part of the transformation */
+ inline AffinePart affine() { return take_affine_part::run(m_matrix); }
+
+ /** \returns a read-only expression of the translation vector of the transformation */
+ inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }
+ /** \returns a writable expression of the translation vector of the transformation */
+ inline TranslationPart translation() { return TranslationPart(m_matrix,0,Dim); }
+
+ /** \returns an expression of the product between the transform \c *this and a matrix expression \a other
+ *
+ * The right hand side \a other might be either:
+ * \li a vector of size Dim,
+ * \li an homogeneous vector of size Dim+1,
+ * \li a set of vectors of size Dim x Dynamic,
+ * \li a set of homogeneous vectors of size Dim+1 x Dynamic,
+ * \li a linear transformation matrix of size Dim x Dim,
+ * \li an affine transformation matrix of size Dim x Dim+1,
+ * \li a transformation matrix of size Dim+1 x Dim+1.
+ */
+ // note: this function is defined here because some compilers cannot find the respective declaration
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE const typename internal::transform_right_product_impl<Transform, OtherDerived>::ResultType
+ operator * (const EigenBase<OtherDerived> &other) const
+ { return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }
+
+ /** \returns the product expression of a transformation matrix \a a times a transform \a b
+ *
+ * The left hand side \a other might be either:
+ * \li a linear transformation matrix of size Dim x Dim,
+ * \li an affine transformation matrix of size Dim x Dim+1,
+ * \li a general transformation matrix of size Dim+1 x Dim+1.
+ */
+ template<typename OtherDerived> friend
+ inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType
+ operator * (const EigenBase<OtherDerived> &a, const Transform &b)
+ { return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }
+
+ /** \returns The product expression of a transform \a a times a diagonal matrix \a b
+ *
+ * The rhs diagonal matrix is interpreted as an affine scaling transformation. The
+ * product results in a Transform of the same type (mode) as the lhs only if the lhs
+ * mode is no isometry. In that case, the returned transform is an affinity.
+ */
+ template<typename DiagonalDerived>
+ inline const TransformTimeDiagonalReturnType
+ operator * (const DiagonalBase<DiagonalDerived> &b) const
+ {
+ TransformTimeDiagonalReturnType res(*this);
+ res.linear() *= b;
+ return res;
+ }
+
+ /** \returns The product expression of a diagonal matrix \a a times a transform \a b
+ *
+ * The lhs diagonal matrix is interpreted as an affine scaling transformation. The
+ * product results in a Transform of the same type (mode) as the lhs only if the lhs
+ * mode is no isometry. In that case, the returned transform is an affinity.
+ */
+ template<typename DiagonalDerived>
+ friend inline TransformTimeDiagonalReturnType
+ operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)
+ {
+ TransformTimeDiagonalReturnType res;
+ res.linear().noalias() = a*b.linear();
+ res.translation().noalias() = a*b.translation();
+ if (Mode!=int(AffineCompact))
+ res.matrix().row(Dim) = b.matrix().row(Dim);
+ return res;
+ }
+
+ template<typename OtherDerived>
+ inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }
+
+ /** Concatenates two transformations */
+ inline const Transform operator * (const Transform& other) const
+ {
+ return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);
+ }
+
+ #ifdef __INTEL_COMPILER
+private:
+ // this intermediate structure permits to workaround a bug in ICC 11:
+ // error: template instantiation resulted in unexpected function type of "Eigen::Transform<double, 3, 32, 0>
+ // (const Eigen::Transform<double, 3, 2, 0> &) const"
+ // (the meaning of a name may have changed since the template declaration -- the type of the template is:
+ // "Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,
+ // Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const")
+ //
+ template<int OtherMode,int OtherOptions> struct icc_11_workaround
+ {
+ typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;
+ typedef typename ProductType::ResultType ResultType;
+ };
+
+public:
+ /** Concatenates two different transformations */
+ template<int OtherMode,int OtherOptions>
+ inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType
+ operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
+ {
+ typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;
+ return ProductType::run(*this,other);
+ }
+ #else
+ /** Concatenates two different transformations */
+ template<int OtherMode,int OtherOptions>
+ inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType
+ operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
+ {
+ return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);
+ }
+ #endif
+
+ /** \sa MatrixBase::setIdentity() */
+ void setIdentity() { m_matrix.setIdentity(); }
+
+ /**
+ * \brief Returns an identity transformation.
+ * \todo In the future this function should be returning a Transform expression.
+ */
+ static const Transform Identity()
+ {
+ return Transform(MatrixType::Identity());
+ }
+
+ template<typename OtherDerived>
+ inline Transform& scale(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& prescale(const MatrixBase<OtherDerived> &other);
+
+ inline Transform& scale(const Scalar& s);
+ inline Transform& prescale(const Scalar& s);
+
+ template<typename OtherDerived>
+ inline Transform& translate(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
+
+ template<typename RotationType>
+ inline Transform& rotate(const RotationType& rotation);
+
+ template<typename RotationType>
+ inline Transform& prerotate(const RotationType& rotation);
+
+ Transform& shear(const Scalar& sx, const Scalar& sy);
+ Transform& preshear(const Scalar& sx, const Scalar& sy);
+
+ inline Transform& operator=(const TranslationType& t);
+ inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
+ inline Transform operator*(const TranslationType& t) const;
+
+ inline Transform& operator=(const UniformScaling<Scalar>& t);
+ inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
+ inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode))> operator*(const UniformScaling<Scalar>& s) const
+ {
+ Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode)),Options> res = *this;
+ res.scale(s.factor());
+ return res;
+ }
+
+ inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linear() *= s; return *this; }
+
+ template<typename Derived>
+ inline Transform& operator=(const RotationBase<Derived,Dim>& r);
+ template<typename Derived>
+ inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
+ template<typename Derived>
+ inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
+
+ const LinearMatrixType rotation() const;
+ template<typename RotationMatrixType, typename ScalingMatrixType>
+ void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
+ template<typename ScalingMatrixType, typename RotationMatrixType>
+ void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
+
+ template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+ Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
+
+ inline Transform inverse(TransformTraits traits = (TransformTraits)Mode) const;
+
+ /** \returns a const pointer to the column major internal matrix */
+ const Scalar* data() const { return m_matrix.data(); }
+ /** \returns a non-const pointer to the column major internal matrix */
+ Scalar* data() { return m_matrix.data(); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast() const
+ { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)
+ {
+ check_template_params();
+ m_matrix = other.matrix().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_matrix.isApprox(other.m_matrix, prec); }
+
+ /** Sets the last row to [0 ... 0 1]
+ */
+ void makeAffine()
+ {
+ internal::transform_make_affine<int(Mode)>::run(m_matrix);
+ }
+
+ /** \internal
+ * \returns the Dim x Dim linear part if the transformation is affine,
+ * and the HDim x Dim part for projective transformations.
+ */
+ inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
+ /** \internal
+ * \returns the Dim x Dim linear part if the transformation is affine,
+ * and the HDim x Dim part for projective transformations.
+ */
+ inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
+
+ /** \internal
+ * \returns the translation part if the transformation is affine,
+ * and the last column for projective transformations.
+ */
+ inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
+ /** \internal
+ * \returns the translation part if the transformation is affine,
+ * and the last column for projective transformations.
+ */
+ inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
+
+
+ #ifdef EIGEN_TRANSFORM_PLUGIN
+ #include EIGEN_TRANSFORM_PLUGIN
+ #endif
+
+protected:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ static EIGEN_STRONG_INLINE void check_template_params()
+ {
+ EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ }
+ #endif
+
+};
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Isometry> Isometry2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Isometry> Isometry3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Isometry> Isometry2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Isometry> Isometry3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Affine> Affine2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Affine> Affine3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Affine> Affine2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Affine> Affine3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,AffineCompact> AffineCompact2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,AffineCompact> AffineCompact3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,AffineCompact> AffineCompact2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,AffineCompact> AffineCompact3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Projective> Projective2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Projective> Projective3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Projective> Projective2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Projective> Projective3d;
+
+/**************************
+*** Optional QT support ***
+**************************/
+
+#ifdef EIGEN_QT_SUPPORT
+/** Initializes \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)
+{
+ check_template_params();
+ *this = other;
+}
+
+/** Set \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QMatrix& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ 0, 0, 1;
+ return *this;
+}
+
+/** \returns a QMatrix from \c *this assuming the dimension is 2.
+ *
+ * \warning this conversion might loss data if \c *this is not affine
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+QMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const
+{
+ check_template_params();
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+}
+
+/** Initializes \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)
+{
+ check_template_params();
+ *this = other;
+}
+
+/** Set \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)
+{
+ check_template_params();
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ if (Mode == int(AffineCompact))
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy();
+ else
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ other.m13(), other.m23(), other.m33();
+ return *this;
+}
+
+/** \returns a QTransform from \c *this assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+QTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ if (Mode == int(AffineCompact))
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+ else
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
+}
+#endif
+
+/*********************
+*** Procedural API ***
+*********************/
+
+/** Applies on the right the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa prescale()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ linearExt().noalias() = (linearExt() * other.asDiagonal());
+ return *this;
+}
+
+/** Applies on the right a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa prescale(Scalar)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ linearExt() *= s;
+ return *this;
+}
+
+/** Applies on the left the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa scale()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ m_matrix.template block<Dim,HDim>(0,0).noalias() = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0));
+ return *this;
+}
+
+/** Applies on the left a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa scale(Scalar)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ m_matrix.template topRows<Dim>() *= s;
+ return *this;
+}
+
+/** Applies on the right the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa pretranslate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translationExt() += linearExt() * other;
+ return *this;
+}
+
+/** Applies on the left the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa translate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ if(int(Mode)==int(Projective))
+ affine() += other * m_matrix.row(Dim);
+ else
+ translation() += other;
+ return *this;
+}
+
+/** Applies on the right the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * The template parameter \a RotationType is the type of the rotation which
+ * must be known by internal::toRotationMatrix<>.
+ *
+ * Natively supported types includes:
+ * - any scalar (2D),
+ * - a Dim x Dim matrix expression,
+ * - a Quaternion (3D),
+ * - a AngleAxis (3D)
+ *
+ * This mechanism is easily extendable to support user types such as Euler angles,
+ * or a pair of Quaternion for 4D rotations.
+ *
+ * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationType>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)
+{
+ linearExt() *= internal::toRotationMatrix<Scalar,Dim>(rotation);
+ return *this;
+}
+
+/** Applies on the left the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * See rotate() for further details.
+ *
+ * \sa rotate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationType>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
+{
+ m_matrix.template block<Dim,HDim>(0,0) = internal::toRotationMatrix<Scalar,Dim>(rotation)
+ * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/** Applies on the right the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa preshear()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ VectorType tmp = linear().col(0)*sy + linear().col(1);
+ linear() << linear().col(0) + linear().col(1)*sx, tmp;
+ return *this;
+}
+
+/** Applies on the left the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa shear()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/******************************************************
+*** Scaling, Translation and Rotation compatibility ***
+******************************************************/
+
+template<typename Scalar, int Dim, int Mode, int Options>
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)
+{
+ linear().setIdentity();
+ translation() = t.vector();
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const
+{
+ Transform res = *this;
+ res.translate(t.vector());
+ return res;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)
+{
+ m_matrix.setZero();
+ linear().diagonal().fill(s.factor());
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename Derived>
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)
+{
+ linear() = internal::toRotationMatrix<Scalar,Dim>(r);
+ translation().setZero();
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename Derived>
+inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const RotationBase<Derived,Dim>& r) const
+{
+ Transform res = *this;
+ res.rotate(r.derived());
+ return res;
+}
+
+/************************
+*** Special functions ***
+************************/
+
+/** \returns the rotation part of the transformation
+ *
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), computeScalingRotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+const typename Transform<Scalar,Dim,Mode,Options>::LinearMatrixType
+Transform<Scalar,Dim,Mode,Options>::rotation() const
+{
+ LinearMatrixType result;
+ computeRotationScaling(&result, (LinearMatrixType*)0);
+ return result;
+}
+
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ *
+ *
+ * \svd_module
+ *
+ * \sa computeScalingRotation(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationMatrixType, typename ScalingMatrixType>
+void Transform<Scalar,Dim,Mode,Options>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
+
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ VectorType sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling) scaling->lazyAssign(svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint());
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->lazyAssign(m * svd.matrixV().adjoint());
+ }
+}
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ *
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename ScalingMatrixType, typename RotationMatrixType>
+void Transform<Scalar,Dim,Mode,Options>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
+
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ VectorType sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling) scaling->lazyAssign(svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint());
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->lazyAssign(m * svd.matrixV().adjoint());
+ }
+}
+
+/** Convenient method to set \c *this from a position, orientation and scale
+ * of a 3D object.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
+{
+ linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);
+ linear() *= scale.asDiagonal();
+ translation() = position;
+ makeAffine();
+ return *this;
+}
+
+namespace internal {
+
+template<int Mode>
+struct transform_make_affine
+{
+ template<typename MatrixType>
+ static void run(MatrixType &mat)
+ {
+ static const int Dim = MatrixType::ColsAtCompileTime-1;
+ mat.template block<1,Dim>(Dim,0).setZero();
+ mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
+ }
+};
+
+template<>
+struct transform_make_affine<AffineCompact>
+{
+ template<typename MatrixType> static void run(MatrixType &) { }
+};
+
+// selector needed to avoid taking the inverse of a 3x4 matrix
+template<typename TransformType, int Mode=TransformType::Mode>
+struct projective_transform_inverse
+{
+ static inline void run(const TransformType&, TransformType&)
+ {}
+};
+
+template<typename TransformType>
+struct projective_transform_inverse<TransformType, Projective>
+{
+ static inline void run(const TransformType& m, TransformType& res)
+ {
+ res.matrix() = m.matrix().inverse();
+ }
+};
+
+} // end namespace internal
+
+
+/**
+ *
+ * \returns the inverse transformation according to some given knowledge
+ * on \c *this.
+ *
+ * \param hint allows to optimize the inversion process when the transformation
+ * is known to be not a general transformation (optional). The possible values are:
+ * - #Projective if the transformation is not necessarily affine, i.e., if the
+ * last row is not guaranteed to be [0 ... 0 1]
+ * - #Affine if the last row can be assumed to be [0 ... 0 1]
+ * - #Isometry if the transformation is only a concatenations of translations
+ * and rotations.
+ * The default is the template class parameter \c Mode.
+ *
+ * \warning unless \a traits is always set to NoShear or NoScaling, this function
+ * requires the generic inverse method of MatrixBase defined in the LU module. If
+ * you forget to include this module, then you will get hard to debug linking errors.
+ *
+ * \sa MatrixBase::inverse()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+Transform<Scalar,Dim,Mode,Options>
+Transform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const
+{
+ Transform res;
+ if (hint == Projective)
+ {
+ internal::projective_transform_inverse<Transform>::run(*this, res);
+ }
+ else
+ {
+ if (hint == Isometry)
+ {
+ res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();
+ }
+ else if(hint&Affine)
+ {
+ res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();
+ }
+ else
+ {
+ eigen_assert(false && "Invalid transform traits in Transform::Inverse");
+ }
+ // translation and remaining parts
+ res.matrix().template topRightCorner<Dim,1>()
+ = - res.matrix().template topLeftCorner<Dim,Dim>() * translation();
+ res.makeAffine(); // we do need this, because in the beginning res is uninitialized
+ }
+ return res;
+}
+
+namespace internal {
+
+/*****************************************************
+*** Specializations of take affine part ***
+*****************************************************/
+
+template<typename TransformType> struct transform_take_affine_part {
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename TransformType::AffinePart AffinePart;
+ typedef typename TransformType::ConstAffinePart ConstAffinePart;
+ static inline AffinePart run(MatrixType& m)
+ { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
+ static inline ConstAffinePart run(const MatrixType& m)
+ { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
+};
+
+template<typename Scalar, int Dim, int Options>
+struct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {
+ typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;
+ static inline MatrixType& run(MatrixType& m) { return m; }
+ static inline const MatrixType& run(const MatrixType& m) { return m; }
+};
+
+/*****************************************************
+*** Specializations of construct from matrix ***
+*****************************************************/
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>
+{
+ static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ {
+ transform->linear() = other;
+ transform->translation().setZero();
+ transform->makeAffine();
+ }
+};
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>
+{
+ static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ {
+ transform->affine() = other;
+ transform->makeAffine();
+ }
+};
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>
+{
+ static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ { transform->matrix() = other; }
+};
+
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>
+{
+ static inline void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)
+ { transform->matrix() = other.template block<Dim,HDim>(0,0); }
+};
+
+/**********************************************************
+*** Specializations of operator* with rhs EigenBase ***
+**********************************************************/
+
+template<int LhsMode,int RhsMode>
+struct transform_product_result
+{
+ enum
+ {
+ Mode =
+ (LhsMode == (int)Projective || RhsMode == (int)Projective ) ? Projective :
+ (LhsMode == (int)Affine || RhsMode == (int)Affine ) ? Affine :
+ (LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :
+ (LhsMode == (int)Isometry || RhsMode == (int)Isometry ) ? Isometry : Projective
+ };
+};
+
+template< typename TransformType, typename MatrixType >
+struct transform_right_product_impl< TransformType, MatrixType, 0 >
+{
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ return T.matrix() * other;
+ }
+};
+
+template< typename TransformType, typename MatrixType >
+struct transform_right_product_impl< TransformType, MatrixType, 1 >
+{
+ enum {
+ Dim = TransformType::Dim,
+ HDim = TransformType::HDim,
+ OtherRows = MatrixType::RowsAtCompileTime,
+ OtherCols = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
+
+ typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;
+
+ ResultType res(other.rows(),other.cols());
+ TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;
+ res.row(OtherRows-1) = other.row(OtherRows-1);
+
+ return res;
+ }
+};
+
+template< typename TransformType, typename MatrixType >
+struct transform_right_product_impl< TransformType, MatrixType, 2 >
+{
+ enum {
+ Dim = TransformType::Dim,
+ HDim = TransformType::HDim,
+ OtherRows = MatrixType::RowsAtCompileTime,
+ OtherCols = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
+
+ typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;
+ ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));
+ TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;
+
+ return res;
+ }
+};
+
+/**********************************************************
+*** Specializations of operator* with lhs EigenBase ***
+**********************************************************/
+
+// generic HDim x HDim matrix * T => Projective
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ { return ResultType(other * tr.matrix()); }
+};
+
+// generic HDim x HDim matrix * AffineCompact => Projective
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();
+ res.matrix().col(Dim) += other.col(Dim);
+ return res;
+ }
+};
+
+// affine matrix * T
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.affine().noalias() = other * tr.matrix();
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ return res;
+ }
+};
+
+// affine matrix * AffineCompact
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();
+ res.translation() += other.col(Dim);
+ return res;
+ }
+};
+
+// linear matrix * T
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other, const TransformType& tr)
+ {
+ TransformType res;
+ if(Mode!=int(AffineCompact))
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ res.matrix().template topRows<Dim>().noalias()
+ = other * tr.matrix().template topRows<Dim>();
+ return res;
+ }
+};
+
+/**********************************************************
+*** Specializations of operator* with another Transform ***
+**********************************************************/
+
+template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >
+{
+ enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };
+ typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res;
+ res.linear() = lhs.linear() * rhs.linear();
+ res.translation() = lhs.linear() * rhs.translation() + lhs.translation();
+ res.makeAffine();
+ return res;
+ }
+};
+
+template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ return ResultType( lhs.matrix() * rhs.matrix() );
+ }
+};
+
+template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res;
+ res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();
+ res.matrix().row(Dim) = rhs.matrix().row(Dim);
+ return res;
+ }
+};
+
+template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());
+ res.matrix().col(Dim) += lhs.matrix().col(Dim);
+ return res;
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSFORM_H
diff --git a/Eigen/src/Geometry/Translation.h b/Eigen/src/Geometry/Translation.h
new file mode 100644
index 0000000..7fda179
--- /dev/null
+++ b/Eigen/src/Geometry/Translation.h
@@ -0,0 +1,206 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSLATION_H
+#define EIGEN_TRANSLATION_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Translation
+ *
+ * \brief Represents a translation transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ * \param _Dim the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a translation transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Scaling, class Transform
+ */
+template<typename _Scalar, int _Dim>
+class Translation
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
+ /** dimension of the space */
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim,Affine> AffineTransformType;
+ /** corresponding isometric transformation type */
+ typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ Translation() {}
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy)
+ {
+ eigen_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ eigen_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the translation transformation from a vector of translation coefficients */
+ explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
+
+ /** \brief Retruns the x-translation by value. **/
+ inline Scalar x() const { return m_coeffs.x(); }
+ /** \brief Retruns the y-translation by value. **/
+ inline Scalar y() const { return m_coeffs.y(); }
+ /** \brief Retruns the z-translation by value. **/
+ inline Scalar z() const { return m_coeffs.z(); }
+
+ /** \brief Retruns the x-translation as a reference. **/
+ inline Scalar& x() { return m_coeffs.x(); }
+ /** \brief Retruns the y-translation as a reference. **/
+ inline Scalar& y() { return m_coeffs.y(); }
+ /** \brief Retruns the z-translation as a reference. **/
+ inline Scalar& z() { return m_coeffs.z(); }
+
+ const VectorType& vector() const { return m_coeffs; }
+ VectorType& vector() { return m_coeffs; }
+
+ const VectorType& translation() const { return m_coeffs; }
+ VectorType& translation() { return m_coeffs; }
+
+ /** Concatenates two translation */
+ inline Translation operator* (const Translation& other) const
+ { return Translation(m_coeffs + other.m_coeffs); }
+
+ /** Concatenates a translation and a uniform scaling */
+ inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
+
+ /** Concatenates a translation and a linear transformation */
+ template<typename OtherDerived>
+ inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
+
+ /** Concatenates a translation and a rotation */
+ template<typename Derived>
+ inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * IsometryTransformType(r); }
+
+ /** \returns the concatenation of a linear transformation \a l with the translation \a t */
+ // its a nightmare to define a templated friend function outside its declaration
+ template<typename OtherDerived> friend
+ inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
+ {
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear() = linear.derived();
+ res.translation() = linear.derived() * t.m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+ }
+
+ /** Concatenates a translation and a transformation */
+ template<int Mode, int Options>
+ inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const
+ {
+ Transform<Scalar,Dim,Mode> res = t;
+ res.pretranslate(m_coeffs);
+ return res;
+ }
+
+ /** Applies translation to vector */
+ inline VectorType operator* (const VectorType& other) const
+ { return m_coeffs + other; }
+
+ /** \returns the inverse translation (opposite) */
+ Translation inverse() const { return Translation(-m_coeffs); }
+
+ Translation& operator=(const Translation& other)
+ {
+ m_coeffs = other.m_coeffs;
+ return *this;
+ }
+
+ static const Translation Identity() { return Translation(VectorType::Zero()); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
+ { m_coeffs = other.vector().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Translation<float, 2> Translation2f;
+typedef Translation<double,2> Translation2d;
+typedef Translation<float, 3> Translation3f;
+typedef Translation<double,3> Translation3d;
+//@}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::AffineTransformType
+Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
+{
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal().fill(other.factor());
+ res.translation() = m_coeffs;
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+inline typename Translation<Scalar,Dim>::AffineTransformType
+Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
+{
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear() = linear.derived();
+ res.translation() = m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSLATION_H
diff --git a/Eigen/src/Geometry/Umeyama.h b/Eigen/src/Geometry/Umeyama.h
new file mode 100644
index 0000000..5e20662
--- /dev/null
+++ b/Eigen/src/Geometry/Umeyama.h
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UMEYAMA_H
+#define EIGEN_UMEYAMA_H
+
+// This file requires the user to include
+// * Eigen/Core
+// * Eigen/LU
+// * Eigen/SVD
+// * Eigen/Array
+
+namespace Eigen {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+// These helpers are required since it allows to use mixed types as parameters
+// for the Umeyama. The problem with mixed parameters is that the return type
+// cannot trivially be deduced when float and double types are mixed.
+namespace internal {
+
+// Compile time return type deduction for different MatrixBase types.
+// Different means here different alignment and parameters but the same underlying
+// real scalar type.
+template<typename MatrixType, typename OtherMatrixType>
+struct umeyama_transform_matrix_type
+{
+ enum {
+ MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),
+
+ // When possible we want to choose some small fixed size value since the result
+ // is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want.
+ HomogeneousDimension = int(MinRowsAtCompileTime) == Dynamic ? Dynamic : int(MinRowsAtCompileTime)+1
+ };
+
+ typedef Matrix<typename traits<MatrixType>::Scalar,
+ HomogeneousDimension,
+ HomogeneousDimension,
+ AutoAlign | (traits<MatrixType>::Flags & RowMajorBit ? RowMajor : ColMajor),
+ HomogeneousDimension,
+ HomogeneousDimension
+ > type;
+};
+
+}
+
+#endif
+
+/**
+* \geometry_module \ingroup Geometry_Module
+*
+* \brief Returns the transformation between two point sets.
+*
+* The algorithm is based on:
+* "Least-squares estimation of transformation parameters between two point patterns",
+* Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573
+*
+* It estimates parameters \f$ c, \mathbf{R}, \f$ and \f$ \mathbf{t} \f$ such that
+* \f{align*}
+* \frac{1}{n} \sum_{i=1}^n \vert\vert y_i - (c\mathbf{R}x_i + \mathbf{t}) \vert\vert_2^2
+* \f}
+* is minimized.
+*
+* The algorithm is based on the analysis of the covariance matrix
+* \f$ \Sigma_{\mathbf{x}\mathbf{y}} \in \mathbb{R}^{d \times d} \f$
+* of the input point sets \f$ \mathbf{x} \f$ and \f$ \mathbf{y} \f$ where
+* \f$d\f$ is corresponding to the dimension (which is typically small).
+* The analysis is involving the SVD having a complexity of \f$O(d^3)\f$
+* though the actual computational effort lies in the covariance
+* matrix computation which has an asymptotic lower bound of \f$O(dm)\f$ when
+* the input point sets have dimension \f$d \times m\f$.
+*
+* Currently the method is working only for floating point matrices.
+*
+* \todo Should the return type of umeyama() become a Transform?
+*
+* \param src Source points \f$ \mathbf{x} = \left( x_1, \hdots, x_n \right) \f$.
+* \param dst Destination points \f$ \mathbf{y} = \left( y_1, \hdots, y_n \right) \f$.
+* \param with_scaling Sets \f$ c=1 \f$ when <code>false</code> is passed.
+* \return The homogeneous transformation
+* \f{align*}
+* T = \begin{bmatrix} c\mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{bmatrix}
+* \f}
+* minimizing the resudiual above. This transformation is always returned as an
+* Eigen::Matrix.
+*/
+template <typename Derived, typename OtherDerived>
+typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type
+umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true)
+{
+ typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;
+ typedef typename internal::traits<TransformationMatrixType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename Derived::Index Index;
+
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename internal::traits<OtherDerived>::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ enum { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
+
+ typedef Matrix<Scalar, Dimension, 1> VectorType;
+ typedef Matrix<Scalar, Dimension, Dimension> MatrixType;
+ typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
+
+ const Index m = src.rows(); // dimension
+ const Index n = src.cols(); // number of measurements
+
+ // required for demeaning ...
+ const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);
+
+ // computation of mean
+ const VectorType src_mean = src.rowwise().sum() * one_over_n;
+ const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
+
+ // demeaning of src and dst points
+ const RowMajorMatrixType src_demean = src.colwise() - src_mean;
+ const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
+
+ // Eq. (36)-(37)
+ const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
+
+ // Eq. (38)
+ const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();
+
+ JacobiSVD<MatrixType> svd(sigma, ComputeFullU | ComputeFullV);
+
+ // Initialize the resulting transformation with an identity matrix...
+ TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);
+
+ // Eq. (39)
+ VectorType S = VectorType::Ones(m);
+ if (sigma.determinant()<Scalar(0)) S(m-1) = Scalar(-1);
+
+ // Eq. (40) and (43)
+ const VectorType& d = svd.singularValues();
+ Index rank = 0; for (Index i=0; i<m; ++i) if (!internal::isMuchSmallerThan(d.coeff(i),d.coeff(0))) ++rank;
+ if (rank == m-1) {
+ if ( svd.matrixU().determinant() * svd.matrixV().determinant() > Scalar(0) ) {
+ Rt.block(0,0,m,m).noalias() = svd.matrixU()*svd.matrixV().transpose();
+ } else {
+ const Scalar s = S(m-1); S(m-1) = Scalar(-1);
+ Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
+ S(m-1) = s;
+ }
+ } else {
+ Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
+ }
+
+ if (with_scaling)
+ {
+ // Eq. (42)
+ const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);
+
+ // Eq. (41)
+ Rt.col(m).head(m) = dst_mean;
+ Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;
+ Rt.block(0,0,m,m) *= c;
+ }
+ else
+ {
+ Rt.col(m).head(m) = dst_mean;
+ Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;
+ }
+
+ return Rt;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_UMEYAMA_H
diff --git a/Eigen/src/Geometry/arch/CMakeLists.txt b/Eigen/src/Geometry/arch/CMakeLists.txt
new file mode 100644
index 0000000..1267a79
--- /dev/null
+++ b/Eigen/src/Geometry/arch/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Geometry_arch_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Geometry_arch_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Geometry/arch COMPONENT Devel
+ )
diff --git a/Eigen/src/Geometry/arch/Geometry_SSE.h b/Eigen/src/Geometry/arch/Geometry_SSE.h
new file mode 100644
index 0000000..3d8284f
--- /dev/null
+++ b/Eigen/src/Geometry/arch/Geometry_SSE.h
@@ -0,0 +1,115 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GEOMETRY_SSE_H
+#define EIGEN_GEOMETRY_SSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<class Derived, class OtherDerived>
+struct quat_product<Architecture::SSE, Derived, OtherDerived, float, Aligned>
+{
+ static inline Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+ {
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
+ Quaternion<float> res;
+ __m128 a = _a.coeffs().template packet<Aligned>(0);
+ __m128 b = _b.coeffs().template packet<Aligned>(0);
+ __m128 flip1 = _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a,1,2,0,2),
+ vec4f_swizzle1(b,2,0,1,2)),mask);
+ __m128 flip2 = _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a,3,3,3,1),
+ vec4f_swizzle1(b,0,1,2,1)),mask);
+ pstore(&res.x(),
+ _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,vec4f_swizzle1(b,3,3,3,3)),
+ _mm_mul_ps(vec4f_swizzle1(a,2,0,1,0),
+ vec4f_swizzle1(b,1,2,0,0))),
+ _mm_add_ps(flip1,flip2)));
+ return res;
+ }
+};
+
+template<typename VectorLhs,typename VectorRhs>
+struct cross3_impl<Architecture::SSE,VectorLhs,VectorRhs,float,true>
+{
+ static inline typename plain_matrix_type<VectorLhs>::type
+ run(const VectorLhs& lhs, const VectorRhs& rhs)
+ {
+ __m128 a = lhs.template packet<VectorLhs::Flags&AlignedBit ? Aligned : Unaligned>(0);
+ __m128 b = rhs.template packet<VectorRhs::Flags&AlignedBit ? Aligned : Unaligned>(0);
+ __m128 mul1=_mm_mul_ps(vec4f_swizzle1(a,1,2,0,3),vec4f_swizzle1(b,2,0,1,3));
+ __m128 mul2=_mm_mul_ps(vec4f_swizzle1(a,2,0,1,3),vec4f_swizzle1(b,1,2,0,3));
+ typename plain_matrix_type<VectorLhs>::type res;
+ pstore(&res.x(),_mm_sub_ps(mul1,mul2));
+ return res;
+ }
+};
+
+
+
+
+template<class Derived, class OtherDerived>
+struct quat_product<Architecture::SSE, Derived, OtherDerived, double, Aligned>
+{
+ static inline Quaternion<double> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+ {
+ const Packet2d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
+
+ Quaternion<double> res;
+
+ const double* a = _a.coeffs().data();
+ Packet2d b_xy = _b.coeffs().template packet<Aligned>(0);
+ Packet2d b_zw = _b.coeffs().template packet<Aligned>(2);
+ Packet2d a_xx = pset1<Packet2d>(a[0]);
+ Packet2d a_yy = pset1<Packet2d>(a[1]);
+ Packet2d a_zz = pset1<Packet2d>(a[2]);
+ Packet2d a_ww = pset1<Packet2d>(a[3]);
+
+ // two temporaries:
+ Packet2d t1, t2;
+
+ /*
+ * t1 = ww*xy + yy*zw
+ * t2 = zz*xy - xx*zw
+ * res.xy = t1 +/- swap(t2)
+ */
+ t1 = padd(pmul(a_ww, b_xy), pmul(a_yy, b_zw));
+ t2 = psub(pmul(a_zz, b_xy), pmul(a_xx, b_zw));
+#ifdef EIGEN_VECTORIZE_SSE3
+ EIGEN_UNUSED_VARIABLE(mask)
+ pstore(&res.x(), _mm_addsub_pd(t1, preverse(t2)));
+#else
+ pstore(&res.x(), padd(t1, pxor(mask,preverse(t2))));
+#endif
+
+ /*
+ * t1 = ww*zw - yy*xy
+ * t2 = zz*zw + xx*xy
+ * res.zw = t1 -/+ swap(t2) = swap( swap(t1) +/- t2)
+ */
+ t1 = psub(pmul(a_ww, b_zw), pmul(a_yy, b_xy));
+ t2 = padd(pmul(a_zz, b_zw), pmul(a_xx, b_xy));
+#ifdef EIGEN_VECTORIZE_SSE3
+ EIGEN_UNUSED_VARIABLE(mask)
+ pstore(&res.z(), preverse(_mm_addsub_pd(preverse(t1), t2)));
+#else
+ pstore(&res.z(), psub(t1, pxor(mask,preverse(t2))));
+#endif
+
+ return res;
+}
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GEOMETRY_SSE_H
diff --git a/Eigen/src/Householder/BlockHouseholder.h b/Eigen/src/Householder/BlockHouseholder.h
new file mode 100644
index 0000000..60dbea5
--- /dev/null
+++ b/Eigen/src/Householder/BlockHouseholder.h
@@ -0,0 +1,68 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Vincent Lejeune
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLOCK_HOUSEHOLDER_H
+#define EIGEN_BLOCK_HOUSEHOLDER_H
+
+// This file contains some helper function to deal with block householder reflectors
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal */
+template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
+void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
+{
+ typedef typename TriangularFactorType::Index Index;
+ typedef typename VectorsType::Scalar Scalar;
+ const Index nbVecs = vectors.cols();
+ eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
+
+ for(Index i = 0; i < nbVecs; i++)
+ {
+ Index rs = vectors.rows() - i;
+ Scalar Vii = vectors(i,i);
+ vectors.const_cast_derived().coeffRef(i,i) = Scalar(1);
+ triFactor.col(i).head(i).noalias() = -hCoeffs(i) * vectors.block(i, 0, rs, i).adjoint()
+ * vectors.col(i).tail(rs);
+ vectors.const_cast_derived().coeffRef(i, i) = Vii;
+ // FIXME add .noalias() once the triangular product can work inplace
+ triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
+ * triFactor.col(i).head(i);
+ triFactor(i,i) = hCoeffs(i);
+ }
+}
+
+/** \internal */
+template<typename MatrixType,typename VectorsType,typename CoeffsType>
+void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs)
+{
+ typedef typename MatrixType::Index Index;
+ enum { TFactorSize = MatrixType::ColsAtCompileTime };
+ Index nbVecs = vectors.cols();
+ Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, ColMajor> T(nbVecs,nbVecs);
+ make_block_householder_triangular_factor(T, vectors, hCoeffs);
+
+ const TriangularView<const VectorsType, UnitLower>& V(vectors);
+
+ // A -= V T V^* A
+ Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,0,
+ VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;
+ // FIXME add .noalias() once the triangular product can work inplace
+ tmp = T.template triangularView<Upper>().adjoint() * tmp;
+ mat.noalias() -= V * tmp;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLOCK_HOUSEHOLDER_H
diff --git a/Eigen/src/Householder/CMakeLists.txt b/Eigen/src/Householder/CMakeLists.txt
new file mode 100644
index 0000000..ce4937d
--- /dev/null
+++ b/Eigen/src/Householder/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Householder_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Householder_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Householder COMPONENT Devel
+ )
diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h
new file mode 100644
index 0000000..32112af
--- /dev/null
+++ b/Eigen/src/Householder/Householder.h
@@ -0,0 +1,171 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOUSEHOLDER_H
+#define EIGEN_HOUSEHOLDER_H
+
+namespace Eigen {
+
+namespace internal {
+template<int n> struct decrement_size
+{
+ enum {
+ ret = n==Dynamic ? n : n-1
+ };
+};
+}
+
+/** Computes the elementary reflector H such that:
+ * \f$ H *this = [ beta 0 ... 0]^T \f$
+ * where the transformation H is:
+ * \f$ H = I - tau v v^*\f$
+ * and the vector v is:
+ * \f$ v^T = [1 essential^T] \f$
+ *
+ * The essential part of the vector \c v is stored in *this.
+ *
+ * On output:
+ * \param tau the scaling factor of the Householder transformation
+ * \param beta the result of H * \c *this
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
+{
+ VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
+ makeHouseholder(essentialPart, tau, beta);
+}
+
+/** Computes the elementary reflector H such that:
+ * \f$ H *this = [ beta 0 ... 0]^T \f$
+ * where the transformation H is:
+ * \f$ H = I - tau v v^*\f$
+ * and the vector v is:
+ * \f$ v^T = [1 essential^T] \f$
+ *
+ * On output:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param beta the result of H * \c *this
+ *
+ * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+void MatrixBase<Derived>::makeHouseholder(
+ EssentialPart& essential,
+ Scalar& tau,
+ RealScalar& beta) const
+{
+ using std::sqrt;
+ using numext::conj;
+
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
+ VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
+
+ RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
+ Scalar c0 = coeff(0);
+
+ if(tailSqNorm == RealScalar(0) && numext::imag(c0)==RealScalar(0))
+ {
+ tau = RealScalar(0);
+ beta = numext::real(c0);
+ essential.setZero();
+ }
+ else
+ {
+ beta = sqrt(numext::abs2(c0) + tailSqNorm);
+ if (numext::real(c0)>=RealScalar(0))
+ beta = -beta;
+ essential = tail / (c0 - beta);
+ tau = conj((beta - c0) / beta);
+ }
+}
+
+/** Apply the elementary reflector H given by
+ * \f$ H = I - tau v v^*\f$
+ * with
+ * \f$ v^T = [1 essential^T] \f$
+ * from the left to a vector or matrix.
+ *
+ * On input:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param workspace a pointer to working space with at least
+ * this->cols() * essential.size() entries
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+void MatrixBase<Derived>::applyHouseholderOnTheLeft(
+ const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace)
+{
+ if(rows() == 1)
+ {
+ *this *= Scalar(1)-tau;
+ }
+ else
+ {
+ Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
+ Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
+ tmp.noalias() = essential.adjoint() * bottom;
+ tmp += this->row(0);
+ this->row(0) -= tau * tmp;
+ bottom.noalias() -= tau * essential * tmp;
+ }
+}
+
+/** Apply the elementary reflector H given by
+ * \f$ H = I - tau v v^*\f$
+ * with
+ * \f$ v^T = [1 essential^T] \f$
+ * from the right to a vector or matrix.
+ *
+ * On input:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param workspace a pointer to working space with at least
+ * this->cols() * essential.size() entries
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
+ * MatrixBase::applyHouseholderOnTheLeft()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+void MatrixBase<Derived>::applyHouseholderOnTheRight(
+ const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace)
+{
+ if(cols() == 1)
+ {
+ *this *= Scalar(1)-tau;
+ }
+ else
+ {
+ Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
+ Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
+ tmp.noalias() = right * essential.conjugate();
+ tmp += this->col(0);
+ this->col(0) -= tau * tmp;
+ right.noalias() -= tau * tmp * essential.transpose();
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOUSEHOLDER_H
diff --git a/Eigen/src/Householder/HouseholderSequence.h b/Eigen/src/Householder/HouseholderSequence.h
new file mode 100644
index 0000000..d800ca1
--- /dev/null
+++ b/Eigen/src/Householder/HouseholderSequence.h
@@ -0,0 +1,441 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H
+#define EIGEN_HOUSEHOLDER_SEQUENCE_H
+
+namespace Eigen {
+
+/** \ingroup Householder_Module
+ * \householder_module
+ * \class HouseholderSequence
+ * \brief Sequence of Householder reflections acting on subspaces with decreasing size
+ * \tparam VectorsType type of matrix containing the Householder vectors
+ * \tparam CoeffsType type of vector containing the Householder coefficients
+ * \tparam Side either OnTheLeft (the default) or OnTheRight
+ *
+ * This class represents a product sequence of Householder reflections where the first Householder reflection
+ * acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by
+ * the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace
+ * spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but
+ * one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections
+ * are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods
+ * HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(),
+ * and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence.
+ *
+ * More precisely, the class %HouseholderSequence represents an \f$ n \times n \f$ matrix \f$ H \f$ of the
+ * form \f$ H = \prod_{i=0}^{n-1} H_i \f$ where the i-th Householder reflection is \f$ H_i = I - h_i v_i
+ * v_i^* \f$. The i-th Householder coefficient \f$ h_i \f$ is a scalar and the i-th Householder vector \f$
+ * v_i \f$ is a vector of the form
+ * \f[
+ * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
+ * \f]
+ * The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector.
+ *
+ * Typical usages are listed below, where H is a HouseholderSequence:
+ * \code
+ * A.applyOnTheRight(H); // A = A * H
+ * A.applyOnTheLeft(H); // A = H * A
+ * A.applyOnTheRight(H.adjoint()); // A = A * H^*
+ * A.applyOnTheLeft(H.adjoint()); // A = H^* * A
+ * MatrixXd Q = H; // conversion to a dense matrix
+ * \endcode
+ * In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate operators.
+ *
+ * See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example.
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+
+namespace internal {
+
+template<typename VectorsType, typename CoeffsType, int Side>
+struct traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
+{
+ typedef typename VectorsType::Scalar Scalar;
+ typedef typename VectorsType::Index Index;
+ typedef typename VectorsType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime
+ : traits<VectorsType>::ColsAtCompileTime,
+ ColsAtCompileTime = RowsAtCompileTime,
+ MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime
+ : traits<VectorsType>::MaxColsAtCompileTime,
+ MaxColsAtCompileTime = MaxRowsAtCompileTime,
+ Flags = 0
+ };
+};
+
+template<typename VectorsType, typename CoeffsType, int Side>
+struct hseq_side_dependent_impl
+{
+ typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType;
+ typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;
+ typedef typename VectorsType::Index Index;
+ static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
+ {
+ Index start = k+1+h.m_shift;
+ return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1);
+ }
+};
+
+template<typename VectorsType, typename CoeffsType>
+struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>
+{
+ typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType;
+ typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;
+ typedef typename VectorsType::Index Index;
+ static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
+ {
+ Index start = k+1+h.m_shift;
+ return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose();
+ }
+};
+
+template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type
+{
+ typedef typename scalar_product_traits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
+ ResultScalar;
+ typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
+ 0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;
+};
+
+} // end namespace internal
+
+template<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence
+ : public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> >
+{
+ typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType;
+
+ public:
+ enum {
+ RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime
+ };
+ typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;
+ typedef typename VectorsType::Index Index;
+
+ typedef HouseholderSequence<
+ typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,
+ VectorsType>::type,
+ typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,
+ CoeffsType>::type,
+ Side
+ > ConjugateReturnType;
+
+ /** \brief Constructor.
+ * \param[in] v %Matrix containing the essential parts of the Householder vectors
+ * \param[in] h Vector containing the Householder coefficients
+ *
+ * Constructs the Householder sequence with coefficients given by \p h and vectors given by \p v. The
+ * i-th Householder coefficient \f$ h_i \f$ is given by \p h(i) and the essential part of the i-th
+ * Householder vector \f$ v_i \f$ is given by \p v(k,i) with \p k > \p i (the subdiagonal part of the
+ * i-th column). If \p v has fewer columns than rows, then the Householder sequence contains as many
+ * Householder reflections as there are columns.
+ *
+ * \note The %HouseholderSequence object stores \p v and \p h by reference.
+ *
+ * Example: \include HouseholderSequence_HouseholderSequence.cpp
+ * Output: \verbinclude HouseholderSequence_HouseholderSequence.out
+ *
+ * \sa setLength(), setShift()
+ */
+ HouseholderSequence(const VectorsType& v, const CoeffsType& h)
+ : m_vectors(v), m_coeffs(h), m_trans(false), m_length(v.diagonalSize()),
+ m_shift(0)
+ {
+ }
+
+ /** \brief Copy constructor. */
+ HouseholderSequence(const HouseholderSequence& other)
+ : m_vectors(other.m_vectors),
+ m_coeffs(other.m_coeffs),
+ m_trans(other.m_trans),
+ m_length(other.m_length),
+ m_shift(other.m_shift)
+ {
+ }
+
+ /** \brief Number of rows of transformation viewed as a matrix.
+ * \returns Number of rows
+ * \details This equals the dimension of the space that the transformation acts on.
+ */
+ Index rows() const { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); }
+
+ /** \brief Number of columns of transformation viewed as a matrix.
+ * \returns Number of columns
+ * \details This equals the dimension of the space that the transformation acts on.
+ */
+ Index cols() const { return rows(); }
+
+ /** \brief Essential part of a Householder vector.
+ * \param[in] k Index of Householder reflection
+ * \returns Vector containing non-trivial entries of k-th Householder vector
+ *
+ * This function returns the essential part of the Householder vector \f$ v_i \f$. This is a vector of
+ * length \f$ n-i \f$ containing the last \f$ n-i \f$ entries of the vector
+ * \f[
+ * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
+ * \f]
+ * The index \f$ i \f$ equals \p k + shift(), corresponding to the k-th column of the matrix \p v
+ * passed to the constructor.
+ *
+ * \sa setShift(), shift()
+ */
+ const EssentialVectorType essentialVector(Index k) const
+ {
+ eigen_assert(k >= 0 && k < m_length);
+ return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k);
+ }
+
+ /** \brief %Transpose of the Householder sequence. */
+ HouseholderSequence transpose() const
+ {
+ return HouseholderSequence(*this).setTrans(!m_trans);
+ }
+
+ /** \brief Complex conjugate of the Householder sequence. */
+ ConjugateReturnType conjugate() const
+ {
+ return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
+ .setTrans(m_trans)
+ .setLength(m_length)
+ .setShift(m_shift);
+ }
+
+ /** \brief Adjoint (conjugate transpose) of the Householder sequence. */
+ ConjugateReturnType adjoint() const
+ {
+ return conjugate().setTrans(!m_trans);
+ }
+
+ /** \brief Inverse of the Householder sequence (equals the adjoint). */
+ ConjugateReturnType inverse() const { return adjoint(); }
+
+ /** \internal */
+ template<typename DestType> inline void evalTo(DestType& dst) const
+ {
+ Matrix<Scalar, DestType::RowsAtCompileTime, 1,
+ AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows());
+ evalTo(dst, workspace);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ void evalTo(Dest& dst, Workspace& workspace) const
+ {
+ workspace.resize(rows());
+ Index vecs = m_length;
+ if( internal::is_same<typename internal::remove_all<VectorsType>::type,Dest>::value
+ && internal::extract_data(dst) == internal::extract_data(m_vectors))
+ {
+ // in-place
+ dst.diagonal().setOnes();
+ dst.template triangularView<StrictlyUpper>().setZero();
+ for(Index k = vecs-1; k >= 0; --k)
+ {
+ Index cornerSize = rows() - k - m_shift;
+ if(m_trans)
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+ else
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+
+ // clear the off diagonal vector
+ dst.col(k).tail(rows()-k-1).setZero();
+ }
+ // clear the remaining columns if needed
+ for(Index k = 0; k<cols()-vecs ; ++k)
+ dst.col(k).tail(rows()-k-1).setZero();
+ }
+ else
+ {
+ dst.setIdentity(rows(), rows());
+ for(Index k = vecs-1; k >= 0; --k)
+ {
+ Index cornerSize = rows() - k - m_shift;
+ if(m_trans)
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
+ else
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
+ }
+ }
+ }
+
+ /** \internal */
+ template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
+ {
+ Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows());
+ applyThisOnTheRight(dst, workspace);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const
+ {
+ workspace.resize(dst.rows());
+ for(Index k = 0; k < m_length; ++k)
+ {
+ Index actual_k = m_trans ? m_length-k-1 : k;
+ dst.rightCols(rows()-m_shift-actual_k)
+ .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
+ }
+ }
+
+ /** \internal */
+ template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
+ {
+ Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace(dst.cols());
+ applyThisOnTheLeft(dst, workspace);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace) const
+ {
+ workspace.resize(dst.cols());
+ for(Index k = 0; k < m_length; ++k)
+ {
+ Index actual_k = m_trans ? k : m_length-k-1;
+ dst.bottomRows(rows()-m_shift-actual_k)
+ .applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
+ }
+ }
+
+ /** \brief Computes the product of a Householder sequence with a matrix.
+ * \param[in] other %Matrix being multiplied.
+ * \returns Expression object representing the product.
+ *
+ * This function computes \f$ HM \f$ where \f$ H \f$ is the Householder sequence represented by \p *this
+ * and \f$ M \f$ is the matrix \p other.
+ */
+ template<typename OtherDerived>
+ typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const
+ {
+ typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type
+ res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>());
+ applyThisOnTheLeft(res);
+ return res;
+ }
+
+ template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl;
+
+ /** \brief Sets the length of the Householder sequence.
+ * \param [in] length New value for the length.
+ *
+ * By default, the length \f$ n \f$ of the Householder sequence \f$ H = H_0 H_1 \ldots H_{n-1} \f$ is set
+ * to the number of columns of the matrix \p v passed to the constructor, or the number of rows if that
+ * is smaller. After this function is called, the length equals \p length.
+ *
+ * \sa length()
+ */
+ HouseholderSequence& setLength(Index length)
+ {
+ m_length = length;
+ return *this;
+ }
+
+ /** \brief Sets the shift of the Householder sequence.
+ * \param [in] shift New value for the shift.
+ *
+ * By default, a %HouseholderSequence object represents \f$ H = H_0 H_1 \ldots H_{n-1} \f$ and the i-th
+ * column of the matrix \p v passed to the constructor corresponds to the i-th Householder
+ * reflection. After this function is called, the object represents \f$ H = H_{\mathrm{shift}}
+ * H_{\mathrm{shift}+1} \ldots H_{n-1} \f$ and the i-th column of \p v corresponds to the (shift+i)-th
+ * Householder reflection.
+ *
+ * \sa shift()
+ */
+ HouseholderSequence& setShift(Index shift)
+ {
+ m_shift = shift;
+ return *this;
+ }
+
+ Index length() const { return m_length; } /**< \brief Returns the length of the Householder sequence. */
+ Index shift() const { return m_shift; } /**< \brief Returns the shift of the Householder sequence. */
+
+ /* Necessary for .adjoint() and .conjugate() */
+ template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence;
+
+ protected:
+
+ /** \brief Sets the transpose flag.
+ * \param [in] trans New value of the transpose flag.
+ *
+ * By default, the transpose flag is not set. If the transpose flag is set, then this object represents
+ * \f$ H^T = H_{n-1}^T \ldots H_1^T H_0^T \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$.
+ *
+ * \sa trans()
+ */
+ HouseholderSequence& setTrans(bool trans)
+ {
+ m_trans = trans;
+ return *this;
+ }
+
+ bool trans() const { return m_trans; } /**< \brief Returns the transpose flag. */
+
+ typename VectorsType::Nested m_vectors;
+ typename CoeffsType::Nested m_coeffs;
+ bool m_trans;
+ Index m_length;
+ Index m_shift;
+};
+
+/** \brief Computes the product of a matrix with a Householder sequence.
+ * \param[in] other %Matrix being multiplied.
+ * \param[in] h %HouseholderSequence being multiplied.
+ * \returns Expression object representing the product.
+ *
+ * This function computes \f$ MH \f$ where \f$ M \f$ is the matrix \p other and \f$ H \f$ is the
+ * Householder sequence represented by \p h.
+ */
+template<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side>
+typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h)
+{
+ typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type
+ res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>());
+ h.applyThisOnTheRight(res);
+ return res;
+}
+
+/** \ingroup Householder_Module \householder_module
+ * \brief Convenience function for constructing a Householder sequence.
+ * \returns A HouseholderSequence constructed from the specified arguments.
+ */
+template<typename VectorsType, typename CoeffsType>
+HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h)
+{
+ return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h);
+}
+
+/** \ingroup Householder_Module \householder_module
+ * \brief Convenience function for constructing a Householder sequence.
+ * \returns A HouseholderSequence constructed from the specified arguments.
+ * \details This function differs from householderSequence() in that the template argument \p OnTheSide of
+ * the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft.
+ */
+template<typename VectorsType, typename CoeffsType>
+HouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h)
+{
+ return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H
diff --git a/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
new file mode 100644
index 0000000..73ca9bf
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BASIC_PRECONDITIONERS_H
+#define EIGEN_BASIC_PRECONDITIONERS_H
+
+namespace Eigen {
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A preconditioner based on the digonal entries
+ *
+ * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
+ * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+ * \code
+ * A.diagonal().asDiagonal() . x = b
+ * \endcode
+ *
+ * \tparam _Scalar the type of the scalar.
+ *
+ * This preconditioner is suitable for both selfadjoint and general problems.
+ * The diagonal entries are pre-inverted and stored into a dense vector.
+ *
+ * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
+ *
+ */
+template <typename _Scalar>
+class DiagonalPreconditioner
+{
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef typename Vector::Index Index;
+
+ public:
+ // this typedef is only to export the scalar type and compile-time dimensions to solve_retval
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+
+ DiagonalPreconditioner() : m_isInitialized(false) {}
+
+ template<typename MatType>
+ DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols())
+ {
+ compute(mat);
+ }
+
+ Index rows() const { return m_invdiag.size(); }
+ Index cols() const { return m_invdiag.size(); }
+
+ template<typename MatType>
+ DiagonalPreconditioner& analyzePattern(const MatType& )
+ {
+ return *this;
+ }
+
+ template<typename MatType>
+ DiagonalPreconditioner& factorize(const MatType& mat)
+ {
+ m_invdiag.resize(mat.cols());
+ for(int j=0; j<mat.outerSize(); ++j)
+ {
+ typename MatType::InnerIterator it(mat,j);
+ while(it && it.index()!=j) ++it;
+ if(it && it.index()==j)
+ m_invdiag(j) = Scalar(1)/it.value();
+ else
+ m_invdiag(j) = 0;
+ }
+ m_isInitialized = true;
+ return *this;
+ }
+
+ template<typename MatType>
+ DiagonalPreconditioner& compute(const MatType& mat)
+ {
+ return factorize(mat);
+ }
+
+ template<typename Rhs, typename Dest>
+ void _solve(const Rhs& b, Dest& x) const
+ {
+ x = m_invdiag.array() * b.array() ;
+ }
+
+ template<typename Rhs> inline const internal::solve_retval<DiagonalPreconditioner, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
+ eigen_assert(m_invdiag.size()==b.rows()
+ && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<DiagonalPreconditioner, Rhs>(*this, b.derived());
+ }
+
+ protected:
+ Vector m_invdiag;
+ bool m_isInitialized;
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<DiagonalPreconditioner<_MatrixType>, Rhs>
+ : solve_retval_base<DiagonalPreconditioner<_MatrixType>, Rhs>
+{
+ typedef DiagonalPreconditioner<_MatrixType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A naive preconditioner which approximates any matrix as the identity matrix
+ *
+ * \sa class DiagonalPreconditioner
+ */
+class IdentityPreconditioner
+{
+ public:
+
+ IdentityPreconditioner() {}
+
+ template<typename MatrixType>
+ IdentityPreconditioner(const MatrixType& ) {}
+
+ template<typename MatrixType>
+ IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }
+
+ template<typename MatrixType>
+ IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }
+
+ template<typename MatrixType>
+ IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
+
+ template<typename Rhs>
+ inline const Rhs& solve(const Rhs& b) const { return b; }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_BASIC_PRECONDITIONERS_H
diff --git a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
new file mode 100644
index 0000000..2625c4d
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
@@ -0,0 +1,262 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BICGSTAB_H
+#define EIGEN_BICGSTAB_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level bi conjugate gradient stabilized algorithm
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A preconditioner being able to efficiently solve for an
+ * approximation of Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ * \return false in the case of numerical issue, for example a break down of BiCGSTAB.
+ */
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, int& iters,
+ typename Dest::RealScalar& tol_error)
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ RealScalar tol = tol_error;
+ int maxIters = iters;
+
+ int n = mat.cols();
+ VectorType r = rhs - mat * x;
+ VectorType r0 = r;
+
+ RealScalar r0_sqnorm = r0.squaredNorm();
+ RealScalar rhs_sqnorm = rhs.squaredNorm();
+ if(rhs_sqnorm == 0)
+ {
+ x.setZero();
+ return true;
+ }
+ Scalar rho = 1;
+ Scalar alpha = 1;
+ Scalar w = 1;
+
+ VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
+ VectorType y(n), z(n);
+ VectorType kt(n), ks(n);
+
+ VectorType s(n), t(n);
+
+ RealScalar tol2 = tol*tol;
+ RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
+ int i = 0;
+ int restarts = 0;
+
+ while ( r.squaredNorm()/rhs_sqnorm > tol2 && i<maxIters )
+ {
+ Scalar rho_old = rho;
+
+ rho = r0.dot(r);
+ if (abs(rho) < eps2*r0_sqnorm)
+ {
+ // The new residual vector became too orthogonal to the arbitrarily choosen direction r0
+ // Let's restart with a new r0:
+ r0 = r;
+ rho = r0_sqnorm = r.squaredNorm();
+ if(restarts++ == 0)
+ i = 0;
+ }
+ Scalar beta = (rho/rho_old) * (alpha / w);
+ p = r + beta * (p - w * v);
+
+ y = precond.solve(p);
+
+ v.noalias() = mat * y;
+
+ alpha = rho / r0.dot(v);
+ s = r - alpha * v;
+
+ z = precond.solve(s);
+ t.noalias() = mat * z;
+
+ RealScalar tmp = t.squaredNorm();
+ if(tmp>RealScalar(0))
+ w = t.dot(s) / tmp;
+ else
+ w = Scalar(0);
+ x += alpha * y + w * z;
+ r = s - w * t;
+ ++i;
+ }
+ tol_error = sqrt(r.squaredNorm()/rhs_sqnorm);
+ iters = i;
+ return true;
+}
+
+}
+
+template< typename _MatrixType,
+ typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
+class BiCGSTAB;
+
+namespace internal {
+
+template< typename _MatrixType, typename _Preconditioner>
+struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Preconditioner Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A bi conjugate gradient stabilized solver for sparse square problems
+ *
+ * This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient
+ * stabilized algorithm. The vectors x and b can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ * \code
+ * int n = 10000;
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A(n,n);
+ * // fill A and b
+ * BiCGSTAB<SparseMatrix<double> > solver;
+ * solver.compute(A);
+ * x = solver.solve(b);
+ * std::cout << "#iterations: " << solver.iterations() << std::endl;
+ * std::cout << "estimated error: " << solver.error() << std::endl;
+ * // update b, and solve again
+ * x = solver.solve(b);
+ * \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename _MatrixType, typename _Preconditioner>
+class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >
+{
+ typedef IterativeSolverBase<BiCGSTAB> Base;
+ using Base::mp_matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+public:
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef _Preconditioner Preconditioner;
+
+public:
+
+ /** Default constructor. */
+ BiCGSTAB() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ BiCGSTAB(const MatrixType& A) : Base(A) {}
+
+ ~BiCGSTAB() {}
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
+ * \a x0 as an initial solution.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs,typename Guess>
+ inline const internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess>
+ solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
+ {
+ eigen_assert(m_isInitialized && "BiCGSTAB is not initialized.");
+ eigen_assert(Base::rows()==b.rows()
+ && "BiCGSTAB::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval_with_guess
+ <BiCGSTAB, Rhs, Guess>(*this, b.derived(), x0);
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solveWithGuess(const Rhs& b, Dest& x) const
+ {
+ bool failed = false;
+ for(int j=0; j<b.cols(); ++j)
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ typename Dest::ColXpr xj(x,j);
+ if(!internal::bicgstab(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))
+ failed = true;
+ }
+ m_info = failed ? NumericalIssue
+ : m_error <= Base::m_tolerance ? Success
+ : NoConvergence;
+ m_isInitialized = true;
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const Rhs& b, Dest& x) const
+ {
+// x.setZero();
+ x = b;
+ _solveWithGuess(b,x);
+ }
+
+protected:
+
+};
+
+
+namespace internal {
+
+ template<typename _MatrixType, typename _Preconditioner, typename Rhs>
+struct solve_retval<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs>
+ : solve_retval_base<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs>
+{
+ typedef BiCGSTAB<_MatrixType, _Preconditioner> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BICGSTAB_H
diff --git a/Eigen/src/IterativeLinearSolvers/CMakeLists.txt b/Eigen/src/IterativeLinearSolvers/CMakeLists.txt
new file mode 100644
index 0000000..59ccc00
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_IterativeLinearSolvers_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_IterativeLinearSolvers_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/IterativeLinearSolvers COMPONENT Devel
+ )
diff --git a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
new file mode 100644
index 0000000..8ba4a8d
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
@@ -0,0 +1,255 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONJUGATE_GRADIENT_H
+#define EIGEN_CONJUGATE_GRADIENT_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level conjugate gradient algorithm
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A preconditioner being able to efficiently solve for an
+ * approximation of Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ */
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+EIGEN_DONT_INLINE
+void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, int& iters,
+ typename Dest::RealScalar& tol_error)
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ RealScalar tol = tol_error;
+ int maxIters = iters;
+
+ int n = mat.cols();
+
+ VectorType residual = rhs - mat * x; //initial residual
+
+ RealScalar rhsNorm2 = rhs.squaredNorm();
+ if(rhsNorm2 == 0)
+ {
+ x.setZero();
+ iters = 0;
+ tol_error = 0;
+ return;
+ }
+ RealScalar threshold = tol*tol*rhsNorm2;
+ RealScalar residualNorm2 = residual.squaredNorm();
+ if (residualNorm2 < threshold)
+ {
+ iters = 0;
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ return;
+ }
+
+ VectorType p(n);
+ p = precond.solve(residual); //initial search direction
+
+ VectorType z(n), tmp(n);
+ RealScalar absNew = numext::real(residual.dot(p)); // the square of the absolute value of r scaled by invM
+ int i = 0;
+ while(i < maxIters)
+ {
+ tmp.noalias() = mat * p; // the bottleneck of the algorithm
+
+ Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
+ x += alpha * p; // update solution
+ residual -= alpha * tmp; // update residue
+
+ residualNorm2 = residual.squaredNorm();
+ if(residualNorm2 < threshold)
+ break;
+
+ z = precond.solve(residual); // approximately solve for "A z = residual"
+
+ RealScalar absOld = absNew;
+ absNew = numext::real(residual.dot(z)); // update the absolute value of r
+ RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
+ p = z + beta * p; // update search direction
+ i++;
+ }
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ iters = i;
+}
+
+}
+
+template< typename _MatrixType, int _UpLo=Lower,
+ typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
+class ConjugateGradient;
+
+namespace internal {
+
+template< typename _MatrixType, int _UpLo, typename _Preconditioner>
+struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Preconditioner Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A conjugate gradient solver for sparse self-adjoint problems
+ *
+ * This class allows to solve for A.x = b sparse linear problems using a conjugate gradient algorithm.
+ * The sparse matrix A must be selfadjoint. The vectors x and b can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower,
+ * Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.
+ * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ * \code
+ * int n = 10000;
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A(n,n);
+ * // fill A and b
+ * ConjugateGradient<SparseMatrix<double> > cg;
+ * cg.compute(A);
+ * x = cg.solve(b);
+ * std::cout << "#iterations: " << cg.iterations() << std::endl;
+ * std::cout << "estimated error: " << cg.error() << std::endl;
+ * // update b, and solve again
+ * x = cg.solve(b);
+ * \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename _MatrixType, int _UpLo, typename _Preconditioner>
+class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
+{
+ typedef IterativeSolverBase<ConjugateGradient> Base;
+ using Base::mp_matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+public:
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef _Preconditioner Preconditioner;
+
+ enum {
+ UpLo = _UpLo
+ };
+
+public:
+
+ /** Default constructor. */
+ ConjugateGradient() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ ConjugateGradient(const MatrixType& A) : Base(A) {}
+
+ ~ConjugateGradient() {}
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
+ * \a x0 as an initial solution.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs,typename Guess>
+ inline const internal::solve_retval_with_guess<ConjugateGradient, Rhs, Guess>
+ solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
+ {
+ eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
+ eigen_assert(Base::rows()==b.rows()
+ && "ConjugateGradient::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval_with_guess
+ <ConjugateGradient, Rhs, Guess>(*this, b.derived(), x0);
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solveWithGuess(const Rhs& b, Dest& x) const
+ {
+ typedef typename internal::conditional<UpLo==(Lower|Upper),
+ const MatrixType&,
+ SparseSelfAdjointView<const MatrixType, UpLo>
+ >::type MatrixWrapperType;
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ for(int j=0; j<b.cols(); ++j)
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ typename Dest::ColXpr xj(x,j);
+ internal::conjugate_gradient(MatrixWrapperType(*mp_matrix), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
+ }
+
+ m_isInitialized = true;
+ m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const Rhs& b, Dest& x) const
+ {
+ x.setZero();
+ _solveWithGuess(b,x);
+ }
+
+protected:
+
+};
+
+
+namespace internal {
+
+template<typename _MatrixType, int _UpLo, typename _Preconditioner, typename Rhs>
+struct solve_retval<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner>, Rhs>
+ : solve_retval_base<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner>, Rhs>
+{
+ typedef ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONJUGATE_GRADIENT_H
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
new file mode 100644
index 0000000..4c169aa
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
@@ -0,0 +1,469 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INCOMPLETE_LUT_H
+#define EIGEN_INCOMPLETE_LUT_H
+
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Compute a quick-sort split of a vector
+ * On output, the vector row is permuted such that its elements satisfy
+ * abs(row(i)) >= abs(row(ncut)) if i<ncut
+ * abs(row(i)) <= abs(row(ncut)) if i>ncut
+ * \param row The vector of values
+ * \param ind The array of index for the elements in @p row
+ * \param ncut The number of largest elements to keep
+ **/
+template <typename VectorV, typename VectorI, typename Index>
+Index QuickSplit(VectorV &row, VectorI &ind, Index ncut)
+{
+ typedef typename VectorV::RealScalar RealScalar;
+ using std::swap;
+ using std::abs;
+ Index mid;
+ Index n = row.size(); /* length of the vector */
+ Index first, last ;
+
+ ncut--; /* to fit the zero-based indices */
+ first = 0;
+ last = n-1;
+ if (ncut < first || ncut > last ) return 0;
+
+ do {
+ mid = first;
+ RealScalar abskey = abs(row(mid));
+ for (Index j = first + 1; j <= last; j++) {
+ if ( abs(row(j)) > abskey) {
+ ++mid;
+ swap(row(mid), row(j));
+ swap(ind(mid), ind(j));
+ }
+ }
+ /* Interchange for the pivot element */
+ swap(row(mid), row(first));
+ swap(ind(mid), ind(first));
+
+ if (mid > ncut) last = mid - 1;
+ else if (mid < ncut ) first = mid + 1;
+ } while (mid != ncut );
+
+ return 0; /* mid is equal to ncut */
+}
+
+}// end namespace internal
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \class IncompleteLUT
+ * \brief Incomplete LU factorization with dual-threshold strategy
+ *
+ * During the numerical factorization, two dropping rules are used :
+ * 1) any element whose magnitude is less than some tolerance is dropped.
+ * This tolerance is obtained by multiplying the input tolerance @p droptol
+ * by the average magnitude of all the original elements in the current row.
+ * 2) After the elimination of the row, only the @p fill largest elements in
+ * the L part and the @p fill largest elements in the U part are kept
+ * (in addition to the diagonal element ). Note that @p fill is computed from
+ * the input parameter @p fillfactor which is used the ratio to control the fill_in
+ * relatively to the initial number of nonzero elements.
+ *
+ * The two extreme cases are when @p droptol=0 (to keep all the @p fill*2 largest elements)
+ * and when @p fill=n/2 with @p droptol being different to zero.
+ *
+ * References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization,
+ * Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994.
+ *
+ * NOTE : The following implementation is derived from the ILUT implementation
+ * in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota
+ * released under the terms of the GNU LGPL:
+ * http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README
+ * However, Yousef Saad gave us permission to relicense his ILUT code to MPL2.
+ * See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012:
+ * http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html
+ * alternatively, on GMANE:
+ * http://comments.gmane.org/gmane.comp.lib.eigen/3302
+ */
+template <typename _Scalar>
+class IncompleteLUT : internal::noncopyable
+{
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef SparseMatrix<Scalar,RowMajor> FactorType;
+ typedef SparseMatrix<Scalar,ColMajor> PermutType;
+ typedef typename FactorType::Index Index;
+
+ public:
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+
+ IncompleteLUT()
+ : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10),
+ m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false)
+ {}
+
+ template<typename MatrixType>
+ IncompleteLUT(const MatrixType& mat, const RealScalar& droptol=NumTraits<Scalar>::dummy_precision(), int fillfactor = 10)
+ : m_droptol(droptol),m_fillfactor(fillfactor),
+ m_analysisIsOk(false),m_factorizationIsOk(false),m_isInitialized(false)
+ {
+ eigen_assert(fillfactor != 0);
+ compute(mat);
+ }
+
+ Index rows() const { return m_lu.rows(); }
+
+ Index cols() const { return m_lu.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "IncompleteLUT is not initialized.");
+ return m_info;
+ }
+
+ template<typename MatrixType>
+ void analyzePattern(const MatrixType& amat);
+
+ template<typename MatrixType>
+ void factorize(const MatrixType& amat);
+
+ /**
+ * Compute an incomplete LU factorization with dual threshold on the matrix mat
+ * No pivoting is done in this version
+ *
+ **/
+ template<typename MatrixType>
+ IncompleteLUT<Scalar>& compute(const MatrixType& amat)
+ {
+ analyzePattern(amat);
+ factorize(amat);
+ return *this;
+ }
+
+ void setDroptol(const RealScalar& droptol);
+ void setFillfactor(int fillfactor);
+
+ template<typename Rhs, typename Dest>
+ void _solve(const Rhs& b, Dest& x) const
+ {
+ x = m_Pinv * b;
+ x = m_lu.template triangularView<UnitLower>().solve(x);
+ x = m_lu.template triangularView<Upper>().solve(x);
+ x = m_P * x;
+ }
+
+ template<typename Rhs> inline const internal::solve_retval<IncompleteLUT, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "IncompleteLUT is not initialized.");
+ eigen_assert(cols()==b.rows()
+ && "IncompleteLUT::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<IncompleteLUT, Rhs>(*this, b.derived());
+ }
+
+protected:
+
+ /** keeps off-diagonal entries; drops diagonal entries */
+ struct keep_diag {
+ inline bool operator() (const Index& row, const Index& col, const Scalar&) const
+ {
+ return row!=col;
+ }
+ };
+
+protected:
+
+ FactorType m_lu;
+ RealScalar m_droptol;
+ int m_fillfactor;
+ bool m_analysisIsOk;
+ bool m_factorizationIsOk;
+ bool m_isInitialized;
+ ComputationInfo m_info;
+ PermutationMatrix<Dynamic,Dynamic,Index> m_P; // Fill-reducing permutation
+ PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv; // Inverse permutation
+};
+
+/**
+ * Set control parameter droptol
+ * \param droptol Drop any element whose magnitude is less than this tolerance
+ **/
+template<typename Scalar>
+void IncompleteLUT<Scalar>::setDroptol(const RealScalar& droptol)
+{
+ this->m_droptol = droptol;
+}
+
+/**
+ * Set control parameter fillfactor
+ * \param fillfactor This is used to compute the number @p fill_in of largest elements to keep on each row.
+ **/
+template<typename Scalar>
+void IncompleteLUT<Scalar>::setFillfactor(int fillfactor)
+{
+ this->m_fillfactor = fillfactor;
+}
+
+template <typename Scalar>
+template<typename _MatrixType>
+void IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat)
+{
+ // Compute the Fill-reducing permutation
+ SparseMatrix<Scalar,ColMajor, Index> mat1 = amat;
+ SparseMatrix<Scalar,ColMajor, Index> mat2 = amat.transpose();
+ // Symmetrize the pattern
+ // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice.
+ // on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered...
+ SparseMatrix<Scalar,ColMajor, Index> AtA = mat2 + mat1;
+ AtA.prune(keep_diag());
+ internal::minimum_degree_ordering<Scalar, Index>(AtA, m_P); // Then compute the AMD ordering...
+
+ m_Pinv = m_P.inverse(); // ... and the inverse permutation
+
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_isInitialized = false;
+}
+
+template <typename Scalar>
+template<typename _MatrixType>
+void IncompleteLUT<Scalar>::factorize(const _MatrixType& amat)
+{
+ using std::sqrt;
+ using std::swap;
+ using std::abs;
+
+ eigen_assert((amat.rows() == amat.cols()) && "The factorization should be done on a square matrix");
+ Index n = amat.cols(); // Size of the matrix
+ m_lu.resize(n,n);
+ // Declare Working vectors and variables
+ Vector u(n) ; // real values of the row -- maximum size is n --
+ VectorXi ju(n); // column position of the values in u -- maximum size is n
+ VectorXi jr(n); // Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1
+
+ // Apply the fill-reducing permutation
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ SparseMatrix<Scalar,RowMajor, Index> mat;
+ mat = amat.twistedBy(m_Pinv);
+
+ // Initialization
+ jr.fill(-1);
+ ju.fill(0);
+ u.fill(0);
+
+ // number of largest elements to keep in each row:
+ Index fill_in = static_cast<Index> (amat.nonZeros()*m_fillfactor)/n+1;
+ if (fill_in > n) fill_in = n;
+
+ // number of largest nonzero elements to keep in the L and the U part of the current row:
+ Index nnzL = fill_in/2;
+ Index nnzU = nnzL;
+ m_lu.reserve(n * (nnzL + nnzU + 1));
+
+ // global loop over the rows of the sparse matrix
+ for (Index ii = 0; ii < n; ii++)
+ {
+ // 1 - copy the lower and the upper part of the row i of mat in the working vector u
+
+ Index sizeu = 1; // number of nonzero elements in the upper part of the current row
+ Index sizel = 0; // number of nonzero elements in the lower part of the current row
+ ju(ii) = ii;
+ u(ii) = 0;
+ jr(ii) = ii;
+ RealScalar rownorm = 0;
+
+ typename FactorType::InnerIterator j_it(mat, ii); // Iterate through the current row ii
+ for (; j_it; ++j_it)
+ {
+ Index k = j_it.index();
+ if (k < ii)
+ {
+ // copy the lower part
+ ju(sizel) = k;
+ u(sizel) = j_it.value();
+ jr(k) = sizel;
+ ++sizel;
+ }
+ else if (k == ii)
+ {
+ u(ii) = j_it.value();
+ }
+ else
+ {
+ // copy the upper part
+ Index jpos = ii + sizeu;
+ ju(jpos) = k;
+ u(jpos) = j_it.value();
+ jr(k) = jpos;
+ ++sizeu;
+ }
+ rownorm += numext::abs2(j_it.value());
+ }
+
+ // 2 - detect possible zero row
+ if(rownorm==0)
+ {
+ m_info = NumericalIssue;
+ return;
+ }
+ // Take the 2-norm of the current row as a relative tolerance
+ rownorm = sqrt(rownorm);
+
+ // 3 - eliminate the previous nonzero rows
+ Index jj = 0;
+ Index len = 0;
+ while (jj < sizel)
+ {
+ // In order to eliminate in the correct order,
+ // we must select first the smallest column index among ju(jj:sizel)
+ Index k;
+ Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); // k is relative to the segment
+ k += jj;
+ if (minrow != ju(jj))
+ {
+ // swap the two locations
+ Index j = ju(jj);
+ swap(ju(jj), ju(k));
+ jr(minrow) = jj; jr(j) = k;
+ swap(u(jj), u(k));
+ }
+ // Reset this location
+ jr(minrow) = -1;
+
+ // Start elimination
+ typename FactorType::InnerIterator ki_it(m_lu, minrow);
+ while (ki_it && ki_it.index() < minrow) ++ki_it;
+ eigen_internal_assert(ki_it && ki_it.col()==minrow);
+ Scalar fact = u(jj) / ki_it.value();
+
+ // drop too small elements
+ if(abs(fact) <= m_droptol)
+ {
+ jj++;
+ continue;
+ }
+
+ // linear combination of the current row ii and the row minrow
+ ++ki_it;
+ for (; ki_it; ++ki_it)
+ {
+ Scalar prod = fact * ki_it.value();
+ Index j = ki_it.index();
+ Index jpos = jr(j);
+ if (jpos == -1) // fill-in element
+ {
+ Index newpos;
+ if (j >= ii) // dealing with the upper part
+ {
+ newpos = ii + sizeu;
+ sizeu++;
+ eigen_internal_assert(sizeu<=n);
+ }
+ else // dealing with the lower part
+ {
+ newpos = sizel;
+ sizel++;
+ eigen_internal_assert(sizel<=ii);
+ }
+ ju(newpos) = j;
+ u(newpos) = -prod;
+ jr(j) = newpos;
+ }
+ else
+ u(jpos) -= prod;
+ }
+ // store the pivot element
+ u(len) = fact;
+ ju(len) = minrow;
+ ++len;
+
+ jj++;
+ } // end of the elimination on the row ii
+
+ // reset the upper part of the pointer jr to zero
+ for(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1;
+
+ // 4 - partially sort and insert the elements in the m_lu matrix
+
+ // sort the L-part of the row
+ sizel = len;
+ len = (std::min)(sizel, nnzL);
+ typename Vector::SegmentReturnType ul(u.segment(0, sizel));
+ typename VectorXi::SegmentReturnType jul(ju.segment(0, sizel));
+ internal::QuickSplit(ul, jul, len);
+
+ // store the largest m_fill elements of the L part
+ m_lu.startVec(ii);
+ for(Index k = 0; k < len; k++)
+ m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);
+
+ // store the diagonal element
+ // apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization)
+ if (u(ii) == Scalar(0))
+ u(ii) = sqrt(m_droptol) * rownorm;
+ m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii);
+
+ // sort the U-part of the row
+ // apply the dropping rule first
+ len = 0;
+ for(Index k = 1; k < sizeu; k++)
+ {
+ if(abs(u(ii+k)) > m_droptol * rownorm )
+ {
+ ++len;
+ u(ii + len) = u(ii + k);
+ ju(ii + len) = ju(ii + k);
+ }
+ }
+ sizeu = len + 1; // +1 to take into account the diagonal element
+ len = (std::min)(sizeu, nnzU);
+ typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1));
+ typename VectorXi::SegmentReturnType juu(ju.segment(ii+1, sizeu-1));
+ internal::QuickSplit(uu, juu, len);
+
+ // store the largest elements of the U part
+ for(Index k = ii + 1; k < ii + len; k++)
+ m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);
+ }
+
+ m_lu.finalize();
+ m_lu.makeCompressed();
+
+ m_factorizationIsOk = true;
+ m_isInitialized = m_factorizationIsOk;
+ m_info = Success;
+}
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<IncompleteLUT<_MatrixType>, Rhs>
+ : solve_retval_base<IncompleteLUT<_MatrixType>, Rhs>
+{
+ typedef IncompleteLUT<_MatrixType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_INCOMPLETE_LUT_H
diff --git a/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
new file mode 100644
index 0000000..2036922
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
@@ -0,0 +1,254 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ITERATIVE_SOLVER_BASE_H
+#define EIGEN_ITERATIVE_SOLVER_BASE_H
+
+namespace Eigen {
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief Base class for linear iterative solvers
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename Derived>
+class IterativeSolverBase : internal::noncopyable
+{
+public:
+ typedef typename internal::traits<Derived>::MatrixType MatrixType;
+ typedef typename internal::traits<Derived>::Preconditioner Preconditioner;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+public:
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** Default constructor. */
+ IterativeSolverBase()
+ : mp_matrix(0)
+ {
+ init();
+ }
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ IterativeSolverBase(const MatrixType& A)
+ {
+ init();
+ compute(A);
+ }
+
+ ~IterativeSolverBase() {}
+
+ /** Initializes the iterative solver for the sparcity pattern of the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly call analyzePattern on the preconditioner. In the future
+ * we might, for instance, implement column reodering for faster matrix vector products.
+ */
+ Derived& analyzePattern(const MatrixType& A)
+ {
+ m_preconditioner.analyzePattern(A);
+ m_isInitialized = true;
+ m_analysisIsOk = true;
+ m_info = Success;
+ return derived();
+ }
+
+ /** Initializes the iterative solver with the numerical values of the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly call factorize on the preconditioner.
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ Derived& factorize(const MatrixType& A)
+ {
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ mp_matrix = &A;
+ m_preconditioner.factorize(A);
+ m_factorizationIsOk = true;
+ m_info = Success;
+ return derived();
+ }
+
+ /** Initializes the iterative solver with the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly initialized/compute the preconditioner. In the future
+ * we might, for instance, implement column reodering for faster matrix vector products.
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ Derived& compute(const MatrixType& A)
+ {
+ mp_matrix = &A;
+ m_preconditioner.compute(A);
+ m_isInitialized = true;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = true;
+ m_info = Success;
+ return derived();
+ }
+
+ /** \internal */
+ Index rows() const { return mp_matrix ? mp_matrix->rows() : 0; }
+ /** \internal */
+ Index cols() const { return mp_matrix ? mp_matrix->cols() : 0; }
+
+ /** \returns the tolerance threshold used by the stopping criteria */
+ RealScalar tolerance() const { return m_tolerance; }
+
+ /** Sets the tolerance threshold used by the stopping criteria */
+ Derived& setTolerance(const RealScalar& tolerance)
+ {
+ m_tolerance = tolerance;
+ return derived();
+ }
+
+ /** \returns a read-write reference to the preconditioner for custom configuration. */
+ Preconditioner& preconditioner() { return m_preconditioner; }
+
+ /** \returns a read-only reference to the preconditioner. */
+ const Preconditioner& preconditioner() const { return m_preconditioner; }
+
+ /** \returns the max number of iterations */
+ int maxIterations() const
+ {
+ return (mp_matrix && m_maxIterations<0) ? mp_matrix->cols() : m_maxIterations;
+ }
+
+ /** Sets the max number of iterations */
+ Derived& setMaxIterations(int maxIters)
+ {
+ m_maxIterations = maxIters;
+ return derived();
+ }
+
+ /** \returns the number of iterations performed during the last solve */
+ int iterations() const
+ {
+ eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
+ return m_iterations;
+ }
+
+ /** \returns the tolerance error reached during the last solve */
+ RealScalar error() const
+ {
+ eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
+ return m_error;
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs> inline const internal::solve_retval<Derived, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "IterativeSolverBase::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<Derived, Rhs>(derived(), b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<IterativeSolverBase, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "IterativeSolverBase::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<IterativeSolverBase, Rhs>(*this, b.derived());
+ }
+
+ /** \returns Success if the iterations converged, and NoConvergence otherwise. */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ return m_info;
+ }
+
+ /** \internal */
+ template<typename Rhs, typename DestScalar, int DestOptions, typename DestIndex>
+ void _solve_sparse(const Rhs& b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
+ {
+ eigen_assert(rows()==b.rows());
+
+ int rhsCols = b.cols();
+ int size = b.rows();
+ Eigen::Matrix<DestScalar,Dynamic,1> tb(size);
+ Eigen::Matrix<DestScalar,Dynamic,1> tx(size);
+ for(int k=0; k<rhsCols; ++k)
+ {
+ tb = b.col(k);
+ tx = derived().solve(tb);
+ dest.col(k) = tx.sparseView(0);
+ }
+ }
+
+protected:
+ void init()
+ {
+ m_isInitialized = false;
+ m_analysisIsOk = false;
+ m_factorizationIsOk = false;
+ m_maxIterations = -1;
+ m_tolerance = NumTraits<Scalar>::epsilon();
+ }
+ const MatrixType* mp_matrix;
+ Preconditioner m_preconditioner;
+
+ int m_maxIterations;
+ RealScalar m_tolerance;
+
+ mutable RealScalar m_error;
+ mutable int m_iterations;
+ mutable ComputationInfo m_info;
+ mutable bool m_isInitialized, m_analysisIsOk, m_factorizationIsOk;
+};
+
+namespace internal {
+
+template<typename Derived, typename Rhs>
+struct sparse_solve_retval<IterativeSolverBase<Derived>, Rhs>
+ : sparse_solve_retval_base<IterativeSolverBase<Derived>, Rhs>
+{
+ typedef IterativeSolverBase<Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec().derived()._solve_sparse(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ITERATIVE_SOLVER_BASE_H
diff --git a/Eigen/src/Jacobi/CMakeLists.txt b/Eigen/src/Jacobi/CMakeLists.txt
new file mode 100644
index 0000000..490dac6
--- /dev/null
+++ b/Eigen/src/Jacobi/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Jacobi_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Jacobi_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Jacobi COMPONENT Devel
+ )
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
new file mode 100644
index 0000000..956f72d
--- /dev/null
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -0,0 +1,433 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_JACOBI_H
+#define EIGEN_JACOBI_H
+
+namespace Eigen {
+
+/** \ingroup Jacobi_Module
+ * \jacobi_module
+ * \class JacobiRotation
+ * \brief Rotation given by a cosine-sine pair.
+ *
+ * This class represents a Jacobi or Givens rotation.
+ * This is a 2D rotation in the plane \c J of angle \f$ \theta \f$ defined by
+ * its cosine \c c and sine \c s as follow:
+ * \f$ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) \f$
+ *
+ * You can apply the respective counter-clockwise rotation to a column vector \c v by
+ * applying its adjoint on the left: \f$ v = J^* v \f$ that translates to the following Eigen code:
+ * \code
+ * v.applyOnTheLeft(J.adjoint());
+ * \endcode
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar> class JacobiRotation
+{
+ public:
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** Default constructor without any initialization. */
+ JacobiRotation() {}
+
+ /** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */
+ JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
+
+ Scalar& c() { return m_c; }
+ Scalar c() const { return m_c; }
+ Scalar& s() { return m_s; }
+ Scalar s() const { return m_s; }
+
+ /** Concatenates two planar rotation */
+ JacobiRotation operator*(const JacobiRotation& other)
+ {
+ using numext::conj;
+ return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
+ conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
+ }
+
+ /** Returns the transposed transformation */
+ JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }
+
+ /** Returns the adjoint transformation */
+ JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }
+
+ template<typename Derived>
+ bool makeJacobi(const MatrixBase<Derived>&, typename Derived::Index p, typename Derived::Index q);
+ bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);
+
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z=0);
+
+ protected:
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, internal::true_type);
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, internal::false_type);
+
+ Scalar m_c, m_s;
+};
+
+/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the selfadjoint 2x2 matrix
+ * \f$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )\f$ yields a diagonal matrix \f$ A = J^* B J \f$
+ *
+ * \sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ if(y == Scalar(0))
+ {
+ m_c = Scalar(1);
+ m_s = Scalar(0);
+ return false;
+ }
+ else
+ {
+ RealScalar tau = (x-z)/(RealScalar(2)*abs(y));
+ RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
+ RealScalar t;
+ if(tau>RealScalar(0))
+ {
+ t = RealScalar(1) / (tau + w);
+ }
+ else
+ {
+ t = RealScalar(1) / (tau - w);
+ }
+ RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+ RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));
+ m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;
+ m_c = n;
+ return true;
+ }
+}
+
+/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 selfadjoint matrix
+ * \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )\f$ yields
+ * a diagonal matrix \f$ A = J^* B J \f$
+ *
+ * Example: \include Jacobi_makeJacobi.cpp
+ * Output: \verbinclude Jacobi_makeJacobi.out
+ *
+ * \sa JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+template<typename Derived>
+inline bool JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, typename Derived::Index p, typename Derived::Index q)
+{
+ return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));
+}
+
+/** Makes \c *this as a Givens rotation \c G such that applying \f$ G^* \f$ to the left of the vector
+ * \f$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )\f$ yields:
+ * \f$ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )\f$.
+ *
+ * The value of \a z is returned if \a z is not null (the default is null).
+ * Also note that G is built such that the cosine is always real.
+ *
+ * Example: \include Jacobi_makeGivens.cpp
+ * Output: \verbinclude Jacobi_makeGivens.out
+ *
+ * This function implements the continuous Givens rotation generation algorithm
+ * found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem.
+ * LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z)
+{
+ makeGivens(p, q, z, typename internal::conditional<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>::type());
+}
+
+
+// specialization for complexes
+template<typename Scalar>
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
+{
+ using std::sqrt;
+ using std::abs;
+ using numext::conj;
+
+ if(q==Scalar(0))
+ {
+ m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);
+ m_s = 0;
+ if(r) *r = m_c * p;
+ }
+ else if(p==Scalar(0))
+ {
+ m_c = 0;
+ m_s = -q/abs(q);
+ if(r) *r = abs(q);
+ }
+ else
+ {
+ RealScalar p1 = numext::norm1(p);
+ RealScalar q1 = numext::norm1(q);
+ if(p1>=q1)
+ {
+ Scalar ps = p / p1;
+ RealScalar p2 = numext::abs2(ps);
+ Scalar qs = q / p1;
+ RealScalar q2 = numext::abs2(qs);
+
+ RealScalar u = sqrt(RealScalar(1) + q2/p2);
+ if(numext::real(p)<RealScalar(0))
+ u = -u;
+
+ m_c = Scalar(1)/u;
+ m_s = -qs*conj(ps)*(m_c/p2);
+ if(r) *r = p * u;
+ }
+ else
+ {
+ Scalar ps = p / q1;
+ RealScalar p2 = numext::abs2(ps);
+ Scalar qs = q / q1;
+ RealScalar q2 = numext::abs2(qs);
+
+ RealScalar u = q1 * sqrt(p2 + q2);
+ if(numext::real(p)<RealScalar(0))
+ u = -u;
+
+ p1 = abs(p);
+ ps = p/p1;
+ m_c = p1/u;
+ m_s = -conj(ps) * (q/u);
+ if(r) *r = ps * u;
+ }
+ }
+}
+
+// specialization for reals
+template<typename Scalar>
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)
+{
+ using std::sqrt;
+ using std::abs;
+ if(q==Scalar(0))
+ {
+ m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);
+ m_s = Scalar(0);
+ if(r) *r = abs(p);
+ }
+ else if(p==Scalar(0))
+ {
+ m_c = Scalar(0);
+ m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);
+ if(r) *r = abs(q);
+ }
+ else if(abs(p) > abs(q))
+ {
+ Scalar t = q/p;
+ Scalar u = sqrt(Scalar(1) + numext::abs2(t));
+ if(p<Scalar(0))
+ u = -u;
+ m_c = Scalar(1)/u;
+ m_s = -t * m_c;
+ if(r) *r = p * u;
+ }
+ else
+ {
+ Scalar t = p/q;
+ Scalar u = sqrt(Scalar(1) + numext::abs2(t));
+ if(q<Scalar(0))
+ u = -u;
+ m_s = -Scalar(1)/u;
+ m_c = -t * m_s;
+ if(r) *r = q * u;
+ }
+
+}
+
+/****************************************************************************************
+* Implementation of MatrixBase methods
+****************************************************************************************/
+
+/** \jacobi_module
+ * Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
+ * \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+namespace internal {
+template<typename VectorX, typename VectorY, typename OtherScalar>
+void apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<OtherScalar>& j);
+}
+
+/** \jacobi_module
+ * Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
+ * with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
+ *
+ * \sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
+ */
+template<typename Derived>
+template<typename OtherScalar>
+inline void MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)
+{
+ RowXpr x(this->row(p));
+ RowXpr y(this->row(q));
+ internal::apply_rotation_in_the_plane(x, y, j);
+}
+
+/** \ingroup Jacobi_Module
+ * Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
+ * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
+ *
+ * \sa class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()
+ */
+template<typename Derived>
+template<typename OtherScalar>
+inline void MatrixBase<Derived>::applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j)
+{
+ ColXpr x(this->col(p));
+ ColXpr y(this->col(q));
+ internal::apply_rotation_in_the_plane(x, y, j.transpose());
+}
+
+namespace internal {
+template<typename VectorX, typename VectorY, typename OtherScalar>
+void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<OtherScalar>& j)
+{
+ typedef typename VectorX::Index Index;
+ typedef typename VectorX::Scalar Scalar;
+ enum { PacketSize = packet_traits<Scalar>::size };
+ typedef typename packet_traits<Scalar>::type Packet;
+ eigen_assert(_x.size() == _y.size());
+ Index size = _x.size();
+ Index incrx = _x.innerStride();
+ Index incry = _y.innerStride();
+
+ Scalar* EIGEN_RESTRICT x = &_x.coeffRef(0);
+ Scalar* EIGEN_RESTRICT y = &_y.coeffRef(0);
+
+ OtherScalar c = j.c();
+ OtherScalar s = j.s();
+ if (c==OtherScalar(1) && s==OtherScalar(0))
+ return;
+
+ /*** dynamic-size vectorized paths ***/
+
+ if(VectorX::SizeAtCompileTime == Dynamic &&
+ (VectorX::Flags & VectorY::Flags & PacketAccessBit) &&
+ ((incrx==1 && incry==1) || PacketSize == 1))
+ {
+ // both vectors are sequentially stored in memory => vectorization
+ enum { Peeling = 2 };
+
+ Index alignedStart = internal::first_aligned(y, size);
+ Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
+
+ const Packet pc = pset1<Packet>(c);
+ const Packet ps = pset1<Packet>(s);
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,false> pcj;
+
+ for(Index i=0; i<alignedStart; ++i)
+ {
+ Scalar xi = x[i];
+ Scalar yi = y[i];
+ x[i] = c * xi + numext::conj(s) * yi;
+ y[i] = -s * xi + numext::conj(c) * yi;
+ }
+
+ Scalar* EIGEN_RESTRICT px = x + alignedStart;
+ Scalar* EIGEN_RESTRICT py = y + alignedStart;
+
+ if(internal::first_aligned(x, size)==alignedStart)
+ {
+ for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)
+ {
+ Packet xi = pload<Packet>(px);
+ Packet yi = pload<Packet>(py);
+ pstore(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ px += PacketSize;
+ py += PacketSize;
+ }
+ }
+ else
+ {
+ Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);
+ for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)
+ {
+ Packet xi = ploadu<Packet>(px);
+ Packet xi1 = ploadu<Packet>(px+PacketSize);
+ Packet yi = pload <Packet>(py);
+ Packet yi1 = pload <Packet>(py+PacketSize);
+ pstoreu(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstoreu(px+PacketSize, padd(pmul(pc,xi1),pcj.pmul(ps,yi1)));
+ pstore (py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pmul(ps,xi1)));
+ px += Peeling*PacketSize;
+ py += Peeling*PacketSize;
+ }
+ if(alignedEnd!=peelingEnd)
+ {
+ Packet xi = ploadu<Packet>(x+peelingEnd);
+ Packet yi = pload <Packet>(y+peelingEnd);
+ pstoreu(x+peelingEnd, padd(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ }
+ }
+
+ for(Index i=alignedEnd; i<size; ++i)
+ {
+ Scalar xi = x[i];
+ Scalar yi = y[i];
+ x[i] = c * xi + numext::conj(s) * yi;
+ y[i] = -s * xi + numext::conj(c) * yi;
+ }
+ }
+
+ /*** fixed-size vectorized path ***/
+ else if(VectorX::SizeAtCompileTime != Dynamic &&
+ (VectorX::Flags & VectorY::Flags & PacketAccessBit) &&
+ (VectorX::Flags & VectorY::Flags & AlignedBit))
+ {
+ const Packet pc = pset1<Packet>(c);
+ const Packet ps = pset1<Packet>(s);
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,false> pcj;
+ Scalar* EIGEN_RESTRICT px = x;
+ Scalar* EIGEN_RESTRICT py = y;
+ for(Index i=0; i<size; i+=PacketSize)
+ {
+ Packet xi = pload<Packet>(px);
+ Packet yi = pload<Packet>(py);
+ pstore(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ px += PacketSize;
+ py += PacketSize;
+ }
+ }
+
+ /*** non-vectorized path ***/
+ else
+ {
+ for(Index i=0; i<size; ++i)
+ {
+ Scalar xi = *x;
+ Scalar yi = *y;
+ *x = c * xi + numext::conj(s) * yi;
+ *y = -s * xi + numext::conj(c) * yi;
+ x += incrx;
+ y += incry;
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBI_H
diff --git a/Eigen/src/LU/CMakeLists.txt b/Eigen/src/LU/CMakeLists.txt
new file mode 100644
index 0000000..e0d8d78
--- /dev/null
+++ b/Eigen/src/LU/CMakeLists.txt
@@ -0,0 +1,8 @@
+FILE(GLOB Eigen_LU_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_LU_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/LU COMPONENT Devel
+ )
+
+ADD_SUBDIRECTORY(arch)
diff --git a/Eigen/src/LU/Determinant.h b/Eigen/src/LU/Determinant.h
new file mode 100644
index 0000000..bb8e78a
--- /dev/null
+++ b/Eigen/src/LU/Determinant.h
@@ -0,0 +1,101 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DETERMINANT_H
+#define EIGEN_DETERMINANT_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+inline const typename Derived::Scalar bruteforce_det3_helper
+(const MatrixBase<Derived>& matrix, int a, int b, int c)
+{
+ return matrix.coeff(0,a)
+ * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
+}
+
+template<typename Derived>
+const typename Derived::Scalar bruteforce_det4_helper
+(const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
+{
+ return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
+ * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
+}
+
+template<typename Derived,
+ int DeterminantType = Derived::RowsAtCompileTime
+> struct determinant_impl
+{
+ static inline typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)
+ return typename traits<Derived>::Scalar(1);
+ return m.partialPivLu().determinant();
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 1>
+{
+ static inline typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return m.coeff(0,0);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 2>
+{
+ static inline typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 3>
+{
+ static inline typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return bruteforce_det3_helper(m,0,1,2)
+ - bruteforce_det3_helper(m,1,0,2)
+ + bruteforce_det3_helper(m,2,0,1);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 4>
+{
+ static typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ // trick by Martin Costabel to compute 4x4 det with only 30 muls
+ return bruteforce_det4_helper(m,0,1,2,3)
+ - bruteforce_det4_helper(m,0,2,1,3)
+ + bruteforce_det4_helper(m,0,3,1,2)
+ + bruteforce_det4_helper(m,1,2,0,3)
+ - bruteforce_det4_helper(m,1,3,0,2)
+ + bruteforce_det4_helper(m,2,3,0,1);
+ }
+};
+
+} // end namespace internal
+
+/** \lu_module
+ *
+ * \returns the determinant of this matrix
+ */
+template<typename Derived>
+inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::nested<Derived,Base::RowsAtCompileTime>::type Nested;
+ return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DETERMINANT_H
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
new file mode 100644
index 0000000..26bc714
--- /dev/null
+++ b/Eigen/src/LU/FullPivLU.h
@@ -0,0 +1,751 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LU_H
+#define EIGEN_LU_H
+
+namespace Eigen {
+
+/** \ingroup LU_Module
+ *
+ * \class FullPivLU
+ *
+ * \brief LU decomposition of a matrix with complete pivoting, and related features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the LU decomposition
+ *
+ * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is
+ * decomposed as \f$ A = P^{-1} L U Q^{-1} \f$ where L is unit-lower-triangular, U is
+ * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU
+ * decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any
+ * zeros are at the end.
+ *
+ * This decomposition provides the generic approach to solving systems of linear equations, computing
+ * the rank, invertibility, inverse, kernel, and determinant.
+ *
+ * This LU decomposition is very stable and well tested with large matrices. However there are use cases where the SVD
+ * decomposition is inherently more stable and/or flexible. For example, when computing the kernel of a matrix,
+ * working with the SVD allows to select the smallest singular values of the matrix, something that
+ * the LU decomposition doesn't see.
+ *
+ * The data of the LU decomposition can be directly accessed through the methods matrixLU(),
+ * permutationP(), permutationQ().
+ *
+ * As an exemple, here is how the original matrix can be retrieved:
+ * \include class_FullPivLU.cpp
+ * Output: \verbinclude class_FullPivLU.out
+ *
+ * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()
+ */
+template<typename _MatrixType> class FullPivLU
+{
+ public:
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename internal::traits<MatrixType>::StorageKind StorageKind;
+ typedef typename MatrixType::Index Index;
+ typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
+ typedef typename internal::plain_col_type<MatrixType, Index>::type IntColVectorType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType;
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationPType;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LU::compute(const MatrixType&).
+ */
+ FullPivLU();
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa FullPivLU()
+ */
+ FullPivLU(Index rows, Index cols);
+
+ /** Constructor.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ * It is required to be nonzero.
+ */
+ FullPivLU(const MatrixType& matrix);
+
+ /** Computes the LU decomposition of the given matrix.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ * It is required to be nonzero.
+ *
+ * \returns a reference to *this
+ */
+ FullPivLU& compute(const MatrixType& matrix);
+
+ /** \returns the LU decomposition matrix: the upper-triangular part is U, the
+ * unit-lower-triangular part is L (at least for square matrices; in the non-square
+ * case, special care is needed, see the documentation of class FullPivLU).
+ *
+ * \sa matrixL(), matrixU()
+ */
+ inline const MatrixType& matrixLU() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_lu;
+ }
+
+ /** \returns the number of nonzero pivots in the LU decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of U.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ /** \returns the permutation matrix P
+ *
+ * \sa permutationQ()
+ */
+ inline const PermutationPType& permutationP() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_p;
+ }
+
+ /** \returns the permutation matrix Q
+ *
+ * \sa permutationP()
+ */
+ inline const PermutationQType& permutationQ() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_q;
+ }
+
+ /** \returns the kernel of the matrix, also called its null-space. The columns of the returned matrix
+ * will form a basis of the kernel.
+ *
+ * \note If the kernel has dimension zero, then the returned matrix is a column-vector filled with zeros.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ *
+ * Example: \include FullPivLU_kernel.cpp
+ * Output: \verbinclude FullPivLU_kernel.out
+ *
+ * \sa image()
+ */
+ inline const internal::kernel_retval<FullPivLU> kernel() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return internal::kernel_retval<FullPivLU>(*this);
+ }
+
+ /** \returns the image of the matrix, also called its column-space. The columns of the returned matrix
+ * will form a basis of the kernel.
+ *
+ * \param originalMatrix the original matrix, of which *this is the LU decomposition.
+ * The reason why it is needed to pass it here, is that this allows
+ * a large optimization, as otherwise this method would need to reconstruct it
+ * from the LU decomposition.
+ *
+ * \note If the image has dimension zero, then the returned matrix is a column-vector filled with zeros.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ *
+ * Example: \include FullPivLU_image.cpp
+ * Output: \verbinclude FullPivLU_image.out
+ *
+ * \sa kernel()
+ */
+ inline const internal::image_retval<FullPivLU>
+ image(const MatrixType& originalMatrix) const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return internal::image_retval<FullPivLU>(*this, originalMatrix);
+ }
+
+ /** \return a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the LU decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
+ * the only requirement in order for the equation to make sense is that
+ * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.
+ *
+ * \returns a solution.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ * \note_about_using_kernel_to_study_multiple_solutions
+ *
+ * Example: \include FullPivLU_solve.cpp
+ * Output: \verbinclude FullPivLU_solve.out
+ *
+ * \sa TriangularView::solve(), kernel(), inverse()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<FullPivLU, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return internal::solve_retval<FullPivLU, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the LU decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the LU decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers
+ * optimized paths.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ *
+ * \sa MatrixBase::determinant()
+ */
+ typename internal::traits<MatrixType>::Scalar determinant() const;
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * LU decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ FullPivLU& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code lu.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ FullPivLU& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * m_lu.diagonalSize();
+ }
+
+ /** \returns the rank of the matrix of which *this is the LU decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the LU decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return isInjective() && (m_lu.rows() == m_lu.cols());
+ }
+
+ /** \returns the inverse of the matrix of which *this is the LU decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ *
+ * \sa MatrixBase::inverse()
+ */
+ inline const internal::solve_retval<FullPivLU,typename MatrixType::IdentityReturnType> inverse() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the inverse of a non-square matrix!");
+ return internal::solve_retval<FullPivLU,typename MatrixType::IdentityReturnType>
+ (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()));
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+ inline Index rows() const { return m_lu.rows(); }
+ inline Index cols() const { return m_lu.cols(); }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_lu;
+ PermutationPType m_p;
+ PermutationQType m_q;
+ IntColVectorType m_rowsTranspositions;
+ IntRowVectorType m_colsTranspositions;
+ Index m_det_pq, m_nonzero_pivots;
+ RealScalar m_maxpivot, m_prescribedThreshold;
+ bool m_isInitialized, m_usePrescribedThreshold;
+};
+
+template<typename MatrixType>
+FullPivLU<MatrixType>::FullPivLU()
+ : m_isInitialized(false), m_usePrescribedThreshold(false)
+{
+}
+
+template<typename MatrixType>
+FullPivLU<MatrixType>::FullPivLU(Index rows, Index cols)
+ : m_lu(rows, cols),
+ m_p(rows),
+ m_q(cols),
+ m_rowsTranspositions(rows),
+ m_colsTranspositions(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+{
+}
+
+template<typename MatrixType>
+FullPivLU<MatrixType>::FullPivLU(const MatrixType& matrix)
+ : m_lu(matrix.rows(), matrix.cols()),
+ m_p(matrix.rows()),
+ m_q(matrix.cols()),
+ m_rowsTranspositions(matrix.rows()),
+ m_colsTranspositions(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+{
+ compute(matrix);
+}
+
+template<typename MatrixType>
+FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
+{
+ check_template_parameters();
+
+ // the permutations are stored as int indices, so just to be sure:
+ eigen_assert(matrix.rows()<=NumTraits<int>::highest() && matrix.cols()<=NumTraits<int>::highest());
+
+ m_isInitialized = true;
+ m_lu = matrix;
+
+ const Index size = matrix.diagonalSize();
+ const Index rows = matrix.rows();
+ const Index cols = matrix.cols();
+
+ // will store the transpositions, before we accumulate them at the end.
+ // can't accumulate on-the-fly because that will be done in reverse order for the rows.
+ m_rowsTranspositions.resize(matrix.rows());
+ m_colsTranspositions.resize(matrix.cols());
+ Index number_of_transpositions = 0; // number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ // First, we need to find the pivot.
+
+ // biggest coefficient in the remaining bottom-right corner (starting at row k, col k)
+ Index row_of_biggest_in_corner, col_of_biggest_in_corner;
+ RealScalar biggest_in_corner;
+ biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)
+ .cwiseAbs()
+ .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+ row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner,
+ col_of_biggest_in_corner += k; // need to add k to them.
+
+ if(biggest_in_corner==RealScalar(0))
+ {
+ // before exiting, make sure to initialize the still uninitialized transpositions
+ // in a sane state without destroying what we already have.
+ m_nonzero_pivots = k;
+ for(Index i = k; i < size; ++i)
+ {
+ m_rowsTranspositions.coeffRef(i) = i;
+ m_colsTranspositions.coeffRef(i) = i;
+ }
+ break;
+ }
+
+ if(biggest_in_corner > m_maxpivot) m_maxpivot = biggest_in_corner;
+
+ // Now that we've found the pivot, we need to apply the row/col swaps to
+ // bring it to the location (k,k).
+
+ m_rowsTranspositions.coeffRef(k) = row_of_biggest_in_corner;
+ m_colsTranspositions.coeffRef(k) = col_of_biggest_in_corner;
+ if(k != row_of_biggest_in_corner) {
+ m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+ if(k != col_of_biggest_in_corner) {
+ m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+
+ // Now that the pivot is at the right location, we update the remaining
+ // bottom-right corner by Gaussian elimination.
+
+ if(k<rows-1)
+ m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);
+ if(k<size-1)
+ m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);
+ }
+
+ // the main loop is over, we still have to accumulate the transpositions to find the
+ // permutations P and Q
+
+ m_p.setIdentity(rows);
+ for(Index k = size-1; k >= 0; --k)
+ m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));
+
+ m_q.setIdentity(cols);
+ for(Index k = 0; k < size; ++k)
+ m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));
+
+ m_det_pq = (number_of_transpositions%2) ? -1 : 1;
+ return *this;
+}
+
+template<typename MatrixType>
+typename internal::traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the determinant of a non-square matrix!");
+ return Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: \f$ P^{-1} L U Q^{-1} \f$.
+ * This function is provided for debug purposes. */
+template<typename MatrixType>
+MatrixType FullPivLU<MatrixType>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ const Index smalldim = (std::min)(m_lu.rows(), m_lu.cols());
+ // LU
+ MatrixType res(m_lu.rows(),m_lu.cols());
+ // FIXME the .toDenseMatrix() should not be needed...
+ res = m_lu.leftCols(smalldim)
+ .template triangularView<UnitLower>().toDenseMatrix()
+ * m_lu.topRows(smalldim)
+ .template triangularView<Upper>().toDenseMatrix();
+
+ // P^{-1}(LU)
+ res = m_p.inverse() * res;
+
+ // (P^{-1}LU)Q^{-1}
+ res = res * m_q.inverse();
+
+ return res;
+}
+
+/********* Implementation of kernel() **************************************************/
+
+namespace internal {
+template<typename _MatrixType>
+struct kernel_retval<FullPivLU<_MatrixType> >
+ : kernel_retval_base<FullPivLU<_MatrixType> >
+{
+ EIGEN_MAKE_KERNEL_HELPERS(FullPivLU<_MatrixType>)
+
+ enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(
+ MatrixType::MaxColsAtCompileTime,
+ MatrixType::MaxRowsAtCompileTime)
+ };
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ using std::abs;
+ const Index cols = dec().matrixLU().cols(), dimker = cols - rank();
+ if(dimker == 0)
+ {
+ // The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's
+ // avoid crashing/asserting as that depends on floating point calculations. Let's
+ // just return a single column vector filled with zeros.
+ dst.setZero();
+ return;
+ }
+
+ /* Let us use the following lemma:
+ *
+ * Lemma: If the matrix A has the LU decomposition PAQ = LU,
+ * then Ker A = Q(Ker U).
+ *
+ * Proof: trivial: just keep in mind that P, Q, L are invertible.
+ */
+
+ /* Thus, all we need to do is to compute Ker U, and then apply Q.
+ *
+ * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end.
+ * Thus, the diagonal of U ends with exactly
+ * dimKer zero's. Let us use that to construct dimKer linearly
+ * independent vectors in Ker U.
+ */
+
+ Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());
+ RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();
+ Index p = 0;
+ for(Index i = 0; i < dec().nonzeroPivots(); ++i)
+ if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)
+ pivots.coeffRef(p++) = i;
+ eigen_internal_assert(p == rank());
+
+ // we construct a temporaty trapezoid matrix m, by taking the U matrix and
+ // permuting the rows and cols to bring the nonnegligible pivots to the top of
+ // the main diagonal. We need that to be able to apply our triangular solvers.
+ // FIXME when we get triangularView-for-rectangular-matrices, this can be simplified
+ Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, MatrixType::Options,
+ MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime>
+ m(dec().matrixLU().block(0, 0, rank(), cols));
+ for(Index i = 0; i < rank(); ++i)
+ {
+ if(i) m.row(i).head(i).setZero();
+ m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);
+ }
+ m.block(0, 0, rank(), rank());
+ m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero();
+ for(Index i = 0; i < rank(); ++i)
+ m.col(i).swap(m.col(pivots.coeff(i)));
+
+ // ok, we have our trapezoid matrix, we can apply the triangular solver.
+ // notice that the math behind this suggests that we should apply this to the
+ // negative of the RHS, but for performance we just put the negative sign elsewhere, see below.
+ m.topLeftCorner(rank(), rank())
+ .template triangularView<Upper>().solveInPlace(
+ m.topRightCorner(rank(), dimker)
+ );
+
+ // now we must undo the column permutation that we had applied!
+ for(Index i = rank()-1; i >= 0; --i)
+ m.col(i).swap(m.col(pivots.coeff(i)));
+
+ // see the negative sign in the next line, that's what we were talking about above.
+ for(Index i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);
+ for(Index i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();
+ for(Index k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);
+ }
+};
+
+/***** Implementation of image() *****************************************************/
+
+template<typename _MatrixType>
+struct image_retval<FullPivLU<_MatrixType> >
+ : image_retval_base<FullPivLU<_MatrixType> >
+{
+ EIGEN_MAKE_IMAGE_HELPERS(FullPivLU<_MatrixType>)
+
+ enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(
+ MatrixType::MaxColsAtCompileTime,
+ MatrixType::MaxRowsAtCompileTime)
+ };
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ using std::abs;
+ if(rank() == 0)
+ {
+ // The Image is just {0}, so it doesn't have a basis properly speaking, but let's
+ // avoid crashing/asserting as that depends on floating point calculations. Let's
+ // just return a single column vector filled with zeros.
+ dst.setZero();
+ return;
+ }
+
+ Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());
+ RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();
+ Index p = 0;
+ for(Index i = 0; i < dec().nonzeroPivots(); ++i)
+ if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)
+ pivots.coeffRef(p++) = i;
+ eigen_internal_assert(p == rank());
+
+ for(Index i = 0; i < rank(); ++i)
+ dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));
+ }
+};
+
+/***** Implementation of solve() *****************************************************/
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<FullPivLU<_MatrixType>, Rhs>
+ : solve_retval_base<FullPivLU<_MatrixType>, Rhs>
+{
+ EIGEN_MAKE_SOLVE_HELPERS(FullPivLU<_MatrixType>,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}.
+ * So we proceed as follows:
+ * Step 1: compute c = P * rhs.
+ * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.
+ * Step 3: replace c by the solution x to Ux = c. May or may not exist.
+ * Step 4: result = Q * c;
+ */
+
+ const Index rows = dec().rows(), cols = dec().cols(),
+ nonzero_pivots = dec().nonzeroPivots();
+ eigen_assert(rhs().rows() == rows);
+ const Index smalldim = (std::min)(rows, cols);
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename Rhs::PlainObject c(rhs().rows(), rhs().cols());
+
+ // Step 1
+ c = dec().permutationP() * rhs();
+
+ // Step 2
+ dec().matrixLU()
+ .topLeftCorner(smalldim,smalldim)
+ .template triangularView<UnitLower>()
+ .solveInPlace(c.topRows(smalldim));
+ if(rows>cols)
+ {
+ c.bottomRows(rows-cols)
+ -= dec().matrixLU().bottomRows(rows-cols)
+ * c.topRows(cols);
+ }
+
+ // Step 3
+ dec().matrixLU()
+ .topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ // Step 4
+ for(Index i = 0; i < nonzero_pivots; ++i)
+ dst.row(dec().permutationQ().indices().coeff(i)) = c.row(i);
+ for(Index i = nonzero_pivots; i < dec().matrixLU().cols(); ++i)
+ dst.row(dec().permutationQ().indices().coeff(i)).setZero();
+ }
+};
+
+} // end namespace internal
+
+/******* MatrixBase methods *****************************************************************/
+
+/** \lu_module
+ *
+ * \return the full-pivoting LU decomposition of \c *this.
+ *
+ * \sa class FullPivLU
+ */
+template<typename Derived>
+inline const FullPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::fullPivLu() const
+{
+ return FullPivLU<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LU_H
diff --git a/Eigen/src/LU/Inverse.h b/Eigen/src/LU/Inverse.h
new file mode 100644
index 0000000..3cf8871
--- /dev/null
+++ b/Eigen/src/LU/Inverse.h
@@ -0,0 +1,400 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INVERSE_H
+#define EIGEN_INVERSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************
+*** General case implementation ***
+**********************************/
+
+template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
+struct compute_inverse
+{
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ result = matrix.partialPivLu().inverse();
+ }
+};
+
+template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
+struct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ };
+
+/****************************
+*** Size 1 implementation ***
+****************************/
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 1>
+{
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ result.coeffRef(0,0) = Scalar(1) / matrix.coeff(0,0);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
+{
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& result,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ determinant = matrix.coeff(0,0);
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;
+ }
+};
+
+/****************************
+*** Size 2 implementation ***
+****************************/
+
+template<typename MatrixType, typename ResultType>
+inline void compute_inverse_size2_helper(
+ const MatrixType& matrix, const typename ResultType::Scalar& invdet,
+ ResultType& result)
+{
+ result.coeffRef(0,0) = matrix.coeff(1,1) * invdet;
+ result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
+ result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
+ result.coeffRef(1,1) = matrix.coeff(0,0) * invdet;
+}
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 2>
+{
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename ResultType::Scalar Scalar;
+ const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();
+ compute_inverse_size2_helper(matrix, invdet, result);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
+{
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ typedef typename ResultType::Scalar Scalar;
+ determinant = matrix.determinant();
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(!invertible) return;
+ const Scalar invdet = Scalar(1) / determinant;
+ compute_inverse_size2_helper(matrix, invdet, inverse);
+ }
+};
+
+/****************************
+*** Size 3 implementation ***
+****************************/
+
+template<typename MatrixType, int i, int j>
+inline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m)
+{
+ enum {
+ i1 = (i+1) % 3,
+ i2 = (i+2) % 3,
+ j1 = (j+1) % 3,
+ j2 = (j+2) % 3
+ };
+ return m.coeff(i1, j1) * m.coeff(i2, j2)
+ - m.coeff(i1, j2) * m.coeff(i2, j1);
+}
+
+template<typename MatrixType, typename ResultType>
+inline void compute_inverse_size3_helper(
+ const MatrixType& matrix,
+ const typename ResultType::Scalar& invdet,
+ const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,
+ ResultType& result)
+{
+ result.row(0) = cofactors_col0 * invdet;
+ result.coeffRef(1,0) = cofactor_3x3<MatrixType,0,1>(matrix) * invdet;
+ result.coeffRef(1,1) = cofactor_3x3<MatrixType,1,1>(matrix) * invdet;
+ result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet;
+ result.coeffRef(2,0) = cofactor_3x3<MatrixType,0,2>(matrix) * invdet;
+ result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet;
+ result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet;
+}
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 3>
+{
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename ResultType::Scalar Scalar;
+ Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;
+ cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
+ cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
+ cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
+ const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
+ const Scalar invdet = Scalar(1) / det;
+ compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
+{
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ typedef typename ResultType::Scalar Scalar;
+ Matrix<Scalar,3,1> cofactors_col0;
+ cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
+ cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
+ cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
+ determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(!invertible) return;
+ const Scalar invdet = Scalar(1) / determinant;
+ compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
+ }
+};
+
+/****************************
+*** Size 4 implementation ***
+****************************/
+
+template<typename Derived>
+inline const typename Derived::Scalar general_det3_helper
+(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
+{
+ return matrix.coeff(i1,j1)
+ * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
+}
+
+template<typename MatrixType, int i, int j>
+inline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix)
+{
+ enum {
+ i1 = (i+1) % 4,
+ i2 = (i+2) % 4,
+ i3 = (i+3) % 4,
+ j1 = (j+1) % 4,
+ j2 = (j+2) % 4,
+ j3 = (j+3) % 4
+ };
+ return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
+ + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
+ + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
+}
+
+template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
+struct compute_inverse_size4
+{
+ static void run(const MatrixType& matrix, ResultType& result)
+ {
+ result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix);
+ result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);
+ result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix);
+ result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);
+ result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix);
+ result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);
+ result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix);
+ result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);
+ result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);
+ result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix);
+ result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);
+ result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix);
+ result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);
+ result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix);
+ result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);
+ result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix);
+ result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 4>
+ : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,
+ MatrixType, ResultType>
+{
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
+{
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ determinant = matrix.determinant();
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
+ }
+};
+
+/*************************
+*** MatrixBase methods ***
+*************************/
+
+template<typename MatrixType>
+struct traits<inverse_impl<MatrixType> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename MatrixType>
+struct inverse_impl : public ReturnByValue<inverse_impl<MatrixType> >
+{
+ typedef typename MatrixType::Index Index;
+ typedef typename internal::eval<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+ MatrixTypeNested m_matrix;
+
+ inverse_impl(const MatrixType& matrix)
+ : m_matrix(matrix)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ const int Size = EIGEN_PLAIN_ENUM_MIN(MatrixType::ColsAtCompileTime,Dest::ColsAtCompileTime);
+ EIGEN_ONLY_USED_FOR_DEBUG(Size);
+ eigen_assert(( (Size<=1) || (Size>4) || (extract_data(m_matrix)!=extract_data(dst)))
+ && "Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
+
+ compute_inverse<MatrixTypeNestedCleaned, Dest>::run(m_matrix, dst);
+ }
+};
+
+} // end namespace internal
+
+/** \lu_module
+ *
+ * \returns the matrix inverse of this matrix.
+ *
+ * For small fixed sizes up to 4x4, this method uses cofactors.
+ * In the general case, this method uses class PartialPivLU.
+ *
+ * \note This matrix must be invertible, otherwise the result is undefined. If you need an
+ * invertibility check, do the following:
+ * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
+ * \li for the general case, use class FullPivLU.
+ *
+ * Example: \include MatrixBase_inverse.cpp
+ * Output: \verbinclude MatrixBase_inverse.out
+ *
+ * \sa computeInverseAndDetWithCheck()
+ */
+template<typename Derived>
+inline const internal::inverse_impl<Derived> MatrixBase<Derived>::inverse() const
+{
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
+ eigen_assert(rows() == cols());
+ return internal::inverse_impl<Derived>(derived());
+}
+
+/** \lu_module
+ *
+ * Computation of matrix inverse and determinant, with invertibility check.
+ *
+ * This is only for fixed-size square matrices of size up to 4x4.
+ *
+ * \param inverse Reference to the matrix in which to store the inverse.
+ * \param determinant Reference to the variable in which to store the determinant.
+ * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
+ * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
+ * The matrix will be declared invertible if the absolute value of its
+ * determinant is greater than this threshold.
+ *
+ * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
+ * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
+ *
+ * \sa inverse(), computeInverseWithCheck()
+ */
+template<typename Derived>
+template<typename ResultType>
+inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold
+ ) const
+{
+ // i'd love to put some static assertions there, but SFINAE means that they have no effect...
+ eigen_assert(rows() == cols());
+ // for 2x2, it's worth giving a chance to avoid evaluating.
+ // for larger sizes, evaluating has negligible cost and limits code size.
+ typedef typename internal::conditional<
+ RowsAtCompileTime == 2,
+ typename internal::remove_all<typename internal::nested<Derived, 2>::type>::type,
+ PlainObject
+ >::type MatrixType;
+ internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run
+ (derived(), absDeterminantThreshold, inverse, determinant, invertible);
+}
+
+/** \lu_module
+ *
+ * Computation of matrix inverse, with invertibility check.
+ *
+ * This is only for fixed-size square matrices of size up to 4x4.
+ *
+ * \param inverse Reference to the matrix in which to store the inverse.
+ * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
+ * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
+ * The matrix will be declared invertible if the absolute value of its
+ * determinant is greater than this threshold.
+ *
+ * Example: \include MatrixBase_computeInverseWithCheck.cpp
+ * Output: \verbinclude MatrixBase_computeInverseWithCheck.out
+ *
+ * \sa inverse(), computeInverseAndDetWithCheck()
+ */
+template<typename Derived>
+template<typename ResultType>
+inline void MatrixBase<Derived>::computeInverseWithCheck(
+ ResultType& inverse,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold
+ ) const
+{
+ RealScalar determinant;
+ // i'd love to put some static assertions there, but SFINAE means that they have no effect...
+ eigen_assert(rows() == cols());
+ computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_INVERSE_H
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
new file mode 100644
index 0000000..7d1db94
--- /dev/null
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -0,0 +1,509 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARTIALLU_H
+#define EIGEN_PARTIALLU_H
+
+namespace Eigen {
+
+/** \ingroup LU_Module
+ *
+ * \class PartialPivLU
+ *
+ * \brief LU decomposition of a matrix with partial pivoting, and related features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the LU decomposition
+ *
+ * This class represents a LU decomposition of a \b square \b invertible matrix, with partial pivoting: the matrix A
+ * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P
+ * is a permutation matrix.
+ *
+ * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible
+ * matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class
+ * does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the
+ * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.
+ *
+ * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided
+ * by class FullPivLU.
+ *
+ * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class,
+ * such as rank computation. If you need these features, use class FullPivLU.
+ *
+ * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses
+ * in the general case.
+ * On the other hand, it is \b not suitable to determine whether a given matrix is invertible.
+ *
+ * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().
+ *
+ * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU
+ */
+template<typename _MatrixType> class PartialPivLU
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename internal::traits<MatrixType>::StorageKind StorageKind;
+ typedef typename MatrixType::Index Index;
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
+ typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
+
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via PartialPivLU::compute(const MatrixType&).
+ */
+ PartialPivLU();
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa PartialPivLU()
+ */
+ PartialPivLU(Index size);
+
+ /** Constructor.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ *
+ * \warning The matrix should have full rank (e.g. if it's square, it should be invertible).
+ * If you need to deal with non-full rank, use class FullPivLU instead.
+ */
+ PartialPivLU(const MatrixType& matrix);
+
+ PartialPivLU& compute(const MatrixType& matrix);
+
+ /** \returns the LU decomposition matrix: the upper-triangular part is U, the
+ * unit-lower-triangular part is L (at least for square matrices; in the non-square
+ * case, special care is needed, see the documentation of class FullPivLU).
+ *
+ * \sa matrixL(), matrixU()
+ */
+ inline const MatrixType& matrixLU() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return m_lu;
+ }
+
+ /** \returns the permutation matrix P.
+ */
+ inline const PermutationType& permutationP() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return m_p;
+ }
+
+ /** This method returns the solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the LU decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
+ * the only requirement in order for the equation to make sense is that
+ * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.
+ *
+ * \returns the solution.
+ *
+ * Example: \include PartialPivLU_solve.cpp
+ * Output: \verbinclude PartialPivLU_solve.out
+ *
+ * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution
+ * theoretically exists and is unique regardless of b.
+ *
+ * \sa TriangularView::solve(), inverse(), computeInverse()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<PartialPivLU, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return internal::solve_retval<PartialPivLU, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the inverse of the matrix of which *this is the LU decomposition.
+ *
+ * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for
+ * invertibility, use class FullPivLU instead.
+ *
+ * \sa MatrixBase::inverse(), LU::inverse()
+ */
+ inline const internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType> inverse() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType>
+ (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()));
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the LU decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the LU decomposition has already been computed.
+ *
+ * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers
+ * optimized paths.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ *
+ * \sa MatrixBase::determinant()
+ */
+ typename internal::traits<MatrixType>::Scalar determinant() const;
+
+ MatrixType reconstructedMatrix() const;
+
+ inline Index rows() const { return m_lu.rows(); }
+ inline Index cols() const { return m_lu.cols(); }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_lu;
+ PermutationType m_p;
+ TranspositionType m_rowsTranspositions;
+ Index m_det_p;
+ bool m_isInitialized;
+};
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>::PartialPivLU()
+ : m_lu(),
+ m_p(),
+ m_rowsTranspositions(),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+}
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>::PartialPivLU(Index size)
+ : m_lu(size, size),
+ m_p(size),
+ m_rowsTranspositions(size),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+}
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>::PartialPivLU(const MatrixType& matrix)
+ : m_lu(matrix.rows(), matrix.rows()),
+ m_p(matrix.rows()),
+ m_rowsTranspositions(matrix.rows()),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+ compute(matrix);
+}
+
+namespace internal {
+
+/** \internal This is the blocked version of fullpivlu_unblocked() */
+template<typename Scalar, int StorageOrder, typename PivIndex>
+struct partial_lu_impl
+{
+ // FIXME add a stride to Map, so that the following mapping becomes easier,
+ // another option would be to create an expression being able to automatically
+ // warp any Map, Matrix, and Block expressions as a unique type, but since that's exactly
+ // a Map + stride, why not adding a stride to Map, and convenient ctors from a Matrix,
+ // and Block.
+ typedef Map<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > MapLU;
+ typedef Block<MapLU, Dynamic, Dynamic> MatrixType;
+ typedef Block<MatrixType,Dynamic,Dynamic> BlockType;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \internal performs the LU decomposition in-place of the matrix \a lu
+ * using an unblocked algorithm.
+ *
+ * In addition, this function returns the row transpositions in the
+ * vector \a row_transpositions which must have a size equal to the number
+ * of columns of the matrix \a lu, and an integer \a nb_transpositions
+ * which returns the actual number of transpositions.
+ *
+ * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
+ */
+ static Index unblocked_lu(MatrixType& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)
+ {
+ const Index rows = lu.rows();
+ const Index cols = lu.cols();
+ const Index size = (std::min)(rows,cols);
+ nb_transpositions = 0;
+ Index first_zero_pivot = -1;
+ for(Index k = 0; k < size; ++k)
+ {
+ Index rrows = rows-k-1;
+ Index rcols = cols-k-1;
+
+ Index row_of_biggest_in_col;
+ RealScalar biggest_in_corner
+ = lu.col(k).tail(rows-k).cwiseAbs().maxCoeff(&row_of_biggest_in_col);
+ row_of_biggest_in_col += k;
+
+ row_transpositions[k] = PivIndex(row_of_biggest_in_col);
+
+ if(biggest_in_corner != RealScalar(0))
+ {
+ if(k != row_of_biggest_in_col)
+ {
+ lu.row(k).swap(lu.row(row_of_biggest_in_col));
+ ++nb_transpositions;
+ }
+
+ // FIXME shall we introduce a safe quotient expression in cas 1/lu.coeff(k,k)
+ // overflow but not the actual quotient?
+ lu.col(k).tail(rrows) /= lu.coeff(k,k);
+ }
+ else if(first_zero_pivot==-1)
+ {
+ // the pivot is exactly zero, we record the index of the first pivot which is exactly 0,
+ // and continue the factorization such we still have A = PLU
+ first_zero_pivot = k;
+ }
+
+ if(k<rows-1)
+ lu.bottomRightCorner(rrows,rcols).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rcols);
+ }
+ return first_zero_pivot;
+ }
+
+ /** \internal performs the LU decomposition in-place of the matrix represented
+ * by the variables \a rows, \a cols, \a lu_data, and \a lu_stride using a
+ * recursive, blocked algorithm.
+ *
+ * In addition, this function returns the row transpositions in the
+ * vector \a row_transpositions which must have a size equal to the number
+ * of columns of the matrix \a lu, and an integer \a nb_transpositions
+ * which returns the actual number of transpositions.
+ *
+ * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
+ *
+ * \note This very low level interface using pointers, etc. is to:
+ * 1 - reduce the number of instanciations to the strict minimum
+ * 2 - avoid infinite recursion of the instanciations with Block<Block<Block<...> > >
+ */
+ static Index blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions, Index maxBlockSize=256)
+ {
+ MapLU lu1(lu_data,StorageOrder==RowMajor?rows:luStride,StorageOrder==RowMajor?luStride:cols);
+ MatrixType lu(lu1,0,0,rows,cols);
+
+ const Index size = (std::min)(rows,cols);
+
+ // if the matrix is too small, no blocking:
+ if(size<=16)
+ {
+ return unblocked_lu(lu, row_transpositions, nb_transpositions);
+ }
+
+ // automatically adjust the number of subdivisions to the size
+ // of the matrix so that there is enough sub blocks:
+ Index blockSize;
+ {
+ blockSize = size/8;
+ blockSize = (blockSize/16)*16;
+ blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize);
+ }
+
+ nb_transpositions = 0;
+ Index first_zero_pivot = -1;
+ for(Index k = 0; k < size; k+=blockSize)
+ {
+ Index bs = (std::min)(size-k,blockSize); // actual size of the block
+ Index trows = rows - k - bs; // trailing rows
+ Index tsize = size - k - bs; // trailing size
+
+ // partition the matrix:
+ // A00 | A01 | A02
+ // lu = A_0 | A_1 | A_2 = A10 | A11 | A12
+ // A20 | A21 | A22
+ BlockType A_0(lu,0,0,rows,k);
+ BlockType A_2(lu,0,k+bs,rows,tsize);
+ BlockType A11(lu,k,k,bs,bs);
+ BlockType A12(lu,k,k+bs,bs,tsize);
+ BlockType A21(lu,k+bs,k,trows,bs);
+ BlockType A22(lu,k+bs,k+bs,trows,tsize);
+
+ PivIndex nb_transpositions_in_panel;
+ // recursively call the blocked LU algorithm on [A11^T A21^T]^T
+ // with a very small blocking size:
+ Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,
+ row_transpositions+k, nb_transpositions_in_panel, 16);
+ if(ret>=0 && first_zero_pivot==-1)
+ first_zero_pivot = k+ret;
+
+ nb_transpositions += nb_transpositions_in_panel;
+ // update permutations and apply them to A_0
+ for(Index i=k; i<k+bs; ++i)
+ {
+ Index piv = (row_transpositions[i] += k);
+ A_0.row(i).swap(A_0.row(piv));
+ }
+
+ if(trows)
+ {
+ // apply permutations to A_2
+ for(Index i=k;i<k+bs; ++i)
+ A_2.row(i).swap(A_2.row(row_transpositions[i]));
+
+ // A12 = A11^-1 A12
+ A11.template triangularView<UnitLower>().solveInPlace(A12);
+
+ A22.noalias() -= A21 * A12;
+ }
+ }
+ return first_zero_pivot;
+ }
+};
+
+/** \internal performs the LU decomposition with partial pivoting in-place.
+ */
+template<typename MatrixType, typename TranspositionType>
+void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, typename TranspositionType::Index& nb_transpositions)
+{
+ eigen_assert(lu.cols() == row_transpositions.size());
+ eigen_assert((&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1);
+
+ partial_lu_impl
+ <typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor, typename TranspositionType::Index>
+ ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions);
+}
+
+} // end namespace internal
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const MatrixType& matrix)
+{
+ check_template_parameters();
+
+ // the row permutation is stored as int indices, so just to be sure:
+ eigen_assert(matrix.rows()<NumTraits<int>::highest());
+
+ m_lu = matrix;
+
+ eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
+ const Index size = matrix.rows();
+
+ m_rowsTranspositions.resize(size);
+
+ typename TranspositionType::Index nb_transpositions;
+ internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);
+ m_det_p = (nb_transpositions%2) ? -1 : 1;
+
+ m_p = m_rowsTranspositions;
+
+ m_isInitialized = true;
+ return *this;
+}
+
+template<typename MatrixType>
+typename internal::traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return Scalar(m_det_p) * m_lu.diagonal().prod();
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^{-1} L U.
+ * This function is provided for debug purpose. */
+template<typename MatrixType>
+MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ // LU
+ MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()
+ * m_lu.template triangularView<Upper>();
+
+ // P^{-1}(LU)
+ res = m_p.inverse() * res;
+
+ return res;
+}
+
+/***** Implementation of solve() *****************************************************/
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<PartialPivLU<_MatrixType>, Rhs>
+ : solve_retval_base<PartialPivLU<_MatrixType>, Rhs>
+{
+ EIGEN_MAKE_SOLVE_HELPERS(PartialPivLU<_MatrixType>,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
+ * So we proceed as follows:
+ * Step 1: compute c = Pb.
+ * Step 2: replace c by the solution x to Lx = c.
+ * Step 3: replace c by the solution x to Ux = c.
+ */
+
+ eigen_assert(rhs().rows() == dec().matrixLU().rows());
+
+ // Step 1
+ dst = dec().permutationP() * rhs();
+
+ // Step 2
+ dec().matrixLU().template triangularView<UnitLower>().solveInPlace(dst);
+
+ // Step 3
+ dec().matrixLU().template triangularView<Upper>().solveInPlace(dst);
+ }
+};
+
+} // end namespace internal
+
+/******** MatrixBase methods *******/
+
+/** \lu_module
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::partialPivLu() const
+{
+ return PartialPivLU<PlainObject>(eval());
+}
+
+#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+/** \lu_module
+ *
+ * Synonym of partialPivLu().
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::lu() const
+{
+ return PartialPivLU<PlainObject>(eval());
+}
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIALLU_H
diff --git a/Eigen/src/LU/PartialPivLU_MKL.h b/Eigen/src/LU/PartialPivLU_MKL.h
new file mode 100644
index 0000000..9035953
--- /dev/null
+++ b/Eigen/src/LU/PartialPivLU_MKL.h
@@ -0,0 +1,85 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * LU decomposition with partial pivoting based on LAPACKE_?getrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_PARTIALLU_LAPACK_H
+#define EIGEN_PARTIALLU_LAPACK_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_LU_PARTPIV(EIGTYPE, MKLTYPE, MKLPREFIX) \
+template<int StorageOrder> \
+struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \
+{ \
+ /* \internal performs the LU decomposition in-place of the matrix represented */ \
+ static lapack_int blocked_lu(lapack_int rows, lapack_int cols, EIGTYPE* lu_data, lapack_int luStride, lapack_int* row_transpositions, lapack_int& nb_transpositions, lapack_int maxBlockSize=256) \
+ { \
+ EIGEN_UNUSED_VARIABLE(maxBlockSize);\
+ lapack_int matrix_order, first_zero_pivot; \
+ lapack_int m, n, lda, *ipiv, info; \
+ EIGTYPE* a; \
+/* Set up parameters for ?getrf */ \
+ matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
+ lda = luStride; \
+ a = lu_data; \
+ ipiv = row_transpositions; \
+ m = rows; \
+ n = cols; \
+ nb_transpositions = 0; \
+\
+ info = LAPACKE_##MKLPREFIX##getrf( matrix_order, m, n, (MKLTYPE*)a, lda, ipiv ); \
+\
+ for(int i=0;i<m;i++) { ipiv[i]--; if (ipiv[i]!=i) nb_transpositions++; } \
+\
+ eigen_assert(info >= 0); \
+/* something should be done with nb_transpositions */ \
+\
+ first_zero_pivot = info; \
+ return first_zero_pivot; \
+ } \
+};
+
+EIGEN_MKL_LU_PARTPIV(double, double, d)
+EIGEN_MKL_LU_PARTPIV(float, float, s)
+EIGEN_MKL_LU_PARTPIV(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_LU_PARTPIV(scomplex, MKL_Complex8, c)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIALLU_LAPACK_H
diff --git a/Eigen/src/LU/arch/CMakeLists.txt b/Eigen/src/LU/arch/CMakeLists.txt
new file mode 100644
index 0000000..f6b7ed9
--- /dev/null
+++ b/Eigen/src/LU/arch/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_LU_arch_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_LU_arch_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/LU/arch COMPONENT Devel
+ )
diff --git a/Eigen/src/LU/arch/Inverse_SSE.h b/Eigen/src/LU/arch/Inverse_SSE.h
new file mode 100644
index 0000000..60b7a23
--- /dev/null
+++ b/Eigen/src/LU/arch/Inverse_SSE.h
@@ -0,0 +1,329 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2001 Intel Corporation
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// The SSE code for the 4x4 float and double matrix inverse in this file
+// comes from the following Intel's library:
+// http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/
+//
+// Here is the respective copyright and license statement:
+//
+// Copyright (c) 2001 Intel Corporation.
+//
+// Permition is granted to use, copy, distribute and prepare derivative works
+// of this library for any purpose and without fee, provided, that the above
+// copyright notice and this statement appear in all copies.
+// Intel makes no representations about the suitability of this software for
+// any purpose, and specifically disclaims all warranties.
+// See LEGAL.TXT for all the legal information.
+
+#ifndef EIGEN_INVERSE_SSE_H
+#define EIGEN_INVERSE_SSE_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType>
+{
+ enum {
+ MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
+ ResultAlignment = bool(ResultType::Flags&AlignedBit),
+ StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
+ };
+
+ static void run(const MatrixType& matrix, ResultType& result)
+ {
+ EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 };
+
+ // Load the full matrix into registers
+ __m128 _L1 = matrix.template packet<MatrixAlignment>( 0);
+ __m128 _L2 = matrix.template packet<MatrixAlignment>( 4);
+ __m128 _L3 = matrix.template packet<MatrixAlignment>( 8);
+ __m128 _L4 = matrix.template packet<MatrixAlignment>(12);
+
+ // The inverse is calculated using "Divide and Conquer" technique. The
+ // original matrix is divide into four 2x2 sub-matrices. Since each
+ // register holds four matrix element, the smaller matrices are
+ // represented as a registers. Hence we get a better locality of the
+ // calculations.
+
+ __m128 A, B, C, D; // the four sub-matrices
+ if(!StorageOrdersMatch)
+ {
+ A = _mm_unpacklo_ps(_L1, _L2);
+ B = _mm_unpacklo_ps(_L3, _L4);
+ C = _mm_unpackhi_ps(_L1, _L2);
+ D = _mm_unpackhi_ps(_L3, _L4);
+ }
+ else
+ {
+ A = _mm_movelh_ps(_L1, _L2);
+ B = _mm_movehl_ps(_L2, _L1);
+ C = _mm_movelh_ps(_L3, _L4);
+ D = _mm_movehl_ps(_L4, _L3);
+ }
+
+ __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices
+ DC, AB;
+ __m128 dA, dB, dC, dD; // determinant of the sub-matrices
+ __m128 det, d, d1, d2;
+ __m128 rd; // reciprocal of the determinant
+
+ // AB = A# * B
+ AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);
+ AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));
+ // DC = D# * C
+ DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);
+ DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));
+
+ // dA = |A|
+ dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);
+ dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));
+ // dB = |B|
+ dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);
+ dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));
+
+ // dC = |C|
+ dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);
+ dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));
+ // dD = |D|
+ dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);
+ dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));
+
+ // d = trace(AB*DC) = trace(A#*B*D#*C)
+ d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);
+
+ // iD = C*A#*B
+ iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));
+ iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));
+ // iA = B*D#*C
+ iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));
+ iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));
+
+ // d = trace(AB*DC) = trace(A#*B*D#*C) [continue]
+ d = _mm_add_ps(d, _mm_movehl_ps(d, d));
+ d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));
+ d1 = _mm_mul_ss(dA,dD);
+ d2 = _mm_mul_ss(dB,dC);
+
+ // iD = D*|A| - C*A#*B
+ iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);
+
+ // iA = A*|D| - B*D#*C;
+ iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);
+
+ // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
+ det = _mm_sub_ss(_mm_add_ss(d1,d2),d);
+ rd = _mm_div_ss(_mm_set_ss(1.0f), det);
+
+// #ifdef ZERO_SINGULAR
+// rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd);
+// #endif
+
+ // iB = D * (A#B)# = D*B#*A
+ iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));
+ iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));
+ // iC = A * (D#C)# = A*C#*D
+ iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));
+ iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));
+
+ rd = _mm_shuffle_ps(rd,rd,0);
+ rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP));
+
+ // iB = C*|B| - D*B#*A
+ iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);
+
+ // iC = B*|C| - A*C#*D;
+ iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);
+
+ // iX = iX / det
+ iA = _mm_mul_ps(rd,iA);
+ iB = _mm_mul_ps(rd,iB);
+ iC = _mm_mul_ps(rd,iC);
+ iD = _mm_mul_ps(rd,iD);
+
+ result.template writePacket<ResultAlignment>( 0, _mm_shuffle_ps(iA,iB,0x77));
+ result.template writePacket<ResultAlignment>( 4, _mm_shuffle_ps(iA,iB,0x22));
+ result.template writePacket<ResultAlignment>( 8, _mm_shuffle_ps(iC,iD,0x77));
+ result.template writePacket<ResultAlignment>(12, _mm_shuffle_ps(iC,iD,0x22));
+ }
+
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType>
+{
+ enum {
+ MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
+ ResultAlignment = bool(ResultType::Flags&AlignedBit),
+ StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
+ };
+ static void run(const MatrixType& matrix, ResultType& result)
+ {
+ const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
+ const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+
+ // The inverse is calculated using "Divide and Conquer" technique. The
+ // original matrix is divide into four 2x2 sub-matrices. Since each
+ // register of the matrix holds two element, the smaller matrices are
+ // consisted of two registers. Hence we get a better locality of the
+ // calculations.
+
+ // the four sub-matrices
+ __m128d A1, A2, B1, B2, C1, C2, D1, D2;
+
+ if(StorageOrdersMatch)
+ {
+ A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2);
+ A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6);
+ C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
+ C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
+ }
+ else
+ {
+ __m128d tmp;
+ A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2);
+ A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6);
+ tmp = A1;
+ A1 = _mm_unpacklo_pd(A1,A2);
+ A2 = _mm_unpackhi_pd(tmp,A2);
+ tmp = C1;
+ C1 = _mm_unpacklo_pd(C1,C2);
+ C2 = _mm_unpackhi_pd(tmp,C2);
+
+ B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
+ B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
+ tmp = B1;
+ B1 = _mm_unpacklo_pd(B1,B2);
+ B2 = _mm_unpackhi_pd(tmp,B2);
+ tmp = D1;
+ D1 = _mm_unpacklo_pd(D1,D2);
+ D2 = _mm_unpackhi_pd(tmp,D2);
+ }
+
+ __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices
+ DC1, DC2, AB1, AB2;
+ __m128d dA, dB, dC, dD; // determinant of the sub-matrices
+ __m128d det, d1, d2, rd;
+
+ // dA = |A|
+ dA = _mm_shuffle_pd(A2, A2, 1);
+ dA = _mm_mul_pd(A1, dA);
+ dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));
+ // dB = |B|
+ dB = _mm_shuffle_pd(B2, B2, 1);
+ dB = _mm_mul_pd(B1, dB);
+ dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));
+
+ // AB = A# * B
+ AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));
+ AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));
+ AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));
+ AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));
+
+ // dC = |C|
+ dC = _mm_shuffle_pd(C2, C2, 1);
+ dC = _mm_mul_pd(C1, dC);
+ dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));
+ // dD = |D|
+ dD = _mm_shuffle_pd(D2, D2, 1);
+ dD = _mm_mul_pd(D1, dD);
+ dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));
+
+ // DC = D# * C
+ DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));
+ DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));
+ DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));
+ DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));
+
+ // rd = trace(AB*DC) = trace(A#*B*D#*C)
+ d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));
+ d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));
+ rd = _mm_add_pd(d1, d2);
+ rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));
+
+ // iD = C*A#*B
+ iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));
+ iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));
+ iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));
+ iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));
+
+ // iA = B*D#*C
+ iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));
+ iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));
+ iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));
+ iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));
+
+ // iD = D*|A| - C*A#*B
+ dA = _mm_shuffle_pd(dA,dA,0);
+ iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);
+ iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);
+
+ // iA = A*|D| - B*D#*C;
+ dD = _mm_shuffle_pd(dD,dD,0);
+ iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);
+ iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);
+
+ d1 = _mm_mul_sd(dA, dD);
+ d2 = _mm_mul_sd(dB, dC);
+
+ // iB = D * (A#B)# = D*B#*A
+ iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));
+ iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));
+ iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));
+ iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));
+
+ // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
+ det = _mm_add_sd(d1, d2);
+ det = _mm_sub_sd(det, rd);
+
+ // iC = A * (D#C)# = A*C#*D
+ iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));
+ iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));
+ iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));
+ iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));
+
+ rd = _mm_div_sd(_mm_set_sd(1.0), det);
+// #ifdef ZERO_SINGULAR
+// rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd);
+// #endif
+ rd = _mm_shuffle_pd(rd,rd,0);
+
+ // iB = C*|B| - D*B#*A
+ dB = _mm_shuffle_pd(dB,dB,0);
+ iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);
+ iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);
+
+ d1 = _mm_xor_pd(rd, _Sign_PN);
+ d2 = _mm_xor_pd(rd, _Sign_NP);
+
+ // iC = B*|C| - A*C#*D;
+ dC = _mm_shuffle_pd(dC,dC,0);
+ iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);
+ iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);
+
+ result.template writePacket<ResultAlignment>( 0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1)); // iA# / det
+ result.template writePacket<ResultAlignment>( 4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));
+ result.template writePacket<ResultAlignment>( 2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1)); // iB# / det
+ result.template writePacket<ResultAlignment>( 6, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));
+ result.template writePacket<ResultAlignment>( 8, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1)); // iC# / det
+ result.template writePacket<ResultAlignment>(12, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));
+ result.template writePacket<ResultAlignment>(10, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1)); // iD# / det
+ result.template writePacket<ResultAlignment>(14, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_INVERSE_SSE_H
diff --git a/Eigen/src/MetisSupport/CMakeLists.txt b/Eigen/src/MetisSupport/CMakeLists.txt
new file mode 100644
index 0000000..2bad314
--- /dev/null
+++ b/Eigen/src/MetisSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_MetisSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_MetisSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/MetisSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/MetisSupport/MetisSupport.h b/Eigen/src/MetisSupport/MetisSupport.h
new file mode 100644
index 0000000..f2bbef2
--- /dev/null
+++ b/Eigen/src/MetisSupport/MetisSupport.h
@@ -0,0 +1,137 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef METIS_SUPPORT_H
+#define METIS_SUPPORT_H
+
+namespace Eigen {
+/**
+ * Get the fill-reducing ordering from the METIS package
+ *
+ * If A is the original matrix and Ap is the permuted matrix,
+ * the fill-reducing permutation is defined as follows :
+ * Row (column) i of A is the matperm(i) row (column) of Ap.
+ * WARNING: As computed by METIS, this corresponds to the vector iperm (instead of perm)
+ */
+template <typename Index>
+class MetisOrdering
+{
+public:
+ typedef PermutationMatrix<Dynamic,Dynamic,Index> PermutationType;
+ typedef Matrix<Index,Dynamic,1> IndexVector;
+
+ template <typename MatrixType>
+ void get_symmetrized_graph(const MatrixType& A)
+ {
+ Index m = A.cols();
+ eigen_assert((A.rows() == A.cols()) && "ONLY FOR SQUARED MATRICES");
+ // Get the transpose of the input matrix
+ MatrixType At = A.transpose();
+ // Get the number of nonzeros elements in each row/col of At+A
+ Index TotNz = 0;
+ IndexVector visited(m);
+ visited.setConstant(-1);
+ for (int j = 0; j < m; j++)
+ {
+ // Compute the union structure of of A(j,:) and At(j,:)
+ visited(j) = j; // Do not include the diagonal element
+ // Get the nonzeros in row/column j of A
+ for (typename MatrixType::InnerIterator it(A, j); it; ++it)
+ {
+ Index idx = it.index(); // Get the row index (for column major) or column index (for row major)
+ if (visited(idx) != j )
+ {
+ visited(idx) = j;
+ ++TotNz;
+ }
+ }
+ //Get the nonzeros in row/column j of At
+ for (typename MatrixType::InnerIterator it(At, j); it; ++it)
+ {
+ Index idx = it.index();
+ if(visited(idx) != j)
+ {
+ visited(idx) = j;
+ ++TotNz;
+ }
+ }
+ }
+ // Reserve place for A + At
+ m_indexPtr.resize(m+1);
+ m_innerIndices.resize(TotNz);
+
+ // Now compute the real adjacency list of each column/row
+ visited.setConstant(-1);
+ Index CurNz = 0;
+ for (int j = 0; j < m; j++)
+ {
+ m_indexPtr(j) = CurNz;
+
+ visited(j) = j; // Do not include the diagonal element
+ // Add the pattern of row/column j of A to A+At
+ for (typename MatrixType::InnerIterator it(A,j); it; ++it)
+ {
+ Index idx = it.index(); // Get the row index (for column major) or column index (for row major)
+ if (visited(idx) != j )
+ {
+ visited(idx) = j;
+ m_innerIndices(CurNz) = idx;
+ CurNz++;
+ }
+ }
+ //Add the pattern of row/column j of At to A+At
+ for (typename MatrixType::InnerIterator it(At, j); it; ++it)
+ {
+ Index idx = it.index();
+ if(visited(idx) != j)
+ {
+ visited(idx) = j;
+ m_innerIndices(CurNz) = idx;
+ ++CurNz;
+ }
+ }
+ }
+ m_indexPtr(m) = CurNz;
+ }
+
+ template <typename MatrixType>
+ void operator() (const MatrixType& A, PermutationType& matperm)
+ {
+ Index m = A.cols();
+ IndexVector perm(m),iperm(m);
+ // First, symmetrize the matrix graph.
+ get_symmetrized_graph(A);
+ int output_error;
+
+ // Call the fill-reducing routine from METIS
+ output_error = METIS_NodeND(&m, m_indexPtr.data(), m_innerIndices.data(), NULL, NULL, perm.data(), iperm.data());
+
+ if(output_error != METIS_OK)
+ {
+ //FIXME The ordering interface should define a class of possible errors
+ std::cerr << "ERROR WHILE CALLING THE METIS PACKAGE \n";
+ return;
+ }
+
+ // Get the fill-reducing permutation
+ //NOTE: If Ap is the permuted matrix then perm and iperm vectors are defined as follows
+ // Row (column) i of Ap is the perm(i) row(column) of A, and row (column) i of A is the iperm(i) row(column) of Ap
+
+ matperm.resize(m);
+ for (int j = 0; j < m; j++)
+ matperm.indices()(iperm(j)) = j;
+
+ }
+
+ protected:
+ IndexVector m_indexPtr; // Pointer to the adjacenccy list of each row/column
+ IndexVector m_innerIndices; // Adjacency list
+};
+
+}// end namespace eigen
+#endif
diff --git a/Eigen/src/OrderingMethods/Amd.h b/Eigen/src/OrderingMethods/Amd.h
new file mode 100644
index 0000000..1c28bdf
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Amd.h
@@ -0,0 +1,447 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+/*
+
+NOTE: this routine has been adapted from the CSparse library:
+
+Copyright (c) 2006, Timothy A. Davis.
+http://www.cise.ufl.edu/research/sparse/CSparse
+
+CSparse is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+CSparse is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+*/
+
+#include "../Core/util/NonMPL2.h"
+
+#ifndef EIGEN_SPARSE_AMD_H
+#define EIGEN_SPARSE_AMD_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename T> inline T amd_flip(const T& i) { return -i-2; }
+template<typename T> inline T amd_unflip(const T& i) { return i<0 ? amd_flip(i) : i; }
+template<typename T0, typename T1> inline bool amd_marked(const T0* w, const T1& j) { return w[j]<0; }
+template<typename T0, typename T1> inline void amd_mark(const T0* w, const T1& j) { return w[j] = amd_flip(w[j]); }
+
+/* clear w */
+template<typename Index>
+static int cs_wclear (Index mark, Index lemax, Index *w, Index n)
+{
+ Index k;
+ if(mark < 2 || (mark + lemax < 0))
+ {
+ for(k = 0; k < n; k++)
+ if(w[k] != 0)
+ w[k] = 1;
+ mark = 2;
+ }
+ return (mark); /* at this point, w[0..n-1] < mark holds */
+}
+
+/* depth-first search and postorder of a tree rooted at node j */
+template<typename Index>
+Index cs_tdfs(Index j, Index k, Index *head, const Index *next, Index *post, Index *stack)
+{
+ int i, p, top = 0;
+ if(!head || !next || !post || !stack) return (-1); /* check inputs */
+ stack[0] = j; /* place j on the stack */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack[top]; /* p = top of stack */
+ i = head[p]; /* i = youngest child of p */
+ if(i == -1)
+ {
+ top--; /* p has no unordered children left */
+ post[k++] = p; /* node p is the kth postordered node */
+ }
+ else
+ {
+ head[p] = next[i]; /* remove i from children of p */
+ stack[++top] = i; /* start dfs on child node i */
+ }
+ }
+ return k;
+}
+
+
+/** \internal
+ * \ingroup OrderingMethods_Module
+ * Approximate minimum degree ordering algorithm.
+ * \returns the permutation P reducing the fill-in of the input matrix \a C
+ * The input matrix \a C must be a selfadjoint compressed column major SparseMatrix object. Both the upper and lower parts have to be stored, but the diagonal entries are optional.
+ * On exit the values of C are destroyed */
+template<typename Scalar, typename Index>
+void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,Index>& C, PermutationMatrix<Dynamic,Dynamic,Index>& perm)
+{
+ using std::sqrt;
+
+ int d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
+ k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
+ ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t;
+ unsigned int h;
+
+ Index n = C.cols();
+ dense = std::max<Index> (16, Index(10 * sqrt(double(n)))); /* find dense threshold */
+ dense = std::min<Index> (n-2, dense);
+
+ Index cnz = C.nonZeros();
+ perm.resize(n+1);
+ t = cnz + cnz/5 + 2*n; /* add elbow room to C */
+ C.resizeNonZeros(t);
+
+ Index* W = new Index[8*(n+1)]; /* get workspace */
+ Index* len = W;
+ Index* nv = W + (n+1);
+ Index* next = W + 2*(n+1);
+ Index* head = W + 3*(n+1);
+ Index* elen = W + 4*(n+1);
+ Index* degree = W + 5*(n+1);
+ Index* w = W + 6*(n+1);
+ Index* hhead = W + 7*(n+1);
+ Index* last = perm.indices().data(); /* use P as workspace for last */
+
+ /* --- Initialize quotient graph ---------------------------------------- */
+ Index* Cp = C.outerIndexPtr();
+ Index* Ci = C.innerIndexPtr();
+ for(k = 0; k < n; k++)
+ len[k] = Cp[k+1] - Cp[k];
+ len[n] = 0;
+ nzmax = t;
+
+ for(i = 0; i <= n; i++)
+ {
+ head[i] = -1; // degree list i is empty
+ last[i] = -1;
+ next[i] = -1;
+ hhead[i] = -1; // hash list i is empty
+ nv[i] = 1; // node i is just one node
+ w[i] = 1; // node i is alive
+ elen[i] = 0; // Ek of node i is empty
+ degree[i] = len[i]; // degree of node i
+ }
+ mark = internal::cs_wclear<Index>(0, 0, w, n); /* clear w */
+ elen[n] = -2; /* n is a dead element */
+ Cp[n] = -1; /* n is a root of assembly tree */
+ w[n] = 0; /* n is a dead element */
+
+ /* --- Initialize degree lists ------------------------------------------ */
+ for(i = 0; i < n; i++)
+ {
+ bool has_diag = false;
+ for(p = Cp[i]; p<Cp[i+1]; ++p)
+ if(Ci[p]==i)
+ {
+ has_diag = true;
+ break;
+ }
+
+ d = degree[i];
+ if(d == 1) /* node i is empty */
+ {
+ elen[i] = -2; /* element i is dead */
+ nel++;
+ Cp[i] = -1; /* i is a root of assembly tree */
+ w[i] = 0;
+ }
+ else if(d > dense || !has_diag) /* node i is dense or has no structural diagonal element */
+ {
+ nv[i] = 0; /* absorb i into element n */
+ elen[i] = -1; /* node i is dead */
+ nel++;
+ Cp[i] = amd_flip (n);
+ nv[n]++;
+ }
+ else
+ {
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put node i in degree list d */
+ head[d] = i;
+ }
+ }
+
+ elen[n] = -2; /* n is a dead element */
+ Cp[n] = -1; /* n is a root of assembly tree */
+ w[n] = 0; /* n is a dead element */
+
+ while (nel < n) /* while (selecting pivots) do */
+ {
+ /* --- Select node of minimum approximate degree -------------------- */
+ for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}
+ if(next[k] != -1) last[next[k]] = -1;
+ head[mindeg] = next[k]; /* remove k from degree list */
+ elenk = elen[k]; /* elenk = |Ek| */
+ nvk = nv[k]; /* # of nodes k represents */
+ nel += nvk; /* nv[k] nodes of A eliminated */
+
+ /* --- Garbage collection ------------------------------------------- */
+ if(elenk > 0 && cnz + mindeg >= nzmax)
+ {
+ for(j = 0; j < n; j++)
+ {
+ if((p = Cp[j]) >= 0) /* j is a live node or element */
+ {
+ Cp[j] = Ci[p]; /* save first entry of object */
+ Ci[p] = amd_flip (j); /* first entry is now amd_flip(j) */
+ }
+ }
+ for(q = 0, p = 0; p < cnz; ) /* scan all of memory */
+ {
+ if((j = amd_flip (Ci[p++])) >= 0) /* found object j */
+ {
+ Ci[q] = Cp[j]; /* restore first entry of object */
+ Cp[j] = q++; /* new pointer to object j */
+ for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];
+ }
+ }
+ cnz = q; /* Ci[cnz...nzmax-1] now free */
+ }
+
+ /* --- Construct new element ---------------------------------------- */
+ dk = 0;
+ nv[k] = -nvk; /* flag k as in Lk */
+ p = Cp[k];
+ pk1 = (elenk == 0) ? p : cnz; /* do in place if elen[k] == 0 */
+ pk2 = pk1;
+ for(k1 = 1; k1 <= elenk + 1; k1++)
+ {
+ if(k1 > elenk)
+ {
+ e = k; /* search the nodes in k */
+ pj = p; /* list of nodes starts at Ci[pj]*/
+ ln = len[k] - elenk; /* length of list of nodes in k */
+ }
+ else
+ {
+ e = Ci[p++]; /* search the nodes in e */
+ pj = Cp[e];
+ ln = len[e]; /* length of list of nodes in e */
+ }
+ for(k2 = 1; k2 <= ln; k2++)
+ {
+ i = Ci[pj++];
+ if((nvi = nv[i]) <= 0) continue; /* node i dead, or seen */
+ dk += nvi; /* degree[Lk] += size of node i */
+ nv[i] = -nvi; /* negate nv[i] to denote i in Lk*/
+ Ci[pk2++] = i; /* place i in Lk */
+ if(next[i] != -1) last[next[i]] = last[i];
+ if(last[i] != -1) /* remove i from degree list */
+ {
+ next[last[i]] = next[i];
+ }
+ else
+ {
+ head[degree[i]] = next[i];
+ }
+ }
+ if(e != k)
+ {
+ Cp[e] = amd_flip (k); /* absorb e into k */
+ w[e] = 0; /* e is now a dead element */
+ }
+ }
+ if(elenk != 0) cnz = pk2; /* Ci[cnz...nzmax] is free */
+ degree[k] = dk; /* external degree of k - |Lk\i| */
+ Cp[k] = pk1; /* element k is in Ci[pk1..pk2-1] */
+ len[k] = pk2 - pk1;
+ elen[k] = -2; /* k is now an element */
+
+ /* --- Find set differences ----------------------------------------- */
+ mark = internal::cs_wclear<Index>(mark, lemax, w, n); /* clear w if necessary */
+ for(pk = pk1; pk < pk2; pk++) /* scan 1: find |Le\Lk| */
+ {
+ i = Ci[pk];
+ if((eln = elen[i]) <= 0) continue;/* skip if elen[i] empty */
+ nvi = -nv[i]; /* nv[i] was negated */
+ wnvi = mark - nvi;
+ for(p = Cp[i]; p <= Cp[i] + eln - 1; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] >= mark)
+ {
+ w[e] -= nvi; /* decrement |Le\Lk| */
+ }
+ else if(w[e] != 0) /* ensure e is a live element */
+ {
+ w[e] = degree[e] + wnvi; /* 1st time e seen in scan 1 */
+ }
+ }
+ }
+
+ /* --- Degree update ------------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++) /* scan2: degree update */
+ {
+ i = Ci[pk]; /* consider node i in Lk */
+ p1 = Cp[i];
+ p2 = p1 + elen[i] - 1;
+ pn = p1;
+ for(h = 0, d = 0, p = p1; p <= p2; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] != 0) /* e is an unabsorbed element */
+ {
+ dext = w[e] - mark; /* dext = |Le\Lk| */
+ if(dext > 0)
+ {
+ d += dext; /* sum up the set differences */
+ Ci[pn++] = e; /* keep e in Ei */
+ h += e; /* compute the hash of node i */
+ }
+ else
+ {
+ Cp[e] = amd_flip (k); /* aggressive absorb. e->k */
+ w[e] = 0; /* e is a dead element */
+ }
+ }
+ }
+ elen[i] = pn - p1 + 1; /* elen[i] = |Ei| */
+ p3 = pn;
+ p4 = p1 + len[i];
+ for(p = p2 + 1; p < p4; p++) /* prune edges in Ai */
+ {
+ j = Ci[p];
+ if((nvj = nv[j]) <= 0) continue; /* node j dead or in Lk */
+ d += nvj; /* degree(i) += |j| */
+ Ci[pn++] = j; /* place j in node list of i */
+ h += j; /* compute hash for node i */
+ }
+ if(d == 0) /* check for mass elimination */
+ {
+ Cp[i] = amd_flip (k); /* absorb i into k */
+ nvi = -nv[i];
+ dk -= nvi; /* |Lk| -= |i| */
+ nvk += nvi; /* |k| += nv[i] */
+ nel += nvi;
+ nv[i] = 0;
+ elen[i] = -1; /* node i is dead */
+ }
+ else
+ {
+ degree[i] = std::min<Index> (degree[i], d); /* update degree(i) */
+ Ci[pn] = Ci[p3]; /* move first node to end */
+ Ci[p3] = Ci[p1]; /* move 1st el. to end of Ei */
+ Ci[p1] = k; /* add k as 1st element in of Ei */
+ len[i] = pn - p1 + 1; /* new len of adj. list of node i */
+ h %= n; /* finalize hash of i */
+ next[i] = hhead[h]; /* place i in hash bucket */
+ hhead[h] = i;
+ last[i] = h; /* save hash of i in last[i] */
+ }
+ } /* scan2 is done */
+ degree[k] = dk; /* finalize |Lk| */
+ lemax = std::max<Index>(lemax, dk);
+ mark = internal::cs_wclear<Index>(mark+lemax, lemax, w, n); /* clear w */
+
+ /* --- Supernode detection ------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++)
+ {
+ i = Ci[pk];
+ if(nv[i] >= 0) continue; /* skip if i is dead */
+ h = last[i]; /* scan hash bucket of node i */
+ i = hhead[h];
+ hhead[h] = -1; /* hash bucket will be empty */
+ for(; i != -1 && next[i] != -1; i = next[i], mark++)
+ {
+ ln = len[i];
+ eln = elen[i];
+ for(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark;
+ jlast = i;
+ for(j = next[i]; j != -1; ) /* compare i with all j */
+ {
+ ok = (len[j] == ln) && (elen[j] == eln);
+ for(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++)
+ {
+ if(w[Ci[p]] != mark) ok = 0; /* compare i and j*/
+ }
+ if(ok) /* i and j are identical */
+ {
+ Cp[j] = amd_flip (i); /* absorb j into i */
+ nv[i] += nv[j];
+ nv[j] = 0;
+ elen[j] = -1; /* node j is dead */
+ j = next[j]; /* delete j from hash bucket */
+ next[jlast] = j;
+ }
+ else
+ {
+ jlast = j; /* j and i are different */
+ j = next[j];
+ }
+ }
+ }
+ }
+
+ /* --- Finalize new element------------------------------------------ */
+ for(p = pk1, pk = pk1; pk < pk2; pk++) /* finalize Lk */
+ {
+ i = Ci[pk];
+ if((nvi = -nv[i]) <= 0) continue;/* skip if i is dead */
+ nv[i] = nvi; /* restore nv[i] */
+ d = degree[i] + dk - nvi; /* compute external degree(i) */
+ d = std::min<Index> (d, n - nel - nvi);
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put i back in degree list */
+ last[i] = -1;
+ head[d] = i;
+ mindeg = std::min<Index> (mindeg, d); /* find new minimum degree */
+ degree[i] = d;
+ Ci[p++] = i; /* place i in Lk */
+ }
+ nv[k] = nvk; /* # nodes absorbed into k */
+ if((len[k] = p-pk1) == 0) /* length of adj list of element k*/
+ {
+ Cp[k] = -1; /* k is a root of the tree */
+ w[k] = 0; /* k is now a dead element */
+ }
+ if(elenk != 0) cnz = p; /* free unused space in Lk */
+ }
+
+ /* --- Postordering ----------------------------------------------------- */
+ for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);/* fix assembly tree */
+ for(j = 0; j <= n; j++) head[j] = -1;
+ for(j = n; j >= 0; j--) /* place unordered nodes in lists */
+ {
+ if(nv[j] > 0) continue; /* skip if j is an element */
+ next[j] = head[Cp[j]]; /* place j in list of its parent */
+ head[Cp[j]] = j;
+ }
+ for(e = n; e >= 0; e--) /* place elements in lists */
+ {
+ if(nv[e] <= 0) continue; /* skip unless e is an element */
+ if(Cp[e] != -1)
+ {
+ next[e] = head[Cp[e]]; /* place e in list of its parent */
+ head[Cp[e]] = e;
+ }
+ }
+ for(k = 0, i = 0; i <= n; i++) /* postorder the assembly tree */
+ {
+ if(Cp[i] == -1) k = internal::cs_tdfs<Index>(i, k, head, next, perm.indices().data(), w);
+ }
+
+ perm.indices().conservativeResize(n);
+
+ delete[] W;
+}
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_AMD_H
diff --git a/Eigen/src/OrderingMethods/CMakeLists.txt b/Eigen/src/OrderingMethods/CMakeLists.txt
new file mode 100644
index 0000000..9f4bb27
--- /dev/null
+++ b/Eigen/src/OrderingMethods/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_OrderingMethods_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_OrderingMethods_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/OrderingMethods COMPONENT Devel
+ )
diff --git a/Eigen/src/OrderingMethods/Eigen_Colamd.h b/Eigen/src/OrderingMethods/Eigen_Colamd.h
new file mode 100644
index 0000000..44548f6
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Eigen_Colamd.h
@@ -0,0 +1,1850 @@
+// // This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is modified from the colamd/symamd library. The copyright is below
+
+// The authors of the code itself are Stefan I. Larimore and Timothy A.
+// Davis (davis@cise.ufl.edu), University of Florida. The algorithm was
+// developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+// Ng, Oak Ridge National Laboratory.
+//
+// Date:
+//
+// September 8, 2003. Version 2.3.
+//
+// Acknowledgements:
+//
+// This work was supported by the National Science Foundation, under
+// grants DMS-9504974 and DMS-9803599.
+//
+// Notice:
+//
+// Copyright (c) 1998-2003 by the University of Florida.
+// All Rights Reserved.
+//
+// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+//
+// Permission is hereby granted to use, copy, modify, and/or distribute
+// this program, provided that the Copyright, this License, and the
+// Availability of the original version is retained on all copies and made
+// accessible to the end-user of any code or package that includes COLAMD
+// or any modified version of COLAMD.
+//
+// Availability:
+//
+// The colamd/symamd library is available at
+//
+// http://www.cise.ufl.edu/research/sparse/colamd/
+
+// This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h
+// file. It is required by the colamd.c, colamdmex.c, and symamdmex.c
+// files, and by any C code that calls the routines whose prototypes are
+// listed below, or that uses the colamd/symamd definitions listed below.
+
+#ifndef EIGEN_COLAMD_H
+#define EIGEN_COLAMD_H
+
+namespace internal {
+/* Ensure that debugging is turned off: */
+#ifndef COLAMD_NDEBUG
+#define COLAMD_NDEBUG
+#endif /* NDEBUG */
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */
+#define COLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..6] are currently used. */
+#define COLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define COLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define COLAMD_DENSE_COL 1
+
+/* stats [2]: memory defragmentation count output statistic */
+#define COLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+#define COLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define COLAMD_INFO1 4
+#define COLAMD_INFO2 5
+#define COLAMD_INFO3 6
+
+/* error codes returned in stats [3]: */
+#define COLAMD_OK (0)
+#define COLAMD_OK_BUT_JUMBLED (1)
+#define COLAMD_ERROR_A_not_present (-1)
+#define COLAMD_ERROR_p_not_present (-2)
+#define COLAMD_ERROR_nrow_negative (-3)
+#define COLAMD_ERROR_ncol_negative (-4)
+#define COLAMD_ERROR_nnz_negative (-5)
+#define COLAMD_ERROR_p0_nonzero (-6)
+#define COLAMD_ERROR_A_too_small (-7)
+#define COLAMD_ERROR_col_length_negative (-8)
+#define COLAMD_ERROR_row_index_out_of_bounds (-9)
+#define COLAMD_ERROR_out_of_memory (-10)
+#define COLAMD_ERROR_internal_error (-999)
+
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+#define COLAMD_MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define COLAMD_MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+
+/* -------------------------------------------------------------------------- */
+
+#define COLAMD_EMPTY (-1)
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+/* ========================================================================== */
+/* === Colamd reporting mechanism =========================================== */
+/* ========================================================================== */
+
+// == Row and Column structures ==
+template <typename Index>
+struct colamd_col
+{
+ Index start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Index length ; /* number of rows in this column */
+ union
+ {
+ Index thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Index parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Index score ; /* the score used to maintain heap, if col is alive */
+ Index order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ Index headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Index hash ; /* hash value, if col is not in a degree list */
+ Index prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Index degree_next ; /* next column, if col is in a degree list */
+ Index hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+};
+
+template <typename Index>
+struct Colamd_Row
+{
+ Index start ; /* index for A of first col in this row */
+ Index length ; /* number of principal columns in this row */
+ union
+ {
+ Index degree ; /* number of principal & non-principal columns in row */
+ Index p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Index mark ; /* for computing set differences and marking dead rows*/
+ Index first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+};
+
+/* ========================================================================== */
+/* === Colamd recommended memory size ======================================= */
+/* ========================================================================== */
+
+/*
+ The recommended length Alen of the array A passed to colamd is given by
+ the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any
+ argument is negative. 2*nnz space is required for the row and column
+ indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd. An additional n_col space is the minimal amount of "elbow room",
+ and nnz/5 more space is recommended for run time efficiency.
+
+ This macro is not needed when using symamd.
+
+ Explicit typecast to Index added Sept. 23, 2002, COLAMD version 2.2, to avoid
+ gcc -pedantic warning messages.
+*/
+template <typename Index>
+inline Index colamd_c(Index n_col)
+{ return Index( ((n_col) + 1) * sizeof (colamd_col<Index>) / sizeof (Index) ) ; }
+
+template <typename Index>
+inline Index colamd_r(Index n_row)
+{ return Index(((n_row) + 1) * sizeof (Colamd_Row<Index>) / sizeof (Index)); }
+
+// Prototypes of non-user callable routines
+template <typename Index>
+static Index init_rows_cols (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> col [], Index A [], Index p [], Index stats[COLAMD_STATS] );
+
+template <typename Index>
+static void init_scoring (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], double knobs[COLAMD_KNOBS], Index *p_n_row2, Index *p_n_col2, Index *p_max_deg);
+
+template <typename Index>
+static Index find_ordering (Index n_row, Index n_col, Index Alen, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], Index n_col2, Index max_deg, Index pfree);
+
+template <typename Index>
+static void order_children (Index n_col, colamd_col<Index> Col [], Index p []);
+
+template <typename Index>
+static void detect_super_cols (colamd_col<Index> Col [], Index A [], Index head [], Index row_start, Index row_length ) ;
+
+template <typename Index>
+static Index garbage_collection (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index *pfree) ;
+
+template <typename Index>
+static inline Index clear_mark (Index n_row, Colamd_Row<Index> Row [] ) ;
+
+/* === No debugging ========================================================= */
+
+#define COLAMD_DEBUG0(params) ;
+#define COLAMD_DEBUG1(params) ;
+#define COLAMD_DEBUG2(params) ;
+#define COLAMD_DEBUG3(params) ;
+#define COLAMD_DEBUG4(params) ;
+
+#define COLAMD_ASSERT(expression) ((void) 0)
+
+
+/**
+ * \brief Returns the recommended value of Alen
+ *
+ * Returns recommended value of Alen for use by colamd.
+ * Returns -1 if any input argument is negative.
+ * The use of this routine or macro is optional.
+ * Note that the macro uses its arguments more than once,
+ * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.
+ *
+ * \param nnz nonzeros in A
+ * \param n_row number of rows in A
+ * \param n_col number of columns in A
+ * \return recommended value of Alen for use by colamd
+ */
+template <typename Index>
+inline Index colamd_recommended ( Index nnz, Index n_row, Index n_col)
+{
+ if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)
+ return (-1);
+ else
+ return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5));
+}
+
+/**
+ * \brief set default parameters The use of this routine is optional.
+ *
+ * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col)
+ * entries are removed prior to ordering. Columns with more than
+ * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to
+ * ordering, and placed last in the output column ordering.
+ *
+ * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
+ * respectively, in colamd.h. Default values of these two knobs
+ * are both 0.5. Currently, only knobs [0] and knobs [1] are
+ * used, but future versions may use more knobs. If so, they will
+ * be properly set to their defaults by the future version of
+ * colamd_set_defaults, so that the code that calls colamd will
+ * not need to change, assuming that you either use
+ * colamd_set_defaults, or pass a (double *) NULL pointer as the
+ * knobs array to colamd or symamd.
+ *
+ * \param knobs parameter settings for colamd
+ */
+
+static inline void colamd_set_defaults(double knobs[COLAMD_KNOBS])
+{
+ /* === Local variables ================================================== */
+
+ int i ;
+
+ if (!knobs)
+ {
+ return ; /* no knobs to initialize */
+ }
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [COLAMD_DENSE_ROW] = 0.5 ; /* ignore rows over 50% dense */
+ knobs [COLAMD_DENSE_COL] = 0.5 ; /* ignore columns over 50% dense */
+}
+
+/**
+ * \brief Computes a column ordering using the column approximate minimum degree ordering
+ *
+ * Computes a column ordering (Q) of A such that P(AQ)=LU or
+ * (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ * operations than factorizing the unpermuted matrix A or A'A,
+ * respectively.
+ *
+ *
+ * \param n_row number of rows in A
+ * \param n_col number of columns in A
+ * \param Alen, size of the array A
+ * \param A row indices of the matrix, of size ALen
+ * \param p column pointers of A, of size n_col+1
+ * \param knobs parameter settings for colamd
+ * \param stats colamd output statistics and error codes
+ */
+template <typename Index>
+static bool colamd(Index n_row, Index n_col, Index Alen, Index *A, Index *p, double knobs[COLAMD_KNOBS], Index stats[COLAMD_STATS])
+{
+ /* === Local variables ================================================== */
+
+ Index i ; /* loop index */
+ Index nnz ; /* nonzeros in A */
+ Index Row_size ; /* size of Row [], in integers */
+ Index Col_size ; /* size of Col [], in integers */
+ Index need ; /* minimum required length of A */
+ Colamd_Row<Index> *Row ; /* pointer into A of Row [0..n_row] array */
+ colamd_col<Index> *Col ; /* pointer into A of Col [0..n_col] array */
+ Index n_col2 ; /* number of non-dense, non-empty columns */
+ Index n_row2 ; /* number of non-dense, non-empty rows */
+ Index ngarbage ; /* number of garbage collections performed */
+ Index max_deg ; /* maximum row degree */
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
+
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ COLAMD_DEBUG0 (("colamd: stats not present\n")) ;
+ return (false) ;
+ }
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+ if (!A) /* A is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ COLAMD_DEBUG0 (("colamd: A not present\n")) ;
+ return (false) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ COLAMD_DEBUG0 (("colamd: p not present\n")) ;
+ return (false) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
+ stats [COLAMD_INFO1] = n_row ;
+ COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
+ return (false) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n_col ;
+ COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
+ return (false) ;
+ }
+
+ nnz = p [n_col] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
+ return (false) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
+ return (false) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ colamd_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ Col_size = colamd_c (n_col) ;
+ Row_size = colamd_r (n_row) ;
+ need = 2*nnz + n_col + Col_size + Row_size ;
+
+ if (need > Alen)
+ {
+ /* not enough space in array A to perform the ordering */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
+ stats [COLAMD_INFO1] = need ;
+ stats [COLAMD_INFO2] = Alen ;
+ COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
+ return (false) ;
+ }
+
+ Alen -= Col_size + Row_size ;
+ Col = (colamd_col<Index> *) &A [Alen] ;
+ Row = (Colamd_Row<Index> *) &A [Alen + Col_size] ;
+
+ /* === Construct the row and column data structures ===================== */
+
+ if (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
+ {
+ /* input matrix is invalid */
+ COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (false) ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz) ;
+
+ /* === Order the non-principal columns ================================== */
+
+ Eigen::internal::order_children (n_col, Col, p) ;
+
+ /* === Return statistics in stats ======================================= */
+
+ stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;
+ stats [COLAMD_DENSE_COL] = n_col - n_col2 ;
+ stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
+ COLAMD_DEBUG0 (("colamd: done.\n")) ;
+ return (true) ;
+}
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns false if the matrix is invalid,
+ true otherwise. Not user-callable.
+*/
+template <typename Index>
+static Index init_rows_cols /* returns true if OK, or false otherwise */
+ (
+ /* === Parameters ======================================================= */
+
+ Index n_row, /* number of rows of A */
+ Index n_col, /* number of columns of A */
+ Colamd_Row<Index> Row [], /* of size n_row+1 */
+ colamd_col<Index> Col [], /* of size n_col+1 */
+ Index A [], /* row indices of A, of size Alen */
+ Index p [], /* pointers to columns in A, of size n_col+1 */
+ Index stats [COLAMD_STATS] /* colamd statistics */
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index col ; /* a column index */
+ Index row ; /* a row index */
+ Index *cp ; /* a column pointer */
+ Index *cp_end ; /* a pointer to the end of a column */
+ Index *rp ; /* a row pointer */
+ Index *rp_end ; /* a pointer to the end of a row */
+ Index last_row ; /* previous row */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = Col [col].length ;
+ COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
+ return (false) ;
+ }
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = COLAMD_EMPTY ;
+ Col [col].shared4.degree_next = COLAMD_EMPTY ;
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ last_row = -1 ;
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ stats [COLAMD_INFO3] = n_row ;
+ COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
+ return (false) ;
+ }
+
+ if (row <= last_row || Row [row].shared2.mark == col)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ (stats [COLAMD_INFO3]) ++ ;
+ COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
+ }
+
+ if (Row [row].shared2.mark != col)
+ {
+ Row [row].length++ ;
+ }
+ else
+ {
+ /* this is a repeated entry in the column, */
+ /* it will be removed */
+ Col [col].length-- ;
+ }
+
+ /* mark the row as having been seen in this column */
+ Row [row].shared2.mark = col ;
+
+ last_row = row ;
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ Row [0].shared2.mark = -1 ;
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ /* === Create row form ================================================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ /* if cols jumbled, watch for repeated row indices */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ if (Row [row].shared2.mark != col)
+ {
+ A [(Row [row].shared1.p)++] = col ;
+ Row [row].shared2.mark = col ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* if cols not jumbled, we don't need the mark (this is faster) */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* === See if we need to re-create columns ============================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
+
+
+ /* === Compute col pointers ========================================= */
+
+ /* col form of the matrix starts at A [0]. */
+ /* Note, we may have a gap between the col form and the row */
+ /* form if there were duplicate entries, if so, it will be */
+ /* removed upon the first garbage collection */
+ Col [0].start = 0 ;
+ p [0] = Col [0].start ;
+ for (col = 1 ; col < n_col ; col++)
+ {
+ /* note that the lengths here are for pruned columns, i.e. */
+ /* no duplicate row indices will exist for these columns */
+ Col [col].start = Col [col-1].start + Col [col-1].length ;
+ p [col] = Col [col].start ;
+ }
+
+ /* === Re-create col form =========================================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ A [(p [*rp++])++] = row ;
+ }
+ }
+ }
+
+ /* === Done. Matrix is not (or no longer) jumbled ====================== */
+
+ return (true) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+template <typename Index>
+static void init_scoring
+ (
+ /* === Parameters ======================================================= */
+
+ Index n_row, /* number of rows of A */
+ Index n_col, /* number of columns of A */
+ Colamd_Row<Index> Row [], /* of size n_row+1 */
+ colamd_col<Index> Col [], /* of size n_col+1 */
+ Index A [], /* column form and row form of A */
+ Index head [], /* of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameters */
+ Index *p_n_row2, /* number of non-dense, non-empty rows */
+ Index *p_n_col2, /* number of non-dense, non-empty columns */
+ Index *p_max_deg /* maximum row degree */
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index c ; /* a column index */
+ Index r, row ; /* a row index */
+ Index *cp ; /* a column pointer */
+ Index deg ; /* degree of a row or column */
+ Index *cp_end ; /* a pointer to the end of a column */
+ Index *new_cp ; /* new column pointer */
+ Index col_length ; /* length of pruned column */
+ Index score ; /* current column score */
+ Index n_col2 ; /* number of non-dense, non-empty columns */
+ Index n_row2 ; /* number of non-dense, non-empty rows */
+ Index dense_row_count ; /* remove rows with more entries than this */
+ Index dense_col_count ; /* remove cols with more entries than this */
+ Index min_score ; /* smallest column score */
+ Index max_deg ; /* maximum row degree */
+ Index next_col ; /* Used to add to degree list.*/
+
+
+ /* === Extract knobs ==================================================== */
+
+ dense_row_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ;
+ dense_col_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ;
+ COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* === Kill empty columns =============================================== */
+
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = COLAMD_MAX (max_deg, deg) ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = COLAMD_MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Index) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ else
+ {
+ /* set column length and set score */
+ COLAMD_ASSERT (score >= 0) ;
+ COLAMD_ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+ /* === Initialize degree lists ========================================== */
+
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = COLAMD_EMPTY ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (COL_IS_ALIVE (c))
+ {
+ COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (score >= 0) ;
+ COLAMD_ASSERT (score <= n_col) ;
+ COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = COLAMD_EMPTY ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != COLAMD_EMPTY)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = COLAMD_MIN (min_score, score) ;
+
+
+ }
+ }
+
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+template <typename Index>
+static Index find_ordering /* return the number of garbage collections */
+ (
+ /* === Parameters ======================================================= */
+
+ Index n_row, /* number of rows of A */
+ Index n_col, /* number of columns of A */
+ Index Alen, /* size of A, 2*nnz + n_col or larger */
+ Colamd_Row<Index> Row [], /* of size n_row+1 */
+ colamd_col<Index> Col [], /* of size n_col+1 */
+ Index A [], /* column form and row form of A */
+ Index head [], /* of size n_col+1 */
+ Index n_col2, /* Remaining columns to order */
+ Index max_deg, /* Maximum row degree */
+ Index pfree /* index of first free slot (2*nnz on entry) */
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index k ; /* current pivot ordering step */
+ Index pivot_col ; /* current pivot column */
+ Index *cp ; /* a column pointer */
+ Index *rp ; /* a row pointer */
+ Index pivot_row ; /* current pivot row */
+ Index *new_cp ; /* modified column pointer */
+ Index *new_rp ; /* modified row pointer */
+ Index pivot_row_start ; /* pointer to start of pivot row */
+ Index pivot_row_degree ; /* number of columns in pivot row */
+ Index pivot_row_length ; /* number of supercolumns in pivot row */
+ Index pivot_col_score ; /* score of pivot column */
+ Index needed_memory ; /* free space needed for pivot row */
+ Index *cp_end ; /* pointer to the end of a column */
+ Index *rp_end ; /* pointer to the end of a row */
+ Index row ; /* a row index */
+ Index col ; /* a column index */
+ Index max_score ; /* maximum possible score */
+ Index cur_score ; /* score of current column */
+ unsigned int hash ; /* hash value for supernode detection */
+ Index head_column ; /* head of hash bucket */
+ Index first_col ; /* first column in hash bucket */
+ Index tag_mark ; /* marker value for mark array */
+ Index row_mark ; /* Row [row].shared2.mark */
+ Index set_difference ; /* set difference size of row with pivot row */
+ Index min_score ; /* smallest column score */
+ Index col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Index max_mark ; /* maximum value of tag_mark */
+ Index pivot_col_thickness ; /* number of columns represented by pivot col */
+ Index prev_col ; /* Used by Dlist operations. */
+ Index next_col ; /* Used by Dlist operations. */
+ Index ngarbage ; /* number of garbage collections performed */
+
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */
+ tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ;
+
+ /* get pivot column from head of minimum degree list */
+ while (head [min_score] == COLAMD_EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != COLAMD_EMPTY)
+ {
+ Col [next_col].shared3.prev = COLAMD_EMPTY ;
+ }
+
+ COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ;
+ COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ k += pivot_col_thickness ;
+ COLAMD_ASSERT (pivot_col_thickness > 0) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = COLAMD_MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ COLAMD_ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
+
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ COLAMD_ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ }
+ }
+ }
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ;
+ max_deg = COLAMD_MAX (max_deg, pivot_row_degree) ;
+
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+ COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = COLAMD_EMPTY ;
+ COLAMD_ASSERT (pivot_row_length == 0) ;
+ }
+ COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ COLAMD_DEBUG3 (("Pivot row: ")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ COLAMD_DEBUG3 (("Col: %d\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ COLAMD_ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+ COLAMD_ASSERT (cur_score <= n_col) ;
+ COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ;
+ if (prev_col == COLAMD_EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != COLAMD_EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ COLAMD_ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ COLAMD_ASSERT (set_difference >= 0) ;
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0)
+ {
+ COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+
+ /* === Add up set differences for each column ======================= */
+
+ COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ COLAMD_ASSERT(row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ COLAMD_ASSERT (row_mark > tag_mark) ;
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = COLAMD_MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Index) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ COLAMD_ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ hash %= n_col + 1 ;
+
+ COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
+ COLAMD_ASSERT (hash <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > COLAMD_EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Index) hash ;
+ COLAMD_ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* === Clear mark =================================================== */
+
+ tag_mark += (max_deg + 1) ;
+ if (tag_mark >= max_mark)
+ {
+ COLAMD_DEBUG2 (("clearing tag_mark\n")) ;
+ tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
+ }
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = COLAMD_MIN (cur_score, max_score) ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+
+ /* === Place column back in degree list ========================= */
+
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+ COLAMD_ASSERT (cur_score <= n_col) ;
+ COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = COLAMD_EMPTY ;
+ if (next_col != COLAMD_EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = COLAMD_MIN (min_score, cur_score) ;
+
+ }
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0)
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Index) (new_rp - &A[pivot_row_start]) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* pivot row is no longer dead */
+ }
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children ======================================================= */
+/* ========================================================================== */
+
+/*
+ The find_ordering routine has ordered all of the principal columns (the
+ representatives of the supercolumns). The non-principal columns have not
+ yet been ordered. This routine orders those columns by walking up the
+ parent tree (a column is a child of the column which absorbed it). The
+ final permutation vector is then placed in p [0 ... n_col-1], with p [0]
+ being the first column, and p [n_col-1] being the last. It doesn't look
+ like it at first glance, but be assured that this routine takes time linear
+ in the number of columns. Although not immediately obvious, the time
+ taken by this routine is O (n_col), that is, linear in the number of
+ columns. Not user-callable.
+*/
+template <typename Index>
+static inline void order_children
+(
+ /* === Parameters ======================================================= */
+
+ Index n_col, /* number of columns of A */
+ colamd_col<Index> Col [], /* of size n_col+1 */
+ Index p [] /* p [0 ... n_col-1] is the column permutation*/
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index i ; /* loop counter for all columns */
+ Index c ; /* column index */
+ Index parent ; /* index of column's parent */
+ Index order ; /* column's order */
+
+ /* === Order each non-principal column ================================== */
+
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* find an un-ordered non-principal column */
+ COLAMD_ASSERT (COL_IS_DEAD (i)) ;
+ if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY)
+ {
+ parent = i ;
+ /* once found, find its principal parent */
+ do
+ {
+ parent = Col [parent].shared1.parent ;
+ } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;
+
+ /* now, order all un-ordered non-principal columns along path */
+ /* to this parent. collapse tree at the same time */
+ c = i ;
+ /* get order of parent */
+ order = Col [parent].shared2.order ;
+
+ do
+ {
+ COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ;
+
+ /* order this column */
+ Col [c].shared2.order = order++ ;
+ /* collaps tree */
+ Col [c].shared1.parent = parent ;
+
+ /* get immediate parent of this column */
+ c = Col [c].shared1.parent ;
+
+ /* continue until we hit an ordered column. There are */
+ /* guarranteed not to be anymore unordered columns */
+ /* above an ordered column */
+ } while (Col [c].shared2.order == COLAMD_EMPTY) ;
+
+ /* re-order the super_col parent to largest order for this group */
+ Col [parent].shared2.order = order ;
+ }
+ }
+
+ /* === Generate the permutation ========================================= */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ p [Col [c].shared2.order] = c ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+template <typename Index>
+static void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+ colamd_col<Index> Col [], /* of size n_col+1 */
+ Index A [], /* row indices of A */
+ Index head [], /* head of degree lists and hash buckets */
+ Index row_start, /* pointer to set of columns to check */
+ Index row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ Index hash ; /* hash value for a column */
+ Index *rp ; /* pointer to a row */
+ Index c ; /* a column index */
+ Index super_c ; /* column index of the column to absorb into */
+ Index *cp1 ; /* column pointer for column super_c */
+ Index *cp2 ; /* column pointer for column c */
+ Index length ; /* length of column super_c */
+ Index prev_c ; /* column preceding c in hash bucket */
+ Index i ; /* loop counter */
+ Index *rp_end ; /* pointer to the end of the row */
+ Index col ; /* a column index in the row to check */
+ Index head_column ; /* first column in hash bucket or degree list */
+ Index first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ COLAMD_ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > COLAMD_EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != COLAMD_EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ;
+ COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ COLAMD_ASSERT (c != super_c) ;
+ COLAMD_ASSERT (COL_IS_ALIVE (c)) ;
+ COLAMD_ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ COLAMD_ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ COLAMD_ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+ /* order c later, in order_children() */
+ Col [c].shared2.order = COLAMD_EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > COLAMD_EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = COLAMD_EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = COLAMD_EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all avaliable memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+template <typename Index>
+static Index garbage_collection /* returns the new value of pfree */
+ (
+ /* === Parameters ======================================================= */
+
+ Index n_row, /* number of rows */
+ Index n_col, /* number of columns */
+ Colamd_Row<Index> Row [], /* row info */
+ colamd_col<Index> Col [], /* column info */
+ Index A [], /* A [0 ... Alen-1] holds the matrix */
+ Index *pfree /* &A [0] ... pfree is in use */
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index *psrc ; /* source pointer */
+ Index *pdest ; /* destination pointer */
+ Index j ; /* counter */
+ Index r ; /* a row index */
+ Index c ; /* a column index */
+ Index length ; /* length of a row or column */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ COLAMD_ASSERT (pdest <= psrc) ;
+ Col [c].start = (Index) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Index) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ if (Row [r].length == 0)
+ {
+ /* this row is of zero length. cannot compact it, so kill it */
+ COLAMD_DEBUG3 (("Defrag row kill\n")) ;
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+
+ }
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ COLAMD_ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
+
+ /* move and compact the row */
+ COLAMD_ASSERT (pdest <= psrc) ;
+ Row [r].start = (Index) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Index) (pdest - &A [Row [r].start]) ;
+
+ }
+ }
+ /* ensure we found all the rows */
+ COLAMD_ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Index) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+template <typename Index>
+static inline Index clear_mark /* return the new value for tag_mark */
+ (
+ /* === Parameters ======================================================= */
+
+ Index n_row, /* number of rows in A */
+ Colamd_Row<Index> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
+ )
+{
+ /* === Local variables ================================================== */
+
+ Index r ;
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+ return (1) ;
+}
+
+
+} // namespace internal
+#endif
diff --git a/Eigen/src/OrderingMethods/Ordering.h b/Eigen/src/OrderingMethods/Ordering.h
new file mode 100644
index 0000000..f3c31f9
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Ordering.h
@@ -0,0 +1,154 @@
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ORDERING_H
+#define EIGEN_ORDERING_H
+
+namespace Eigen {
+
+#include "Eigen_Colamd.h"
+
+namespace internal {
+
+/** \internal
+ * \ingroup OrderingMethods_Module
+ * \returns the symmetric pattern A^T+A from the input matrix A.
+ * FIXME: The values should not be considered here
+ */
+template<typename MatrixType>
+void ordering_helper_at_plus_a(const MatrixType& mat, MatrixType& symmat)
+{
+ MatrixType C;
+ C = mat.transpose(); // NOTE: Could be costly
+ for (int i = 0; i < C.rows(); i++)
+ {
+ for (typename MatrixType::InnerIterator it(C, i); it; ++it)
+ it.valueRef() = 0.0;
+ }
+ symmat = C + mat;
+}
+
+}
+
+#ifndef EIGEN_MPL2_ONLY
+
+/** \ingroup OrderingMethods_Module
+ * \class AMDOrdering
+ *
+ * Functor computing the \em approximate \em minimum \em degree ordering
+ * If the matrix is not structurally symmetric, an ordering of A^T+A is computed
+ * \tparam Index The type of indices of the matrix
+ * \sa COLAMDOrdering
+ */
+template <typename Index>
+class AMDOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+
+ /** Compute the permutation vector from a sparse matrix
+ * This routine is much faster if the input matrix is column-major
+ */
+ template <typename MatrixType>
+ void operator()(const MatrixType& mat, PermutationType& perm)
+ {
+ // Compute the symmetric pattern
+ SparseMatrix<typename MatrixType::Scalar, ColMajor, Index> symm;
+ internal::ordering_helper_at_plus_a(mat,symm);
+
+ // Call the AMD routine
+ //m_mat.prune(keep_diag());
+ internal::minimum_degree_ordering(symm, perm);
+ }
+
+ /** Compute the permutation with a selfadjoint matrix */
+ template <typename SrcType, unsigned int SrcUpLo>
+ void operator()(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat, PermutationType& perm)
+ {
+ SparseMatrix<typename SrcType::Scalar, ColMajor, Index> C; C = mat;
+
+ // Call the AMD routine
+ // m_mat.prune(keep_diag()); //Remove the diagonal elements
+ internal::minimum_degree_ordering(C, perm);
+ }
+};
+
+#endif // EIGEN_MPL2_ONLY
+
+/** \ingroup OrderingMethods_Module
+ * \class NaturalOrdering
+ *
+ * Functor computing the natural ordering (identity)
+ *
+ * \note Returns an empty permutation matrix
+ * \tparam Index The type of indices of the matrix
+ */
+template <typename Index>
+class NaturalOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+
+ /** Compute the permutation vector from a column-major sparse matrix */
+ template <typename MatrixType>
+ void operator()(const MatrixType& /*mat*/, PermutationType& perm)
+ {
+ perm.resize(0);
+ }
+
+};
+
+/** \ingroup OrderingMethods_Module
+ * \class COLAMDOrdering
+ *
+ * Functor computing the \em column \em approximate \em minimum \em degree ordering
+ * The matrix should be in column-major and \b compressed format (see SparseMatrix::makeCompressed()).
+ */
+template<typename Index>
+class COLAMDOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+ typedef Matrix<Index, Dynamic, 1> IndexVector;
+
+ /** Compute the permutation vector \a perm form the sparse matrix \a mat
+ * \warning The input sparse matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ */
+ template <typename MatrixType>
+ void operator() (const MatrixType& mat, PermutationType& perm)
+ {
+ eigen_assert(mat.isCompressed() && "COLAMDOrdering requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to COLAMDOrdering");
+
+ Index m = mat.rows();
+ Index n = mat.cols();
+ Index nnz = mat.nonZeros();
+ // Get the recommended value of Alen to be used by colamd
+ Index Alen = internal::colamd_recommended(nnz, m, n);
+ // Set the default parameters
+ double knobs [COLAMD_KNOBS];
+ Index stats [COLAMD_STATS];
+ internal::colamd_set_defaults(knobs);
+
+ IndexVector p(n+1), A(Alen);
+ for(Index i=0; i <= n; i++) p(i) = mat.outerIndexPtr()[i];
+ for(Index i=0; i < nnz; i++) A(i) = mat.innerIndexPtr()[i];
+ // Call Colamd routine to compute the ordering
+ Index info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats);
+ EIGEN_UNUSED_VARIABLE(info);
+ eigen_assert( info && "COLAMD failed " );
+
+ perm.resize(n);
+ for (Index i = 0; i < n; i++) perm.indices()(p(i)) = i;
+ }
+};
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/PaStiXSupport/CMakeLists.txt b/Eigen/src/PaStiXSupport/CMakeLists.txt
new file mode 100644
index 0000000..28c657e
--- /dev/null
+++ b/Eigen/src/PaStiXSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_PastixSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_PastixSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/PaStiXSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/PaStiXSupport/PaStiXSupport.h b/Eigen/src/PaStiXSupport/PaStiXSupport.h
new file mode 100644
index 0000000..a955287
--- /dev/null
+++ b/Eigen/src/PaStiXSupport/PaStiXSupport.h
@@ -0,0 +1,721 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PASTIXSUPPORT_H
+#define EIGEN_PASTIXSUPPORT_H
+
+namespace Eigen {
+
+/** \ingroup PaStiXSupport_Module
+ * \brief Interface to the PaStix solver
+ *
+ * This class is used to solve the linear systems A.X = B via the PaStix library.
+ * The matrix can be either real or complex, symmetric or not.
+ *
+ * \sa TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType, bool IsStrSym = false> class PastixLU;
+template<typename _MatrixType, int Options> class PastixLLT;
+template<typename _MatrixType, int Options> class PastixLDLT;
+
+namespace internal
+{
+
+ template<class Pastix> struct pastix_traits;
+
+ template<typename _MatrixType>
+ struct pastix_traits< PastixLU<_MatrixType> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+ template<typename _MatrixType, int Options>
+ struct pastix_traits< PastixLLT<_MatrixType,Options> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+ template<typename _MatrixType, int Options>
+ struct pastix_traits< PastixLDLT<_MatrixType,Options> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+ void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
+ }
+
+ void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
+ }
+
+ void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<COMPLEX*>(vals), perm, invp, reinterpret_cast<COMPLEX*>(x), nbrhs, iparm, dparm);
+ }
+
+ void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<DCOMPLEX*>(vals), perm, invp, reinterpret_cast<DCOMPLEX*>(x), nbrhs, iparm, dparm);
+ }
+
+ // Convert the matrix to Fortran-style Numbering
+ template <typename MatrixType>
+ void c_to_fortran_numbering (MatrixType& mat)
+ {
+ if ( !(mat.outerIndexPtr()[0]) )
+ {
+ int i;
+ for(i = 0; i <= mat.rows(); ++i)
+ ++mat.outerIndexPtr()[i];
+ for(i = 0; i < mat.nonZeros(); ++i)
+ ++mat.innerIndexPtr()[i];
+ }
+ }
+
+ // Convert to C-style Numbering
+ template <typename MatrixType>
+ void fortran_to_c_numbering (MatrixType& mat)
+ {
+ // Check the Numbering
+ if ( mat.outerIndexPtr()[0] == 1 )
+ { // Convert to C-style numbering
+ int i;
+ for(i = 0; i <= mat.rows(); ++i)
+ --mat.outerIndexPtr()[i];
+ for(i = 0; i < mat.nonZeros(); ++i)
+ --mat.innerIndexPtr()[i];
+ }
+ }
+}
+
+// This is the base class to interface with PaStiX functions.
+// Users should not used this class directly.
+template <class Derived>
+class PastixBase : internal::noncopyable
+{
+ public:
+ typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType;
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
+
+ public:
+
+ PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false), m_pastixdata(0), m_size(0)
+ {
+ init();
+ }
+
+ ~PastixBase()
+ {
+ clean();
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<PastixBase, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Pastix solver is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<PastixBase, Rhs>(*this, b.derived());
+ }
+
+ template<typename Rhs,typename Dest>
+ bool _solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;
+
+ Derived& derived()
+ {
+ return *static_cast<Derived*>(this);
+ }
+ const Derived& derived() const
+ {
+ return *static_cast<const Derived*>(this);
+ }
+
+ /** Returns a reference to the integer vector IPARM of PaStiX parameters
+ * to modify the default parameters.
+ * The statistics related to the different phases of factorization and solve are saved here as well
+ * \sa analyzePattern() factorize()
+ */
+ Array<Index,IPARM_SIZE,1>& iparm()
+ {
+ return m_iparm;
+ }
+
+ /** Return a reference to a particular index parameter of the IPARM vector
+ * \sa iparm()
+ */
+
+ int& iparm(int idxparam)
+ {
+ return m_iparm(idxparam);
+ }
+
+ /** Returns a reference to the double vector DPARM of PaStiX parameters
+ * The statistics related to the different phases of factorization and solve are saved here as well
+ * \sa analyzePattern() factorize()
+ */
+ Array<RealScalar,IPARM_SIZE,1>& dparm()
+ {
+ return m_dparm;
+ }
+
+
+ /** Return a reference to a particular index parameter of the DPARM vector
+ * \sa dparm()
+ */
+ double& dparm(int idxparam)
+ {
+ return m_dparm(idxparam);
+ }
+
+ inline Index cols() const { return m_size; }
+ inline Index rows() const { return m_size; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the PaStiX reports a problem
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<PastixBase, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Pastix LU, LLT or LDLT is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<PastixBase, Rhs>(*this, b.derived());
+ }
+
+ protected:
+
+ // Initialize the Pastix data structure, check the matrix
+ void init();
+
+ // Compute the ordering and the symbolic factorization
+ void analyzePattern(ColSpMatrix& mat);
+
+ // Compute the numerical factorization
+ void factorize(ColSpMatrix& mat);
+
+ // Free all the data allocated by Pastix
+ void clean()
+ {
+ eigen_assert(m_initisOk && "The Pastix structure should be allocated first");
+ m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;
+ m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+ m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+ }
+
+ void compute(ColSpMatrix& mat);
+
+ int m_initisOk;
+ int m_analysisIsOk;
+ int m_factorizationIsOk;
+ bool m_isInitialized;
+ mutable ComputationInfo m_info;
+ mutable pastix_data_t *m_pastixdata; // Data structure for pastix
+ mutable int m_comm; // The MPI communicator identifier
+ mutable Matrix<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters
+ mutable Matrix<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters
+ mutable Matrix<Index,Dynamic,1> m_perm; // Permutation vector
+ mutable Matrix<Index,Dynamic,1> m_invp; // Inverse permutation vector
+ mutable int m_size; // Size of the matrix
+};
+
+ /** Initialize the PaStiX data structure.
+ *A first call to this function fills iparm and dparm with the default PaStiX parameters
+ * \sa iparm() dparm()
+ */
+template <class Derived>
+void PastixBase<Derived>::init()
+{
+ m_size = 0;
+ m_iparm.setZero(IPARM_SIZE);
+ m_dparm.setZero(DPARM_SIZE);
+
+ m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
+ pastix(&m_pastixdata, MPI_COMM_WORLD,
+ 0, 0, 0, 0,
+ 0, 0, 0, 1, m_iparm.data(), m_dparm.data());
+
+ m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;
+ m_iparm[IPARM_VERBOSE] = 2;
+ m_iparm[IPARM_ORDERING] = API_ORDER_SCOTCH;
+ m_iparm[IPARM_INCOMPLETE] = API_NO;
+ m_iparm[IPARM_OOC_LIMIT] = 2000;
+ m_iparm[IPARM_RHS_MAKING] = API_RHS_B;
+ m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+
+ m_iparm(IPARM_START_TASK) = API_TASK_INIT;
+ m_iparm(IPARM_END_TASK) = API_TASK_INIT;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+ 0, 0, 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER)) {
+ m_info = InvalidInput;
+ m_initisOk = false;
+ }
+ else {
+ m_info = Success;
+ m_initisOk = true;
+ }
+}
+
+template <class Derived>
+void PastixBase<Derived>::compute(ColSpMatrix& mat)
+{
+ eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");
+
+ analyzePattern(mat);
+ factorize(mat);
+
+ m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+ m_isInitialized = m_factorizationIsOk;
+}
+
+
+template <class Derived>
+void PastixBase<Derived>::analyzePattern(ColSpMatrix& mat)
+{
+ eigen_assert(m_initisOk && "The initialization of PaSTiX failed");
+
+ // clean previous calls
+ if(m_size>0)
+ clean();
+
+ m_size = mat.rows();
+ m_perm.resize(m_size);
+ m_invp.resize(m_size);
+
+ m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;
+ m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+ mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER))
+ {
+ m_info = NumericalIssue;
+ m_analysisIsOk = false;
+ }
+ else
+ {
+ m_info = Success;
+ m_analysisIsOk = true;
+ }
+}
+
+template <class Derived>
+void PastixBase<Derived>::factorize(ColSpMatrix& mat)
+{
+// if(&m_cpyMat != &mat) m_cpyMat = mat;
+ eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase");
+ m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;
+ m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;
+ m_size = mat.rows();
+
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+ mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER))
+ {
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ m_isInitialized = false;
+ }
+ else
+ {
+ m_info = Success;
+ m_factorizationIsOk = true;
+ m_isInitialized = true;
+ }
+}
+
+/* Solve the system */
+template<typename Base>
+template<typename Rhs,typename Dest>
+bool PastixBase<Base>::_solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const
+{
+ eigen_assert(m_isInitialized && "The matrix should be factorized first");
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ int rhs = 1;
+
+ x = b; /* on return, x is overwritten by the computed solution */
+
+ for (int i = 0; i < b.cols(); i++){
+ m_iparm[IPARM_START_TASK] = API_TASK_SOLVE;
+ m_iparm[IPARM_END_TASK] = API_TASK_REFINE;
+
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, x.rows(), 0, 0, 0,
+ m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
+ }
+
+ // Check the returned error
+ m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue;
+
+ return m_iparm(IPARM_ERROR_NUMBER)==0;
+}
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLU
+ * \brief Sparse direct LU solver based on PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B with a supernodal LU
+ * factorization in the PaStiX library. The matrix A should be squared and nonsingular
+ * PaStiX requires that the matrix A has a symmetric structural pattern.
+ * This interface can symmetrize the input matrix otherwise.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false
+ * NOTE : Note that if the analysis and factorization phase are called separately,
+ * the input matrix will be symmetrized at each call, hence it is advised to
+ * symmetrize the matrix in a end-user program and set \p IsStrSym to true
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ *
+ */
+template<typename _MatrixType, bool IsStrSym>
+class PastixLU : public PastixBase< PastixLU<_MatrixType> >
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef PastixBase<PastixLU<MatrixType> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+ typedef typename MatrixType::Index Index;
+
+ public:
+ PastixLU() : Base()
+ {
+ init();
+ }
+
+ PastixLU(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+ /** Compute the LU supernodal factorization of \p matrix.
+ * iparm and dparm can be used to tune the PaStiX parameters.
+ * see the PaStiX user's manual
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ m_structureIsUptodate = false;
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+ /** Compute the LU symbolic factorization of \p matrix using its sparsity pattern.
+ * Several ordering methods can be used at this step. See the PaStiX user's manual.
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ m_structureIsUptodate = false;
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+
+ /** Compute the LU supernodal factorization of \p matrix
+ * WARNING The matrix \p matrix should have the same structural pattern
+ * as the same used in the analysis phase.
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+ protected:
+
+ void init()
+ {
+ m_structureIsUptodate = false;
+ m_iparm(IPARM_SYM) = API_SYM_NO;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ if(IsStrSym)
+ out = matrix;
+ else
+ {
+ if(!m_structureIsUptodate)
+ {
+ // update the transposed structure
+ m_transposedStructure = matrix.transpose();
+
+ // Set the elements of the matrix to zero
+ for (Index j=0; j<m_transposedStructure.outerSize(); ++j)
+ for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it)
+ it.valueRef() = 0.0;
+
+ m_structureIsUptodate = true;
+ }
+
+ out = m_transposedStructure + matrix;
+ }
+ internal::c_to_fortran_numbering(out);
+ }
+
+ using Base::m_iparm;
+ using Base::m_dparm;
+
+ ColSpMatrix m_transposedStructure;
+ bool m_structureIsUptodate;
+};
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLLT
+ * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization
+ * available in the PaStiX library. The matrix A should be symmetric and positive definite
+ * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+ * The vectors or matrices X and B can be either dense or sparse
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType, int _UpLo>
+class PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> >
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+
+ public:
+ enum { UpLo = _UpLo };
+ PastixLLT() : Base()
+ {
+ init();
+ }
+
+ PastixLLT(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ /** Compute the L factor of the LL^T supernodal factorization of \p matrix
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+
+ /** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+ /** Compute the LL^T supernodal numerical factorization of \p matrix
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+ protected:
+ using Base::m_iparm;
+
+ void init()
+ {
+ m_iparm(IPARM_SYM) = API_SYM_YES;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ // Pastix supports only lower, column-major matrices
+ out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+ internal::c_to_fortran_numbering(out);
+ }
+};
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLDLT
+ * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization
+ * available in the PaStiX library. The matrix A should be symmetric and positive definite
+ * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+ * The vectors or matrices X and B can be either dense or sparse
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType, int _UpLo>
+class PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> >
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+
+ public:
+ enum { UpLo = _UpLo };
+ PastixLDLT():Base()
+ {
+ init();
+ }
+
+ PastixLDLT(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ /** Compute the L and D factors of the LDL^T factorization of \p matrix
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+
+ /** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+ /** Compute the LDL^T supernodal numerical factorization of \p matrix
+ *
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+
+ protected:
+ using Base::m_iparm;
+
+ void init()
+ {
+ m_iparm(IPARM_SYM) = API_SYM_YES;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ // Pastix supports only lower, column-major matrices
+ out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+ internal::c_to_fortran_numbering(out);
+ }
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<PastixBase<_MatrixType>, Rhs>
+ : solve_retval_base<PastixBase<_MatrixType>, Rhs>
+{
+ typedef PastixBase<_MatrixType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+template<typename _MatrixType, typename Rhs>
+struct sparse_solve_retval<PastixBase<_MatrixType>, Rhs>
+ : sparse_solve_retval_base<PastixBase<_MatrixType>, Rhs>
+{
+ typedef PastixBase<_MatrixType> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/PardisoSupport/CMakeLists.txt b/Eigen/src/PardisoSupport/CMakeLists.txt
new file mode 100644
index 0000000..a097ab4
--- /dev/null
+++ b/Eigen/src/PardisoSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_PardisoSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_PardisoSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/PardisoSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/PardisoSupport/PardisoSupport.h b/Eigen/src/PardisoSupport/PardisoSupport.h
new file mode 100644
index 0000000..18cd7d8
--- /dev/null
+++ b/Eigen/src/PardisoSupport/PardisoSupport.h
@@ -0,0 +1,592 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL PARDISO
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_PARDISOSUPPORT_H
+#define EIGEN_PARDISOSUPPORT_H
+
+namespace Eigen {
+
+template<typename _MatrixType> class PardisoLU;
+template<typename _MatrixType, int Options=Upper> class PardisoLLT;
+template<typename _MatrixType, int Options=Upper> class PardisoLDLT;
+
+namespace internal
+{
+ template<typename Index>
+ struct pardiso_run_selector
+ {
+ static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
+ Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
+ {
+ Index error = 0;
+ ::pardiso(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
+ return error;
+ }
+ };
+ template<>
+ struct pardiso_run_selector<long long int>
+ {
+ typedef long long int Index;
+ static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
+ Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
+ {
+ Index error = 0;
+ ::pardiso_64(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
+ return error;
+ }
+ };
+
+ template<class Pardiso> struct pardiso_traits;
+
+ template<typename _MatrixType>
+ struct pardiso_traits< PardisoLU<_MatrixType> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+ template<typename _MatrixType, int Options>
+ struct pardiso_traits< PardisoLLT<_MatrixType, Options> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+ template<typename _MatrixType, int Options>
+ struct pardiso_traits< PardisoLDLT<_MatrixType, Options> >
+ {
+ typedef _MatrixType MatrixType;
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef typename _MatrixType::Index Index;
+ };
+
+}
+
+template<class Derived>
+class PardisoImpl
+{
+ typedef internal::pardiso_traits<Derived> Traits;
+ public:
+ typedef typename Traits::MatrixType MatrixType;
+ typedef typename Traits::Scalar Scalar;
+ typedef typename Traits::RealScalar RealScalar;
+ typedef typename Traits::Index Index;
+ typedef SparseMatrix<Scalar,RowMajor,Index> SparseMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef Matrix<Index, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<Index, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef Array<Index,64,1,DontAlign> ParameterType;
+ enum {
+ ScalarIsComplex = NumTraits<Scalar>::IsComplex
+ };
+
+ PardisoImpl()
+ {
+ eigen_assert((sizeof(Index) >= sizeof(_INTEGER_t) && sizeof(Index) <= 8) && "Non-supported index type");
+ m_iparm.setZero();
+ m_msglvl = 0; // No output
+ m_initialized = false;
+ }
+
+ ~PardisoImpl()
+ {
+ pardisoRelease();
+ }
+
+ inline Index cols() const { return m_size; }
+ inline Index rows() const { return m_size; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_initialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** \warning for advanced usage only.
+ * \returns a reference to the parameter array controlling PARDISO.
+ * See the PARDISO manual to know how to use it. */
+ ParameterType& pardisoParameterArray()
+ {
+ return m_iparm;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ Derived& analyzePattern(const MatrixType& matrix);
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ Derived& factorize(const MatrixType& matrix);
+
+ Derived& compute(const MatrixType& matrix);
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<PardisoImpl, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_initialized && "Pardiso solver is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<PardisoImpl, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<PardisoImpl, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_initialized && "Pardiso solver is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<PardisoImpl, Rhs>(*this, b.derived());
+ }
+
+ Derived& derived()
+ {
+ return *static_cast<Derived*>(this);
+ }
+ const Derived& derived() const
+ {
+ return *static_cast<const Derived*>(this);
+ }
+
+ template<typename BDerived, typename XDerived>
+ bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const;
+
+ protected:
+ void pardisoRelease()
+ {
+ if(m_initialized) // Factorization ran at least once
+ {
+ internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, -1, m_size, 0, 0, 0, m_perm.data(), 0,
+ m_iparm.data(), m_msglvl, 0, 0);
+ }
+ }
+
+ void pardisoInit(int type)
+ {
+ m_type = type;
+ bool symmetric = std::abs(m_type) < 10;
+ m_iparm[0] = 1; // No solver default
+ m_iparm[1] = 3; // use Metis for the ordering
+ m_iparm[2] = 1; // Numbers of processors, value of OMP_NUM_THREADS
+ m_iparm[3] = 0; // No iterative-direct algorithm
+ m_iparm[4] = 0; // No user fill-in reducing permutation
+ m_iparm[5] = 0; // Write solution into x
+ m_iparm[6] = 0; // Not in use
+ m_iparm[7] = 2; // Max numbers of iterative refinement steps
+ m_iparm[8] = 0; // Not in use
+ m_iparm[9] = 13; // Perturb the pivot elements with 1E-13
+ m_iparm[10] = symmetric ? 0 : 1; // Use nonsymmetric permutation and scaling MPS
+ m_iparm[11] = 0; // Not in use
+ m_iparm[12] = symmetric ? 0 : 1; // Maximum weighted matching algorithm is switched-off (default for symmetric).
+ // Try m_iparm[12] = 1 in case of inappropriate accuracy
+ m_iparm[13] = 0; // Output: Number of perturbed pivots
+ m_iparm[14] = 0; // Not in use
+ m_iparm[15] = 0; // Not in use
+ m_iparm[16] = 0; // Not in use
+ m_iparm[17] = -1; // Output: Number of nonzeros in the factor LU
+ m_iparm[18] = -1; // Output: Mflops for LU factorization
+ m_iparm[19] = 0; // Output: Numbers of CG Iterations
+
+ m_iparm[20] = 0; // 1x1 pivoting
+ m_iparm[26] = 0; // No matrix checker
+ m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
+ m_iparm[34] = 1; // C indexing
+ m_iparm[59] = 1; // Automatic switch between In-Core and Out-of-Core modes
+ }
+
+ protected:
+ // cached data to reduce reallocation, etc.
+
+ void manageErrorCode(Index error)
+ {
+ switch(error)
+ {
+ case 0:
+ m_info = Success;
+ break;
+ case -4:
+ case -7:
+ m_info = NumericalIssue;
+ break;
+ default:
+ m_info = InvalidInput;
+ }
+ }
+
+ mutable SparseMatrixType m_matrix;
+ ComputationInfo m_info;
+ bool m_initialized, m_analysisIsOk, m_factorizationIsOk;
+ Index m_type, m_msglvl;
+ mutable void *m_pt[64];
+ mutable ParameterType m_iparm;
+ mutable IntColVectorType m_perm;
+ Index m_size;
+
+ private:
+ PardisoImpl(PardisoImpl &) {}
+};
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
+{
+ m_size = a.rows();
+ eigen_assert(a.rows() == a.cols());
+
+ pardisoRelease();
+ memset(m_pt, 0, sizeof(m_pt));
+ m_perm.setZero(m_size);
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 12, m_size,
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+
+ manageErrorCode(error);
+ m_analysisIsOk = true;
+ m_factorizationIsOk = true;
+ m_initialized = true;
+ return derived();
+}
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
+{
+ m_size = a.rows();
+ eigen_assert(m_size == a.cols());
+
+ pardisoRelease();
+ memset(m_pt, 0, sizeof(m_pt));
+ m_perm.setZero(m_size);
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 11, m_size,
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+
+ manageErrorCode(error);
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_initialized = true;
+ return derived();
+}
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ eigen_assert(m_size == a.rows() && m_size == a.cols());
+
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 22, m_size,
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+
+ manageErrorCode(error);
+ m_factorizationIsOk = true;
+ return derived();
+}
+
+template<class Base>
+template<typename BDerived,typename XDerived>
+bool PardisoImpl<Base>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const
+{
+ if(m_iparm[0] == 0) // Factorization was not computed
+ return false;
+
+ //Index n = m_matrix.rows();
+ Index nrhs = Index(b.cols());
+ eigen_assert(m_size==b.rows());
+ eigen_assert(((MatrixBase<BDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major right hand sides are not supported");
+ eigen_assert(((MatrixBase<XDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major matrices of unknowns are not supported");
+ eigen_assert(((nrhs == 1) || b.outerStride() == b.rows()));
+
+
+// switch (transposed) {
+// case SvNoTrans : m_iparm[11] = 0 ; break;
+// case SvTranspose : m_iparm[11] = 2 ; break;
+// case SvAdjoint : m_iparm[11] = 1 ; break;
+// default:
+// //std::cerr << "Eigen: transposition option \"" << transposed << "\" not supported by the PARDISO backend\n";
+// m_iparm[11] = 0;
+// }
+
+ Scalar* rhs_ptr = const_cast<Scalar*>(b.derived().data());
+ Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp;
+
+ // Pardiso cannot solve in-place
+ if(rhs_ptr == x.derived().data())
+ {
+ tmp = b;
+ rhs_ptr = tmp.data();
+ }
+
+ Index error;
+ error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 33, m_size,
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), nrhs, m_iparm.data(), m_msglvl,
+ rhs_ptr, x.derived().data());
+
+ return error==0;
+}
+
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLU
+ * \brief A sparse direct LU factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename MatrixType>
+class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
+{
+ protected:
+ typedef PardisoImpl< PardisoLU<MatrixType> > Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLU<MatrixType> >;
+
+ public:
+
+ using Base::compute;
+ using Base::solve;
+
+ PardisoLU()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 13 : 11);
+ }
+
+ PardisoLU(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 13 : 11);
+ compute(matrix);
+ }
+ protected:
+ void getMatrix(const MatrixType& matrix)
+ {
+ m_matrix = matrix;
+ }
+
+ private:
+ PardisoLU(PardisoLU& ) {}
+};
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLLT
+ * \brief A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LL^T Cholesky factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
+ * Upper|Lower can be used to tell both triangular parts can be used as input.
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename MatrixType, int _UpLo>
+class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >
+{
+ protected:
+ typedef PardisoImpl< PardisoLLT<MatrixType,_UpLo> > Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::Index Index;
+ typedef typename Base::RealScalar RealScalar;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLLT<MatrixType,_UpLo> >;
+
+ public:
+
+ enum { UpLo = _UpLo };
+ using Base::compute;
+ using Base::solve;
+
+ PardisoLLT()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 4 : 2);
+ }
+
+ PardisoLLT(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 4 : 2);
+ compute(matrix);
+ }
+
+ protected:
+
+ void getMatrix(const MatrixType& matrix)
+ {
+ // PARDISO supports only upper, row-major matrices
+ PermutationMatrix<Dynamic,Dynamic,Index> p_null;
+ m_matrix.resize(matrix.rows(), matrix.cols());
+ m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
+ }
+
+ private:
+ PardisoLLT(PardisoLLT& ) {}
+};
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLDLT
+ * \brief A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LDL^T Cholesky factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A is assumed to be selfajoint and positive definite.
+ * For complex matrices, A can also be symmetric only, see the \a Options template parameter.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.
+ * Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.
+ * Upper|Lower can be used to tell both triangular parts can be used as input.
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename MatrixType, int Options>
+class PardisoLDLT : public PardisoImpl< PardisoLDLT<MatrixType,Options> >
+{
+ protected:
+ typedef PardisoImpl< PardisoLDLT<MatrixType,Options> > Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::Index Index;
+ typedef typename Base::RealScalar RealScalar;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;
+
+ public:
+
+ using Base::compute;
+ using Base::solve;
+ enum { UpLo = Options&(Upper|Lower) };
+
+ PardisoLDLT()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
+ }
+
+ PardisoLDLT(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
+ compute(matrix);
+ }
+
+ void getMatrix(const MatrixType& matrix)
+ {
+ // PARDISO supports only upper, row-major matrices
+ PermutationMatrix<Dynamic,Dynamic,Index> p_null;
+ m_matrix.resize(matrix.rows(), matrix.cols());
+ m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
+ }
+
+ private:
+ PardisoLDLT(PardisoLDLT& ) {}
+};
+
+namespace internal {
+
+template<typename _Derived, typename Rhs>
+struct solve_retval<PardisoImpl<_Derived>, Rhs>
+ : solve_retval_base<PardisoImpl<_Derived>, Rhs>
+{
+ typedef PardisoImpl<_Derived> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+template<typename Derived, typename Rhs>
+struct sparse_solve_retval<PardisoImpl<Derived>, Rhs>
+ : sparse_solve_retval_base<PardisoImpl<Derived>, Rhs>
+{
+ typedef PardisoImpl<Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARDISOSUPPORT_H
diff --git a/Eigen/src/QR/CMakeLists.txt b/Eigen/src/QR/CMakeLists.txt
new file mode 100644
index 0000000..96f43d7
--- /dev/null
+++ b/Eigen/src/QR/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_QR_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_QR_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/QR COMPONENT Devel
+ )
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
new file mode 100644
index 0000000..567eab7
--- /dev/null
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -0,0 +1,580 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
+#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
+
+namespace Eigen {
+
+/** \ingroup QR_Module
+ *
+ * \class ColPivHouseholderQR
+ *
+ * \brief Householder rank-revealing QR decomposition of a matrix with column-pivoting
+ *
+ * \param MatrixType the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
+ * upper triangular matrix.
+ *
+ * This decomposition performs column pivoting in order to be rank-revealing and improve
+ * numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
+ *
+ * \sa MatrixBase::colPivHouseholderQr()
+ */
+template<typename _MatrixType> class ColPivHouseholderQR
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
+ typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;
+ typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
+
+ private:
+
+ typedef typename PermutationType::Index PermIndexType;
+
+ public:
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).
+ */
+ ColPivHouseholderQR()
+ : m_qr(),
+ m_hCoeffs(),
+ m_colsPermutation(),
+ m_colsTranspositions(),
+ m_temp(),
+ m_colSqNorms(),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa ColPivHouseholderQR()
+ */
+ ColPivHouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_colsPermutation(PermIndexType(cols)),
+ m_colsTranspositions(cols),
+ m_temp(cols),
+ m_colSqNorms(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * ColPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ ColPivHouseholderQR(const MatrixType& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_colsPermutation(PermIndexType(matrix.cols())),
+ m_colsTranspositions(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_colSqNorms(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ compute(matrix);
+ }
+
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the QR decomposition, if any exists.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns a solution.
+ *
+ * \note The case where b is a matrix is not yet implemented. Also, this
+ * code is space inefficient.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include ColPivHouseholderQR_solve.cpp
+ * Output: \verbinclude ColPivHouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<ColPivHouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return internal::solve_retval<ColPivHouseholderQR, Rhs>(*this, b.derived());
+ }
+
+ HouseholderSequenceType householderQ(void) const;
+ HouseholderSequenceType matrixQ(void) const
+ {
+ return householderQ();
+ }
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ /** \returns a reference to the matrix where the result Householder QR is stored
+ * \warning The strict lower part of this matrix contains internal values.
+ * Only the upper triangular part should be referenced. To get it, use
+ * \code matrixR().template triangularView<Upper>() \endcode
+ * For rank-deficient matrices, use
+ * \code
+ * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>()
+ * \endcode
+ */
+ const MatrixType& matrixR() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ ColPivHouseholderQR& compute(const MatrixType& matrix);
+
+ /** \returns a const reference to the column permutation matrix */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_colsPermutation;
+ }
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ /** \returns the rank of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return isInjective() && isSurjective();
+ }
+
+ /** \returns the inverse of the matrix of which *this is the QR decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ */
+ inline const
+ internal::solve_retval<ColPivHouseholderQR, typename MatrixType::IdentityReturnType>
+ inverse() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return internal::solve_retval<ColPivHouseholderQR,typename MatrixType::IdentityReturnType>
+ (*this, MatrixType::Identity(m_qr.rows(), m_qr.cols()));
+ }
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * QR decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ ColPivHouseholderQR& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code qr.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ ColPivHouseholderQR& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
+ }
+
+ /** \returns the number of nonzero pivots in the QR decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of R.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ /** \brief Reports whether the QR factorization was succesful.
+ *
+ * \note This function always returns \c Success. It is provided for compatibility
+ * with other factorization routines.
+ * \returns \c Success
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return Success;
+ }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ PermutationType m_colsPermutation;
+ IntRowVectorType m_colsTranspositions;
+ RowVectorType m_temp;
+ RealRowVectorType m_colSqNorms;
+ bool m_isInitialized, m_usePrescribedThreshold;
+ RealScalar m_prescribedThreshold, m_maxpivot;
+ Index m_nonzero_pivots;
+ Index m_det_pq;
+};
+
+template<typename MatrixType>
+typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class ColPivHouseholderQR, ColPivHouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
+{
+ check_template_parameters();
+
+ using std::abs;
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+ Index size = matrix.diagonalSize();
+
+ // the column permutation is stored as int indices, so just to be sure:
+ eigen_assert(cols<=NumTraits<int>::highest());
+
+ m_qr = matrix;
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ m_colsTranspositions.resize(matrix.cols());
+ Index number_of_transpositions = 0;
+
+ m_colSqNorms.resize(cols);
+ for(Index k = 0; k < cols; ++k)
+ m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm();
+
+ RealScalar threshold_helper = m_colSqNorms.maxCoeff() * numext::abs2(NumTraits<Scalar>::epsilon()) / RealScalar(rows);
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ // first, we look up in our table m_colSqNorms which column has the biggest squared norm
+ Index biggest_col_index;
+ RealScalar biggest_col_sq_norm = m_colSqNorms.tail(cols-k).maxCoeff(&biggest_col_index);
+ biggest_col_index += k;
+
+ // since our table m_colSqNorms accumulates imprecision at every step, we must now recompute
+ // the actual squared norm of the selected column.
+ // Note that not doing so does result in solve() sometimes returning inf/nan values
+ // when running the unit test with 1000 repetitions.
+ biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm();
+
+ // we store that back into our table: it can't hurt to correct our table.
+ m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;
+
+ // Track the number of meaningful pivots but do not stop the decomposition to make
+ // sure that the initial matrix is properly reproduced. See bug 941.
+ if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
+ m_nonzero_pivots = k;
+
+ // apply the transposition to the columns
+ m_colsTranspositions.coeffRef(k) = biggest_col_index;
+ if(k != biggest_col_index) {
+ m_qr.col(k).swap(m_qr.col(biggest_col_index));
+ std::swap(m_colSqNorms.coeffRef(k), m_colSqNorms.coeffRef(biggest_col_index));
+ ++number_of_transpositions;
+ }
+
+ // generate the householder vector, store it below the diagonal
+ RealScalar beta;
+ m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+
+ // apply the householder transformation to the diagonal coefficient
+ m_qr.coeffRef(k,k) = beta;
+
+ // remember the maximum absolute value of diagonal coefficients
+ if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+
+ // apply the householder transformation
+ m_qr.bottomRightCorner(rows-k, cols-k-1)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
+
+ // update our table of squared norms of the columns
+ m_colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2();
+ }
+
+ m_colsPermutation.setIdentity(PermIndexType(cols));
+ for(PermIndexType k = 0; k < size/*m_nonzero_pivots*/; ++k)
+ m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));
+
+ m_det_pq = (number_of_transpositions%2) ? -1 : 1;
+ m_isInitialized = true;
+
+ return *this;
+}
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<ColPivHouseholderQR<_MatrixType>, Rhs>
+ : solve_retval_base<ColPivHouseholderQR<_MatrixType>, Rhs>
+{
+ EIGEN_MAKE_SOLVE_HELPERS(ColPivHouseholderQR<_MatrixType>,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ eigen_assert(rhs().rows() == dec().rows());
+
+ const Index cols = dec().cols(),
+ nonzero_pivots = dec().nonzeroPivots();
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename Rhs::PlainObject c(rhs());
+
+ // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
+ c.applyOnTheLeft(householderSequence(dec().matrixQR(), dec().hCoeffs())
+ .setLength(dec().nonzeroPivots())
+ .transpose()
+ );
+
+ dec().matrixR()
+ .topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ for(Index i = 0; i < nonzero_pivots; ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);
+ for(Index i = nonzero_pivots; i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();
+ }
+};
+
+} // end namespace internal
+
+/** \returns the matrix Q as a sequence of householder transformations.
+ * You can extract the meaningful part only by using:
+ * \code qr.householderQ().setLength(qr.nonzeroPivots()) \endcode*/
+template<typename MatrixType>
+typename ColPivHouseholderQR<MatrixType>::HouseholderSequenceType ColPivHouseholderQR<MatrixType>
+ ::householderQ() const
+{
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
+}
+
+/** \return the column-pivoting Householder QR decomposition of \c *this.
+ *
+ * \sa class ColPivHouseholderQR
+ */
+template<typename Derived>
+const ColPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::colPivHouseholderQr() const
+{
+ return ColPivHouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
diff --git a/Eigen/src/QR/ColPivHouseholderQR_MKL.h b/Eigen/src/QR/ColPivHouseholderQR_MKL.h
new file mode 100644
index 0000000..b5b1983
--- /dev/null
+++ b/Eigen/src/QR/ColPivHouseholderQR_MKL.h
@@ -0,0 +1,99 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Householder QR decomposition of a matrix with column pivoting based on
+ * LAPACKE_?geqp3 function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H
+#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_QR_COLPIV(EIGTYPE, MKLTYPE, MKLPREFIX, EIGCOLROW, MKLCOLROW) \
+template<> inline \
+ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >& \
+ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >::compute( \
+ const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix) \
+\
+{ \
+ using std::abs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
+ typedef MatrixType::Scalar Scalar; \
+ typedef MatrixType::RealScalar RealScalar; \
+ Index rows = matrix.rows();\
+ Index cols = matrix.cols();\
+ Index size = matrix.diagonalSize();\
+\
+ m_qr = matrix;\
+ m_hCoeffs.resize(size);\
+\
+ m_colsTranspositions.resize(cols);\
+ /*Index number_of_transpositions = 0;*/ \
+\
+ m_nonzero_pivots = 0; \
+ m_maxpivot = RealScalar(0);\
+ m_colsPermutation.resize(cols); \
+ m_colsPermutation.indices().setZero(); \
+\
+ lapack_int lda = m_qr.outerStride(), i; \
+ lapack_int matrix_order = MKLCOLROW; \
+ LAPACKE_##MKLPREFIX##geqp3( matrix_order, rows, cols, (MKLTYPE*)m_qr.data(), lda, (lapack_int*)m_colsPermutation.indices().data(), (MKLTYPE*)m_hCoeffs.data()); \
+ m_isInitialized = true; \
+ m_maxpivot=m_qr.diagonal().cwiseAbs().maxCoeff(); \
+ m_hCoeffs.adjointInPlace(); \
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold(); \
+ lapack_int *perm = m_colsPermutation.indices().data(); \
+ for(i=0;i<size;i++) { \
+ m_nonzero_pivots += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\
+ } \
+ for(i=0;i<cols;i++) perm[i]--;\
+\
+ /*m_det_pq = (number_of_transpositions%2) ? -1 : 1; // TODO: It's not needed now; fix upon availability in Eigen */ \
+\
+ return *this; \
+}
+
+EIGEN_MKL_QR_COLPIV(double, double, d, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_QR_COLPIV(float, float, s, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_QR_COLPIV(dcomplex, MKL_Complex16, z, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_QR_COLPIV(scomplex, MKL_Complex8, c, ColMajor, LAPACK_COL_MAJOR)
+
+EIGEN_MKL_QR_COLPIV(double, double, d, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_QR_COLPIV(float, float, s, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_QR_COLPIV(dcomplex, MKL_Complex16, z, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_QR_COLPIV(scomplex, MKL_Complex8, c, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
new file mode 100644
index 0000000..0b39966
--- /dev/null
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -0,0 +1,622 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType;
+
+template<typename MatrixType>
+struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+}
+
+/** \ingroup QR_Module
+ *
+ * \class FullPivHouseholderQR
+ *
+ * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
+ *
+ * \param MatrixType the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
+ * upper triangular matrix.
+ *
+ * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
+ * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
+ *
+ * \sa MatrixBase::fullPivHouseholderQr()
+ */
+template<typename _MatrixType> class FullPivHouseholderQR
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef Matrix<Index, 1,
+ EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1,
+ EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> IntDiagSizeVectorType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef typename internal::plain_col_type<MatrixType>::type ColVectorType;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).
+ */
+ FullPivHouseholderQR()
+ : m_qr(),
+ m_hCoeffs(),
+ m_rows_transpositions(),
+ m_cols_transpositions(),
+ m_cols_permutation(),
+ m_temp(),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa FullPivHouseholderQR()
+ */
+ FullPivHouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_rows_transpositions((std::min)(rows,cols)),
+ m_cols_transpositions((std::min)(rows,cols)),
+ m_cols_permutation(cols),
+ m_temp(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ FullPivHouseholderQR(const MatrixType& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
+ m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_permutation(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ compute(matrix);
+ }
+
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * \c *this is the QR decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,
+ * and an arbitrary solution otherwise.
+ *
+ * \note The case where b is a matrix is not yet implemented. Also, this
+ * code is space inefficient.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include FullPivHouseholderQR_solve.cpp
+ * Output: \verbinclude FullPivHouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<FullPivHouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return internal::solve_retval<FullPivHouseholderQR, Rhs>(*this, b.derived());
+ }
+
+ /** \returns Expression object representing the matrix Q
+ */
+ MatrixQReturnType matrixQ(void) const;
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ FullPivHouseholderQR& compute(const MatrixType& matrix);
+
+ /** \returns a const reference to the column permutation matrix */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_cols_permutation;
+ }
+
+ /** \returns a const reference to the vector of indices representing the rows transpositions */
+ const IntDiagSizeVectorType& rowsTranspositions() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_rows_transpositions;
+ }
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ /** \returns the rank of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return isInjective() && isSurjective();
+ }
+
+ /** \returns the inverse of the matrix of which *this is the QR decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ */ inline const
+ internal::solve_retval<FullPivHouseholderQR, typename MatrixType::IdentityReturnType>
+ inverse() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return internal::solve_retval<FullPivHouseholderQR,typename MatrixType::IdentityReturnType>
+ (*this, MatrixType::Identity(m_qr.rows(), m_qr.cols()));
+ }
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * QR decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ FullPivHouseholderQR& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code qr.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ FullPivHouseholderQR& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
+ }
+
+ /** \returns the number of nonzero pivots in the QR decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of U.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ IntDiagSizeVectorType m_rows_transpositions;
+ IntDiagSizeVectorType m_cols_transpositions;
+ PermutationType m_cols_permutation;
+ RowVectorType m_temp;
+ bool m_isInitialized, m_usePrescribedThreshold;
+ RealScalar m_prescribedThreshold, m_maxpivot;
+ Index m_nonzero_pivots;
+ RealScalar m_precision;
+ Index m_det_pq;
+};
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
+{
+ check_template_parameters();
+
+ using std::abs;
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+ Index size = (std::min)(rows,cols);
+
+ m_qr = matrix;
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);
+
+ m_rows_transpositions.resize(size);
+ m_cols_transpositions.resize(size);
+ Index number_of_transpositions = 0;
+
+ RealScalar biggest(0);
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for (Index k = 0; k < size; ++k)
+ {
+ Index row_of_biggest_in_corner, col_of_biggest_in_corner;
+ RealScalar biggest_in_corner;
+
+ biggest_in_corner = m_qr.bottomRightCorner(rows-k, cols-k)
+ .cwiseAbs()
+ .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+ row_of_biggest_in_corner += k;
+ col_of_biggest_in_corner += k;
+ if(k==0) biggest = biggest_in_corner;
+
+ // if the corner is negligible, then we have less than full rank, and we can finish early
+ if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))
+ {
+ m_nonzero_pivots = k;
+ for(Index i = k; i < size; i++)
+ {
+ m_rows_transpositions.coeffRef(i) = i;
+ m_cols_transpositions.coeffRef(i) = i;
+ m_hCoeffs.coeffRef(i) = Scalar(0);
+ }
+ break;
+ }
+
+ m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;
+ m_cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;
+ if(k != row_of_biggest_in_corner) {
+ m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));
+ ++number_of_transpositions;
+ }
+ if(k != col_of_biggest_in_corner) {
+ m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+
+ RealScalar beta;
+ m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+ m_qr.coeffRef(k,k) = beta;
+
+ // remember the maximum absolute value of diagonal coefficients
+ if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+
+ m_qr.bottomRightCorner(rows-k, cols-k-1)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
+ }
+
+ m_cols_permutation.setIdentity(cols);
+ for(Index k = 0; k < size; ++k)
+ m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));
+
+ m_det_pq = (number_of_transpositions%2) ? -1 : 1;
+ m_isInitialized = true;
+
+ return *this;
+}
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<FullPivHouseholderQR<_MatrixType>, Rhs>
+ : solve_retval_base<FullPivHouseholderQR<_MatrixType>, Rhs>
+{
+ EIGEN_MAKE_SOLVE_HELPERS(FullPivHouseholderQR<_MatrixType>,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ const Index rows = dec().rows(), cols = dec().cols();
+ eigen_assert(rhs().rows() == rows);
+
+ // FIXME introduce nonzeroPivots() and use it here. and more generally,
+ // make the same improvements in this dec as in FullPivLU.
+ if(dec().rank()==0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename Rhs::PlainObject c(rhs());
+
+ Matrix<Scalar,1,Rhs::ColsAtCompileTime> temp(rhs().cols());
+ for (Index k = 0; k < dec().rank(); ++k)
+ {
+ Index remainingSize = rows-k;
+ c.row(k).swap(c.row(dec().rowsTranspositions().coeff(k)));
+ c.bottomRightCorner(remainingSize, rhs().cols())
+ .applyHouseholderOnTheLeft(dec().matrixQR().col(k).tail(remainingSize-1),
+ dec().hCoeffs().coeff(k), &temp.coeffRef(0));
+ }
+
+ dec().matrixQR()
+ .topLeftCorner(dec().rank(), dec().rank())
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(dec().rank()));
+
+ for(Index i = 0; i < dec().rank(); ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);
+ for(Index i = dec().rank(); i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();
+ }
+};
+
+/** \ingroup QR_Module
+ *
+ * \brief Expression type for return value of FullPivHouseholderQR::matrixQ()
+ *
+ * \tparam MatrixType type of underlying dense matrix
+ */
+template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType
+ : public ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
+{
+public:
+ typedef typename MatrixType::Index Index;
+ typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,
+ MatrixType::MaxRowsAtCompileTime> WorkVectorType;
+
+ FullPivHouseholderQRMatrixQReturnType(const MatrixType& qr,
+ const HCoeffsType& hCoeffs,
+ const IntDiagSizeVectorType& rowsTranspositions)
+ : m_qr(qr),
+ m_hCoeffs(hCoeffs),
+ m_rowsTranspositions(rowsTranspositions)
+ {}
+
+ template <typename ResultType>
+ void evalTo(ResultType& result) const
+ {
+ const Index rows = m_qr.rows();
+ WorkVectorType workspace(rows);
+ evalTo(result, workspace);
+ }
+
+ template <typename ResultType>
+ void evalTo(ResultType& result, WorkVectorType& workspace) const
+ {
+ using numext::conj;
+ // compute the product H'_0 H'_1 ... H'_n-1,
+ // where H_k is the k-th Householder transformation I - h_k v_k v_k'
+ // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
+ const Index rows = m_qr.rows();
+ const Index cols = m_qr.cols();
+ const Index size = (std::min)(rows, cols);
+ workspace.resize(rows);
+ result.setIdentity(rows, rows);
+ for (Index k = size-1; k >= 0; k--)
+ {
+ result.block(k, k, rows-k, rows-k)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));
+ result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));
+ }
+ }
+
+ Index rows() const { return m_qr.rows(); }
+ Index cols() const { return m_qr.rows(); }
+
+protected:
+ typename MatrixType::Nested m_qr;
+ typename HCoeffsType::Nested m_hCoeffs;
+ typename IntDiagSizeVectorType::Nested m_rowsTranspositions;
+};
+
+} // end namespace internal
+
+template<typename MatrixType>
+inline typename FullPivHouseholderQR<MatrixType>::MatrixQReturnType FullPivHouseholderQR<MatrixType>::matrixQ() const
+{
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);
+}
+
+/** \return the full-pivoting Householder QR decomposition of \c *this.
+ *
+ * \sa class FullPivHouseholderQR
+ */
+template<typename Derived>
+const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::fullPivHouseholderQr() const
+{
+ return FullPivHouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h
new file mode 100644
index 0000000..343a664
--- /dev/null
+++ b/Eigen/src/QR/HouseholderQR.h
@@ -0,0 +1,388 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Vincent Lejeune
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QR_H
+#define EIGEN_QR_H
+
+namespace Eigen {
+
+/** \ingroup QR_Module
+ *
+ *
+ * \class HouseholderQR
+ *
+ * \brief Householder QR decomposition of a matrix
+ *
+ * \param MatrixType the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a QR decomposition of a matrix \b A into matrices \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{A} = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b Q a unitary matrix and \b R an upper triangular matrix.
+ * The result is stored in a compact way compatible with LAPACK.
+ *
+ * Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
+ * If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.
+ *
+ * This Householder QR decomposition is faster, but less numerically stable and less feature-full than
+ * FullPivHouseholderQR or ColPivHouseholderQR.
+ *
+ * \sa MatrixBase::householderQr()
+ */
+template<typename _MatrixType> class HouseholderQR
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via HouseholderQR::compute(const MatrixType&).
+ */
+ HouseholderQR() : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa HouseholderQR()
+ */
+ HouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_temp(cols),
+ m_isInitialized(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * HouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ HouseholderQR(const MatrixType& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_temp(matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix);
+ }
+
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the QR decomposition, if any exists.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns a solution.
+ *
+ * \note The case where b is a matrix is not yet implemented. Also, this
+ * code is space inefficient.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include HouseholderQR_solve.cpp
+ * Output: \verbinclude HouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<HouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ return internal::solve_retval<HouseholderQR, Rhs>(*this, b.derived());
+ }
+
+ /** This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.
+ *
+ * The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object.
+ * Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:
+ *
+ * Example: \include HouseholderQR_householderQ.cpp
+ * Output: \verbinclude HouseholderQR_householderQ.out
+ */
+ HouseholderSequenceType householderQ() const
+ {
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
+ }
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ * in a LAPACK-compatible way.
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ HouseholderQR& compute(const MatrixType& matrix);
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ RowVectorType m_temp;
+ bool m_isInitialized;
+};
+
+template<typename MatrixType>
+typename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar HouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+namespace internal {
+
+/** \internal */
+template<typename MatrixQR, typename HCoeffs>
+void householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, typename MatrixQR::Scalar* tempData = 0)
+{
+ typedef typename MatrixQR::Index Index;
+ typedef typename MatrixQR::Scalar Scalar;
+ typedef typename MatrixQR::RealScalar RealScalar;
+ Index rows = mat.rows();
+ Index cols = mat.cols();
+ Index size = (std::min)(rows,cols);
+
+ eigen_assert(hCoeffs.size() == size);
+
+ typedef Matrix<Scalar,MatrixQR::ColsAtCompileTime,1> TempType;
+ TempType tempVector;
+ if(tempData==0)
+ {
+ tempVector.resize(cols);
+ tempData = tempVector.data();
+ }
+
+ for(Index k = 0; k < size; ++k)
+ {
+ Index remainingRows = rows - k;
+ Index remainingCols = cols - k - 1;
+
+ RealScalar beta;
+ mat.col(k).tail(remainingRows).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);
+ mat.coeffRef(k,k) = beta;
+
+ // apply H to remaining part of m_qr from the left
+ mat.bottomRightCorner(remainingRows, remainingCols)
+ .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), hCoeffs.coeffRef(k), tempData+k+1);
+ }
+}
+
+/** \internal */
+template<typename MatrixQR, typename HCoeffs,
+ typename MatrixQRScalar = typename MatrixQR::Scalar,
+ bool InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 && HCoeffs::InnerStrideAtCompileTime == 1)>
+struct householder_qr_inplace_blocked
+{
+ // This is specialized for MKL-supported Scalar types in HouseholderQR_MKL.h
+ static void run(MatrixQR& mat, HCoeffs& hCoeffs,
+ typename MatrixQR::Index maxBlockSize=32,
+ typename MatrixQR::Scalar* tempData = 0)
+ {
+ typedef typename MatrixQR::Index Index;
+ typedef typename MatrixQR::Scalar Scalar;
+ typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;
+
+ Index rows = mat.rows();
+ Index cols = mat.cols();
+ Index size = (std::min)(rows, cols);
+
+ typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;
+ TempType tempVector;
+ if(tempData==0)
+ {
+ tempVector.resize(cols);
+ tempData = tempVector.data();
+ }
+
+ Index blockSize = (std::min)(maxBlockSize,size);
+
+ Index k = 0;
+ for (k = 0; k < size; k += blockSize)
+ {
+ Index bs = (std::min)(size-k,blockSize); // actual size of the block
+ Index tcols = cols - k - bs; // trailing columns
+ Index brows = rows-k; // rows of the block
+
+ // partition the matrix:
+ // A00 | A01 | A02
+ // mat = A10 | A11 | A12
+ // A20 | A21 | A22
+ // and performs the qr dec of [A11^T A12^T]^T
+ // and update [A21^T A22^T]^T using level 3 operations.
+ // Finally, the algorithm continue on A22
+
+ BlockType A11_21 = mat.block(k,k,brows,bs);
+ Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);
+
+ householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);
+
+ if(tcols)
+ {
+ BlockType A21_22 = mat.block(k,k+bs,brows,tcols);
+ apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint());
+ }
+ }
+ }
+};
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<HouseholderQR<_MatrixType>, Rhs>
+ : solve_retval_base<HouseholderQR<_MatrixType>, Rhs>
+{
+ EIGEN_MAKE_SOLVE_HELPERS(HouseholderQR<_MatrixType>,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ const Index rows = dec().rows(), cols = dec().cols();
+ const Index rank = (std::min)(rows, cols);
+ eigen_assert(rhs().rows() == rows);
+
+ typename Rhs::PlainObject c(rhs());
+
+ // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
+ c.applyOnTheLeft(householderSequence(
+ dec().matrixQR().leftCols(rank),
+ dec().hCoeffs().head(rank)).transpose()
+ );
+
+ dec().matrixQR()
+ .topLeftCorner(rank, rank)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(rank));
+
+ dst.topRows(rank) = c.topRows(rank);
+ dst.bottomRows(cols-rank).setZero();
+ }
+};
+
+} // end namespace internal
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class HouseholderQR, HouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType& matrix)
+{
+ check_template_parameters();
+
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+ Index size = (std::min)(rows,cols);
+
+ m_qr = matrix;
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data());
+
+ m_isInitialized = true;
+ return *this;
+}
+
+/** \return the Householder QR decomposition of \c *this.
+ *
+ * \sa class HouseholderQR
+ */
+template<typename Derived>
+const HouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::householderQr() const
+{
+ return HouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_QR_H
diff --git a/Eigen/src/QR/HouseholderQR_MKL.h b/Eigen/src/QR/HouseholderQR_MKL.h
new file mode 100644
index 0000000..b80f1b4
--- /dev/null
+++ b/Eigen/src/QR/HouseholderQR_MKL.h
@@ -0,0 +1,71 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Householder QR decomposition of a matrix w/o pivoting based on
+ * LAPACKE_?geqrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_QR_MKL_H
+#define EIGEN_QR_MKL_H
+
+#include "../Core/util/MKL_support.h"
+
+namespace Eigen {
+
+ namespace internal {
+
+ /** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_QR_NOPIV(EIGTYPE, MKLTYPE, MKLPREFIX) \
+template<typename MatrixQR, typename HCoeffs> \
+struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \
+{ \
+ static void run(MatrixQR& mat, HCoeffs& hCoeffs, \
+ typename MatrixQR::Index = 32, \
+ typename MatrixQR::Scalar* = 0) \
+ { \
+ lapack_int m = (lapack_int) mat.rows(); \
+ lapack_int n = (lapack_int) mat.cols(); \
+ lapack_int lda = (lapack_int) mat.outerStride(); \
+ lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
+ LAPACKE_##MKLPREFIX##geqrf( matrix_order, m, n, (MKLTYPE*)mat.data(), lda, (MKLTYPE*)hCoeffs.data()); \
+ hCoeffs.adjointInPlace(); \
+ } \
+};
+
+EIGEN_MKL_QR_NOPIV(double, double, d)
+EIGEN_MKL_QR_NOPIV(float, float, s)
+EIGEN_MKL_QR_NOPIV(dcomplex, MKL_Complex16, z)
+EIGEN_MKL_QR_NOPIV(scomplex, MKL_Complex8, c)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_QR_MKL_H
diff --git a/Eigen/src/SPQRSupport/CMakeLists.txt b/Eigen/src/SPQRSupport/CMakeLists.txt
new file mode 100644
index 0000000..4968bea
--- /dev/null
+++ b/Eigen/src/SPQRSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SPQRSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SPQRSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SPQRSupport/ COMPONENT Devel
+ )
diff --git a/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
new file mode 100644
index 0000000..de00877
--- /dev/null
+++ b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
@@ -0,0 +1,338 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SUITESPARSEQRSUPPORT_H
+#define EIGEN_SUITESPARSEQRSUPPORT_H
+
+namespace Eigen {
+
+ template<typename MatrixType> class SPQR;
+ template<typename SPQRType> struct SPQRMatrixQReturnType;
+ template<typename SPQRType> struct SPQRMatrixQTransposeReturnType;
+ template <typename SPQRType, typename Derived> struct SPQR_QProduct;
+ namespace internal {
+ template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> >
+ {
+ typedef typename SPQRType::MatrixType ReturnType;
+ };
+ template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> >
+ {
+ typedef typename SPQRType::MatrixType ReturnType;
+ };
+ template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> >
+ {
+ typedef typename Derived::PlainObject ReturnType;
+ };
+ } // End namespace internal
+
+/**
+ * \ingroup SPQRSupport_Module
+ * \class SPQR
+ * \brief Sparse QR factorization based on SuiteSparseQR library
+ *
+ * This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition
+ * of sparse matrices. The result is then used to solve linear leasts_square systems.
+ * Clearly, a QR factorization is returned such that A*P = Q*R where :
+ *
+ * P is the column permutation. Use colsPermutation() to get it.
+ *
+ * Q is the orthogonal matrix represented as Householder reflectors.
+ * Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose.
+ * You can then apply it to a vector.
+ *
+ * R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix.
+ * NOTE : The Index type of R is always UF_long. You can get it with SPQR::Index
+ *
+ * \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>
+ * NOTE
+ *
+ */
+template<typename _MatrixType>
+class SPQR
+{
+ public:
+ typedef typename _MatrixType::Scalar Scalar;
+ typedef typename _MatrixType::RealScalar RealScalar;
+ typedef UF_long Index ;
+ typedef SparseMatrix<Scalar, ColMajor, Index> MatrixType;
+ typedef PermutationMatrix<Dynamic, Dynamic> PermutationType;
+ public:
+ SPQR()
+ : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
+ {
+ cholmod_l_start(&m_cc);
+ }
+
+ SPQR(const _MatrixType& matrix)
+ : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
+ {
+ cholmod_l_start(&m_cc);
+ compute(matrix);
+ }
+
+ ~SPQR()
+ {
+ SPQR_free();
+ cholmod_l_finish(&m_cc);
+ }
+ void SPQR_free()
+ {
+ cholmod_l_free_sparse(&m_H, &m_cc);
+ cholmod_l_free_sparse(&m_cR, &m_cc);
+ cholmod_l_free_dense(&m_HTau, &m_cc);
+ std::free(m_E);
+ std::free(m_HPinv);
+ }
+
+ void compute(const _MatrixType& matrix)
+ {
+ if(m_isInitialized) SPQR_free();
+
+ MatrixType mat(matrix);
+
+ /* Compute the default threshold as in MatLab, see:
+ * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+ * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
+ */
+ RealScalar pivotThreshold = m_tolerance;
+ if(m_useDefaultThreshold)
+ {
+ using std::max;
+ RealScalar max2Norm = 0.0;
+ for (int j = 0; j < mat.cols(); j++) max2Norm = (max)(max2Norm, mat.col(j).norm());
+ if(max2Norm==RealScalar(0))
+ max2Norm = RealScalar(1);
+ pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
+ }
+
+ cholmod_sparse A;
+ A = viewAsCholmod(mat);
+ Index col = matrix.cols();
+ m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A,
+ &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);
+
+ if (!m_cR)
+ {
+ m_info = NumericalIssue;
+ m_isInitialized = false;
+ return;
+ }
+ m_info = Success;
+ m_isInitialized = true;
+ m_isRUpToDate = false;
+ }
+ /**
+ * Get the number of rows of the input matrix and the Q matrix
+ */
+ inline Index rows() const {return m_cR->nrow; }
+
+ /**
+ * Get the number of columns of the input matrix.
+ */
+ inline Index cols() const { return m_cR->ncol; }
+
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<SPQR, Rhs> solve(const MatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
+ eigen_assert(this->rows()==B.rows()
+ && "SPQR::solve(): invalid number of rows of the right hand side matrix B");
+ return internal::solve_retval<SPQR, Rhs>(*this, B.derived());
+ }
+
+ template<typename Rhs, typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
+ eigen_assert(b.cols()==1 && "This method is for vectors only");
+
+ //Compute Q^T * b
+ typename Dest::PlainObject y, y2;
+ y = matrixQ().transpose() * b;
+
+ // Solves with the triangular matrix R
+ Index rk = this->rank();
+ y2 = y;
+ y.resize((std::max)(cols(),Index(y.rows())),y.cols());
+ y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));
+
+ // Apply the column permutation
+ // colsPermutation() performs a copy of the permutation,
+ // so let's apply it manually:
+ for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
+ for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
+
+// y.bottomRows(y.rows()-rk).setZero();
+// dest = colsPermutation() * y.topRows(cols());
+
+ m_info = Success;
+ }
+
+ /** \returns the sparse triangular factor R. It is a sparse matrix
+ */
+ const MatrixType matrixR() const
+ {
+ eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
+ if(!m_isRUpToDate) {
+ m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::Index>(*m_cR);
+ m_isRUpToDate = true;
+ }
+ return m_R;
+ }
+ /// Get an expression of the matrix Q
+ SPQRMatrixQReturnType<SPQR> matrixQ() const
+ {
+ return SPQRMatrixQReturnType<SPQR>(*this);
+ }
+ /// Get the permutation that was applied to columns of A
+ PermutationType colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ Index n = m_cR->ncol;
+ PermutationType colsPerm(n);
+ for(Index j = 0; j <n; j++) colsPerm.indices()(j) = m_E[j];
+ return colsPerm;
+
+ }
+ /**
+ * Gets the rank of the matrix.
+ * It should be equal to matrixQR().cols if the matrix is full-rank
+ */
+ Index rank() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_cc.SPQR_istat[4];
+ }
+ /// Set the fill-reducing ordering method to be used
+ void setSPQROrdering(int ord) { m_ordering = ord;}
+ /// Set the tolerance tol to treat columns with 2-norm < =tol as zero
+ void setPivotThreshold(const RealScalar& tol)
+ {
+ m_useDefaultThreshold = false;
+ m_tolerance = tol;
+ }
+
+ /** \returns a pointer to the SPQR workspace */
+ cholmod_common *cholmodCommon() const { return &m_cc; }
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the sparse QR can not be computed
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+ protected:
+ bool m_isInitialized;
+ bool m_analysisIsOk;
+ bool m_factorizationIsOk;
+ mutable bool m_isRUpToDate;
+ mutable ComputationInfo m_info;
+ int m_ordering; // Ordering method to use, see SPQR's manual
+ int m_allow_tol; // Allow to use some tolerance during numerical factorization.
+ RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero
+ mutable cholmod_sparse *m_cR; // The sparse R factor in cholmod format
+ mutable MatrixType m_R; // The sparse matrix R in Eigen format
+ mutable Index *m_E; // The permutation applied to columns
+ mutable cholmod_sparse *m_H; //The householder vectors
+ mutable Index *m_HPinv; // The row permutation of H
+ mutable cholmod_dense *m_HTau; // The Householder coefficients
+ mutable Index m_rank; // The rank of the matrix
+ mutable cholmod_common m_cc; // Workspace and parameters
+ bool m_useDefaultThreshold; // Use default threshold
+ template<typename ,typename > friend struct SPQR_QProduct;
+};
+
+template <typename SPQRType, typename Derived>
+struct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> >
+{
+ typedef typename SPQRType::Scalar Scalar;
+ typedef typename SPQRType::Index Index;
+ //Define the constructor to get reference to argument types
+ SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}
+
+ inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); }
+ inline Index cols() const { return m_other.cols(); }
+ // Assign to a vector
+ template<typename ResType>
+ void evalTo(ResType& res) const
+ {
+ cholmod_dense y_cd;
+ cholmod_dense *x_cd;
+ int method = m_transpose ? SPQR_QTX : SPQR_QX;
+ cholmod_common *cc = m_spqr.cholmodCommon();
+ y_cd = viewAsCholmod(m_other.const_cast_derived());
+ x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc);
+ res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol);
+ cholmod_l_free_dense(&x_cd, cc);
+ }
+ const SPQRType& m_spqr;
+ const Derived& m_other;
+ bool m_transpose;
+
+};
+template<typename SPQRType>
+struct SPQRMatrixQReturnType{
+
+ SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
+ template<typename Derived>
+ SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false);
+ }
+ SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const
+ {
+ return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
+ }
+ // To use for operations with the transpose of Q
+ SPQRMatrixQTransposeReturnType<SPQRType> transpose() const
+ {
+ return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
+ }
+ const SPQRType& m_spqr;
+};
+
+template<typename SPQRType>
+struct SPQRMatrixQTransposeReturnType{
+ SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
+ template<typename Derived>
+ SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true);
+ }
+ const SPQRType& m_spqr;
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<SPQR<_MatrixType>, Rhs>
+ : solve_retval_base<SPQR<_MatrixType>, Rhs>
+{
+ typedef SPQR<_MatrixType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+} // end namespace internal
+
+}// End namespace Eigen
+#endif
diff --git a/Eigen/src/SVD/CMakeLists.txt b/Eigen/src/SVD/CMakeLists.txt
new file mode 100644
index 0000000..55efc44
--- /dev/null
+++ b/Eigen/src/SVD/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SVD_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SVD_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SVD COMPONENT Devel
+ )
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
new file mode 100644
index 0000000..1b29774
--- /dev/null
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -0,0 +1,976 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_JACOBISVD_H
+#define EIGEN_JACOBISVD_H
+
+namespace Eigen {
+
+namespace internal {
+// forward declaration (needed by ICC)
+// the empty body is required by MSVC
+template<typename MatrixType, int QRPreconditioner,
+ bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct svd_precondition_2x2_block_to_be_real {};
+
+/*** QR preconditioners (R-SVD)
+ ***
+ *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
+ *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
+ *** JacobiSVD which by itself is only able to work on square matrices.
+ ***/
+
+enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
+
+template<typename MatrixType, int QRPreconditioner, int Case>
+struct qr_preconditioner_should_do_anything
+{
+ enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
+ b = MatrixType::RowsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime != Dynamic &&
+ MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
+ ret = !( (QRPreconditioner == NoQRPreconditioner) ||
+ (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
+ (Case == PreconditionIfMoreRowsThanCols && bool(b)) )
+ };
+};
+
+template<typename MatrixType, int QRPreconditioner, int Case,
+ bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret
+> struct qr_preconditioner_impl {};
+
+template<typename MatrixType, int QRPreconditioner, int Case>
+class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
+{
+public:
+ typedef typename MatrixType::Index Index;
+ void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
+ bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
+ {
+ return false;
+ }
+};
+
+/*** preconditioner using FullPivHouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ enum
+ {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
+ };
+ typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
+
+ void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
+ {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ }
+
+ bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
+ if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+ return true;
+ }
+ return false;
+ }
+private:
+ typedef FullPivHouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ WorkspaceType m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ enum
+ {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ Options = MatrixType::Options
+ };
+ typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
+ {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.cols(), svd.rows());
+ }
+ m_adjoint.resize(svd.cols(), svd.rows());
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ }
+
+ bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
+ if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+ return true;
+ }
+ else return false;
+ }
+private:
+ typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** preconditioner using ColPivHouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+
+ void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
+ {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+ }
+
+ bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+ else if(svd.m_computeThinU)
+ {
+ svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+ }
+ if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+ return true;
+ }
+ return false;
+ }
+
+private:
+ typedef ColPivHouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ typename internal::plain_col_type<MatrixType>::type m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ enum
+ {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ Options = MatrixType::Options
+ };
+
+ typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
+ {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.cols(), svd.rows());
+ }
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+ m_adjoint.resize(svd.cols(), svd.rows());
+ }
+
+ bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+ else if(svd.m_computeThinV)
+ {
+ svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+ }
+ if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+ return true;
+ }
+ else return false;
+ }
+
+private:
+ typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** preconditioner using HouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+
+ void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
+ {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+ }
+
+ bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+ else if(svd.m_computeThinU)
+ {
+ svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+ }
+ if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
+ return true;
+ }
+ return false;
+ }
+private:
+ typedef HouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ typename internal::plain_col_type<MatrixType>::type m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ enum
+ {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ Options = MatrixType::Options
+ };
+
+ typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
+ {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ m_qr.~QRType();
+ ::new (&m_qr) QRType(svd.cols(), svd.rows());
+ }
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+ m_adjoint.resize(svd.cols(), svd.rows());
+ }
+
+ bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+ {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+ else if(svd.m_computeThinV)
+ {
+ svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+ }
+ if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
+ return true;
+ }
+ else return false;
+ }
+
+private:
+ typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** 2x2 SVD implementation
+ ***
+ *** JacobiSVD consists in performing a series of 2x2 SVD subproblems
+ ***/
+
+template<typename MatrixType, int QRPreconditioner>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
+{
+ typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
+ typedef typename SVD::Index Index;
+ static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
+};
+
+template<typename MatrixType, int QRPreconditioner>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
+{
+ typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename SVD::Index Index;
+ static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
+ {
+ using std::sqrt;
+ Scalar z;
+ JacobiRotation<Scalar> rot;
+ RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
+
+ if(n==0)
+ {
+ z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+ work_matrix.row(p) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
+ if(work_matrix.coeff(q,q)!=Scalar(0))
+ {
+ z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+ work_matrix.row(q) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+ }
+ // otherwise the second row is already zero, so we have nothing to do.
+ }
+ else
+ {
+ rot.c() = conj(work_matrix.coeff(p,p)) / n;
+ rot.s() = work_matrix.coeff(q,p) / n;
+ work_matrix.applyOnTheLeft(p,q,rot);
+ if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
+ if(work_matrix.coeff(p,q) != Scalar(0))
+ {
+ Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+ work_matrix.col(q) *= z;
+ if(svd.computeV()) svd.m_matrixV.col(q) *= z;
+ }
+ if(work_matrix.coeff(q,q) != Scalar(0))
+ {
+ z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+ work_matrix.row(q) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+ }
+ }
+ }
+};
+
+template<typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
+ JacobiRotation<RealScalar> *j_left,
+ JacobiRotation<RealScalar> *j_right)
+{
+ using std::sqrt;
+ using std::abs;
+ Matrix<RealScalar,2,2> m;
+ m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
+ numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
+ JacobiRotation<RealScalar> rot1;
+ RealScalar t = m.coeff(0,0) + m.coeff(1,1);
+ RealScalar d = m.coeff(1,0) - m.coeff(0,1);
+ if(t == RealScalar(0))
+ {
+ rot1.c() = RealScalar(0);
+ rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+ }
+ else
+ {
+ RealScalar t2d2 = numext::hypot(t,d);
+ rot1.c() = abs(t)/t2d2;
+ rot1.s() = d/t2d2;
+ if(t<RealScalar(0))
+ rot1.s() = -rot1.s();
+ }
+ m.applyOnTheLeft(0,1,rot1);
+ j_right->makeJacobi(m,0,1);
+ *j_left = rot1 * j_right->transpose();
+}
+
+} // end namespace internal
+
+/** \ingroup SVD_Module
+ *
+ *
+ * \class JacobiSVD
+ *
+ * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
+ *
+ * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+ * \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
+ * for the R-SVD step for non-square matrices. See discussion of possible values below.
+ *
+ * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+ * \f[ A = U S V^* \f]
+ * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
+ * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
+ * and right \em singular \em vectors of \a A respectively.
+ *
+ * Singular values are always sorted in decreasing order.
+ *
+ * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly.
+ *
+ * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
+ * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
+ * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
+ * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
+ *
+ * Here's an example demonstrating basic usage:
+ * \include JacobiSVD_basic.cpp
+ * Output: \verbinclude JacobiSVD_basic.out
+ *
+ * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
+ * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and
+ * \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
+ * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
+ *
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
+ * terminate in finite (and reasonable) time.
+ *
+ * The possible values for QRPreconditioner are:
+ * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
+ * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
+ * Contrary to other QRs, it doesn't allow computing thin unitaries.
+ * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
+ * This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
+ * is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
+ * process is more reliable than the optimized bidiagonal SVD iterations.
+ * \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
+ * JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
+ * faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
+ * if QR preconditioning is needed before applying it anyway.
+ *
+ * \sa MatrixBase::jacobiSvd()
+ */
+template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Index Index;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
+ MatrixOptions = MatrixType::Options
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+ MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+ MatrixUType;
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
+ MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
+ MatrixVType;
+ typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowType;
+ typedef typename internal::plain_col_type<MatrixType>::type ColType;
+ typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
+ MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
+ WorkMatrixType;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via JacobiSVD::compute(const MatrixType&).
+ */
+ JacobiSVD()
+ : m_isInitialized(false),
+ m_isAllocated(false),
+ m_usePrescribedThreshold(false),
+ m_computationOptions(0),
+ m_rows(-1), m_cols(-1), m_diagSize(0)
+ {}
+
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem size.
+ * \sa JacobiSVD()
+ */
+ JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
+ : m_isInitialized(false),
+ m_isAllocated(false),
+ m_usePrescribedThreshold(false),
+ m_computationOptions(0),
+ m_rows(-1), m_cols(-1)
+ {
+ allocate(rows, cols, computationOptions);
+ }
+
+ /** \brief Constructor performing the decomposition of given matrix.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+ * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
+ * #ComputeFullV, #ComputeThinV.
+ *
+ * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+ * available with the (non-default) FullPivHouseholderQR preconditioner.
+ */
+ JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
+ : m_isInitialized(false),
+ m_isAllocated(false),
+ m_usePrescribedThreshold(false),
+ m_computationOptions(0),
+ m_rows(-1), m_cols(-1)
+ {
+ compute(matrix, computationOptions);
+ }
+
+ /** \brief Method performing the decomposition of given matrix using custom options.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+ * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
+ * #ComputeFullV, #ComputeThinV.
+ *
+ * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+ * available with the (non-default) FullPivHouseholderQR preconditioner.
+ */
+ JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
+
+ /** \brief Method performing the decomposition of given matrix using current options.
+ *
+ * \param matrix the matrix to decompose
+ *
+ * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
+ */
+ JacobiSVD& compute(const MatrixType& matrix)
+ {
+ return compute(matrix, m_computationOptions);
+ }
+
+ /** \returns the \a U matrix.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+ * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
+ *
+ * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
+ *
+ * This method asserts that you asked for \a U to be computed.
+ */
+ const MatrixUType& matrixU() const
+ {
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
+ return m_matrixU;
+ }
+
+ /** \returns the \a V matrix.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+ * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
+ *
+ * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
+ *
+ * This method asserts that you asked for \a V to be computed.
+ */
+ const MatrixVType& matrixV() const
+ {
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
+ return m_matrixV;
+ }
+
+ /** \returns the vector of singular values.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
+ * returned vector has size \a m. Singular values are always sorted in decreasing order.
+ */
+ const SingularValuesType& singularValues() const
+ {
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ return m_singularValues;
+ }
+
+ /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
+ inline bool computeU() const { return m_computeFullU || m_computeThinU; }
+ /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
+ inline bool computeV() const { return m_computeFullV || m_computeThinV; }
+
+ /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
+ *
+ * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
+ * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<JacobiSVD, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
+ return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the number of singular values that are not exactly 0 */
+ Index nonzeroSingularValues() const
+ {
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ return m_nonzeroSingularValues;
+ }
+
+ /** \returns the rank of the matrix of which \c *this is the SVD.
+ *
+ * \note This method has to determine which singular values should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+ if(m_singularValues.size()==0) return 0;
+ RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
+ Index i = m_nonzeroSingularValues-1;
+ while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
+ return i+1;
+ }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
+ * which need to determine when singular values are to be considered nonzero.
+ * This is not used for the SVD decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold().
+ * The default is \c NumTraits<Scalar>::epsilon()
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A singular value will be considered nonzero if its value is strictly greater than
+ * \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ JacobiSVD& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code svd.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ JacobiSVD& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
+ }
+
+ inline Index rows() const { return m_rows; }
+ inline Index cols() const { return m_cols; }
+
+ private:
+ void allocate(Index rows, Index cols, unsigned int computationOptions);
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ }
+
+ protected:
+ MatrixUType m_matrixU;
+ MatrixVType m_matrixV;
+ SingularValuesType m_singularValues;
+ WorkMatrixType m_workMatrix;
+ bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
+ bool m_computeFullU, m_computeThinU;
+ bool m_computeFullV, m_computeThinV;
+ unsigned int m_computationOptions;
+ Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
+ RealScalar m_prescribedThreshold;
+
+ template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
+ friend struct internal::svd_precondition_2x2_block_to_be_real;
+ template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>
+ friend struct internal::qr_preconditioner_impl;
+
+ internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
+ internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
+ MatrixType m_scaledMatrix;
+};
+
+template<typename MatrixType, int QRPreconditioner>
+void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)
+{
+ eigen_assert(rows >= 0 && cols >= 0);
+
+ if (m_isAllocated &&
+ rows == m_rows &&
+ cols == m_cols &&
+ computationOptions == m_computationOptions)
+ {
+ return;
+ }
+
+ m_rows = rows;
+ m_cols = cols;
+ m_isInitialized = false;
+ m_isAllocated = true;
+ m_computationOptions = computationOptions;
+ m_computeFullU = (computationOptions & ComputeFullU) != 0;
+ m_computeThinU = (computationOptions & ComputeThinU) != 0;
+ m_computeFullV = (computationOptions & ComputeFullV) != 0;
+ m_computeThinV = (computationOptions & ComputeThinV) != 0;
+ eigen_assert(!(m_computeFullU && m_computeThinU) && "JacobiSVD: you can't ask for both full and thin U");
+ eigen_assert(!(m_computeFullV && m_computeThinV) && "JacobiSVD: you can't ask for both full and thin V");
+ eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
+ "JacobiSVD: thin U and V are only available when your matrix has a dynamic number of columns.");
+ if (QRPreconditioner == FullPivHouseholderQRPreconditioner)
+ {
+ eigen_assert(!(m_computeThinU || m_computeThinV) &&
+ "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
+ "Use the ColPivHouseholderQR preconditioner instead.");
+ }
+ m_diagSize = (std::min)(m_rows, m_cols);
+ m_singularValues.resize(m_diagSize);
+ if(RowsAtCompileTime==Dynamic)
+ m_matrixU.resize(m_rows, m_computeFullU ? m_rows
+ : m_computeThinU ? m_diagSize
+ : 0);
+ if(ColsAtCompileTime==Dynamic)
+ m_matrixV.resize(m_cols, m_computeFullV ? m_cols
+ : m_computeThinV ? m_diagSize
+ : 0);
+ m_workMatrix.resize(m_diagSize, m_diagSize);
+
+ if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this);
+ if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this);
+ if(m_cols!=m_cols) m_scaledMatrix.resize(rows,cols);
+}
+
+template<typename MatrixType, int QRPreconditioner>
+JacobiSVD<MatrixType, QRPreconditioner>&
+JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
+{
+ check_template_parameters();
+
+ using std::abs;
+ allocate(matrix.rows(), matrix.cols(), computationOptions);
+
+ // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
+ // only worsening the precision of U and V as we accumulate more rotations
+ const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
+
+ // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
+ const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
+
+ // Scaling factor to reduce over/under-flows
+ RealScalar scale = matrix.cwiseAbs().maxCoeff();
+ if(scale==RealScalar(0)) scale = RealScalar(1);
+
+ /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
+
+ if(m_rows!=m_cols)
+ {
+ m_scaledMatrix = matrix / scale;
+ m_qr_precond_morecols.run(*this, m_scaledMatrix);
+ m_qr_precond_morerows.run(*this, m_scaledMatrix);
+ }
+ else
+ {
+ m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;
+ if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows);
+ if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize);
+ if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols);
+ if(m_computeThinV) m_matrixV.setIdentity(m_cols, m_diagSize);
+ }
+
+ /*** step 2. The main Jacobi SVD iteration. ***/
+
+ bool finished = false;
+ while(!finished)
+ {
+ finished = true;
+
+ // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
+
+ for(Index p = 1; p < m_diagSize; ++p)
+ {
+ for(Index q = 0; q < p; ++q)
+ {
+ // if this 2x2 sub-matrix is not diagonal already...
+ // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
+ // keep us iterating forever. Similarly, small denormal numbers are considered zero.
+ using std::max;
+ RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
+ abs(m_workMatrix.coeff(q,q))));
+ // We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
+ if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
+ {
+ finished = false;
+
+ // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
+ internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q);
+ JacobiRotation<RealScalar> j_left, j_right;
+ internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
+
+ // accumulate resulting Jacobi rotations
+ m_workMatrix.applyOnTheLeft(p,q,j_left);
+ if(computeU()) m_matrixU.applyOnTheRight(p,q,j_left.transpose());
+
+ m_workMatrix.applyOnTheRight(p,q,j_right);
+ if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
+ }
+ }
+ }
+ }
+
+ /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
+
+ for(Index i = 0; i < m_diagSize; ++i)
+ {
+ RealScalar a = abs(m_workMatrix.coeff(i,i));
+ m_singularValues.coeffRef(i) = a;
+ if(computeU() && (a!=RealScalar(0))) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
+ }
+
+ /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
+
+ m_nonzeroSingularValues = m_diagSize;
+ for(Index i = 0; i < m_diagSize; i++)
+ {
+ Index pos;
+ RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSize-i).maxCoeff(&pos);
+ if(maxRemainingSingularValue == RealScalar(0))
+ {
+ m_nonzeroSingularValues = i;
+ break;
+ }
+ if(pos)
+ {
+ pos += i;
+ std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
+ if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));
+ if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
+ }
+ }
+
+ m_singularValues *= scale;
+
+ m_isInitialized = true;
+ return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int QRPreconditioner, typename Rhs>
+struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
+ : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
+{
+ typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType;
+ EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ eigen_assert(rhs().rows() == dec().rows());
+
+ // A = U S V^*
+ // So A^{-1} = V S^{-1} U^*
+
+ Matrix<Scalar, Dynamic, Rhs::ColsAtCompileTime, 0, _MatrixType::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime> tmp;
+ Index rank = dec().rank();
+
+ tmp.noalias() = dec().matrixU().leftCols(rank).adjoint() * rhs();
+ tmp = dec().singularValues().head(rank).asDiagonal().inverse() * tmp;
+ dst = dec().matrixV().leftCols(rank) * tmp;
+ }
+};
+} // end namespace internal
+
+/** \svd_module
+ *
+ * \return the singular value decomposition of \c *this computed by two-sided
+ * Jacobi transformations.
+ *
+ * \sa class JacobiSVD
+ */
+template<typename Derived>
+JacobiSVD<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const
+{
+ return JacobiSVD<PlainObject>(*this, computationOptions);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBISVD_H
diff --git a/Eigen/src/SVD/JacobiSVD_MKL.h b/Eigen/src/SVD/JacobiSVD_MKL.h
new file mode 100644
index 0000000..decda75
--- /dev/null
+++ b/Eigen/src/SVD/JacobiSVD_MKL.h
@@ -0,0 +1,92 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Singular Value Decomposition - SVD.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_JACOBISVD_MKL_H
+#define EIGEN_JACOBISVD_MKL_H
+
+#include "Eigen/src/Core/util/MKL_support.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by MKL */
+
+#define EIGEN_MKL_SVD(EIGTYPE, MKLTYPE, MKLRTYPE, MKLPREFIX, EIGCOLROW, MKLCOLROW) \
+template<> inline \
+JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>& \
+JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) \
+{ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
+ typedef MatrixType::Scalar Scalar; \
+ typedef MatrixType::RealScalar RealScalar; \
+ allocate(matrix.rows(), matrix.cols(), computationOptions); \
+\
+ /*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \
+ m_nonzeroSingularValues = m_diagSize; \
+\
+ lapack_int lda = matrix.outerStride(), ldu, ldvt; \
+ lapack_int matrix_order = MKLCOLROW; \
+ char jobu, jobvt; \
+ MKLTYPE *u, *vt, dummy; \
+ jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \
+ jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \
+ if (computeU()) { \
+ ldu = m_matrixU.outerStride(); \
+ u = (MKLTYPE*)m_matrixU.data(); \
+ } else { ldu=1; u=&dummy; }\
+ MatrixType localV; \
+ ldvt = (m_computeFullV) ? m_cols : (m_computeThinV) ? m_diagSize : 1; \
+ if (computeV()) { \
+ localV.resize(ldvt, m_cols); \
+ vt = (MKLTYPE*)localV.data(); \
+ } else { ldvt=1; vt=&dummy; }\
+ Matrix<MKLRTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \
+ MatrixType m_temp; m_temp = matrix; \
+ LAPACKE_##MKLPREFIX##gesvd( matrix_order, jobu, jobvt, m_rows, m_cols, (MKLTYPE*)m_temp.data(), lda, (MKLRTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
+ if (computeV()) m_matrixV = localV.adjoint(); \
+ /* for(int i=0;i<m_diagSize;i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
+ m_isInitialized = true; \
+ return *this; \
+}
+
+EIGEN_MKL_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SVD(float, float, float , s, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SVD(dcomplex, MKL_Complex16, double, z, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_MKL_SVD(scomplex, MKL_Complex8, float , c, ColMajor, LAPACK_COL_MAJOR)
+
+EIGEN_MKL_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_SVD(float, float, float , s, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_SVD(dcomplex, MKL_Complex16, double, z, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_MKL_SVD(scomplex, MKL_Complex8, float , c, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBISVD_MKL_H
diff --git a/Eigen/src/SVD/UpperBidiagonalization.h b/Eigen/src/SVD/UpperBidiagonalization.h
new file mode 100644
index 0000000..587de37
--- /dev/null
+++ b/Eigen/src/SVD/UpperBidiagonalization.h
@@ -0,0 +1,148 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BIDIAGONALIZATION_H
+#define EIGEN_BIDIAGONALIZATION_H
+
+namespace Eigen {
+
+namespace internal {
+// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.
+// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.
+
+template<typename _MatrixType> class UpperBidiagonalization
+{
+ public:
+
+ typedef _MatrixType MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
+ typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0> BidiagonalType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
+ typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
+ typedef HouseholderSequence<
+ const MatrixType,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Diagonal<const MatrixType,0> >
+ > HouseholderUSequenceType;
+ typedef HouseholderSequence<
+ const typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type,
+ Diagonal<const MatrixType,1>,
+ OnTheRight
+ > HouseholderVSequenceType;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via Bidiagonalization::compute(const MatrixType&).
+ */
+ UpperBidiagonalization() : m_householder(), m_bidiagonal(), m_isInitialized(false) {}
+
+ UpperBidiagonalization(const MatrixType& matrix)
+ : m_householder(matrix.rows(), matrix.cols()),
+ m_bidiagonal(matrix.cols(), matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix);
+ }
+
+ UpperBidiagonalization& compute(const MatrixType& matrix);
+
+ const MatrixType& householder() const { return m_householder; }
+ const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
+
+ const HouseholderUSequenceType householderU() const
+ {
+ eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
+ return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
+ }
+
+ const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
+ {
+ eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
+ return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
+ .setLength(m_householder.cols()-1)
+ .setShift(1);
+ }
+
+ protected:
+ MatrixType m_householder;
+ BidiagonalType m_bidiagonal;
+ bool m_isInitialized;
+};
+
+template<typename _MatrixType>
+UpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::compute(const _MatrixType& matrix)
+{
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+
+ eigen_assert(rows >= cols && "UpperBidiagonalization is only for matrices satisfying rows>=cols.");
+
+ m_householder = matrix;
+
+ ColVectorType temp(rows);
+
+ for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)
+ {
+ Index remainingRows = rows - k;
+ Index remainingCols = cols - k - 1;
+
+ // construct left householder transform in-place in m_householder
+ m_householder.col(k).tail(remainingRows)
+ .makeHouseholderInPlace(m_householder.coeffRef(k,k),
+ m_bidiagonal.template diagonal<0>().coeffRef(k));
+ // apply householder transform to remaining part of m_householder on the left
+ m_householder.bottomRightCorner(remainingRows, remainingCols)
+ .applyHouseholderOnTheLeft(m_householder.col(k).tail(remainingRows-1),
+ m_householder.coeff(k,k),
+ temp.data());
+
+ if(k == cols-1) break;
+
+ // construct right householder transform in-place in m_householder
+ m_householder.row(k).tail(remainingCols)
+ .makeHouseholderInPlace(m_householder.coeffRef(k,k+1),
+ m_bidiagonal.template diagonal<1>().coeffRef(k));
+ // apply householder transform to remaining part of m_householder on the left
+ m_householder.bottomRightCorner(remainingRows-1, remainingCols)
+ .applyHouseholderOnTheRight(m_householder.row(k).tail(remainingCols-1).transpose(),
+ m_householder.coeff(k,k+1),
+ temp.data());
+ }
+ m_isInitialized = true;
+ return *this;
+}
+
+#if 0
+/** \return the Householder QR decomposition of \c *this.
+ *
+ * \sa class Bidiagonalization
+ */
+template<typename Derived>
+const UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::bidiagonalization() const
+{
+ return UpperBidiagonalization<PlainObject>(eval());
+}
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BIDIAGONALIZATION_H
diff --git a/Eigen/src/SparseCholesky/CMakeLists.txt b/Eigen/src/SparseCholesky/CMakeLists.txt
new file mode 100644
index 0000000..375a59d
--- /dev/null
+++ b/Eigen/src/SparseCholesky/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SparseCholesky_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SparseCholesky_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseCholesky COMPONENT Devel
+ )
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky.h b/Eigen/src/SparseCholesky/SimplicialCholesky.h
new file mode 100644
index 0000000..e1f96ba
--- /dev/null
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky.h
@@ -0,0 +1,671 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SIMPLICIAL_CHOLESKY_H
+#define EIGEN_SIMPLICIAL_CHOLESKY_H
+
+namespace Eigen {
+
+enum SimplicialCholeskyMode {
+ SimplicialCholeskyLLT,
+ SimplicialCholeskyLDLT
+};
+
+/** \ingroup SparseCholesky_Module
+ * \brief A direct sparse Cholesky factorizations
+ *
+ * These classes provide LL^T and LDL^T Cholesky factorizations of sparse matrices that are
+ * selfadjoint and positive definite. The factorization allows for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ */
+template<typename Derived>
+class SimplicialCholeskyBase : internal::noncopyable
+{
+ public:
+ typedef typename internal::traits<Derived>::MatrixType MatrixType;
+ typedef typename internal::traits<Derived>::OrderingType OrderingType;
+ enum { UpLo = internal::traits<Derived>::UpLo };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ public:
+
+ /** Default constructor */
+ SimplicialCholeskyBase()
+ : m_info(Success), m_isInitialized(false), m_shiftOffset(0), m_shiftScale(1)
+ {}
+
+ SimplicialCholeskyBase(const MatrixType& matrix)
+ : m_info(Success), m_isInitialized(false), m_shiftOffset(0), m_shiftScale(1)
+ {
+ derived().compute(matrix);
+ }
+
+ ~SimplicialCholeskyBase()
+ {
+ }
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index rows() const { return m_matrix.rows(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<SimplicialCholeskyBase, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Simplicial LLT or LDLT is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "SimplicialCholeskyBase::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<SimplicialCholeskyBase, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Simplicial LLT or LDLT is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "SimplicialCholesky::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the permutation P
+ * \sa permutationPinv() */
+ const PermutationMatrix<Dynamic,Dynamic,Index>& permutationP() const
+ { return m_P; }
+
+ /** \returns the inverse P^-1 of the permutation P
+ * \sa permutationP() */
+ const PermutationMatrix<Dynamic,Dynamic,Index>& permutationPinv() const
+ { return m_Pinv; }
+
+ /** Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.
+ *
+ * During the numerical factorization, the diagonal coefficients are transformed by the following linear model:\n
+ * \c d_ii = \a offset + \a scale * \c d_ii
+ *
+ * The default is the identity transformation with \a offset=0, and \a scale=1.
+ *
+ * \returns a reference to \c *this.
+ */
+ Derived& setShift(const RealScalar& offset, const RealScalar& scale = 1)
+ {
+ m_shiftOffset = offset;
+ m_shiftScale = scale;
+ return derived();
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Stream>
+ void dumpMemory(Stream& s)
+ {
+ int total = 0;
+ s << " L: " << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << "Mb" << "\n";
+ s << " diag: " << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << "Mb" << "\n";
+ s << " tree: " << ((total+=m_parent.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " nonzeros: " << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " perm: " << ((total+=m_P.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " perm^-1: " << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " TOTAL: " << (total>> 20) << "Mb" << "\n";
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ eigen_assert(m_matrix.rows()==b.rows());
+
+ if(m_info!=Success)
+ return;
+
+ if(m_P.size()>0)
+ dest = m_P * b;
+ else
+ dest = b;
+
+ if(m_matrix.nonZeros()>0) // otherwise L==I
+ derived().matrixL().solveInPlace(dest);
+
+ if(m_diag.size()>0)
+ dest = m_diag.asDiagonal().inverse() * dest;
+
+ if (m_matrix.nonZeros()>0) // otherwise U==I
+ derived().matrixU().solveInPlace(dest);
+
+ if(m_P.size()>0)
+ dest = m_Pinv * dest;
+ }
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+ protected:
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ template<bool DoLDLT>
+ void compute(const MatrixType& matrix)
+ {
+ eigen_assert(matrix.rows()==matrix.cols());
+ Index size = matrix.cols();
+ CholMatrixType ap(size,size);
+ ordering(matrix, ap);
+ analyzePattern_preordered(ap, DoLDLT);
+ factorize_preordered<DoLDLT>(ap);
+ }
+
+ template<bool DoLDLT>
+ void factorize(const MatrixType& a)
+ {
+ eigen_assert(a.rows()==a.cols());
+ int size = a.cols();
+ CholMatrixType ap(size,size);
+ ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
+ factorize_preordered<DoLDLT>(ap);
+ }
+
+ template<bool DoLDLT>
+ void factorize_preordered(const CholMatrixType& a);
+
+ void analyzePattern(const MatrixType& a, bool doLDLT)
+ {
+ eigen_assert(a.rows()==a.cols());
+ int size = a.cols();
+ CholMatrixType ap(size,size);
+ ordering(a, ap);
+ analyzePattern_preordered(ap,doLDLT);
+ }
+ void analyzePattern_preordered(const CholMatrixType& a, bool doLDLT);
+
+ void ordering(const MatrixType& a, CholMatrixType& ap);
+
+ /** keeps off-diagonal entries; drops diagonal entries */
+ struct keep_diag {
+ inline bool operator() (const Index& row, const Index& col, const Scalar&) const
+ {
+ return row!=col;
+ }
+ };
+
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_factorizationIsOk;
+ bool m_analysisIsOk;
+
+ CholMatrixType m_matrix;
+ VectorType m_diag; // the diagonal coefficients (LDLT mode)
+ VectorXi m_parent; // elimination tree
+ VectorXi m_nonZerosPerCol;
+ PermutationMatrix<Dynamic,Dynamic,Index> m_P; // the permutation
+ PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv; // the inverse permutation
+
+ RealScalar m_shiftOffset;
+ RealScalar m_shiftScale;
+};
+
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLLT;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLDLT;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialCholesky;
+
+namespace internal {
+
+template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Ordering OrderingType;
+ enum { UpLo = _UpLo };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar, ColMajor, Index> CholMatrixType;
+ typedef SparseTriangularView<CholMatrixType, Eigen::Lower> MatrixL;
+ typedef SparseTriangularView<typename CholMatrixType::AdjointReturnType, Eigen::Upper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m; }
+ static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+};
+
+template<typename _MatrixType,int _UpLo, typename _Ordering> struct traits<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Ordering OrderingType;
+ enum { UpLo = _UpLo };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar, ColMajor, Index> CholMatrixType;
+ typedef SparseTriangularView<CholMatrixType, Eigen::UnitLower> MatrixL;
+ typedef SparseTriangularView<typename CholMatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return m; }
+ static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+};
+
+template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
+{
+ typedef _MatrixType MatrixType;
+ typedef _Ordering OrderingType;
+ enum { UpLo = _UpLo };
+};
+
+}
+
+/** \ingroup SparseCholesky_Module
+ * \class SimplicialLLT
+ * \brief A direct sparse LLT Cholesky factorizations
+ *
+ * This class provides a LL^T Cholesky factorizations of sparse matrices that are
+ * selfadjoint and positive definite. The factorization allows for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
+ *
+ * \sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering
+ */
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+ class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
+{
+public:
+ typedef _MatrixType MatrixType;
+ enum { UpLo = _UpLo };
+ typedef SimplicialCholeskyBase<SimplicialLLT> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialLLT> Traits;
+ typedef typename Traits::MatrixL MatrixL;
+ typedef typename Traits::MatrixU MatrixU;
+public:
+ /** Default constructor */
+ SimplicialLLT() : Base() {}
+ /** Constructs and performs the LLT factorization of \a matrix */
+ SimplicialLLT(const MatrixType& matrix)
+ : Base(matrix) {}
+
+ /** \returns an expression of the factor L */
+ inline const MatrixL matrixL() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
+ return Traits::getL(Base::m_matrix);
+ }
+
+ /** \returns an expression of the factor U (= L^*) */
+ inline const MatrixU matrixU() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
+ return Traits::getU(Base::m_matrix);
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialLLT& compute(const MatrixType& matrix)
+ {
+ Base::template compute<false>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, false);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ Base::template factorize<false>(a);
+ }
+
+ /** \returns the determinant of the underlying matrix from the current factorization */
+ Scalar determinant() const
+ {
+ Scalar detL = Base::m_matrix.diagonal().prod();
+ return numext::abs2(detL);
+ }
+};
+
+/** \ingroup SparseCholesky_Module
+ * \class SimplicialLDLT
+ * \brief A direct sparse LDLT Cholesky factorizations without square root.
+ *
+ * This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are
+ * selfadjoint and positive definite. The factorization allows for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
+ *
+ * \sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering
+ */
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+ class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
+{
+public:
+ typedef _MatrixType MatrixType;
+ enum { UpLo = _UpLo };
+ typedef SimplicialCholeskyBase<SimplicialLDLT> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialLDLT> Traits;
+ typedef typename Traits::MatrixL MatrixL;
+ typedef typename Traits::MatrixU MatrixU;
+public:
+ /** Default constructor */
+ SimplicialLDLT() : Base() {}
+
+ /** Constructs and performs the LLT factorization of \a matrix */
+ SimplicialLDLT(const MatrixType& matrix)
+ : Base(matrix) {}
+
+ /** \returns a vector expression of the diagonal D */
+ inline const VectorType vectorD() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Base::m_diag;
+ }
+ /** \returns an expression of the factor L */
+ inline const MatrixL matrixL() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Traits::getL(Base::m_matrix);
+ }
+
+ /** \returns an expression of the factor U (= L^*) */
+ inline const MatrixU matrixU() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Traits::getU(Base::m_matrix);
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialLDLT& compute(const MatrixType& matrix)
+ {
+ Base::template compute<true>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, true);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ Base::template factorize<true>(a);
+ }
+
+ /** \returns the determinant of the underlying matrix from the current factorization */
+ Scalar determinant() const
+ {
+ return Base::m_diag.prod();
+ }
+};
+
+/** \deprecated use SimplicialLDLT or class SimplicialLLT
+ * \ingroup SparseCholesky_Module
+ * \class SimplicialCholesky
+ *
+ * \sa class SimplicialLDLT, class SimplicialLLT
+ */
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+ class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
+{
+public:
+ typedef _MatrixType MatrixType;
+ enum { UpLo = _UpLo };
+ typedef SimplicialCholeskyBase<SimplicialCholesky> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialCholesky> Traits;
+ typedef internal::traits<SimplicialLDLT<MatrixType,UpLo> > LDLTTraits;
+ typedef internal::traits<SimplicialLLT<MatrixType,UpLo> > LLTTraits;
+ public:
+ SimplicialCholesky() : Base(), m_LDLT(true) {}
+
+ SimplicialCholesky(const MatrixType& matrix)
+ : Base(), m_LDLT(true)
+ {
+ compute(matrix);
+ }
+
+ SimplicialCholesky& setMode(SimplicialCholeskyMode mode)
+ {
+ switch(mode)
+ {
+ case SimplicialCholeskyLLT:
+ m_LDLT = false;
+ break;
+ case SimplicialCholeskyLDLT:
+ m_LDLT = true;
+ break;
+ default:
+ break;
+ }
+
+ return *this;
+ }
+
+ inline const VectorType vectorD() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
+ return Base::m_diag;
+ }
+ inline const CholMatrixType rawMatrix() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
+ return Base::m_matrix;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialCholesky& compute(const MatrixType& matrix)
+ {
+ if(m_LDLT)
+ Base::template compute<true>(matrix);
+ else
+ Base::template compute<false>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, m_LDLT);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ if(m_LDLT)
+ Base::template factorize<true>(a);
+ else
+ Base::template factorize<false>(a);
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(Base::m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ eigen_assert(Base::m_matrix.rows()==b.rows());
+
+ if(Base::m_info!=Success)
+ return;
+
+ if(Base::m_P.size()>0)
+ dest = Base::m_P * b;
+ else
+ dest = b;
+
+ if(Base::m_matrix.nonZeros()>0) // otherwise L==I
+ {
+ if(m_LDLT)
+ LDLTTraits::getL(Base::m_matrix).solveInPlace(dest);
+ else
+ LLTTraits::getL(Base::m_matrix).solveInPlace(dest);
+ }
+
+ if(Base::m_diag.size()>0)
+ dest = Base::m_diag.asDiagonal().inverse() * dest;
+
+ if (Base::m_matrix.nonZeros()>0) // otherwise I==I
+ {
+ if(m_LDLT)
+ LDLTTraits::getU(Base::m_matrix).solveInPlace(dest);
+ else
+ LLTTraits::getU(Base::m_matrix).solveInPlace(dest);
+ }
+
+ if(Base::m_P.size()>0)
+ dest = Base::m_Pinv * dest;
+ }
+
+ Scalar determinant() const
+ {
+ if(m_LDLT)
+ {
+ return Base::m_diag.prod();
+ }
+ else
+ {
+ Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod();
+ return numext::abs2(detL);
+ }
+ }
+
+ protected:
+ bool m_LDLT;
+};
+
+template<typename Derived>
+void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, CholMatrixType& ap)
+{
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+ // Note that amd compute the inverse permutation
+ {
+ CholMatrixType C;
+ C = a.template selfadjointView<UpLo>();
+
+ OrderingType ordering;
+ ordering(C,m_Pinv);
+ }
+
+ if(m_Pinv.size()>0)
+ m_P = m_Pinv.inverse();
+ else
+ m_P.resize(0);
+
+ ap.resize(size,size);
+ ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
+}
+
+namespace internal {
+
+template<typename Derived, typename Rhs>
+struct solve_retval<SimplicialCholeskyBase<Derived>, Rhs>
+ : solve_retval_base<SimplicialCholeskyBase<Derived>, Rhs>
+{
+ typedef SimplicialCholeskyBase<Derived> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec().derived()._solve(rhs(),dst);
+ }
+};
+
+template<typename Derived, typename Rhs>
+struct sparse_solve_retval<SimplicialCholeskyBase<Derived>, Rhs>
+ : sparse_solve_retval_base<SimplicialCholeskyBase<Derived>, Rhs>
+{
+ typedef SimplicialCholeskyBase<Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SIMPLICIAL_CHOLESKY_H
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
new file mode 100644
index 0000000..7aaf702
--- /dev/null
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
@@ -0,0 +1,199 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+/*
+
+NOTE: thes functions vave been adapted from the LDL library:
+
+LDL Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
+
+LDL License:
+
+ Your use or distribution of LDL or any modified version of
+ LDL implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+ */
+
+#include "../Core/util/NonMPL2.h"
+
+#ifndef EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
+#define EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
+
+namespace Eigen {
+
+template<typename Derived>
+void SimplicialCholeskyBase<Derived>::analyzePattern_preordered(const CholMatrixType& ap, bool doLDLT)
+{
+ const Index size = ap.rows();
+ m_matrix.resize(size, size);
+ m_parent.resize(size);
+ m_nonZerosPerCol.resize(size);
+
+ ei_declare_aligned_stack_constructed_variable(Index, tags, size, 0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */
+ m_parent[k] = -1; /* parent of k is not yet known */
+ tags[k] = k; /* mark node k as visited */
+ m_nonZerosPerCol[k] = 0; /* count of nonzeros in column k of L */
+ for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)
+ {
+ Index i = it.index();
+ if(i < k)
+ {
+ /* follow path from i to root of etree, stop at flagged node */
+ for(; tags[i] != k; i = m_parent[i])
+ {
+ /* find parent of i if not yet determined */
+ if (m_parent[i] == -1)
+ m_parent[i] = k;
+ m_nonZerosPerCol[i]++; /* L (k,i) is nonzero */
+ tags[i] = k; /* mark i as visited */
+ }
+ }
+ }
+ }
+
+ /* construct Lp index array from m_nonZerosPerCol column counts */
+ Index* Lp = m_matrix.outerIndexPtr();
+ Lp[0] = 0;
+ for(Index k = 0; k < size; ++k)
+ Lp[k+1] = Lp[k] + m_nonZerosPerCol[k] + (doLDLT ? 0 : 1);
+
+ m_matrix.resizeNonZeros(Lp[size]);
+
+ m_isInitialized = true;
+ m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+}
+
+
+template<typename Derived>
+template<bool DoLDLT>
+void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType& ap)
+{
+ using std::sqrt;
+
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ eigen_assert(ap.rows()==ap.cols());
+ const Index size = ap.rows();
+ eigen_assert(m_parent.size()==size);
+ eigen_assert(m_nonZerosPerCol.size()==size);
+
+ const Index* Lp = m_matrix.outerIndexPtr();
+ Index* Li = m_matrix.innerIndexPtr();
+ Scalar* Lx = m_matrix.valuePtr();
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, y, size, 0);
+ ei_declare_aligned_stack_constructed_variable(Index, pattern, size, 0);
+ ei_declare_aligned_stack_constructed_variable(Index, tags, size, 0);
+
+ bool ok = true;
+ m_diag.resize(DoLDLT ? size : 0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ // compute nonzero pattern of kth row of L, in topological order
+ y[k] = 0.0; // Y(0:k) is now all zero
+ Index top = size; // stack for pattern is empty
+ tags[k] = k; // mark node k as visited
+ m_nonZerosPerCol[k] = 0; // count of nonzeros in column k of L
+ for(typename MatrixType::InnerIterator it(ap,k); it; ++it)
+ {
+ Index i = it.index();
+ if(i <= k)
+ {
+ y[i] += numext::conj(it.value()); /* scatter A(i,k) into Y (sum duplicates) */
+ Index len;
+ for(len = 0; tags[i] != k; i = m_parent[i])
+ {
+ pattern[len++] = i; /* L(k,i) is nonzero */
+ tags[i] = k; /* mark i as visited */
+ }
+ while(len > 0)
+ pattern[--top] = pattern[--len];
+ }
+ }
+
+ /* compute numerical values kth row of L (a sparse triangular solve) */
+
+ RealScalar d = numext::real(y[k]) * m_shiftScale + m_shiftOffset; // get D(k,k), apply the shift function, and clear Y(k)
+ y[k] = 0.0;
+ for(; top < size; ++top)
+ {
+ Index i = pattern[top]; /* pattern[top:n-1] is pattern of L(:,k) */
+ Scalar yi = y[i]; /* get and clear Y(i) */
+ y[i] = 0.0;
+
+ /* the nonzero entry L(k,i) */
+ Scalar l_ki;
+ if(DoLDLT)
+ l_ki = yi / m_diag[i];
+ else
+ yi = l_ki = yi / Lx[Lp[i]];
+
+ Index p2 = Lp[i] + m_nonZerosPerCol[i];
+ Index p;
+ for(p = Lp[i] + (DoLDLT ? 0 : 1); p < p2; ++p)
+ y[Li[p]] -= numext::conj(Lx[p]) * yi;
+ d -= numext::real(l_ki * numext::conj(yi));
+ Li[p] = k; /* store L(k,i) in column form of L */
+ Lx[p] = l_ki;
+ ++m_nonZerosPerCol[i]; /* increment count of nonzeros in col i */
+ }
+ if(DoLDLT)
+ {
+ m_diag[k] = d;
+ if(d == RealScalar(0))
+ {
+ ok = false; /* failure, D(k,k) is zero */
+ break;
+ }
+ }
+ else
+ {
+ Index p = Lp[k] + m_nonZerosPerCol[k]++;
+ Li[p] = k ; /* store L(k,k) = sqrt (d) in column k */
+ if(d <= RealScalar(0)) {
+ ok = false; /* failure, matrix is not positive definite */
+ break;
+ }
+ Lx[p] = sqrt(d) ;
+ }
+ }
+
+ m_info = ok ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
diff --git a/Eigen/src/SparseCore/AmbiVector.h b/Eigen/src/SparseCore/AmbiVector.h
new file mode 100644
index 0000000..220c645
--- /dev/null
+++ b/Eigen/src/SparseCore/AmbiVector.h
@@ -0,0 +1,373 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AMBIVECTOR_H
+#define EIGEN_AMBIVECTOR_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Hybrid sparse/dense vector class designed for intensive read-write operations.
+ *
+ * See BasicSparseLLT and SparseProduct for usage examples.
+ */
+template<typename _Scalar, typename _Index>
+class AmbiVector
+{
+ public:
+ typedef _Scalar Scalar;
+ typedef _Index Index;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ AmbiVector(Index size)
+ : m_buffer(0), m_zero(0), m_size(0), m_allocatedSize(0), m_allocatedElements(0), m_mode(-1)
+ {
+ resize(size);
+ }
+
+ void init(double estimatedDensity);
+ void init(int mode);
+
+ Index nonZeros() const;
+
+ /** Specifies a sub-vector to work on */
+ void setBounds(Index start, Index end) { m_start = start; m_end = end; }
+
+ void setZero();
+
+ void restart();
+ Scalar& coeffRef(Index i);
+ Scalar& coeff(Index i);
+
+ class Iterator;
+
+ ~AmbiVector() { delete[] m_buffer; }
+
+ void resize(Index size)
+ {
+ if (m_allocatedSize < size)
+ reallocate(size);
+ m_size = size;
+ }
+
+ Index size() const { return m_size; }
+
+ protected:
+
+ void reallocate(Index size)
+ {
+ // if the size of the matrix is not too large, let's allocate a bit more than needed such
+ // that we can handle dense vector even in sparse mode.
+ delete[] m_buffer;
+ if (size<1000)
+ {
+ Index allocSize = (size * sizeof(ListEl) + sizeof(Scalar) - 1)/sizeof(Scalar);
+ m_allocatedElements = (allocSize*sizeof(Scalar))/sizeof(ListEl);
+ m_buffer = new Scalar[allocSize];
+ }
+ else
+ {
+ m_allocatedElements = (size*sizeof(Scalar))/sizeof(ListEl);
+ m_buffer = new Scalar[size];
+ }
+ m_size = size;
+ m_start = 0;
+ m_end = m_size;
+ }
+
+ void reallocateSparse()
+ {
+ Index copyElements = m_allocatedElements;
+ m_allocatedElements = (std::min)(Index(m_allocatedElements*1.5),m_size);
+ Index allocSize = m_allocatedElements * sizeof(ListEl);
+ allocSize = (allocSize + sizeof(Scalar) - 1)/sizeof(Scalar);
+ Scalar* newBuffer = new Scalar[allocSize];
+ memcpy(newBuffer, m_buffer, copyElements * sizeof(ListEl));
+ delete[] m_buffer;
+ m_buffer = newBuffer;
+ }
+
+ protected:
+ // element type of the linked list
+ struct ListEl
+ {
+ Index next;
+ Index index;
+ Scalar value;
+ };
+
+ // used to store data in both mode
+ Scalar* m_buffer;
+ Scalar m_zero;
+ Index m_size;
+ Index m_start;
+ Index m_end;
+ Index m_allocatedSize;
+ Index m_allocatedElements;
+ Index m_mode;
+
+ // linked list mode
+ Index m_llStart;
+ Index m_llCurrent;
+ Index m_llSize;
+};
+
+/** \returns the number of non zeros in the current sub vector */
+template<typename _Scalar,typename _Index>
+_Index AmbiVector<_Scalar,_Index>::nonZeros() const
+{
+ if (m_mode==IsSparse)
+ return m_llSize;
+ else
+ return m_end - m_start;
+}
+
+template<typename _Scalar,typename _Index>
+void AmbiVector<_Scalar,_Index>::init(double estimatedDensity)
+{
+ if (estimatedDensity>0.1)
+ init(IsDense);
+ else
+ init(IsSparse);
+}
+
+template<typename _Scalar,typename _Index>
+void AmbiVector<_Scalar,_Index>::init(int mode)
+{
+ m_mode = mode;
+ if (m_mode==IsSparse)
+ {
+ m_llSize = 0;
+ m_llStart = -1;
+ }
+}
+
+/** Must be called whenever we might perform a write access
+ * with an index smaller than the previous one.
+ *
+ * Don't worry, this function is extremely cheap.
+ */
+template<typename _Scalar,typename _Index>
+void AmbiVector<_Scalar,_Index>::restart()
+{
+ m_llCurrent = m_llStart;
+}
+
+/** Set all coefficients of current subvector to zero */
+template<typename _Scalar,typename _Index>
+void AmbiVector<_Scalar,_Index>::setZero()
+{
+ if (m_mode==IsDense)
+ {
+ for (Index i=m_start; i<m_end; ++i)
+ m_buffer[i] = Scalar(0);
+ }
+ else
+ {
+ eigen_assert(m_mode==IsSparse);
+ m_llSize = 0;
+ m_llStart = -1;
+ }
+}
+
+template<typename _Scalar,typename _Index>
+_Scalar& AmbiVector<_Scalar,_Index>::coeffRef(_Index i)
+{
+ if (m_mode==IsDense)
+ return m_buffer[i];
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);
+ // TODO factorize the following code to reduce code generation
+ eigen_assert(m_mode==IsSparse);
+ if (m_llSize==0)
+ {
+ // this is the first element
+ m_llStart = 0;
+ m_llCurrent = 0;
+ ++m_llSize;
+ llElements[0].value = Scalar(0);
+ llElements[0].index = i;
+ llElements[0].next = -1;
+ return llElements[0].value;
+ }
+ else if (i<llElements[m_llStart].index)
+ {
+ // this is going to be the new first element of the list
+ ListEl& el = llElements[m_llSize];
+ el.value = Scalar(0);
+ el.index = i;
+ el.next = m_llStart;
+ m_llStart = m_llSize;
+ ++m_llSize;
+ m_llCurrent = m_llStart;
+ return el.value;
+ }
+ else
+ {
+ Index nextel = llElements[m_llCurrent].next;
+ eigen_assert(i>=llElements[m_llCurrent].index && "you must call restart() before inserting an element with lower or equal index");
+ while (nextel >= 0 && llElements[nextel].index<=i)
+ {
+ m_llCurrent = nextel;
+ nextel = llElements[nextel].next;
+ }
+
+ if (llElements[m_llCurrent].index==i)
+ {
+ // the coefficient already exists and we found it !
+ return llElements[m_llCurrent].value;
+ }
+ else
+ {
+ if (m_llSize>=m_allocatedElements)
+ {
+ reallocateSparse();
+ llElements = reinterpret_cast<ListEl*>(m_buffer);
+ }
+ eigen_internal_assert(m_llSize<m_allocatedElements && "internal error: overflow in sparse mode");
+ // let's insert a new coefficient
+ ListEl& el = llElements[m_llSize];
+ el.value = Scalar(0);
+ el.index = i;
+ el.next = llElements[m_llCurrent].next;
+ llElements[m_llCurrent].next = m_llSize;
+ ++m_llSize;
+ return el.value;
+ }
+ }
+ }
+}
+
+template<typename _Scalar,typename _Index>
+_Scalar& AmbiVector<_Scalar,_Index>::coeff(_Index i)
+{
+ if (m_mode==IsDense)
+ return m_buffer[i];
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);
+ eigen_assert(m_mode==IsSparse);
+ if ((m_llSize==0) || (i<llElements[m_llStart].index))
+ {
+ return m_zero;
+ }
+ else
+ {
+ Index elid = m_llStart;
+ while (elid >= 0 && llElements[elid].index<i)
+ elid = llElements[elid].next;
+
+ if (llElements[elid].index==i)
+ return llElements[m_llCurrent].value;
+ else
+ return m_zero;
+ }
+ }
+}
+
+/** Iterator over the nonzero coefficients */
+template<typename _Scalar,typename _Index>
+class AmbiVector<_Scalar,_Index>::Iterator
+{
+ public:
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** Default constructor
+ * \param vec the vector on which we iterate
+ * \param epsilon the minimal value used to prune zero coefficients.
+ * In practice, all coefficients having a magnitude smaller than \a epsilon
+ * are skipped.
+ */
+ Iterator(const AmbiVector& vec, const RealScalar& epsilon = 0)
+ : m_vector(vec)
+ {
+ using std::abs;
+ m_epsilon = epsilon;
+ m_isDense = m_vector.m_mode==IsDense;
+ if (m_isDense)
+ {
+ m_currentEl = 0; // this is to avoid a compilation warning
+ m_cachedValue = 0; // this is to avoid a compilation warning
+ m_cachedIndex = m_vector.m_start-1;
+ ++(*this);
+ }
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
+ m_currentEl = m_vector.m_llStart;
+ while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon)
+ m_currentEl = llElements[m_currentEl].next;
+ if (m_currentEl<0)
+ {
+ m_cachedValue = 0; // this is to avoid a compilation warning
+ m_cachedIndex = -1;
+ }
+ else
+ {
+ m_cachedIndex = llElements[m_currentEl].index;
+ m_cachedValue = llElements[m_currentEl].value;
+ }
+ }
+ }
+
+ Index index() const { return m_cachedIndex; }
+ Scalar value() const { return m_cachedValue; }
+
+ operator bool() const { return m_cachedIndex>=0; }
+
+ Iterator& operator++()
+ {
+ using std::abs;
+ if (m_isDense)
+ {
+ do {
+ ++m_cachedIndex;
+ } while (m_cachedIndex<m_vector.m_end && abs(m_vector.m_buffer[m_cachedIndex])<m_epsilon);
+ if (m_cachedIndex<m_vector.m_end)
+ m_cachedValue = m_vector.m_buffer[m_cachedIndex];
+ else
+ m_cachedIndex=-1;
+ }
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
+ do {
+ m_currentEl = llElements[m_currentEl].next;
+ } while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<m_epsilon);
+ if (m_currentEl<0)
+ {
+ m_cachedIndex = -1;
+ }
+ else
+ {
+ m_cachedIndex = llElements[m_currentEl].index;
+ m_cachedValue = llElements[m_currentEl].value;
+ }
+ }
+ return *this;
+ }
+
+ protected:
+ const AmbiVector& m_vector; // the target vector
+ Index m_currentEl; // the current element in sparse/linked-list mode
+ RealScalar m_epsilon; // epsilon used to prune zero coefficients
+ Index m_cachedIndex; // current coordinate
+ Scalar m_cachedValue; // current value
+ bool m_isDense; // mode of the vector
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_AMBIVECTOR_H
diff --git a/Eigen/src/SparseCore/CMakeLists.txt b/Eigen/src/SparseCore/CMakeLists.txt
new file mode 100644
index 0000000..d860452
--- /dev/null
+++ b/Eigen/src/SparseCore/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SparseCore_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SparseCore_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseCore COMPONENT Devel
+ )
diff --git a/Eigen/src/SparseCore/CompressedStorage.h b/Eigen/src/SparseCore/CompressedStorage.h
new file mode 100644
index 0000000..a667cb5
--- /dev/null
+++ b/Eigen/src/SparseCore/CompressedStorage.h
@@ -0,0 +1,233 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPRESSED_STORAGE_H
+#define EIGEN_COMPRESSED_STORAGE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Stores a sparse set of values as a list of values and a list of indices.
+ *
+ */
+template<typename _Scalar,typename _Index>
+class CompressedStorage
+{
+ public:
+
+ typedef _Scalar Scalar;
+ typedef _Index Index;
+
+ protected:
+
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ public:
+
+ CompressedStorage()
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {}
+
+ CompressedStorage(size_t size)
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {
+ resize(size);
+ }
+
+ CompressedStorage(const CompressedStorage& other)
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {
+ *this = other;
+ }
+
+ CompressedStorage& operator=(const CompressedStorage& other)
+ {
+ resize(other.size());
+ internal::smart_copy(other.m_values, other.m_values + m_size, m_values);
+ internal::smart_copy(other.m_indices, other.m_indices + m_size, m_indices);
+ return *this;
+ }
+
+ void swap(CompressedStorage& other)
+ {
+ std::swap(m_values, other.m_values);
+ std::swap(m_indices, other.m_indices);
+ std::swap(m_size, other.m_size);
+ std::swap(m_allocatedSize, other.m_allocatedSize);
+ }
+
+ ~CompressedStorage()
+ {
+ delete[] m_values;
+ delete[] m_indices;
+ }
+
+ void reserve(size_t size)
+ {
+ size_t newAllocatedSize = m_size + size;
+ if (newAllocatedSize > m_allocatedSize)
+ reallocate(newAllocatedSize);
+ }
+
+ void squeeze()
+ {
+ if (m_allocatedSize>m_size)
+ reallocate(m_size);
+ }
+
+ void resize(size_t size, double reserveSizeFactor = 0)
+ {
+ if (m_allocatedSize<size)
+ reallocate(size + size_t(reserveSizeFactor*double(size)));
+ m_size = size;
+ }
+
+ void append(const Scalar& v, Index i)
+ {
+ Index id = static_cast<Index>(m_size);
+ resize(m_size+1, 1);
+ m_values[id] = v;
+ m_indices[id] = i;
+ }
+
+ inline size_t size() const { return m_size; }
+ inline size_t allocatedSize() const { return m_allocatedSize; }
+ inline void clear() { m_size = 0; }
+
+ inline Scalar& value(size_t i) { return m_values[i]; }
+ inline const Scalar& value(size_t i) const { return m_values[i]; }
+
+ inline Index& index(size_t i) { return m_indices[i]; }
+ inline const Index& index(size_t i) const { return m_indices[i]; }
+
+ static CompressedStorage Map(Index* indices, Scalar* values, size_t size)
+ {
+ CompressedStorage res;
+ res.m_indices = indices;
+ res.m_values = values;
+ res.m_allocatedSize = res.m_size = size;
+ return res;
+ }
+
+ /** \returns the largest \c k such that for all \c j in [0,k) index[\c j]\<\a key */
+ inline Index searchLowerIndex(Index key) const
+ {
+ return searchLowerIndex(0, m_size, key);
+ }
+
+ /** \returns the largest \c k in [start,end) such that for all \c j in [start,k) index[\c j]\<\a key */
+ inline Index searchLowerIndex(size_t start, size_t end, Index key) const
+ {
+ while(end>start)
+ {
+ size_t mid = (end+start)>>1;
+ if (m_indices[mid]<key)
+ start = mid+1;
+ else
+ end = mid;
+ }
+ return static_cast<Index>(start);
+ }
+
+ /** \returns the stored value at index \a key
+ * If the value does not exist, then the value \a defaultValue is returned without any insertion. */
+ inline Scalar at(Index key, const Scalar& defaultValue = Scalar(0)) const
+ {
+ if (m_size==0)
+ return defaultValue;
+ else if (key==m_indices[m_size-1])
+ return m_values[m_size-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+ const size_t id = searchLowerIndex(0,m_size-1,key);
+ return ((id<m_size) && (m_indices[id]==key)) ? m_values[id] : defaultValue;
+ }
+
+ /** Like at(), but the search is performed in the range [start,end) */
+ inline Scalar atInRange(size_t start, size_t end, Index key, const Scalar& defaultValue = Scalar(0)) const
+ {
+ if (start>=end)
+ return Scalar(0);
+ else if (end>start && key==m_indices[end-1])
+ return m_values[end-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+ const size_t id = searchLowerIndex(start,end-1,key);
+ return ((id<end) && (m_indices[id]==key)) ? m_values[id] : defaultValue;
+ }
+
+ /** \returns a reference to the value at index \a key
+ * If the value does not exist, then the value \a defaultValue is inserted
+ * such that the keys are sorted. */
+ inline Scalar& atWithInsertion(Index key, const Scalar& defaultValue = Scalar(0))
+ {
+ size_t id = searchLowerIndex(0,m_size,key);
+ if (id>=m_size || m_indices[id]!=key)
+ {
+ resize(m_size+1,1);
+ for (size_t j=m_size-1; j>id; --j)
+ {
+ m_indices[j] = m_indices[j-1];
+ m_values[j] = m_values[j-1];
+ }
+ m_indices[id] = key;
+ m_values[id] = defaultValue;
+ }
+ return m_values[id];
+ }
+
+ void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())
+ {
+ size_t k = 0;
+ size_t n = size();
+ for (size_t i=0; i<n; ++i)
+ {
+ if (!internal::isMuchSmallerThan(value(i), reference, epsilon))
+ {
+ value(k) = value(i);
+ index(k) = index(i);
+ ++k;
+ }
+ }
+ resize(k,0);
+ }
+
+ protected:
+
+ inline void reallocate(size_t size)
+ {
+ Scalar* newValues = new Scalar[size];
+ Index* newIndices = new Index[size];
+ size_t copySize = (std::min)(size, m_size);
+ // copy
+ internal::smart_copy(m_values, m_values+copySize, newValues);
+ internal::smart_copy(m_indices, m_indices+copySize, newIndices);
+ // delete old stuff
+ delete[] m_values;
+ delete[] m_indices;
+ m_values = newValues;
+ m_indices = newIndices;
+ m_allocatedSize = size;
+ }
+
+ protected:
+ Scalar* m_values;
+ Index* m_indices;
+ size_t m_size;
+ size_t m_allocatedSize;
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPRESSED_STORAGE_H
diff --git a/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h b/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h
new file mode 100644
index 0000000..5c320e2
--- /dev/null
+++ b/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h
@@ -0,0 +1,245 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
+#define EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename ResultType>
+static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+{
+ typedef typename remove_all<Lhs>::type::Scalar Scalar;
+ typedef typename remove_all<Lhs>::type::Index Index;
+
+ // make sure to call innerSize/outerSize since we fake the storage order.
+ Index rows = lhs.innerSize();
+ Index cols = rhs.outerSize();
+ eigen_assert(lhs.outerSize() == rhs.innerSize());
+
+ std::vector<bool> mask(rows,false);
+ Matrix<Scalar,Dynamic,1> values(rows);
+ Matrix<Index,Dynamic,1> indices(rows);
+
+ // estimate the number of non zero entries
+ // given a rhs column containing Y non zeros, we assume that the respective Y columns
+ // of the lhs differs in average of one non zeros, thus the number of non zeros for
+ // the product of a rhs column with the lhs is X+Y where X is the average number of non zero
+ // per column of the lhs.
+ // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)
+ Index estimated_nnz_prod = lhs.nonZeros() + rhs.nonZeros();
+
+ res.setZero();
+ res.reserve(Index(estimated_nnz_prod));
+ // we compute each column of the result, one after the other
+ for (Index j=0; j<cols; ++j)
+ {
+
+ res.startVec(j);
+ Index nnz = 0;
+ for (typename Rhs::InnerIterator rhsIt(rhs, j); rhsIt; ++rhsIt)
+ {
+ Scalar y = rhsIt.value();
+ Index k = rhsIt.index();
+ for (typename Lhs::InnerIterator lhsIt(lhs, k); lhsIt; ++lhsIt)
+ {
+ Index i = lhsIt.index();
+ Scalar x = lhsIt.value();
+ if(!mask[i])
+ {
+ mask[i] = true;
+ values[i] = x * y;
+ indices[nnz] = i;
+ ++nnz;
+ }
+ else
+ values[i] += x * y;
+ }
+ }
+
+ // unordered insertion
+ for(Index k=0; k<nnz; ++k)
+ {
+ Index i = indices[k];
+ res.insertBackByOuterInnerUnordered(j,i) = values[i];
+ mask[i] = false;
+ }
+
+#if 0
+ // alternative ordered insertion code:
+
+ Index t200 = rows/(log2(200)*1.39);
+ Index t = (rows*100)/139;
+
+ // FIXME reserve nnz non zeros
+ // FIXME implement fast sort algorithms for very small nnz
+ // if the result is sparse enough => use a quick sort
+ // otherwise => loop through the entire vector
+ // In order to avoid to perform an expensive log2 when the
+ // result is clearly very sparse we use a linear bound up to 200.
+ //if((nnz<200 && nnz<t200) || nnz * log2(nnz) < t)
+ //res.startVec(j);
+ if(true)
+ {
+ if(nnz>1) std::sort(indices.data(),indices.data()+nnz);
+ for(Index k=0; k<nnz; ++k)
+ {
+ Index i = indices[k];
+ res.insertBackByOuterInner(j,i) = values[i];
+ mask[i] = false;
+ }
+ }
+ else
+ {
+ // dense path
+ for(Index i=0; i<rows; ++i)
+ {
+ if(mask[i])
+ {
+ mask[i] = false;
+ res.insertBackByOuterInner(j,i) = values[i];
+ }
+ }
+ }
+#endif
+
+ }
+ res.finalize();
+}
+
+
+} // end namespace internal
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = (traits<Lhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int RhsStorageOrder = (traits<Rhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int ResStorageOrder = (traits<ResultType>::Flags&RowMajorBit) ? RowMajor : ColMajor>
+struct conservative_sparse_sparse_product_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>
+{
+ typedef typename remove_all<Lhs>::type LhsCleaned;
+ typedef typename LhsCleaned::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+ ColMajorMatrix resCol(lhs.rows(),rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);
+ // sort the non zeros:
+ RowMajorMatrix resRow(resCol);
+ res = resRow;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+ RowMajorMatrix rhsRow = rhs;
+ RowMajorMatrix resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<RowMajorMatrix,Lhs,RowMajorMatrix>(rhsRow, lhs, resRow);
+ res = resRow;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+ RowMajorMatrix lhsRow = lhs;
+ RowMajorMatrix resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,RowMajorMatrix,RowMajorMatrix>(rhs, lhsRow, resRow);
+ res = resRow;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+ RowMajorMatrix resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);
+ res = resRow;
+ }
+};
+
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>
+{
+ typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+ ColMajorMatrix resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+ ColMajorMatrix lhsCol = lhs;
+ ColMajorMatrix resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<ColMajorMatrix,Rhs,ColMajorMatrix>(lhsCol, rhs, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+ ColMajorMatrix rhsCol = rhs;
+ ColMajorMatrix resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Lhs,ColMajorMatrix,ColMajorMatrix>(lhs, rhsCol, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+ RowMajorMatrix resRow(lhs.rows(),rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);
+ // sort the non zeros:
+ ColMajorMatrix resCol(resRow);
+ res = resCol;
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/MappedSparseMatrix.h b/Eigen/src/SparseCore/MappedSparseMatrix.h
new file mode 100644
index 0000000..ab1a266
--- /dev/null
+++ b/Eigen/src/SparseCore/MappedSparseMatrix.h
@@ -0,0 +1,181 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MAPPED_SPARSEMATRIX_H
+#define EIGEN_MAPPED_SPARSEMATRIX_H
+
+namespace Eigen {
+
+/** \class MappedSparseMatrix
+ *
+ * \brief Sparse matrix
+ *
+ * \param _Scalar the scalar type, i.e. the type of the coefficients
+ *
+ * See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
+ *
+ */
+namespace internal {
+template<typename _Scalar, int _Flags, typename _Index>
+struct traits<MappedSparseMatrix<_Scalar, _Flags, _Index> > : traits<SparseMatrix<_Scalar, _Flags, _Index> >
+{};
+}
+
+template<typename _Scalar, int _Flags, typename _Index>
+class MappedSparseMatrix
+ : public SparseMatrixBase<MappedSparseMatrix<_Scalar, _Flags, _Index> >
+{
+ public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(MappedSparseMatrix)
+ enum { IsRowMajor = Base::IsRowMajor };
+
+ protected:
+
+ Index m_outerSize;
+ Index m_innerSize;
+ Index m_nnz;
+ Index* m_outerIndex;
+ Index* m_innerIndices;
+ Scalar* m_values;
+
+ public:
+
+ inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
+ inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
+ inline Index innerSize() const { return m_innerSize; }
+ inline Index outerSize() const { return m_outerSize; }
+
+ bool isCompressed() const { return true; }
+
+ //----------------------------------------
+ // direct access interface
+ inline const Scalar* valuePtr() const { return m_values; }
+ inline Scalar* valuePtr() { return m_values; }
+
+ inline const Index* innerIndexPtr() const { return m_innerIndices; }
+ inline Index* innerIndexPtr() { return m_innerIndices; }
+
+ inline const Index* outerIndexPtr() const { return m_outerIndex; }
+ inline Index* outerIndexPtr() { return m_outerIndex; }
+ //----------------------------------------
+
+ inline Scalar coeff(Index row, Index col) const
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = m_outerIndex[outer];
+ Index end = m_outerIndex[outer+1];
+ if (start==end)
+ return Scalar(0);
+ else if (end>0 && inner==m_innerIndices[end-1])
+ return m_values[end-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+
+ const Index* r = std::lower_bound(&m_innerIndices[start],&m_innerIndices[end-1],inner);
+ const Index id = r-&m_innerIndices[0];
+ return ((*r==inner) && (id<end)) ? m_values[id] : Scalar(0);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = m_outerIndex[outer];
+ Index end = m_outerIndex[outer+1];
+ eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
+ eigen_assert(end>start && "coeffRef cannot be called on a zero coefficient");
+ Index* r = std::lower_bound(&m_innerIndices[start],&m_innerIndices[end],inner);
+ const Index id = r-&m_innerIndices[0];
+ eigen_assert((*r==inner) && (id<end) && "coeffRef cannot be called on a zero coefficient");
+ return m_values[id];
+ }
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const { return m_nnz; }
+
+ inline MappedSparseMatrix(Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr)
+ : m_outerSize(IsRowMajor?rows:cols), m_innerSize(IsRowMajor?cols:rows), m_nnz(nnz), m_outerIndex(outerIndexPtr),
+ m_innerIndices(innerIndexPtr), m_values(valuePtr)
+ {}
+
+ /** Empty destructor */
+ inline ~MappedSparseMatrix() {}
+};
+
+template<typename Scalar, int _Flags, typename _Index>
+class MappedSparseMatrix<Scalar,_Flags,_Index>::InnerIterator
+{
+ public:
+ InnerIterator(const MappedSparseMatrix& mat, Index outer)
+ : m_matrix(mat),
+ m_outer(outer),
+ m_id(mat.outerIndexPtr()[outer]),
+ m_start(m_id),
+ m_end(mat.outerIndexPtr()[outer+1])
+ {}
+
+ inline InnerIterator& operator++() { m_id++; return *this; }
+
+ inline Scalar value() const { return m_matrix.valuePtr()[m_id]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_id]); }
+
+ inline Index index() const { return m_matrix.innerIndexPtr()[m_id]; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ inline operator bool() const { return (m_id < m_end) && (m_id>=m_start); }
+
+ protected:
+ const MappedSparseMatrix& m_matrix;
+ const Index m_outer;
+ Index m_id;
+ const Index m_start;
+ const Index m_end;
+};
+
+template<typename Scalar, int _Flags, typename _Index>
+class MappedSparseMatrix<Scalar,_Flags,_Index>::ReverseInnerIterator
+{
+ public:
+ ReverseInnerIterator(const MappedSparseMatrix& mat, Index outer)
+ : m_matrix(mat),
+ m_outer(outer),
+ m_id(mat.outerIndexPtr()[outer+1]),
+ m_start(mat.outerIndexPtr()[outer]),
+ m_end(m_id)
+ {}
+
+ inline ReverseInnerIterator& operator--() { m_id--; return *this; }
+
+ inline Scalar value() const { return m_matrix.valuePtr()[m_id-1]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_id-1]); }
+
+ inline Index index() const { return m_matrix.innerIndexPtr()[m_id-1]; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ inline operator bool() const { return (m_id <= m_end) && (m_id>m_start); }
+
+ protected:
+ const MappedSparseMatrix& m_matrix;
+ const Index m_outer;
+ Index m_id;
+ const Index m_start;
+ const Index m_end;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_MAPPED_SPARSEMATRIX_H
diff --git a/Eigen/src/SparseCore/SparseBlock.h b/Eigen/src/SparseCore/SparseBlock.h
new file mode 100644
index 0000000..0c90baf
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseBlock.h
@@ -0,0 +1,537 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_BLOCK_H
+#define EIGEN_SPARSE_BLOCK_H
+
+namespace Eigen {
+
+template<typename XprType, int BlockRows, int BlockCols>
+class BlockImpl<XprType,BlockRows,BlockCols,true,Sparse>
+ : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,true> >
+{
+ typedef typename internal::remove_all<typename XprType::Nested>::type _MatrixTypeNested;
+ typedef Block<XprType, BlockRows, BlockCols, true> BlockType;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+protected:
+ enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+
+ class InnerIterator: public XprType::InnerIterator
+ {
+ typedef typename BlockImpl::Index Index;
+ public:
+ inline InnerIterator(const BlockType& xpr, Index outer)
+ : XprType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+ class ReverseInnerIterator: public XprType::ReverseInnerIterator
+ {
+ typedef typename BlockImpl::Index Index;
+ public:
+ inline ReverseInnerIterator(const BlockType& xpr, Index outer)
+ : XprType::ReverseInnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+
+ inline BlockImpl(const XprType& xpr, int i)
+ : m_matrix(xpr), m_outerStart(i), m_outerSize(OuterSize)
+ {}
+
+ inline BlockImpl(const XprType& xpr, int startRow, int startCol, int blockRows, int blockCols)
+ : m_matrix(xpr), m_outerStart(IsRowMajor ? startRow : startCol), m_outerSize(IsRowMajor ? blockRows : blockCols)
+ {}
+
+ inline const Scalar coeff(int row, int col) const
+ {
+ return m_matrix.coeff(row + IsRowMajor ? m_outerStart : 0, col +IsRowMajor ? 0 : m_outerStart);
+ }
+
+ inline const Scalar coeff(int index) const
+ {
+ return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index : m_outerStart);
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ protected:
+
+ typename XprType::Nested m_matrix;
+ Index m_outerStart;
+ const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+ private:
+ Index nonZeros() const;
+};
+
+
+/***************************************************************************
+* specialisation for SparseMatrix
+***************************************************************************/
+
+template<typename _Scalar, int _Options, typename _Index, int BlockRows, int BlockCols>
+class BlockImpl<SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true,Sparse>
+ : public SparseMatrixBase<Block<SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true> >
+{
+ typedef SparseMatrix<_Scalar, _Options, _Index> SparseMatrixType;
+ typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _MatrixTypeNested;
+ typedef Block<SparseMatrixType, BlockRows, BlockCols, true> BlockType;
+ typedef Block<const SparseMatrixType, BlockRows, BlockCols, true> ConstBlockType;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+protected:
+ enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+public:
+
+ class InnerIterator: public SparseMatrixType::InnerIterator
+ {
+ public:
+ inline InnerIterator(const BlockType& xpr, Index outer)
+ : SparseMatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+ class ReverseInnerIterator: public SparseMatrixType::ReverseInnerIterator
+ {
+ public:
+ inline ReverseInnerIterator(const BlockType& xpr, Index outer)
+ : SparseMatrixType::ReverseInnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+
+ inline BlockImpl(const SparseMatrixType& xpr, int i)
+ : m_matrix(xpr), m_outerStart(i), m_outerSize(OuterSize)
+ {}
+
+ inline BlockImpl(const SparseMatrixType& xpr, int startRow, int startCol, int blockRows, int blockCols)
+ : m_matrix(xpr), m_outerStart(IsRowMajor ? startRow : startCol), m_outerSize(IsRowMajor ? blockRows : blockCols)
+ {}
+
+ template<typename OtherDerived>
+ inline BlockType& operator=(const SparseMatrixBase<OtherDerived>& other)
+ {
+ typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _NestedMatrixType;
+ _NestedMatrixType& matrix = const_cast<_NestedMatrixType&>(m_matrix);;
+ // This assignement is slow if this vector set is not empty
+ // and/or it is not at the end of the nonzeros of the underlying matrix.
+
+ // 1 - eval to a temporary to avoid transposition and/or aliasing issues
+ SparseMatrix<Scalar, IsRowMajor ? RowMajor : ColMajor, Index> tmp(other);
+
+ // 2 - let's check whether there is enough allocated memory
+ Index nnz = tmp.nonZeros();
+ Index start = m_outerStart==0 ? 0 : matrix.outerIndexPtr()[m_outerStart]; // starting position of the current block
+ Index end = m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()]; // ending posiiton of the current block
+ Index block_size = end - start; // available room in the current block
+ Index tail_size = m_matrix.outerIndexPtr()[m_matrix.outerSize()] - end;
+
+ Index free_size = m_matrix.isCompressed()
+ ? Index(matrix.data().allocatedSize()) + block_size
+ : block_size;
+
+ if(nnz>free_size)
+ {
+ // realloc manually to reduce copies
+ typename SparseMatrixType::Storage newdata(m_matrix.data().allocatedSize() - block_size + nnz);
+
+ std::memcpy(&newdata.value(0), &m_matrix.data().value(0), start*sizeof(Scalar));
+ std::memcpy(&newdata.index(0), &m_matrix.data().index(0), start*sizeof(Index));
+
+ std::memcpy(&newdata.value(start), &tmp.data().value(0), nnz*sizeof(Scalar));
+ std::memcpy(&newdata.index(start), &tmp.data().index(0), nnz*sizeof(Index));
+
+ std::memcpy(&newdata.value(start+nnz), &matrix.data().value(end), tail_size*sizeof(Scalar));
+ std::memcpy(&newdata.index(start+nnz), &matrix.data().index(end), tail_size*sizeof(Index));
+
+ newdata.resize(m_matrix.outerIndexPtr()[m_matrix.outerSize()] - block_size + nnz);
+
+ matrix.data().swap(newdata);
+ }
+ else
+ {
+ // no need to realloc, simply copy the tail at its respective position and insert tmp
+ matrix.data().resize(start + nnz + tail_size);
+
+ std::memmove(&matrix.data().value(start+nnz), &matrix.data().value(end), tail_size*sizeof(Scalar));
+ std::memmove(&matrix.data().index(start+nnz), &matrix.data().index(end), tail_size*sizeof(Index));
+
+ std::memcpy(&matrix.data().value(start), &tmp.data().value(0), nnz*sizeof(Scalar));
+ std::memcpy(&matrix.data().index(start), &tmp.data().index(0), nnz*sizeof(Index));
+ }
+
+ // update innerNonZeros
+ if(!m_matrix.isCompressed())
+ for(Index j=0; j<m_outerSize.value(); ++j)
+ matrix.innerNonZeroPtr()[m_outerStart+j] = tmp.innerVector(j).nonZeros();
+
+ // update outer index pointers
+ Index p = start;
+ for(Index k=0; k<m_outerSize.value(); ++k)
+ {
+ matrix.outerIndexPtr()[m_outerStart+k] = p;
+ p += tmp.innerVector(k).nonZeros();
+ }
+ std::ptrdiff_t offset = nnz - block_size;
+ for(Index k = m_outerStart + m_outerSize.value(); k<=matrix.outerSize(); ++k)
+ {
+ matrix.outerIndexPtr()[k] += offset;
+ }
+
+ return derived();
+ }
+
+ inline BlockType& operator=(const BlockType& other)
+ {
+ return operator=<BlockType>(other);
+ }
+
+ inline const Scalar* valuePtr() const
+ { return m_matrix.valuePtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+ inline Scalar* valuePtr()
+ { return m_matrix.const_cast_derived().valuePtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+ inline const Index* innerIndexPtr() const
+ { return m_matrix.innerIndexPtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+ inline Index* innerIndexPtr()
+ { return m_matrix.const_cast_derived().innerIndexPtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+ inline const Index* outerIndexPtr() const
+ { return m_matrix.outerIndexPtr() + m_outerStart; }
+ inline Index* outerIndexPtr()
+ { return m_matrix.const_cast_derived().outerIndexPtr() + m_outerStart; }
+
+ Index nonZeros() const
+ {
+ if(m_matrix.isCompressed())
+ return std::size_t(m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()])
+ - std::size_t(m_matrix.outerIndexPtr()[m_outerStart]);
+ else if(m_outerSize.value()==0)
+ return 0;
+ else
+ return Map<const Matrix<Index,OuterSize,1> >(m_matrix.innerNonZeroPtr()+m_outerStart, m_outerSize.value()).sum();
+ }
+
+ inline Scalar& coeffRef(int row, int col)
+ {
+ return m_matrix.const_cast_derived().coeffRef(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(int row, int col) const
+ {
+ return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(int index) const
+ {
+ return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index : m_outerStart);
+ }
+
+ const Scalar& lastCoeff() const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(BlockImpl);
+ eigen_assert(nonZeros()>0);
+ if(m_matrix.isCompressed())
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart+1]-1];
+ else
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart]+m_matrix.innerNonZeroPtr()[m_outerStart]-1];
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ protected:
+
+ typename SparseMatrixType::Nested m_matrix;
+ Index m_outerStart;
+ const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+};
+
+
+template<typename _Scalar, int _Options, typename _Index, int BlockRows, int BlockCols>
+class BlockImpl<const SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true,Sparse>
+ : public SparseMatrixBase<Block<const SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true> >
+{
+ typedef SparseMatrix<_Scalar, _Options, _Index> SparseMatrixType;
+ typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _MatrixTypeNested;
+ typedef Block<const SparseMatrixType, BlockRows, BlockCols, true> BlockType;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+protected:
+ enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+public:
+
+ class InnerIterator: public SparseMatrixType::InnerIterator
+ {
+ public:
+ inline InnerIterator(const BlockType& xpr, Index outer)
+ : SparseMatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+ class ReverseInnerIterator: public SparseMatrixType::ReverseInnerIterator
+ {
+ public:
+ inline ReverseInnerIterator(const BlockType& xpr, Index outer)
+ : SparseMatrixType::ReverseInnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+ {}
+ inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ Index m_outer;
+ };
+
+ inline BlockImpl(const SparseMatrixType& xpr, int i)
+ : m_matrix(xpr), m_outerStart(i), m_outerSize(OuterSize)
+ {}
+
+ inline BlockImpl(const SparseMatrixType& xpr, int startRow, int startCol, int blockRows, int blockCols)
+ : m_matrix(xpr), m_outerStart(IsRowMajor ? startRow : startCol), m_outerSize(IsRowMajor ? blockRows : blockCols)
+ {}
+
+ inline const Scalar* valuePtr() const
+ { return m_matrix.valuePtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+ inline const Index* innerIndexPtr() const
+ { return m_matrix.innerIndexPtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+ inline const Index* outerIndexPtr() const
+ { return m_matrix.outerIndexPtr() + m_outerStart; }
+
+ Index nonZeros() const
+ {
+ if(m_matrix.isCompressed())
+ return std::size_t(m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()])
+ - std::size_t(m_matrix.outerIndexPtr()[m_outerStart]);
+ else if(m_outerSize.value()==0)
+ return 0;
+ else
+ return Map<const Matrix<Index,OuterSize,1> >(m_matrix.innerNonZeroPtr()+m_outerStart, m_outerSize.value()).sum();
+ }
+
+ inline const Scalar coeff(int row, int col) const
+ {
+ return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(int index) const
+ {
+ return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index : m_outerStart);
+ }
+
+ const Scalar& lastCoeff() const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(BlockImpl);
+ eigen_assert(nonZeros()>0);
+ if(m_matrix.isCompressed())
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart+1]-1];
+ else
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart]+m_matrix.innerNonZeroPtr()[m_outerStart]-1];
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ protected:
+
+ typename SparseMatrixType::Nested m_matrix;
+ Index m_outerStart;
+ const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+};
+
+//----------
+
+/** \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+ * is col-major (resp. row-major).
+ */
+template<typename Derived>
+typename SparseMatrixBase<Derived>::InnerVectorReturnType SparseMatrixBase<Derived>::innerVector(Index outer)
+{ return InnerVectorReturnType(derived(), outer); }
+
+/** \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+ * is col-major (resp. row-major). Read-only.
+ */
+template<typename Derived>
+const typename SparseMatrixBase<Derived>::ConstInnerVectorReturnType SparseMatrixBase<Derived>::innerVector(Index outer) const
+{ return ConstInnerVectorReturnType(derived(), outer); }
+
+/** \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+ * is col-major (resp. row-major).
+ */
+template<typename Derived>
+typename SparseMatrixBase<Derived>::InnerVectorsReturnType
+SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize)
+{
+ return Block<Derived,Dynamic,Dynamic,true>(derived(),
+ IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
+ IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);
+
+}
+
+/** \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+ * is col-major (resp. row-major). Read-only.
+ */
+template<typename Derived>
+const typename SparseMatrixBase<Derived>::ConstInnerVectorsReturnType
+SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize) const
+{
+ return Block<const Derived,Dynamic,Dynamic,true>(derived(),
+ IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
+ IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);
+
+}
+
+/** Generic implementation of sparse Block expression.
+ * Real-only.
+ */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl<XprType,BlockRows,BlockCols,InnerPanel,Sparse>
+ : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,InnerPanel> >, internal::no_assignment_operator
+{
+ typedef typename internal::remove_all<typename XprType::Nested>::type _MatrixTypeNested;
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+
+ /** Column or Row constructor
+ */
+ inline BlockImpl(const XprType& xpr, int i)
+ : m_matrix(xpr),
+ m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+ m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+ m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+ m_blockCols(BlockCols==1 ? 1 : xpr.cols())
+ {}
+
+ /** Dynamic-size constructor
+ */
+ inline BlockImpl(const XprType& xpr, int startRow, int startCol, int blockRows, int blockCols)
+ : m_matrix(xpr), m_startRow(startRow), m_startCol(startCol), m_blockRows(blockRows), m_blockCols(blockCols)
+ {}
+
+ inline int rows() const { return m_blockRows.value(); }
+ inline int cols() const { return m_blockCols.value(); }
+
+ inline Scalar& coeffRef(int row, int col)
+ {
+ return m_matrix.const_cast_derived()
+ .coeffRef(row + m_startRow.value(), col + m_startCol.value());
+ }
+
+ inline const Scalar coeff(int row, int col) const
+ {
+ return m_matrix.coeff(row + m_startRow.value(), col + m_startCol.value());
+ }
+
+ inline Scalar& coeffRef(int index)
+ {
+ return m_matrix.const_cast_derived()
+ .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const Scalar coeff(int index) const
+ {
+ return m_matrix
+ .coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const _MatrixTypeNested& nestedExpression() const { return m_matrix; }
+
+ class InnerIterator : public _MatrixTypeNested::InnerIterator
+ {
+ typedef typename _MatrixTypeNested::InnerIterator Base;
+ const BlockType& m_block;
+ Index m_end;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const BlockType& block, Index outer)
+ : Base(block.derived().nestedExpression(), outer + (IsRowMajor ? block.m_startRow.value() : block.m_startCol.value())),
+ m_block(block),
+ m_end(IsRowMajor ? block.m_startCol.value()+block.m_blockCols.value() : block.m_startRow.value()+block.m_blockRows.value())
+ {
+ while( (Base::operator bool()) && (Base::index() < (IsRowMajor ? m_block.m_startCol.value() : m_block.m_startRow.value())) )
+ Base::operator++();
+ }
+
+ inline Index index() const { return Base::index() - (IsRowMajor ? m_block.m_startCol.value() : m_block.m_startRow.value()); }
+ inline Index outer() const { return Base::outer() - (IsRowMajor ? m_block.m_startRow.value() : m_block.m_startCol.value()); }
+ inline Index row() const { return Base::row() - m_block.m_startRow.value(); }
+ inline Index col() const { return Base::col() - m_block.m_startCol.value(); }
+
+ inline operator bool() const { return Base::operator bool() && Base::index() < m_end; }
+ };
+ class ReverseInnerIterator : public _MatrixTypeNested::ReverseInnerIterator
+ {
+ typedef typename _MatrixTypeNested::ReverseInnerIterator Base;
+ const BlockType& m_block;
+ Index m_begin;
+ public:
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator(const BlockType& block, Index outer)
+ : Base(block.derived().nestedExpression(), outer + (IsRowMajor ? block.m_startRow.value() : block.m_startCol.value())),
+ m_block(block),
+ m_begin(IsRowMajor ? block.m_startCol.value() : block.m_startRow.value())
+ {
+ while( (Base::operator bool()) && (Base::index() >= (IsRowMajor ? m_block.m_startCol.value()+block.m_blockCols.value() : m_block.m_startRow.value()+block.m_blockRows.value())) )
+ Base::operator--();
+ }
+
+ inline Index index() const { return Base::index() - (IsRowMajor ? m_block.m_startCol.value() : m_block.m_startRow.value()); }
+ inline Index outer() const { return Base::outer() - (IsRowMajor ? m_block.m_startRow.value() : m_block.m_startCol.value()); }
+ inline Index row() const { return Base::row() - m_block.m_startRow.value(); }
+ inline Index col() const { return Base::col() - m_block.m_startCol.value(); }
+
+ inline operator bool() const { return Base::operator bool() && Base::index() >= m_begin; }
+ };
+ protected:
+ friend class InnerIterator;
+ friend class ReverseInnerIterator;
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+
+ typename XprType::Nested m_matrix;
+ const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+ const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_BLOCK_H
+
diff --git a/Eigen/src/SparseCore/SparseColEtree.h b/Eigen/src/SparseCore/SparseColEtree.h
new file mode 100644
index 0000000..f8745f4
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseColEtree.h
@@ -0,0 +1,206 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/*
+
+ * NOTE: This file is the modified version of sp_coletree.c file in SuperLU
+
+ * -- SuperLU routine (version 3.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * August 1, 2008
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSE_COLETREE_H
+#define SPARSE_COLETREE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** Find the root of the tree/set containing the vertex i : Use Path halving */
+template<typename Index, typename IndexVector>
+Index etree_find (Index i, IndexVector& pp)
+{
+ Index p = pp(i); // Parent
+ Index gp = pp(p); // Grand parent
+ while (gp != p)
+ {
+ pp(i) = gp; // Parent pointer on find path is changed to former grand parent
+ i = gp;
+ p = pp(i);
+ gp = pp(p);
+ }
+ return p;
+}
+
+/** Compute the column elimination tree of a sparse matrix
+ * \param mat The matrix in column-major format.
+ * \param parent The elimination tree
+ * \param firstRowElt The column index of the first element in each row
+ * \param perm The permutation to apply to the column of \b mat
+ */
+template <typename MatrixType, typename IndexVector>
+int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowElt, typename MatrixType::Index *perm=0)
+{
+ typedef typename MatrixType::Index Index;
+ Index nc = mat.cols(); // Number of columns
+ Index m = mat.rows();
+ Index diagSize = (std::min)(nc,m);
+ IndexVector root(nc); // root of subtree of etree
+ root.setZero();
+ IndexVector pp(nc); // disjoint sets
+ pp.setZero(); // Initialize disjoint sets
+ parent.resize(mat.cols());
+ //Compute first nonzero column in each row
+ Index row,col;
+ firstRowElt.resize(m);
+ firstRowElt.setConstant(nc);
+ firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);
+ bool found_diag;
+ for (col = 0; col < nc; col++)
+ {
+ Index pcol = col;
+ if(perm) pcol = perm[col];
+ for (typename MatrixType::InnerIterator it(mat, pcol); it; ++it)
+ {
+ row = it.row();
+ firstRowElt(row) = (std::min)(firstRowElt(row), col);
+ }
+ }
+ /* Compute etree by Liu's algorithm for symmetric matrices,
+ except use (firstRowElt[r],c) in place of an edge (r,c) of A.
+ Thus each row clique in A'*A is replaced by a star
+ centered at its first vertex, which has the same fill. */
+ Index rset, cset, rroot;
+ for (col = 0; col < nc; col++)
+ {
+ found_diag = col>=m;
+ pp(col) = col;
+ cset = col;
+ root(cset) = col;
+ parent(col) = nc;
+ /* The diagonal element is treated here even if it does not exist in the matrix
+ * hence the loop is executed once more */
+ Index pcol = col;
+ if(perm) pcol = perm[col];
+ for (typename MatrixType::InnerIterator it(mat, pcol); it||!found_diag; ++it)
+ { // A sequence of interleaved find and union is performed
+ Index i = col;
+ if(it) i = it.index();
+ if (i == col) found_diag = true;
+
+ row = firstRowElt(i);
+ if (row >= col) continue;
+ rset = internal::etree_find(row, pp); // Find the name of the set containing row
+ rroot = root(rset);
+ if (rroot != col)
+ {
+ parent(rroot) = col;
+ pp(cset) = rset;
+ cset = rset;
+ root(cset) = col;
+ }
+ }
+ }
+ return 0;
+}
+
+/**
+ * Depth-first search from vertex n. No recursion.
+ * This routine was contributed by Cédric Doucet, CEDRAT Group, Meylan, France.
+*/
+template <typename Index, typename IndexVector>
+void nr_etdfs (Index n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, Index postnum)
+{
+ Index current = n, first, next;
+ while (postnum != n)
+ {
+ // No kid for the current node
+ first = first_kid(current);
+
+ // no kid for the current node
+ if (first == -1)
+ {
+ // Numbering this node because it has no kid
+ post(current) = postnum++;
+
+ // looking for the next kid
+ next = next_kid(current);
+ while (next == -1)
+ {
+ // No more kids : back to the parent node
+ current = parent(current);
+ // numbering the parent node
+ post(current) = postnum++;
+
+ // Get the next kid
+ next = next_kid(current);
+ }
+ // stopping criterion
+ if (postnum == n+1) return;
+
+ // Updating current node
+ current = next;
+ }
+ else
+ {
+ current = first;
+ }
+ }
+}
+
+
+/**
+ * \brief Post order a tree
+ * \param n the number of nodes
+ * \param parent Input tree
+ * \param post postordered tree
+ */
+template <typename Index, typename IndexVector>
+void treePostorder(Index n, IndexVector& parent, IndexVector& post)
+{
+ IndexVector first_kid, next_kid; // Linked list of children
+ Index postnum;
+ // Allocate storage for working arrays and results
+ first_kid.resize(n+1);
+ next_kid.setZero(n+1);
+ post.setZero(n+1);
+
+ // Set up structure describing children
+ Index v, dad;
+ first_kid.setConstant(-1);
+ for (v = n-1; v >= 0; v--)
+ {
+ dad = parent(v);
+ next_kid(v) = first_kid(dad);
+ first_kid(dad) = v;
+ }
+
+ // Depth-first search from dummy root vertex #n
+ postnum = 0;
+ internal::nr_etdfs(n, parent, first_kid, next_kid, post, postnum);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // SPARSE_COLETREE_H
diff --git a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
new file mode 100644
index 0000000..60ca769
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
@@ -0,0 +1,325 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_CWISE_BINARY_OP_H
+#define EIGEN_SPARSE_CWISE_BINARY_OP_H
+
+namespace Eigen {
+
+// Here we have to handle 3 cases:
+// 1 - sparse op dense
+// 2 - dense op sparse
+// 3 - sparse op sparse
+// We also need to implement a 4th iterator for:
+// 4 - dense op dense
+// Finally, we also need to distinguish between the product and other operations :
+// configuration returned mode
+// 1 - sparse op dense product sparse
+// generic dense
+// 2 - dense op sparse product sparse
+// generic dense
+// 3 - sparse op sparse product sparse
+// generic sparse
+// 4 - dense op dense product dense
+// generic dense
+
+namespace internal {
+
+template<> struct promote_storage_type<Dense,Sparse>
+{ typedef Sparse ret; };
+
+template<> struct promote_storage_type<Sparse,Dense>
+{ typedef Sparse ret; };
+
+template<typename BinaryOp, typename Lhs, typename Rhs, typename Derived,
+ typename _LhsStorageMode = typename traits<Lhs>::StorageKind,
+ typename _RhsStorageMode = typename traits<Rhs>::StorageKind>
+class sparse_cwise_binary_op_inner_iterator_selector;
+
+} // end namespace internal
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Sparse>
+ : public SparseMatrixBase<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ public:
+ class InnerIterator;
+ class ReverseInnerIterator;
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Derived)
+ CwiseBinaryOpImpl()
+ {
+ typedef typename internal::traits<Lhs>::StorageKind LhsStorageKind;
+ typedef typename internal::traits<Rhs>::StorageKind RhsStorageKind;
+ EIGEN_STATIC_ASSERT((
+ (!internal::is_same<LhsStorageKind,RhsStorageKind>::value)
+ || ((Lhs::Flags&RowMajorBit) == (Rhs::Flags&RowMajorBit))),
+ THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH);
+ }
+};
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOpImpl<BinaryOp,Lhs,Rhs,Sparse>::InnerIterator
+ : public internal::sparse_cwise_binary_op_inner_iterator_selector<BinaryOp,Lhs,Rhs,typename CwiseBinaryOpImpl<BinaryOp,Lhs,Rhs,Sparse>::InnerIterator>
+{
+ public:
+ typedef typename Lhs::Index Index;
+ typedef internal::sparse_cwise_binary_op_inner_iterator_selector<
+ BinaryOp,Lhs,Rhs, InnerIterator> Base;
+
+ // NOTE: we have to prefix Index by "typename Lhs::" to avoid an ICE with VC11
+ EIGEN_STRONG_INLINE InnerIterator(const CwiseBinaryOpImpl& binOp, typename Lhs::Index outer)
+ : Base(binOp.derived(),outer)
+ {}
+};
+
+/***************************************************************************
+* Implementation of inner-iterators
+***************************************************************************/
+
+// template<typename T> struct internal::func_is_conjunction { enum { ret = false }; };
+// template<typename T> struct internal::func_is_conjunction<internal::scalar_product_op<T> > { enum { ret = true }; };
+
+// TODO generalize the internal::scalar_product_op specialization to all conjunctions if any !
+
+namespace internal {
+
+// sparse - sparse (generic)
+template<typename BinaryOp, typename Lhs, typename Rhs, typename Derived>
+class sparse_cwise_binary_op_inner_iterator_selector<BinaryOp, Lhs, Rhs, Derived, Sparse, Sparse>
+{
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> CwiseBinaryXpr;
+ typedef typename traits<CwiseBinaryXpr>::Scalar Scalar;
+ typedef typename traits<CwiseBinaryXpr>::_LhsNested _LhsNested;
+ typedef typename traits<CwiseBinaryXpr>::_RhsNested _RhsNested;
+ typedef typename _LhsNested::InnerIterator LhsIterator;
+ typedef typename _RhsNested::InnerIterator RhsIterator;
+ typedef typename Lhs::Index Index;
+
+ public:
+
+ EIGEN_STRONG_INLINE sparse_cwise_binary_op_inner_iterator_selector(const CwiseBinaryXpr& xpr, Index outer)
+ : m_lhsIter(xpr.lhs(),outer), m_rhsIter(xpr.rhs(),outer), m_functor(xpr.functor())
+ {
+ this->operator++();
+ }
+
+ EIGEN_STRONG_INLINE Derived& operator++()
+ {
+ if (m_lhsIter && m_rhsIter && (m_lhsIter.index() == m_rhsIter.index()))
+ {
+ m_id = m_lhsIter.index();
+ m_value = m_functor(m_lhsIter.value(), m_rhsIter.value());
+ ++m_lhsIter;
+ ++m_rhsIter;
+ }
+ else if (m_lhsIter && (!m_rhsIter || (m_lhsIter.index() < m_rhsIter.index())))
+ {
+ m_id = m_lhsIter.index();
+ m_value = m_functor(m_lhsIter.value(), Scalar(0));
+ ++m_lhsIter;
+ }
+ else if (m_rhsIter && (!m_lhsIter || (m_lhsIter.index() > m_rhsIter.index())))
+ {
+ m_id = m_rhsIter.index();
+ m_value = m_functor(Scalar(0), m_rhsIter.value());
+ ++m_rhsIter;
+ }
+ else
+ {
+ m_value = 0; // this is to avoid a compilation warning
+ m_id = -1;
+ }
+ return *static_cast<Derived*>(this);
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_value; }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_id; }
+ EIGEN_STRONG_INLINE Index row() const { return Lhs::IsRowMajor ? m_lhsIter.row() : index(); }
+ EIGEN_STRONG_INLINE Index col() const { return Lhs::IsRowMajor ? index() : m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_id>=0; }
+
+ protected:
+ LhsIterator m_lhsIter;
+ RhsIterator m_rhsIter;
+ const BinaryOp& m_functor;
+ Scalar m_value;
+ Index m_id;
+};
+
+// sparse - sparse (product)
+template<typename T, typename Lhs, typename Rhs, typename Derived>
+class sparse_cwise_binary_op_inner_iterator_selector<scalar_product_op<T>, Lhs, Rhs, Derived, Sparse, Sparse>
+{
+ typedef scalar_product_op<T> BinaryFunc;
+ typedef CwiseBinaryOp<BinaryFunc, Lhs, Rhs> CwiseBinaryXpr;
+ typedef typename CwiseBinaryXpr::Scalar Scalar;
+ typedef typename traits<CwiseBinaryXpr>::_LhsNested _LhsNested;
+ typedef typename _LhsNested::InnerIterator LhsIterator;
+ typedef typename traits<CwiseBinaryXpr>::_RhsNested _RhsNested;
+ typedef typename _RhsNested::InnerIterator RhsIterator;
+ typedef typename Lhs::Index Index;
+ public:
+
+ EIGEN_STRONG_INLINE sparse_cwise_binary_op_inner_iterator_selector(const CwiseBinaryXpr& xpr, Index outer)
+ : m_lhsIter(xpr.lhs(),outer), m_rhsIter(xpr.rhs(),outer), m_functor(xpr.functor())
+ {
+ while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))
+ {
+ if (m_lhsIter.index() < m_rhsIter.index())
+ ++m_lhsIter;
+ else
+ ++m_rhsIter;
+ }
+ }
+
+ EIGEN_STRONG_INLINE Derived& operator++()
+ {
+ ++m_lhsIter;
+ ++m_rhsIter;
+ while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))
+ {
+ if (m_lhsIter.index() < m_rhsIter.index())
+ ++m_lhsIter;
+ else
+ ++m_rhsIter;
+ }
+ return *static_cast<Derived*>(this);
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_functor(m_lhsIter.value(), m_rhsIter.value()); }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_lhsIter.index(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return (m_lhsIter && m_rhsIter); }
+
+ protected:
+ LhsIterator m_lhsIter;
+ RhsIterator m_rhsIter;
+ const BinaryFunc& m_functor;
+};
+
+// sparse - dense (product)
+template<typename T, typename Lhs, typename Rhs, typename Derived>
+class sparse_cwise_binary_op_inner_iterator_selector<scalar_product_op<T>, Lhs, Rhs, Derived, Sparse, Dense>
+{
+ typedef scalar_product_op<T> BinaryFunc;
+ typedef CwiseBinaryOp<BinaryFunc, Lhs, Rhs> CwiseBinaryXpr;
+ typedef typename CwiseBinaryXpr::Scalar Scalar;
+ typedef typename traits<CwiseBinaryXpr>::_LhsNested _LhsNested;
+ typedef typename traits<CwiseBinaryXpr>::RhsNested RhsNested;
+ typedef typename _LhsNested::InnerIterator LhsIterator;
+ typedef typename Lhs::Index Index;
+ enum { IsRowMajor = (int(Lhs::Flags)&RowMajorBit)==RowMajorBit };
+ public:
+
+ EIGEN_STRONG_INLINE sparse_cwise_binary_op_inner_iterator_selector(const CwiseBinaryXpr& xpr, Index outer)
+ : m_rhs(xpr.rhs()), m_lhsIter(xpr.lhs(),outer), m_functor(xpr.functor()), m_outer(outer)
+ {}
+
+ EIGEN_STRONG_INLINE Derived& operator++()
+ {
+ ++m_lhsIter;
+ return *static_cast<Derived*>(this);
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ { return m_functor(m_lhsIter.value(),
+ m_rhs.coeff(IsRowMajor?m_outer:m_lhsIter.index(),IsRowMajor?m_lhsIter.index():m_outer)); }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_lhsIter.index(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_lhsIter; }
+
+ protected:
+ RhsNested m_rhs;
+ LhsIterator m_lhsIter;
+ const BinaryFunc m_functor;
+ const Index m_outer;
+};
+
+// sparse - dense (product)
+template<typename T, typename Lhs, typename Rhs, typename Derived>
+class sparse_cwise_binary_op_inner_iterator_selector<scalar_product_op<T>, Lhs, Rhs, Derived, Dense, Sparse>
+{
+ typedef scalar_product_op<T> BinaryFunc;
+ typedef CwiseBinaryOp<BinaryFunc, Lhs, Rhs> CwiseBinaryXpr;
+ typedef typename CwiseBinaryXpr::Scalar Scalar;
+ typedef typename traits<CwiseBinaryXpr>::_RhsNested _RhsNested;
+ typedef typename _RhsNested::InnerIterator RhsIterator;
+ typedef typename Lhs::Index Index;
+
+ enum { IsRowMajor = (int(Rhs::Flags)&RowMajorBit)==RowMajorBit };
+ public:
+
+ EIGEN_STRONG_INLINE sparse_cwise_binary_op_inner_iterator_selector(const CwiseBinaryXpr& xpr, Index outer)
+ : m_xpr(xpr), m_rhsIter(xpr.rhs(),outer), m_functor(xpr.functor()), m_outer(outer)
+ {}
+
+ EIGEN_STRONG_INLINE Derived& operator++()
+ {
+ ++m_rhsIter;
+ return *static_cast<Derived*>(this);
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ { return m_functor(m_xpr.lhs().coeff(IsRowMajor?m_outer:m_rhsIter.index(),IsRowMajor?m_rhsIter.index():m_outer), m_rhsIter.value()); }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_rhsIter.index(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_rhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_rhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_rhsIter; }
+
+ protected:
+ const CwiseBinaryXpr& m_xpr;
+ RhsIterator m_rhsIter;
+ const BinaryFunc& m_functor;
+ const Index m_outer;
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of SparseMatrixBase and SparseCwise functions/operators
+***************************************************************************/
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+SparseMatrixBase<Derived>::operator-=(const SparseMatrixBase<OtherDerived> &other)
+{
+ return derived() = derived() - other.derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+SparseMatrixBase<Derived>::operator+=(const SparseMatrixBase<OtherDerived>& other)
+{
+ return derived() = derived() + other.derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE
+SparseMatrixBase<Derived>::cwiseProduct(const MatrixBase<OtherDerived> &other) const
+{
+ return EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_CWISE_BINARY_OP_H
diff --git a/Eigen/src/SparseCore/SparseCwiseUnaryOp.h b/Eigen/src/SparseCore/SparseCwiseUnaryOp.h
new file mode 100644
index 0000000..5a50c78
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseCwiseUnaryOp.h
@@ -0,0 +1,163 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_CWISE_UNARY_OP_H
+#define EIGEN_SPARSE_CWISE_UNARY_OP_H
+
+namespace Eigen {
+
+template<typename UnaryOp, typename MatrixType>
+class CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>
+ : public SparseMatrixBase<CwiseUnaryOp<UnaryOp, MatrixType> >
+{
+ public:
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ typedef CwiseUnaryOp<UnaryOp, MatrixType> Derived;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Derived)
+
+ protected:
+ typedef typename internal::traits<Derived>::_XprTypeNested _MatrixTypeNested;
+ typedef typename _MatrixTypeNested::InnerIterator MatrixTypeIterator;
+ typedef typename _MatrixTypeNested::ReverseInnerIterator MatrixTypeReverseIterator;
+};
+
+template<typename UnaryOp, typename MatrixType>
+class CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::InnerIterator
+ : public CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::MatrixTypeIterator
+{
+ typedef typename CwiseUnaryOpImpl::Scalar Scalar;
+ typedef typename CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::MatrixTypeIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const CwiseUnaryOpImpl& unaryOp, typename CwiseUnaryOpImpl::Index outer)
+ : Base(unaryOp.derived().nestedExpression(),outer), m_functor(unaryOp.derived().functor())
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ { Base::operator++(); return *this; }
+
+ EIGEN_STRONG_INLINE typename CwiseUnaryOpImpl::Scalar value() const { return m_functor(Base::value()); }
+
+ protected:
+ const UnaryOp m_functor;
+ private:
+ typename CwiseUnaryOpImpl::Scalar& valueRef();
+};
+
+template<typename UnaryOp, typename MatrixType>
+class CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::ReverseInnerIterator
+ : public CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::MatrixTypeReverseIterator
+{
+ typedef typename CwiseUnaryOpImpl::Scalar Scalar;
+ typedef typename CwiseUnaryOpImpl<UnaryOp,MatrixType,Sparse>::MatrixTypeReverseIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator(const CwiseUnaryOpImpl& unaryOp, typename CwiseUnaryOpImpl::Index outer)
+ : Base(unaryOp.derived().nestedExpression(),outer), m_functor(unaryOp.derived().functor())
+ {}
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator& operator--()
+ { Base::operator--(); return *this; }
+
+ EIGEN_STRONG_INLINE typename CwiseUnaryOpImpl::Scalar value() const { return m_functor(Base::value()); }
+
+ protected:
+ const UnaryOp m_functor;
+ private:
+ typename CwiseUnaryOpImpl::Scalar& valueRef();
+};
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>
+ : public SparseMatrixBase<CwiseUnaryView<ViewOp, MatrixType> >
+{
+ public:
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ typedef CwiseUnaryView<ViewOp, MatrixType> Derived;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Derived)
+
+ protected:
+ typedef typename internal::traits<Derived>::_MatrixTypeNested _MatrixTypeNested;
+ typedef typename _MatrixTypeNested::InnerIterator MatrixTypeIterator;
+ typedef typename _MatrixTypeNested::ReverseInnerIterator MatrixTypeReverseIterator;
+};
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::InnerIterator
+ : public CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::MatrixTypeIterator
+{
+ typedef typename CwiseUnaryViewImpl::Scalar Scalar;
+ typedef typename CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::MatrixTypeIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const CwiseUnaryViewImpl& unaryOp, typename CwiseUnaryViewImpl::Index outer)
+ : Base(unaryOp.derived().nestedExpression(),outer), m_functor(unaryOp.derived().functor())
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ { Base::operator++(); return *this; }
+
+ EIGEN_STRONG_INLINE typename CwiseUnaryViewImpl::Scalar value() const { return m_functor(Base::value()); }
+ EIGEN_STRONG_INLINE typename CwiseUnaryViewImpl::Scalar& valueRef() { return m_functor(Base::valueRef()); }
+
+ protected:
+ const ViewOp m_functor;
+};
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::ReverseInnerIterator
+ : public CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::MatrixTypeReverseIterator
+{
+ typedef typename CwiseUnaryViewImpl::Scalar Scalar;
+ typedef typename CwiseUnaryViewImpl<ViewOp,MatrixType,Sparse>::MatrixTypeReverseIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator(const CwiseUnaryViewImpl& unaryOp, typename CwiseUnaryViewImpl::Index outer)
+ : Base(unaryOp.derived().nestedExpression(),outer), m_functor(unaryOp.derived().functor())
+ {}
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator& operator--()
+ { Base::operator--(); return *this; }
+
+ EIGEN_STRONG_INLINE typename CwiseUnaryViewImpl::Scalar value() const { return m_functor(Base::value()); }
+ EIGEN_STRONG_INLINE typename CwiseUnaryViewImpl::Scalar& valueRef() { return m_functor(Base::valueRef()); }
+
+ protected:
+ const ViewOp m_functor;
+};
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+SparseMatrixBase<Derived>::operator*=(const Scalar& other)
+{
+ for (Index j=0; j<outerSize(); ++j)
+ for (typename Derived::InnerIterator i(derived(),j); i; ++i)
+ i.valueRef() *= other;
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+SparseMatrixBase<Derived>::operator/=(const Scalar& other)
+{
+ for (Index j=0; j<outerSize(); ++j)
+ for (typename Derived::InnerIterator i(derived(),j); i; ++i)
+ i.valueRef() /= other;
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_CWISE_UNARY_OP_H
diff --git a/Eigen/src/SparseCore/SparseDenseProduct.h b/Eigen/src/SparseCore/SparseDenseProduct.h
new file mode 100644
index 0000000..ccb6ae7
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDenseProduct.h
@@ -0,0 +1,311 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEDENSEPRODUCT_H
+#define EIGEN_SPARSEDENSEPRODUCT_H
+
+namespace Eigen {
+
+template<typename Lhs, typename Rhs, int InnerSize> struct SparseDenseProductReturnType
+{
+ typedef SparseTimeDenseProduct<Lhs,Rhs> Type;
+};
+
+template<typename Lhs, typename Rhs> struct SparseDenseProductReturnType<Lhs,Rhs,1>
+{
+ typedef typename internal::conditional<
+ Lhs::IsRowMajor,
+ SparseDenseOuterProduct<Rhs,Lhs,true>,
+ SparseDenseOuterProduct<Lhs,Rhs,false> >::type Type;
+};
+
+template<typename Lhs, typename Rhs, int InnerSize> struct DenseSparseProductReturnType
+{
+ typedef DenseTimeSparseProduct<Lhs,Rhs> Type;
+};
+
+template<typename Lhs, typename Rhs> struct DenseSparseProductReturnType<Lhs,Rhs,1>
+{
+ typedef typename internal::conditional<
+ Rhs::IsRowMajor,
+ SparseDenseOuterProduct<Rhs,Lhs,true>,
+ SparseDenseOuterProduct<Lhs,Rhs,false> >::type Type;
+};
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, bool Tr>
+struct traits<SparseDenseOuterProduct<Lhs,Rhs,Tr> >
+{
+ typedef Sparse StorageKind;
+ typedef typename scalar_product_traits<typename traits<Lhs>::Scalar,
+ typename traits<Rhs>::Scalar>::ReturnType Scalar;
+ typedef typename Lhs::Index Index;
+ typedef typename Lhs::Nested LhsNested;
+ typedef typename Rhs::Nested RhsNested;
+ typedef typename remove_all<LhsNested>::type _LhsNested;
+ typedef typename remove_all<RhsNested>::type _RhsNested;
+
+ enum {
+ LhsCoeffReadCost = traits<_LhsNested>::CoeffReadCost,
+ RhsCoeffReadCost = traits<_RhsNested>::CoeffReadCost,
+
+ RowsAtCompileTime = Tr ? int(traits<Rhs>::RowsAtCompileTime) : int(traits<Lhs>::RowsAtCompileTime),
+ ColsAtCompileTime = Tr ? int(traits<Lhs>::ColsAtCompileTime) : int(traits<Rhs>::ColsAtCompileTime),
+ MaxRowsAtCompileTime = Tr ? int(traits<Rhs>::MaxRowsAtCompileTime) : int(traits<Lhs>::MaxRowsAtCompileTime),
+ MaxColsAtCompileTime = Tr ? int(traits<Lhs>::MaxColsAtCompileTime) : int(traits<Rhs>::MaxColsAtCompileTime),
+
+ Flags = Tr ? RowMajorBit : 0,
+
+ CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + NumTraits<Scalar>::MulCost
+ };
+};
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs, bool Tr>
+class SparseDenseOuterProduct
+ : public SparseMatrixBase<SparseDenseOuterProduct<Lhs,Rhs,Tr> >
+{
+ public:
+
+ typedef SparseMatrixBase<SparseDenseOuterProduct> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(SparseDenseOuterProduct)
+ typedef internal::traits<SparseDenseOuterProduct> Traits;
+
+ private:
+
+ typedef typename Traits::LhsNested LhsNested;
+ typedef typename Traits::RhsNested RhsNested;
+ typedef typename Traits::_LhsNested _LhsNested;
+ typedef typename Traits::_RhsNested _RhsNested;
+
+ public:
+
+ class InnerIterator;
+
+ EIGEN_STRONG_INLINE SparseDenseOuterProduct(const Lhs& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {
+ EIGEN_STATIC_ASSERT(!Tr,YOU_MADE_A_PROGRAMMING_MISTAKE);
+ }
+
+ EIGEN_STRONG_INLINE SparseDenseOuterProduct(const Rhs& rhs, const Lhs& lhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {
+ EIGEN_STATIC_ASSERT(Tr,YOU_MADE_A_PROGRAMMING_MISTAKE);
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return Tr ? m_rhs.rows() : m_lhs.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return Tr ? m_lhs.cols() : m_rhs.cols(); }
+
+ EIGEN_STRONG_INLINE const _LhsNested& lhs() const { return m_lhs; }
+ EIGEN_STRONG_INLINE const _RhsNested& rhs() const { return m_rhs; }
+
+ protected:
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+};
+
+template<typename Lhs, typename Rhs, bool Transpose>
+class SparseDenseOuterProduct<Lhs,Rhs,Transpose>::InnerIterator : public _LhsNested::InnerIterator
+{
+ typedef typename _LhsNested::InnerIterator Base;
+ typedef typename SparseDenseOuterProduct::Index Index;
+ public:
+ EIGEN_STRONG_INLINE InnerIterator(const SparseDenseOuterProduct& prod, Index outer)
+ : Base(prod.lhs(), 0), m_outer(outer), m_factor(get(prod.rhs(), outer, typename internal::traits<Rhs>::StorageKind() ))
+ { }
+
+ inline Index outer() const { return m_outer; }
+ inline Index row() const { return Transpose ? m_outer : Base::index(); }
+ inline Index col() const { return Transpose ? Base::index() : m_outer; }
+
+ inline Scalar value() const { return Base::value() * m_factor; }
+
+ protected:
+ static Scalar get(const _RhsNested &rhs, Index outer, Dense = Dense())
+ {
+ return rhs.coeff(outer);
+ }
+
+ static Scalar get(const _RhsNested &rhs, Index outer, Sparse = Sparse())
+ {
+ typename Traits::_RhsNested::InnerIterator it(rhs, outer);
+ if (it && it.index()==0)
+ return it.value();
+
+ return Scalar(0);
+ }
+
+ Index m_outer;
+ Scalar m_factor;
+};
+
+namespace internal {
+template<typename Lhs, typename Rhs>
+struct traits<SparseTimeDenseProduct<Lhs,Rhs> >
+ : traits<ProductBase<SparseTimeDenseProduct<Lhs,Rhs>, Lhs, Rhs> >
+{
+ typedef Dense StorageKind;
+ typedef MatrixXpr XprKind;
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType,
+ int LhsStorageOrder = ((SparseLhsType::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor,
+ bool ColPerCol = ((DenseRhsType::Flags&RowMajorBit)==0) || DenseRhsType::ColsAtCompileTime==1>
+struct sparse_time_dense_product_impl;
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, RowMajor, true>
+{
+ typedef typename internal::remove_all<SparseLhsType>::type Lhs;
+ typedef typename internal::remove_all<DenseRhsType>::type Rhs;
+ typedef typename internal::remove_all<DenseResType>::type Res;
+ typedef typename Lhs::Index Index;
+ typedef typename Lhs::InnerIterator LhsInnerIterator;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ for(Index c=0; c<rhs.cols(); ++c)
+ {
+ Index n = lhs.outerSize();
+ for(Index j=0; j<n; ++j)
+ {
+ typename Res::Scalar tmp(0);
+ for(LhsInnerIterator it(lhs,j); it ;++it)
+ tmp += it.value() * rhs.coeff(it.index(),c);
+ res.coeffRef(j,c) += alpha * tmp;
+ }
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, ColMajor, true>
+{
+ typedef typename internal::remove_all<SparseLhsType>::type Lhs;
+ typedef typename internal::remove_all<DenseRhsType>::type Rhs;
+ typedef typename internal::remove_all<DenseResType>::type Res;
+ typedef typename Lhs::InnerIterator LhsInnerIterator;
+ typedef typename Lhs::Index Index;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ for(Index c=0; c<rhs.cols(); ++c)
+ {
+ for(Index j=0; j<lhs.outerSize(); ++j)
+ {
+ typename Res::Scalar rhs_j = alpha * rhs.coeff(j,c);
+ for(LhsInnerIterator it(lhs,j); it ;++it)
+ res.coeffRef(it.index(),c) += it.value() * rhs_j;
+ }
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, RowMajor, false>
+{
+ typedef typename internal::remove_all<SparseLhsType>::type Lhs;
+ typedef typename internal::remove_all<DenseRhsType>::type Rhs;
+ typedef typename internal::remove_all<DenseResType>::type Res;
+ typedef typename Lhs::InnerIterator LhsInnerIterator;
+ typedef typename Lhs::Index Index;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ for(Index j=0; j<lhs.outerSize(); ++j)
+ {
+ typename Res::RowXpr res_j(res.row(j));
+ for(LhsInnerIterator it(lhs,j); it ;++it)
+ res_j += (alpha*it.value()) * rhs.row(it.index());
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, ColMajor, false>
+{
+ typedef typename internal::remove_all<SparseLhsType>::type Lhs;
+ typedef typename internal::remove_all<DenseRhsType>::type Rhs;
+ typedef typename internal::remove_all<DenseResType>::type Res;
+ typedef typename Lhs::InnerIterator LhsInnerIterator;
+ typedef typename Lhs::Index Index;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ for(Index j=0; j<lhs.outerSize(); ++j)
+ {
+ typename Rhs::ConstRowXpr rhs_j(rhs.row(j));
+ for(LhsInnerIterator it(lhs,j); it ;++it)
+ res.row(it.index()) += (alpha*it.value()) * rhs_j;
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType,typename AlphaType>
+inline void sparse_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)
+{
+ sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType>::run(lhs, rhs, res, alpha);
+}
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class SparseTimeDenseProduct
+ : public ProductBase<SparseTimeDenseProduct<Lhs,Rhs>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(SparseTimeDenseProduct)
+
+ SparseTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ internal::sparse_time_dense_product(m_lhs, m_rhs, dest, alpha);
+ }
+
+ private:
+ SparseTimeDenseProduct& operator=(const SparseTimeDenseProduct&);
+};
+
+
+// dense = dense * sparse
+namespace internal {
+template<typename Lhs, typename Rhs>
+struct traits<DenseTimeSparseProduct<Lhs,Rhs> >
+ : traits<ProductBase<DenseTimeSparseProduct<Lhs,Rhs>, Lhs, Rhs> >
+{
+ typedef Dense StorageKind;
+};
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class DenseTimeSparseProduct
+ : public ProductBase<DenseTimeSparseProduct<Lhs,Rhs>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(DenseTimeSparseProduct)
+
+ DenseTimeSparseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ Transpose<const _LhsNested> lhs_t(m_lhs);
+ Transpose<const _RhsNested> rhs_t(m_rhs);
+ Transpose<Dest> dest_t(dest);
+ internal::sparse_time_dense_product(rhs_t, lhs_t, dest_t, alpha);
+ }
+
+ private:
+ DenseTimeSparseProduct& operator=(const DenseTimeSparseProduct&);
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEDENSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseDiagonalProduct.h b/Eigen/src/SparseCore/SparseDiagonalProduct.h
new file mode 100644
index 0000000..1bb590e
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDiagonalProduct.h
@@ -0,0 +1,196 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_DIAGONAL_PRODUCT_H
+#define EIGEN_SPARSE_DIAGONAL_PRODUCT_H
+
+namespace Eigen {
+
+// The product of a diagonal matrix with a sparse matrix can be easily
+// implemented using expression template.
+// We have two consider very different cases:
+// 1 - diag * row-major sparse
+// => each inner vector <=> scalar * sparse vector product
+// => so we can reuse CwiseUnaryOp::InnerIterator
+// 2 - diag * col-major sparse
+// => each inner vector <=> densevector * sparse vector cwise product
+// => again, we can reuse specialization of CwiseBinaryOp::InnerIterator
+// for that particular case
+// The two other cases are symmetric.
+
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct traits<SparseDiagonalProduct<Lhs, Rhs> >
+{
+ typedef typename remove_all<Lhs>::type _Lhs;
+ typedef typename remove_all<Rhs>::type _Rhs;
+ typedef typename _Lhs::Scalar Scalar;
+ typedef typename promote_index_type<typename traits<Lhs>::Index,
+ typename traits<Rhs>::Index>::type Index;
+ typedef Sparse StorageKind;
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = _Lhs::RowsAtCompileTime,
+ ColsAtCompileTime = _Rhs::ColsAtCompileTime,
+
+ MaxRowsAtCompileTime = _Lhs::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = _Rhs::MaxColsAtCompileTime,
+
+ SparseFlags = is_diagonal<_Lhs>::ret ? int(_Rhs::Flags) : int(_Lhs::Flags),
+ Flags = (SparseFlags&RowMajorBit),
+ CoeffReadCost = Dynamic
+ };
+};
+
+enum {SDP_IsDiagonal, SDP_IsSparseRowMajor, SDP_IsSparseColMajor};
+template<typename Lhs, typename Rhs, typename SparseDiagonalProductType, int RhsMode, int LhsMode>
+class sparse_diagonal_product_inner_iterator_selector;
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class SparseDiagonalProduct
+ : public SparseMatrixBase<SparseDiagonalProduct<Lhs,Rhs> >,
+ internal::no_assignment_operator
+{
+ typedef typename Lhs::Nested LhsNested;
+ typedef typename Rhs::Nested RhsNested;
+
+ typedef typename internal::remove_all<LhsNested>::type _LhsNested;
+ typedef typename internal::remove_all<RhsNested>::type _RhsNested;
+
+ enum {
+ LhsMode = internal::is_diagonal<_LhsNested>::ret ? internal::SDP_IsDiagonal
+ : (_LhsNested::Flags&RowMajorBit) ? internal::SDP_IsSparseRowMajor : internal::SDP_IsSparseColMajor,
+ RhsMode = internal::is_diagonal<_RhsNested>::ret ? internal::SDP_IsDiagonal
+ : (_RhsNested::Flags&RowMajorBit) ? internal::SDP_IsSparseRowMajor : internal::SDP_IsSparseColMajor
+ };
+
+ public:
+
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseDiagonalProduct)
+
+ typedef internal::sparse_diagonal_product_inner_iterator_selector
+ <_LhsNested,_RhsNested,SparseDiagonalProduct,LhsMode,RhsMode> InnerIterator;
+
+ // We do not want ReverseInnerIterator for diagonal-sparse products,
+ // but this dummy declaration is needed to make diag * sparse * diag compile.
+ class ReverseInnerIterator;
+
+ EIGEN_STRONG_INLINE SparseDiagonalProduct(const Lhs& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {
+ eigen_assert(lhs.cols() == rhs.rows() && "invalid sparse matrix * diagonal matrix product");
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_lhs.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_rhs.cols(); }
+
+ EIGEN_STRONG_INLINE const _LhsNested& lhs() const { return m_lhs; }
+ EIGEN_STRONG_INLINE const _RhsNested& rhs() const { return m_rhs; }
+
+ protected:
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+};
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
+class sparse_diagonal_product_inner_iterator_selector
+<Lhs,Rhs,SparseDiagonalProductType,SDP_IsDiagonal,SDP_IsSparseRowMajor>
+ : public CwiseUnaryOp<scalar_multiple_op<typename Lhs::Scalar>,const Rhs>::InnerIterator
+{
+ typedef typename CwiseUnaryOp<scalar_multiple_op<typename Lhs::Scalar>,const Rhs>::InnerIterator Base;
+ typedef typename Lhs::Index Index;
+ public:
+ inline sparse_diagonal_product_inner_iterator_selector(
+ const SparseDiagonalProductType& expr, Index outer)
+ : Base(expr.rhs()*(expr.lhs().diagonal().coeff(outer)), outer)
+ {}
+};
+
+template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
+class sparse_diagonal_product_inner_iterator_selector
+<Lhs,Rhs,SparseDiagonalProductType,SDP_IsDiagonal,SDP_IsSparseColMajor>
+ : public CwiseBinaryOp<
+ scalar_product_op<typename Lhs::Scalar>,
+ const typename Rhs::ConstInnerVectorReturnType,
+ const typename Lhs::DiagonalVectorType>::InnerIterator
+{
+ typedef typename CwiseBinaryOp<
+ scalar_product_op<typename Lhs::Scalar>,
+ const typename Rhs::ConstInnerVectorReturnType,
+ const typename Lhs::DiagonalVectorType>::InnerIterator Base;
+ typedef typename Lhs::Index Index;
+ Index m_outer;
+ public:
+ inline sparse_diagonal_product_inner_iterator_selector(
+ const SparseDiagonalProductType& expr, Index outer)
+ : Base(expr.rhs().innerVector(outer) .cwiseProduct(expr.lhs().diagonal()), 0), m_outer(outer)
+ {}
+
+ inline Index outer() const { return m_outer; }
+ inline Index col() const { return m_outer; }
+};
+
+template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
+class sparse_diagonal_product_inner_iterator_selector
+<Lhs,Rhs,SparseDiagonalProductType,SDP_IsSparseColMajor,SDP_IsDiagonal>
+ : public CwiseUnaryOp<scalar_multiple_op<typename Rhs::Scalar>,const Lhs>::InnerIterator
+{
+ typedef typename CwiseUnaryOp<scalar_multiple_op<typename Rhs::Scalar>,const Lhs>::InnerIterator Base;
+ typedef typename Lhs::Index Index;
+ public:
+ inline sparse_diagonal_product_inner_iterator_selector(
+ const SparseDiagonalProductType& expr, Index outer)
+ : Base(expr.lhs()*expr.rhs().diagonal().coeff(outer), outer)
+ {}
+};
+
+template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
+class sparse_diagonal_product_inner_iterator_selector
+<Lhs,Rhs,SparseDiagonalProductType,SDP_IsSparseRowMajor,SDP_IsDiagonal>
+ : public CwiseBinaryOp<
+ scalar_product_op<typename Rhs::Scalar>,
+ const typename Lhs::ConstInnerVectorReturnType,
+ const Transpose<const typename Rhs::DiagonalVectorType> >::InnerIterator
+{
+ typedef typename CwiseBinaryOp<
+ scalar_product_op<typename Rhs::Scalar>,
+ const typename Lhs::ConstInnerVectorReturnType,
+ const Transpose<const typename Rhs::DiagonalVectorType> >::InnerIterator Base;
+ typedef typename Lhs::Index Index;
+ Index m_outer;
+ public:
+ inline sparse_diagonal_product_inner_iterator_selector(
+ const SparseDiagonalProductType& expr, Index outer)
+ : Base(expr.lhs().innerVector(outer) .cwiseProduct(expr.rhs().diagonal().transpose()), 0), m_outer(outer)
+ {}
+
+ inline Index outer() const { return m_outer; }
+ inline Index row() const { return m_outer; }
+};
+
+} // end namespace internal
+
+// SparseMatrixBase functions
+
+template<typename Derived>
+template<typename OtherDerived>
+const SparseDiagonalProduct<Derived,OtherDerived>
+SparseMatrixBase<Derived>::operator*(const DiagonalBase<OtherDerived> &other) const
+{
+ return SparseDiagonalProduct<Derived,OtherDerived>(this->derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_DIAGONAL_PRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseDot.h b/Eigen/src/SparseCore/SparseDot.h
new file mode 100644
index 0000000..db39c9a
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDot.h
@@ -0,0 +1,101 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_DOT_H
+#define EIGEN_SPARSE_DOT_H
+
+namespace Eigen {
+
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(size() == other.size());
+ eigen_assert(other.size()>0 && "you are using a non initialized vector");
+
+ typename Derived::InnerIterator i(derived(),0);
+ Scalar res(0);
+ while (i)
+ {
+ res += numext::conj(i.value()) * other.coeff(i.index());
+ ++i;
+ }
+ return res;
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::dot(const SparseMatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(size() == other.size());
+
+ typedef typename Derived::Nested Nested;
+ typedef typename OtherDerived::Nested OtherNested;
+ typedef typename internal::remove_all<Nested>::type NestedCleaned;
+ typedef typename internal::remove_all<OtherNested>::type OtherNestedCleaned;
+
+ Nested nthis(derived());
+ OtherNested nother(other.derived());
+
+ typename NestedCleaned::InnerIterator i(nthis,0);
+ typename OtherNestedCleaned::InnerIterator j(nother,0);
+ Scalar res(0);
+ while (i && j)
+ {
+ if (i.index()==j.index())
+ {
+ res += numext::conj(i.value()) * j.value();
+ ++i; ++j;
+ }
+ else if (i.index()<j.index())
+ ++i;
+ else
+ ++j;
+ }
+ return res;
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::squaredNorm() const
+{
+ return numext::real((*this).cwiseAbs2().sum());
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::norm() const
+{
+ using std::sqrt;
+ return sqrt(squaredNorm());
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::blueNorm() const
+{
+ return internal::blueNorm_impl(*this);
+}
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_DOT_H
diff --git a/Eigen/src/SparseCore/SparseFuzzy.h b/Eigen/src/SparseCore/SparseFuzzy.h
new file mode 100644
index 0000000..45f36e9
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseFuzzy.h
@@ -0,0 +1,26 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_FUZZY_H
+#define EIGEN_SPARSE_FUZZY_H
+
+// template<typename Derived>
+// template<typename OtherDerived>
+// bool SparseMatrixBase<Derived>::isApprox(
+// const OtherDerived& other,
+// typename NumTraits<Scalar>::Real prec
+// ) const
+// {
+// const typename internal::nested<Derived,2>::type nested(derived());
+// const typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
+// return (nested - otherNested).cwise().abs2().sum()
+// <= prec * prec * (std::min)(nested.cwise().abs2().sum(), otherNested.cwise().abs2().sum());
+// }
+
+#endif // EIGEN_SPARSE_FUZZY_H
diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
new file mode 100644
index 0000000..ba5e3a9
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -0,0 +1,1259 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEMATRIX_H
+#define EIGEN_SPARSEMATRIX_H
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ *
+ * \class SparseMatrix
+ *
+ * \brief A versatible sparse matrix representation
+ *
+ * This class implements a more versatile variants of the common \em compressed row/column storage format.
+ * Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index.
+ * All the non zeros are stored in a single large buffer. Unlike the \em compressed format, there might be extra
+ * space inbetween the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero
+ * can be done with limited memory reallocation and copies.
+ *
+ * A call to the function makeCompressed() turns the matrix into the standard \em compressed format
+ * compatible with many library.
+ *
+ * More details on this storage sceheme are given in the \ref TutorialSparse "manual pages".
+ *
+ * \tparam _Scalar the scalar type, i.e. the type of the coefficients
+ * \tparam _Options Union of bit flags controlling the storage scheme. Currently the only possibility
+ * is ColMajor or RowMajor. The default is 0 which means column-major.
+ * \tparam _Index the type of the indices. It has to be a \b signed type (e.g., short, int, std::ptrdiff_t). Default is \c int.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_SPARSEMATRIX_PLUGIN.
+ */
+
+namespace internal {
+template<typename _Scalar, int _Options, typename _Index>
+struct traits<SparseMatrix<_Scalar, _Options, _Index> >
+{
+ typedef _Scalar Scalar;
+ typedef _Index Index;
+ typedef Sparse StorageKind;
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ Flags = _Options | NestByRefBit | LvalueBit,
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ SupportedAccessPatterns = InnerRandomAccessPattern
+ };
+};
+
+template<typename _Scalar, int _Options, typename _Index, int DiagIndex>
+struct traits<Diagonal<const SparseMatrix<_Scalar, _Options, _Index>, DiagIndex> >
+{
+ typedef SparseMatrix<_Scalar, _Options, _Index> MatrixType;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+
+ typedef _Scalar Scalar;
+ typedef Dense StorageKind;
+ typedef _Index Index;
+ typedef MatrixXpr XprKind;
+
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = 1,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = 1,
+ Flags = 0,
+ CoeffReadCost = _MatrixTypeNested::CoeffReadCost*10
+ };
+};
+
+} // end namespace internal
+
+template<typename _Scalar, int _Options, typename _Index>
+class SparseMatrix
+ : public SparseMatrixBase<SparseMatrix<_Scalar, _Options, _Index> >
+{
+ public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseMatrix)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, +=)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, -=)
+
+ typedef MappedSparseMatrix<Scalar,Flags> Map;
+ using Base::IsRowMajor;
+ typedef internal::CompressedStorage<Scalar,Index> Storage;
+ enum {
+ Options = _Options
+ };
+
+ protected:
+
+ typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;
+
+ Index m_outerSize;
+ Index m_innerSize;
+ Index* m_outerIndex;
+ Index* m_innerNonZeros; // optional, if null then the data is compressed
+ Storage m_data;
+
+ Eigen::Map<Matrix<Index,Dynamic,1> > innerNonZeros() { return Eigen::Map<Matrix<Index,Dynamic,1> >(m_innerNonZeros, m_innerNonZeros?m_outerSize:0); }
+ const Eigen::Map<const Matrix<Index,Dynamic,1> > innerNonZeros() const { return Eigen::Map<const Matrix<Index,Dynamic,1> >(m_innerNonZeros, m_innerNonZeros?m_outerSize:0); }
+
+ public:
+
+ /** \returns whether \c *this is in compressed form. */
+ inline bool isCompressed() const { return m_innerNonZeros==0; }
+
+ /** \returns the number of rows of the matrix */
+ inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
+ /** \returns the number of columns of the matrix */
+ inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
+
+ /** \returns the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major) */
+ inline Index innerSize() const { return m_innerSize; }
+ /** \returns the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major) */
+ inline Index outerSize() const { return m_outerSize; }
+
+ /** \returns a const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline const Scalar* valuePtr() const { return &m_data.value(0); }
+ /** \returns a non-const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline Scalar* valuePtr() { return &m_data.value(0); }
+
+ /** \returns a const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline const Index* innerIndexPtr() const { return &m_data.index(0); }
+ /** \returns a non-const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline Index* innerIndexPtr() { return &m_data.index(0); }
+
+ /** \returns a const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), innerIndexPtr() */
+ inline const Index* outerIndexPtr() const { return m_outerIndex; }
+ /** \returns a non-const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), innerIndexPtr() */
+ inline Index* outerIndexPtr() { return m_outerIndex; }
+
+ /** \returns a const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline const Index* innerNonZeroPtr() const { return m_innerNonZeros; }
+ /** \returns a non-const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline Index* innerNonZeroPtr() { return m_innerNonZeros; }
+
+ /** \internal */
+ inline Storage& data() { return m_data; }
+ /** \internal */
+ inline const Storage& data() const { return m_data; }
+
+ /** \returns the value of the matrix at position \a i, \a j
+ * This function returns Scalar(0) if the element is an explicit \em zero */
+ inline Scalar coeff(Index row, Index col) const
+ {
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+ Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
+ return m_data.atInRange(m_outerIndex[outer], end, inner);
+ }
+
+ /** \returns a non-const reference to the value of the matrix at position \a i, \a j
+ *
+ * If the element does not exist then it is inserted via the insert(Index,Index) function
+ * which itself turns the matrix into a non compressed form if that was not the case.
+ *
+ * This is a O(log(nnz_j)) operation (binary search) plus the cost of insert(Index,Index)
+ * function if the element does not already exist.
+ */
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = m_outerIndex[outer];
+ Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
+ eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
+ if(end<=start)
+ return insert(row,col);
+ const Index p = m_data.searchLowerIndex(start,end-1,inner);
+ if((p<end) && (m_data.index(p)==inner))
+ return m_data.value(p);
+ else
+ return insert(row,col);
+ }
+
+ /** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
+ * The non zero coefficient must \b not already exist.
+ *
+ * If the matrix \c *this is in compressed mode, then \c *this is turned into uncompressed
+ * mode while reserving room for 2 non zeros per inner vector. It is strongly recommended to first
+ * call reserve(const SizesType &) to reserve a more appropriate number of elements per
+ * inner vector that better match your scenario.
+ *
+ * This function performs a sorted insertion in O(1) if the elements of each inner vector are
+ * inserted in increasing inner index order, and in O(nnz_j) for a random insertion.
+ *
+ */
+ Scalar& insert(Index row, Index col)
+ {
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ if(isCompressed())
+ {
+ reserve(Matrix<Index,Dynamic,1>::Constant(outerSize(), 2));
+ }
+ return insertUncompressed(row,col);
+ }
+
+ public:
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ /** Removes all non zeros but keep allocated memory */
+ inline void setZero()
+ {
+ m_data.clear();
+ memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(Index));
+ if(m_innerNonZeros)
+ memset(m_innerNonZeros, 0, (m_outerSize)*sizeof(Index));
+ }
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const
+ {
+ if(m_innerNonZeros)
+ return innerNonZeros().sum();
+ return static_cast<Index>(m_data.size());
+ }
+
+ /** Preallocates \a reserveSize non zeros.
+ *
+ * Precondition: the matrix must be in compressed mode. */
+ inline void reserve(Index reserveSize)
+ {
+ eigen_assert(isCompressed() && "This function does not make sense in non compressed mode.");
+ m_data.reserve(reserveSize);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** Preallocates \a reserveSize[\c j] non zeros for each column (resp. row) \c j.
+ *
+ * This function turns the matrix in non-compressed mode */
+ template<class SizesType>
+ inline void reserve(const SizesType& reserveSizes);
+ #else
+ template<class SizesType>
+ inline void reserve(const SizesType& reserveSizes, const typename SizesType::value_type& enableif = typename SizesType::value_type())
+ {
+ EIGEN_UNUSED_VARIABLE(enableif);
+ reserveInnerVectors(reserveSizes);
+ }
+ template<class SizesType>
+ inline void reserve(const SizesType& reserveSizes, const typename SizesType::Scalar& enableif =
+ #if (!defined(_MSC_VER)) || (_MSC_VER>=1500) // MSVC 2005 fails to compile with this typename
+ typename
+ #endif
+ SizesType::Scalar())
+ {
+ EIGEN_UNUSED_VARIABLE(enableif);
+ reserveInnerVectors(reserveSizes);
+ }
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+ protected:
+ template<class SizesType>
+ inline void reserveInnerVectors(const SizesType& reserveSizes)
+ {
+ if(isCompressed())
+ {
+ std::size_t totalReserveSize = 0;
+ // turn the matrix into non-compressed mode
+ m_innerNonZeros = static_cast<Index*>(std::malloc(m_outerSize * sizeof(Index)));
+ if (!m_innerNonZeros) internal::throw_std_bad_alloc();
+
+ // temporarily use m_innerSizes to hold the new starting points.
+ Index* newOuterIndex = m_innerNonZeros;
+
+ Index count = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ newOuterIndex[j] = count;
+ count += reserveSizes[j] + (m_outerIndex[j+1]-m_outerIndex[j]);
+ totalReserveSize += reserveSizes[j];
+ }
+ m_data.reserve(totalReserveSize);
+ Index previousOuterIndex = m_outerIndex[m_outerSize];
+ for(Index j=m_outerSize-1; j>=0; --j)
+ {
+ Index innerNNZ = previousOuterIndex - m_outerIndex[j];
+ for(Index i=innerNNZ-1; i>=0; --i)
+ {
+ m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
+ m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
+ }
+ previousOuterIndex = m_outerIndex[j];
+ m_outerIndex[j] = newOuterIndex[j];
+ m_innerNonZeros[j] = innerNNZ;
+ }
+ m_outerIndex[m_outerSize] = m_outerIndex[m_outerSize-1] + m_innerNonZeros[m_outerSize-1] + reserveSizes[m_outerSize-1];
+
+ m_data.resize(m_outerIndex[m_outerSize]);
+ }
+ else
+ {
+ Index* newOuterIndex = static_cast<Index*>(std::malloc((m_outerSize+1)*sizeof(Index)));
+ if (!newOuterIndex) internal::throw_std_bad_alloc();
+
+ Index count = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ newOuterIndex[j] = count;
+ Index alreadyReserved = (m_outerIndex[j+1]-m_outerIndex[j]) - m_innerNonZeros[j];
+ Index toReserve = std::max<Index>(reserveSizes[j], alreadyReserved);
+ count += toReserve + m_innerNonZeros[j];
+ }
+ newOuterIndex[m_outerSize] = count;
+
+ m_data.resize(count);
+ for(Index j=m_outerSize-1; j>=0; --j)
+ {
+ Index offset = newOuterIndex[j] - m_outerIndex[j];
+ if(offset>0)
+ {
+ Index innerNNZ = m_innerNonZeros[j];
+ for(Index i=innerNNZ-1; i>=0; --i)
+ {
+ m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
+ m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
+ }
+ }
+ }
+
+ std::swap(m_outerIndex, newOuterIndex);
+ std::free(newOuterIndex);
+ }
+
+ }
+ public:
+
+ //--- low level purely coherent filling ---
+
+ /** \internal
+ * \returns a reference to the non zero coefficient at position \a row, \a col assuming that:
+ * - the nonzero does not already exist
+ * - the new coefficient is the last one according to the storage order
+ *
+ * Before filling a given inner vector you must call the statVec(Index) function.
+ *
+ * After an insertion session, you should call the finalize() function.
+ *
+ * \sa insert, insertBackByOuterInner, startVec */
+ inline Scalar& insertBack(Index row, Index col)
+ {
+ return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row);
+ }
+
+ /** \internal
+ * \sa insertBack, startVec */
+ inline Scalar& insertBackByOuterInner(Index outer, Index inner)
+ {
+ eigen_assert(size_t(m_outerIndex[outer+1]) == m_data.size() && "Invalid ordered insertion (invalid outer index)");
+ eigen_assert( (m_outerIndex[outer+1]-m_outerIndex[outer]==0 || m_data.index(m_data.size()-1)<inner) && "Invalid ordered insertion (invalid inner index)");
+ Index p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+ m_data.append(0, inner);
+ return m_data.value(p);
+ }
+
+ /** \internal
+ * \warning use it only if you know what you are doing */
+ inline Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)
+ {
+ Index p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+ m_data.append(0, inner);
+ return m_data.value(p);
+ }
+
+ /** \internal
+ * \sa insertBack, insertBackByOuterInner */
+ inline void startVec(Index outer)
+ {
+ eigen_assert(m_outerIndex[outer]==Index(m_data.size()) && "You must call startVec for each inner vector sequentially");
+ eigen_assert(m_outerIndex[outer+1]==0 && "You must call startVec for each inner vector sequentially");
+ m_outerIndex[outer+1] = m_outerIndex[outer];
+ }
+
+ /** \internal
+ * Must be called after inserting a set of non zero entries using the low level compressed API.
+ */
+ inline void finalize()
+ {
+ if(isCompressed())
+ {
+ Index size = static_cast<Index>(m_data.size());
+ Index i = m_outerSize;
+ // find the last filled column
+ while (i>=0 && m_outerIndex[i]==0)
+ --i;
+ ++i;
+ while (i<=m_outerSize)
+ {
+ m_outerIndex[i] = size;
+ ++i;
+ }
+ }
+ }
+
+ //---
+
+ template<typename InputIterators>
+ void setFromTriplets(const InputIterators& begin, const InputIterators& end);
+
+ void sumupDuplicates();
+
+ //---
+
+ /** \internal
+ * same as insert(Index,Index) except that the indices are given relative to the storage order */
+ Scalar& insertByOuterInner(Index j, Index i)
+ {
+ return insert(IsRowMajor ? j : i, IsRowMajor ? i : j);
+ }
+
+ /** Turns the matrix into the \em compressed format.
+ */
+ void makeCompressed()
+ {
+ if(isCompressed())
+ return;
+
+ Index oldStart = m_outerIndex[1];
+ m_outerIndex[1] = m_innerNonZeros[0];
+ for(Index j=1; j<m_outerSize; ++j)
+ {
+ Index nextOldStart = m_outerIndex[j+1];
+ Index offset = oldStart - m_outerIndex[j];
+ if(offset>0)
+ {
+ for(Index k=0; k<m_innerNonZeros[j]; ++k)
+ {
+ m_data.index(m_outerIndex[j]+k) = m_data.index(oldStart+k);
+ m_data.value(m_outerIndex[j]+k) = m_data.value(oldStart+k);
+ }
+ }
+ m_outerIndex[j+1] = m_outerIndex[j] + m_innerNonZeros[j];
+ oldStart = nextOldStart;
+ }
+ std::free(m_innerNonZeros);
+ m_innerNonZeros = 0;
+ m_data.resize(m_outerIndex[m_outerSize]);
+ m_data.squeeze();
+ }
+
+ /** Turns the matrix into the uncompressed mode */
+ void uncompress()
+ {
+ if(m_innerNonZeros != 0)
+ return;
+ m_innerNonZeros = static_cast<Index*>(std::malloc(m_outerSize * sizeof(Index)));
+ for (Index i = 0; i < m_outerSize; i++)
+ {
+ m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i];
+ }
+ }
+
+ /** Suppresses all nonzeros which are \b much \b smaller \b than \a reference under the tolerence \a epsilon */
+ void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())
+ {
+ prune(default_prunning_func(reference,epsilon));
+ }
+
+ /** Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate \a keep.
+ * The functor type \a KeepFunc must implement the following function:
+ * \code
+ * bool operator() (const Index& row, const Index& col, const Scalar& value) const;
+ * \endcode
+ * \sa prune(Scalar,RealScalar)
+ */
+ template<typename KeepFunc>
+ void prune(const KeepFunc& keep = KeepFunc())
+ {
+ // TODO optimize the uncompressed mode to avoid moving and allocating the data twice
+ // TODO also implement a unit test
+ makeCompressed();
+
+ Index k = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ Index previousStart = m_outerIndex[j];
+ m_outerIndex[j] = k;
+ Index end = m_outerIndex[j+1];
+ for(Index i=previousStart; i<end; ++i)
+ {
+ if(keep(IsRowMajor?j:m_data.index(i), IsRowMajor?m_data.index(i):j, m_data.value(i)))
+ {
+ m_data.value(k) = m_data.value(i);
+ m_data.index(k) = m_data.index(i);
+ ++k;
+ }
+ }
+ }
+ m_outerIndex[m_outerSize] = k;
+ m_data.resize(k,0);
+ }
+
+ /** Resizes the matrix to a \a rows x \a cols matrix leaving old values untouched.
+ * \sa resizeNonZeros(Index), reserve(), setZero()
+ */
+ void conservativeResize(Index rows, Index cols)
+ {
+ // No change
+ if (this->rows() == rows && this->cols() == cols) return;
+
+ // If one dimension is null, then there is nothing to be preserved
+ if(rows==0 || cols==0) return resize(rows,cols);
+
+ Index innerChange = IsRowMajor ? cols - this->cols() : rows - this->rows();
+ Index outerChange = IsRowMajor ? rows - this->rows() : cols - this->cols();
+ Index newInnerSize = IsRowMajor ? cols : rows;
+
+ // Deals with inner non zeros
+ if (m_innerNonZeros)
+ {
+ // Resize m_innerNonZeros
+ Index *newInnerNonZeros = static_cast<Index*>(std::realloc(m_innerNonZeros, (m_outerSize + outerChange) * sizeof(Index)));
+ if (!newInnerNonZeros) internal::throw_std_bad_alloc();
+ m_innerNonZeros = newInnerNonZeros;
+
+ for(Index i=m_outerSize; i<m_outerSize+outerChange; i++)
+ m_innerNonZeros[i] = 0;
+ }
+ else if (innerChange < 0)
+ {
+ // Inner size decreased: allocate a new m_innerNonZeros
+ m_innerNonZeros = static_cast<Index*>(std::malloc((m_outerSize+outerChange+1) * sizeof(Index)));
+ if (!m_innerNonZeros) internal::throw_std_bad_alloc();
+ for(Index i = 0; i < m_outerSize; i++)
+ m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i];
+ }
+
+ // Change the m_innerNonZeros in case of a decrease of inner size
+ if (m_innerNonZeros && innerChange < 0)
+ {
+ for(Index i = 0; i < m_outerSize + (std::min)(outerChange, Index(0)); i++)
+ {
+ Index &n = m_innerNonZeros[i];
+ Index start = m_outerIndex[i];
+ while (n > 0 && m_data.index(start+n-1) >= newInnerSize) --n;
+ }
+ }
+
+ m_innerSize = newInnerSize;
+
+ // Re-allocate outer index structure if necessary
+ if (outerChange == 0)
+ return;
+
+ Index *newOuterIndex = static_cast<Index*>(std::realloc(m_outerIndex, (m_outerSize + outerChange + 1) * sizeof(Index)));
+ if (!newOuterIndex) internal::throw_std_bad_alloc();
+ m_outerIndex = newOuterIndex;
+ if (outerChange > 0)
+ {
+ Index last = m_outerSize == 0 ? 0 : m_outerIndex[m_outerSize];
+ for(Index i=m_outerSize; i<m_outerSize+outerChange+1; i++)
+ m_outerIndex[i] = last;
+ }
+ m_outerSize += outerChange;
+ }
+
+ /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero.
+ * \sa resizeNonZeros(Index), reserve(), setZero()
+ */
+ void resize(Index rows, Index cols)
+ {
+ const Index outerSize = IsRowMajor ? rows : cols;
+ m_innerSize = IsRowMajor ? cols : rows;
+ m_data.clear();
+ if (m_outerSize != outerSize || m_outerSize==0)
+ {
+ std::free(m_outerIndex);
+ m_outerIndex = static_cast<Index*>(std::malloc((outerSize + 1) * sizeof(Index)));
+ if (!m_outerIndex) internal::throw_std_bad_alloc();
+
+ m_outerSize = outerSize;
+ }
+ if(m_innerNonZeros)
+ {
+ std::free(m_innerNonZeros);
+ m_innerNonZeros = 0;
+ }
+ memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(Index));
+ }
+
+ /** \internal
+ * Resize the nonzero vector to \a size */
+ void resizeNonZeros(Index size)
+ {
+ // TODO remove this function
+ m_data.resize(size);
+ }
+
+ /** \returns a const expression of the diagonal coefficients */
+ const Diagonal<const SparseMatrix> diagonal() const { return *this; }
+
+ /** Default constructor yielding an empty \c 0 \c x \c 0 matrix */
+ inline SparseMatrix()
+ : m_outerSize(-1), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ check_template_parameters();
+ resize(0, 0);
+ }
+
+ /** Constructs a \a rows \c x \a cols empty matrix */
+ inline SparseMatrix(Index rows, Index cols)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ check_template_parameters();
+ resize(rows, cols);
+ }
+
+ /** Constructs a sparse matrix from the sparse expression \a other */
+ template<typename OtherDerived>
+ inline SparseMatrix(const SparseMatrixBase<OtherDerived>& other)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ check_template_parameters();
+ *this = other.derived();
+ }
+
+ /** Constructs a sparse matrix from the sparse selfadjoint view \a other */
+ template<typename OtherDerived, unsigned int UpLo>
+ inline SparseMatrix(const SparseSelfAdjointView<OtherDerived, UpLo>& other)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ check_template_parameters();
+ *this = other;
+ }
+
+ /** Copy constructor (it performs a deep copy) */
+ inline SparseMatrix(const SparseMatrix& other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ check_template_parameters();
+ *this = other.derived();
+ }
+
+ /** \brief Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ SparseMatrix(const ReturnByValue<OtherDerived>& other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ check_template_parameters();
+ initAssignment(other);
+ other.evalTo(*this);
+ }
+
+ /** Swaps the content of two sparse matrices of the same type.
+ * This is a fast operation that simply swaps the underlying pointers and parameters. */
+ inline void swap(SparseMatrix& other)
+ {
+ //EIGEN_DBG_SPARSE(std::cout << "SparseMatrix:: swap\n");
+ std::swap(m_outerIndex, other.m_outerIndex);
+ std::swap(m_innerSize, other.m_innerSize);
+ std::swap(m_outerSize, other.m_outerSize);
+ std::swap(m_innerNonZeros, other.m_innerNonZeros);
+ m_data.swap(other.m_data);
+ }
+
+ /** Sets *this to the identity matrix */
+ inline void setIdentity()
+ {
+ eigen_assert(rows() == cols() && "ONLY FOR SQUARED MATRICES");
+ this->m_data.resize(rows());
+ Eigen::Map<Matrix<Index, Dynamic, 1> >(&this->m_data.index(0), rows()).setLinSpaced(0, rows()-1);
+ Eigen::Map<Matrix<Scalar, Dynamic, 1> >(&this->m_data.value(0), rows()).setOnes();
+ Eigen::Map<Matrix<Index, Dynamic, 1> >(this->m_outerIndex, rows()+1).setLinSpaced(0, rows());
+ }
+ inline SparseMatrix& operator=(const SparseMatrix& other)
+ {
+ if (other.isRValue())
+ {
+ swap(other.const_cast_derived());
+ }
+ else if(this!=&other)
+ {
+ initAssignment(other);
+ if(other.isCompressed())
+ {
+ memcpy(m_outerIndex, other.m_outerIndex, (m_outerSize+1)*sizeof(Index));
+ m_data = other.m_data;
+ }
+ else
+ {
+ Base::operator=(other);
+ }
+ }
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Lhs, typename Rhs>
+ inline SparseMatrix& operator=(const SparseSparseProduct<Lhs,Rhs>& product)
+ { return Base::operator=(product); }
+
+ template<typename OtherDerived>
+ inline SparseMatrix& operator=(const ReturnByValue<OtherDerived>& other)
+ {
+ initAssignment(other);
+ return Base::operator=(other.derived());
+ }
+
+ template<typename OtherDerived>
+ inline SparseMatrix& operator=(const EigenBase<OtherDerived>& other)
+ { return Base::operator=(other.derived()); }
+ #endif
+
+ template<typename OtherDerived>
+ EIGEN_DONT_INLINE SparseMatrix& operator=(const SparseMatrixBase<OtherDerived>& other);
+
+ friend std::ostream & operator << (std::ostream & s, const SparseMatrix& m)
+ {
+ EIGEN_DBG_SPARSE(
+ s << "Nonzero entries:\n";
+ if(m.isCompressed())
+ for (Index i=0; i<m.nonZeros(); ++i)
+ s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
+ else
+ for (Index i=0; i<m.outerSize(); ++i)
+ {
+ Index p = m.m_outerIndex[i];
+ Index pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];
+ Index k=p;
+ for (; k<pe; ++k)
+ s << "(" << m.m_data.value(k) << "," << m.m_data.index(k) << ") ";
+ for (; k<m.m_outerIndex[i+1]; ++k)
+ s << "(_,_) ";
+ }
+ s << std::endl;
+ s << std::endl;
+ s << "Outer pointers:\n";
+ for (Index i=0; i<m.outerSize(); ++i)
+ s << m.m_outerIndex[i] << " ";
+ s << " $" << std::endl;
+ if(!m.isCompressed())
+ {
+ s << "Inner non zeros:\n";
+ for (Index i=0; i<m.outerSize(); ++i)
+ s << m.m_innerNonZeros[i] << " ";
+ s << " $" << std::endl;
+ }
+ s << std::endl;
+ );
+ s << static_cast<const SparseMatrixBase<SparseMatrix>&>(m);
+ return s;
+ }
+
+ /** Destructor */
+ inline ~SparseMatrix()
+ {
+ std::free(m_outerIndex);
+ std::free(m_innerNonZeros);
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** Overloaded for performance */
+ Scalar sum() const;
+#endif
+
+# ifdef EIGEN_SPARSEMATRIX_PLUGIN
+# include EIGEN_SPARSEMATRIX_PLUGIN
+# endif
+
+protected:
+
+ template<typename Other>
+ void initAssignment(const Other& other)
+ {
+ resize(other.rows(), other.cols());
+ if(m_innerNonZeros)
+ {
+ std::free(m_innerNonZeros);
+ m_innerNonZeros = 0;
+ }
+ }
+
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_DONT_INLINE Scalar& insertCompressed(Index row, Index col);
+
+ /** \internal
+ * A vector object that is equal to 0 everywhere but v at the position i */
+ class SingletonVector
+ {
+ Index m_index;
+ Index m_value;
+ public:
+ typedef Index value_type;
+ SingletonVector(Index i, Index v)
+ : m_index(i), m_value(v)
+ {}
+
+ Index operator[](Index i) const { return i==m_index ? m_value : 0; }
+ };
+
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_DONT_INLINE Scalar& insertUncompressed(Index row, Index col);
+
+public:
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_STRONG_INLINE Scalar& insertBackUncompressed(Index row, Index col)
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(!isCompressed());
+ eigen_assert(m_innerNonZeros[outer]<=(m_outerIndex[outer+1] - m_outerIndex[outer]));
+
+ Index p = m_outerIndex[outer] + m_innerNonZeros[outer]++;
+ m_data.index(p) = inner;
+ return (m_data.value(p) = 0);
+ }
+
+private:
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT(NumTraits<Index>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);
+ EIGEN_STATIC_ASSERT((Options&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS);
+ }
+
+ struct default_prunning_func {
+ default_prunning_func(const Scalar& ref, const RealScalar& eps) : reference(ref), epsilon(eps) {}
+ inline bool operator() (const Index&, const Index&, const Scalar& value) const
+ {
+ return !internal::isMuchSmallerThan(value, reference, epsilon);
+ }
+ Scalar reference;
+ RealScalar epsilon;
+ };
+};
+
+template<typename Scalar, int _Options, typename _Index>
+class SparseMatrix<Scalar,_Options,_Index>::InnerIterator
+{
+ public:
+ InnerIterator(const SparseMatrix& mat, Index outer)
+ : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer), m_id(mat.m_outerIndex[outer])
+ {
+ if(mat.isCompressed())
+ m_end = mat.m_outerIndex[outer+1];
+ else
+ m_end = m_id + mat.m_innerNonZeros[outer];
+ }
+
+ inline InnerIterator& operator++() { m_id++; return *this; }
+
+ inline const Scalar& value() const { return m_values[m_id]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id]); }
+
+ inline Index index() const { return m_indices[m_id]; }
+ inline Index outer() const { return m_outer; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ inline operator bool() const { return (m_id < m_end); }
+
+ protected:
+ const Scalar* m_values;
+ const Index* m_indices;
+ const Index m_outer;
+ Index m_id;
+ Index m_end;
+};
+
+template<typename Scalar, int _Options, typename _Index>
+class SparseMatrix<Scalar,_Options,_Index>::ReverseInnerIterator
+{
+ public:
+ ReverseInnerIterator(const SparseMatrix& mat, Index outer)
+ : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer), m_start(mat.m_outerIndex[outer])
+ {
+ if(mat.isCompressed())
+ m_id = mat.m_outerIndex[outer+1];
+ else
+ m_id = m_start + mat.m_innerNonZeros[outer];
+ }
+
+ inline ReverseInnerIterator& operator--() { --m_id; return *this; }
+
+ inline const Scalar& value() const { return m_values[m_id-1]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id-1]); }
+
+ inline Index index() const { return m_indices[m_id-1]; }
+ inline Index outer() const { return m_outer; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ inline operator bool() const { return (m_id > m_start); }
+
+ protected:
+ const Scalar* m_values;
+ const Index* m_indices;
+ const Index m_outer;
+ Index m_id;
+ const Index m_start;
+};
+
+namespace internal {
+
+template<typename InputIterator, typename SparseMatrixType>
+void set_from_triplets(const InputIterator& begin, const InputIterator& end, SparseMatrixType& mat, int Options = 0)
+{
+ EIGEN_UNUSED_VARIABLE(Options);
+ enum { IsRowMajor = SparseMatrixType::IsRowMajor };
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::Index Index;
+ SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor,Index> trMat(mat.rows(),mat.cols());
+
+ if(begin!=end)
+ {
+ // pass 1: count the nnz per inner-vector
+ Matrix<Index,Dynamic,1> wi(trMat.outerSize());
+ wi.setZero();
+ for(InputIterator it(begin); it!=end; ++it)
+ {
+ eigen_assert(it->row()>=0 && it->row()<mat.rows() && it->col()>=0 && it->col()<mat.cols());
+ wi(IsRowMajor ? it->col() : it->row())++;
+ }
+
+ // pass 2: insert all the elements into trMat
+ trMat.reserve(wi);
+ for(InputIterator it(begin); it!=end; ++it)
+ trMat.insertBackUncompressed(it->row(),it->col()) = it->value();
+
+ // pass 3:
+ trMat.sumupDuplicates();
+ }
+
+ // pass 4: transposed copy -> implicit sorting
+ mat = trMat;
+}
+
+}
+
+
+/** Fill the matrix \c *this with the list of \em triplets defined by the iterator range \a begin - \a end.
+ *
+ * A \em triplet is a tuple (i,j,value) defining a non-zero element.
+ * The input list of triplets does not have to be sorted, and can contains duplicated elements.
+ * In any case, the result is a \b sorted and \b compressed sparse matrix where the duplicates have been summed up.
+ * This is a \em O(n) operation, with \em n the number of triplet elements.
+ * The initial contents of \c *this is destroyed.
+ * The matrix \c *this must be properly resized beforehand using the SparseMatrix(Index,Index) constructor,
+ * or the resize(Index,Index) method. The sizes are not extracted from the triplet list.
+ *
+ * The \a InputIterators value_type must provide the following interface:
+ * \code
+ * Scalar value() const; // the value
+ * Scalar row() const; // the row index i
+ * Scalar col() const; // the column index j
+ * \endcode
+ * See for instance the Eigen::Triplet template class.
+ *
+ * Here is a typical usage example:
+ * \code
+ typedef Triplet<double> T;
+ std::vector<T> tripletList;
+ triplets.reserve(estimation_of_entries);
+ for(...)
+ {
+ // ...
+ tripletList.push_back(T(i,j,v_ij));
+ }
+ SparseMatrixType m(rows,cols);
+ m.setFromTriplets(tripletList.begin(), tripletList.end());
+ // m is ready to go!
+ * \endcode
+ *
+ * \warning The list of triplets is read multiple times (at least twice). Therefore, it is not recommended to define
+ * an abstract iterator over a complex data-structure that would be expensive to evaluate. The triplets should rather
+ * be explicitely stored into a std::vector for instance.
+ */
+template<typename Scalar, int _Options, typename _Index>
+template<typename InputIterators>
+void SparseMatrix<Scalar,_Options,_Index>::setFromTriplets(const InputIterators& begin, const InputIterators& end)
+{
+ internal::set_from_triplets(begin, end, *this);
+}
+
+/** \internal */
+template<typename Scalar, int _Options, typename _Index>
+void SparseMatrix<Scalar,_Options,_Index>::sumupDuplicates()
+{
+ eigen_assert(!isCompressed());
+ // TODO, in practice we should be able to use m_innerNonZeros for that task
+ Matrix<Index,Dynamic,1> wi(innerSize());
+ wi.fill(-1);
+ Index count = 0;
+ // for each inner-vector, wi[inner_index] will hold the position of first element into the index/value buffers
+ for(Index j=0; j<outerSize(); ++j)
+ {
+ Index start = count;
+ Index oldEnd = m_outerIndex[j]+m_innerNonZeros[j];
+ for(Index k=m_outerIndex[j]; k<oldEnd; ++k)
+ {
+ Index i = m_data.index(k);
+ if(wi(i)>=start)
+ {
+ // we already meet this entry => accumulate it
+ m_data.value(wi(i)) += m_data.value(k);
+ }
+ else
+ {
+ m_data.value(count) = m_data.value(k);
+ m_data.index(count) = m_data.index(k);
+ wi(i) = count;
+ ++count;
+ }
+ }
+ m_outerIndex[j] = start;
+ }
+ m_outerIndex[m_outerSize] = count;
+
+ // turn the matrix into compressed form
+ std::free(m_innerNonZeros);
+ m_innerNonZeros = 0;
+ m_data.resize(m_outerIndex[m_outerSize]);
+}
+
+template<typename Scalar, int _Options, typename _Index>
+template<typename OtherDerived>
+EIGEN_DONT_INLINE SparseMatrix<Scalar,_Options,_Index>& SparseMatrix<Scalar,_Options,_Index>::operator=(const SparseMatrixBase<OtherDerived>& other)
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
+ if (needToTranspose)
+ {
+ // two passes algorithm:
+ // 1 - compute the number of coeffs per dest inner vector
+ // 2 - do the actual copy/eval
+ // Since each coeff of the rhs has to be evaluated twice, let's evaluate it if needed
+ typedef typename internal::nested<OtherDerived,2>::type OtherCopy;
+ typedef typename internal::remove_all<OtherCopy>::type _OtherCopy;
+ OtherCopy otherCopy(other.derived());
+
+ SparseMatrix dest(other.rows(),other.cols());
+ Eigen::Map<Matrix<Index, Dynamic, 1> > (dest.m_outerIndex,dest.outerSize()).setZero();
+
+ // pass 1
+ // FIXME the above copy could be merged with that pass
+ for (Index j=0; j<otherCopy.outerSize(); ++j)
+ for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
+ ++dest.m_outerIndex[it.index()];
+
+ // prefix sum
+ Index count = 0;
+ Matrix<Index,Dynamic,1> positions(dest.outerSize());
+ for (Index j=0; j<dest.outerSize(); ++j)
+ {
+ Index tmp = dest.m_outerIndex[j];
+ dest.m_outerIndex[j] = count;
+ positions[j] = count;
+ count += tmp;
+ }
+ dest.m_outerIndex[dest.outerSize()] = count;
+ // alloc
+ dest.m_data.resize(count);
+ // pass 2
+ for (Index j=0; j<otherCopy.outerSize(); ++j)
+ {
+ for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
+ {
+ Index pos = positions[it.index()]++;
+ dest.m_data.index(pos) = j;
+ dest.m_data.value(pos) = it.value();
+ }
+ }
+ this->swap(dest);
+ return *this;
+ }
+ else
+ {
+ if(other.isRValue())
+ initAssignment(other.derived());
+ // there is no special optimization
+ return Base::operator=(other.derived());
+ }
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+EIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_Index>::Scalar& SparseMatrix<_Scalar,_Options,_Index>::insertUncompressed(Index row, Index col)
+{
+ eigen_assert(!isCompressed());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index room = m_outerIndex[outer+1] - m_outerIndex[outer];
+ Index innerNNZ = m_innerNonZeros[outer];
+ if(innerNNZ>=room)
+ {
+ // this inner vector is full, we need to reallocate the whole buffer :(
+ reserve(SingletonVector(outer,std::max<Index>(2,innerNNZ)));
+ }
+
+ Index startId = m_outerIndex[outer];
+ Index p = startId + m_innerNonZeros[outer];
+ while ( (p > startId) && (m_data.index(p-1) > inner) )
+ {
+ m_data.index(p) = m_data.index(p-1);
+ m_data.value(p) = m_data.value(p-1);
+ --p;
+ }
+ eigen_assert((p<=startId || m_data.index(p-1)!=inner) && "you cannot insert an element that already exist, you must call coeffRef to this end");
+
+ m_innerNonZeros[outer]++;
+
+ m_data.index(p) = inner;
+ return (m_data.value(p) = 0);
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+EIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_Index>::Scalar& SparseMatrix<_Scalar,_Options,_Index>::insertCompressed(Index row, Index col)
+{
+ eigen_assert(isCompressed());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index previousOuter = outer;
+ if (m_outerIndex[outer+1]==0)
+ {
+ // we start a new inner vector
+ while (previousOuter>=0 && m_outerIndex[previousOuter]==0)
+ {
+ m_outerIndex[previousOuter] = static_cast<Index>(m_data.size());
+ --previousOuter;
+ }
+ m_outerIndex[outer+1] = m_outerIndex[outer];
+ }
+
+ // here we have to handle the tricky case where the outerIndex array
+ // starts with: [ 0 0 0 0 0 1 ...] and we are inserted in, e.g.,
+ // the 2nd inner vector...
+ bool isLastVec = (!(previousOuter==-1 && m_data.size()!=0))
+ && (size_t(m_outerIndex[outer+1]) == m_data.size());
+
+ size_t startId = m_outerIndex[outer];
+ // FIXME let's make sure sizeof(long int) == sizeof(size_t)
+ size_t p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+
+ double reallocRatio = 1;
+ if (m_data.allocatedSize()<=m_data.size())
+ {
+ // if there is no preallocated memory, let's reserve a minimum of 32 elements
+ if (m_data.size()==0)
+ {
+ m_data.reserve(32);
+ }
+ else
+ {
+ // we need to reallocate the data, to reduce multiple reallocations
+ // we use a smart resize algorithm based on the current filling ratio
+ // in addition, we use double to avoid integers overflows
+ double nnzEstimate = double(m_outerIndex[outer])*double(m_outerSize)/double(outer+1);
+ reallocRatio = (nnzEstimate-double(m_data.size()))/double(m_data.size());
+ // furthermore we bound the realloc ratio to:
+ // 1) reduce multiple minor realloc when the matrix is almost filled
+ // 2) avoid to allocate too much memory when the matrix is almost empty
+ reallocRatio = (std::min)((std::max)(reallocRatio,1.5),8.);
+ }
+ }
+ m_data.resize(m_data.size()+1,reallocRatio);
+
+ if (!isLastVec)
+ {
+ if (previousOuter==-1)
+ {
+ // oops wrong guess.
+ // let's correct the outer offsets
+ for (Index k=0; k<=(outer+1); ++k)
+ m_outerIndex[k] = 0;
+ Index k=outer+1;
+ while(m_outerIndex[k]==0)
+ m_outerIndex[k++] = 1;
+ while (k<=m_outerSize && m_outerIndex[k]!=0)
+ m_outerIndex[k++]++;
+ p = 0;
+ --k;
+ k = m_outerIndex[k]-1;
+ while (k>0)
+ {
+ m_data.index(k) = m_data.index(k-1);
+ m_data.value(k) = m_data.value(k-1);
+ k--;
+ }
+ }
+ else
+ {
+ // we are not inserting into the last inner vec
+ // update outer indices:
+ Index j = outer+2;
+ while (j<=m_outerSize && m_outerIndex[j]!=0)
+ m_outerIndex[j++]++;
+ --j;
+ // shift data of last vecs:
+ Index k = m_outerIndex[j]-1;
+ while (k>=Index(p))
+ {
+ m_data.index(k) = m_data.index(k-1);
+ m_data.value(k) = m_data.value(k-1);
+ k--;
+ }
+ }
+ }
+
+ while ( (p > startId) && (m_data.index(p-1) > inner) )
+ {
+ m_data.index(p) = m_data.index(p-1);
+ m_data.value(p) = m_data.value(p-1);
+ --p;
+ }
+
+ m_data.index(p) = inner;
+ return (m_data.value(p) = 0);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEMATRIX_H
diff --git a/Eigen/src/SparseCore/SparseMatrixBase.h b/Eigen/src/SparseCore/SparseMatrixBase.h
new file mode 100644
index 0000000..6b2169a
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseMatrixBase.h
@@ -0,0 +1,454 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEMATRIXBASE_H
+#define EIGEN_SPARSEMATRIXBASE_H
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ *
+ * \class SparseMatrixBase
+ *
+ * \brief Base class of any sparse matrices or sparse expressions
+ *
+ * \tparam Derived
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_SPARSEMATRIXBASE_PLUGIN.
+ */
+template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
+{
+ public:
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Index Index;
+ typedef typename internal::add_const_on_value_type_if_arithmetic<
+ typename internal::packet_traits<Scalar>::type
+ >::type PacketReturnType;
+
+ typedef SparseMatrixBase StorageBaseType;
+ typedef EigenBase<Derived> Base;
+
+ template<typename OtherDerived>
+ Derived& operator=(const EigenBase<OtherDerived> &other)
+ {
+ other.derived().evalTo(derived());
+ return derived();
+ }
+
+ enum {
+
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ /**< The number of rows at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ /**< The number of columns at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+ SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+
+ MaxSizeAtCompileTime = (internal::size_at_compile_time<MaxRowsAtCompileTime,
+ MaxColsAtCompileTime>::ret),
+
+ IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
+ /**< This is set to true if either the number of rows or the number of
+ * columns is known at compile-time to be equal to 1. Indeed, in that case,
+ * we are dealing with a column-vector (if there is only one column) or with
+ * a row-vector (if there is only one row). */
+
+ Flags = internal::traits<Derived>::Flags,
+ /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+ * constructed from this one. See the \ref flags "list of flags".
+ */
+
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ /**< This is a rough measure of how expensive it is to read one coefficient from
+ * this expression.
+ */
+
+ IsRowMajor = Flags&RowMajorBit ? 1 : 0,
+
+ InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
+ : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ _HasDirectAccess = (int(Flags)&DirectAccessBit) ? 1 : 0 // workaround sunCC
+ #endif
+ };
+
+ /** \internal the return type of MatrixBase::adjoint() */
+ typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, Eigen::Transpose<const Derived> >,
+ Transpose<const Derived>
+ >::type AdjointReturnType;
+
+
+ typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor, Index> PlainObject;
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is the "real scalar" type; if the \a Scalar type is already real numbers
+ * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
+ * \a Scalar is \a std::complex<T> then RealScalar is \a T.
+ *
+ * \sa class NumTraits
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** \internal the return type of coeff()
+ */
+ typedef typename internal::conditional<_HasDirectAccess, const Scalar&, Scalar>::type CoeffReturnType;
+
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Matrix<Scalar,Dynamic,Dynamic> > ConstantReturnType;
+
+ /** type of the equivalent square matrix */
+ typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
+ EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
+
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+ inline Derived& const_cast_derived() const
+ { return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::SparseMatrixBase
+# include "../plugins/CommonCwiseUnaryOps.h"
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# include "../plugins/BlockMethods.h"
+# ifdef EIGEN_SPARSEMATRIXBASE_PLUGIN
+# include EIGEN_SPARSEMATRIXBASE_PLUGIN
+# endif
+# undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+ /** \returns the number of rows. \sa cols() */
+ inline Index rows() const { return derived().rows(); }
+ /** \returns the number of columns. \sa rows() */
+ inline Index cols() const { return derived().cols(); }
+ /** \returns the number of coefficients, which is \a rows()*cols().
+ * \sa rows(), cols(). */
+ inline Index size() const { return rows() * cols(); }
+ /** \returns the number of nonzero coefficients which is in practice the number
+ * of stored coefficients. */
+ inline Index nonZeros() const { return derived().nonZeros(); }
+ /** \returns true if either the number of rows or the number of columns is equal to 1.
+ * In other words, this function returns
+ * \code rows()==1 || cols()==1 \endcode
+ * \sa rows(), cols(), IsVectorAtCompileTime. */
+ inline bool isVector() const { return rows()==1 || cols()==1; }
+ /** \returns the size of the storage major dimension,
+ * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
+ Index outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }
+ /** \returns the size of the inner dimension according to the storage order,
+ * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
+ Index innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
+
+ bool isRValue() const { return m_isRValue; }
+ Derived& markAsRValue() { m_isRValue = true; return derived(); }
+
+ SparseMatrixBase() : m_isRValue(false) { /* TODO check flags */ }
+
+
+ template<typename OtherDerived>
+ Derived& operator=(const ReturnByValue<OtherDerived>& other)
+ {
+ other.evalTo(derived());
+ return derived();
+ }
+
+
+ template<typename OtherDerived>
+ inline Derived& operator=(const SparseMatrixBase<OtherDerived>& other)
+ {
+ return assign(other.derived());
+ }
+
+ inline Derived& operator=(const Derived& other)
+ {
+// if (other.isRValue())
+// derived().swap(other.const_cast_derived());
+// else
+ return assign(other.derived());
+ }
+
+ protected:
+
+ template<typename OtherDerived>
+ inline Derived& assign(const OtherDerived& other)
+ {
+ const bool transpose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
+ const Index outerSize = (int(OtherDerived::Flags) & RowMajorBit) ? other.rows() : other.cols();
+ if ((!transpose) && other.isRValue())
+ {
+ // eval without temporary
+ derived().resize(other.rows(), other.cols());
+ derived().setZero();
+ derived().reserve((std::max)(this->rows(),this->cols())*2);
+ for (Index j=0; j<outerSize; ++j)
+ {
+ derived().startVec(j);
+ for (typename OtherDerived::InnerIterator it(other, j); it; ++it)
+ {
+ Scalar v = it.value();
+ derived().insertBackByOuterInner(j,it.index()) = v;
+ }
+ }
+ derived().finalize();
+ }
+ else
+ {
+ assignGeneric(other);
+ }
+ return derived();
+ }
+
+ template<typename OtherDerived>
+ inline void assignGeneric(const OtherDerived& other)
+ {
+ //const bool transpose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
+ eigen_assert(( ((internal::traits<Derived>::SupportedAccessPatterns&OuterRandomAccessPattern)==OuterRandomAccessPattern) ||
+ (!((Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit)))) &&
+ "the transpose operation is supposed to be handled in SparseMatrix::operator=");
+
+ enum { Flip = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit) };
+
+ const Index outerSize = other.outerSize();
+ //typedef typename internal::conditional<transpose, LinkedVectorMatrix<Scalar,Flags&RowMajorBit>, Derived>::type TempType;
+ // thanks to shallow copies, we always eval to a tempary
+ Derived temp(other.rows(), other.cols());
+
+ temp.reserve((std::max)(this->rows(),this->cols())*2);
+ for (Index j=0; j<outerSize; ++j)
+ {
+ temp.startVec(j);
+ for (typename OtherDerived::InnerIterator it(other.derived(), j); it; ++it)
+ {
+ Scalar v = it.value();
+ temp.insertBackByOuterInner(Flip?it.index():j,Flip?j:it.index()) = v;
+ }
+ }
+ temp.finalize();
+
+ derived() = temp.markAsRValue();
+ }
+
+ public:
+
+ template<typename Lhs, typename Rhs>
+ inline Derived& operator=(const SparseSparseProduct<Lhs,Rhs>& product);
+
+ friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)
+ {
+ typedef typename Derived::Nested Nested;
+ typedef typename internal::remove_all<Nested>::type NestedCleaned;
+
+ if (Flags&RowMajorBit)
+ {
+ const Nested nm(m.derived());
+ for (Index row=0; row<nm.outerSize(); ++row)
+ {
+ Index col = 0;
+ for (typename NestedCleaned::InnerIterator it(nm.derived(), row); it; ++it)
+ {
+ for ( ; col<it.index(); ++col)
+ s << "0 ";
+ s << it.value() << " ";
+ ++col;
+ }
+ for ( ; col<m.cols(); ++col)
+ s << "0 ";
+ s << std::endl;
+ }
+ }
+ else
+ {
+ const Nested nm(m.derived());
+ if (m.cols() == 1) {
+ Index row = 0;
+ for (typename NestedCleaned::InnerIterator it(nm.derived(), 0); it; ++it)
+ {
+ for ( ; row<it.index(); ++row)
+ s << "0" << std::endl;
+ s << it.value() << std::endl;
+ ++row;
+ }
+ for ( ; row<m.rows(); ++row)
+ s << "0" << std::endl;
+ }
+ else
+ {
+ SparseMatrix<Scalar, RowMajorBit, Index> trans = m;
+ s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit, Index> >&>(trans);
+ }
+ }
+ return s;
+ }
+
+ template<typename OtherDerived>
+ Derived& operator+=(const SparseMatrixBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ Derived& operator-=(const SparseMatrixBase<OtherDerived>& other);
+
+ Derived& operator*=(const Scalar& other);
+ Derived& operator/=(const Scalar& other);
+
+ #define EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE \
+ CwiseBinaryOp< \
+ internal::scalar_product_op< \
+ typename internal::scalar_product_traits< \
+ typename internal::traits<Derived>::Scalar, \
+ typename internal::traits<OtherDerived>::Scalar \
+ >::ReturnType \
+ >, \
+ const Derived, \
+ const OtherDerived \
+ >
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE const EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE
+ cwiseProduct(const MatrixBase<OtherDerived> &other) const;
+
+ // sparse * sparse
+ template<typename OtherDerived>
+ const typename SparseSparseProductReturnType<Derived,OtherDerived>::Type
+ operator*(const SparseMatrixBase<OtherDerived> &other) const;
+
+ // sparse * diagonal
+ template<typename OtherDerived>
+ const SparseDiagonalProduct<Derived,OtherDerived>
+ operator*(const DiagonalBase<OtherDerived> &other) const;
+
+ // diagonal * sparse
+ template<typename OtherDerived> friend
+ const SparseDiagonalProduct<OtherDerived,Derived>
+ operator*(const DiagonalBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)
+ { return SparseDiagonalProduct<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }
+
+ /** dense * sparse (return a dense object unless it is an outer product) */
+ template<typename OtherDerived> friend
+ const typename DenseSparseProductReturnType<OtherDerived,Derived>::Type
+ operator*(const MatrixBase<OtherDerived>& lhs, const Derived& rhs)
+ { return typename DenseSparseProductReturnType<OtherDerived,Derived>::Type(lhs.derived(),rhs); }
+
+ /** sparse * dense (returns a dense object unless it is an outer product) */
+ template<typename OtherDerived>
+ const typename SparseDenseProductReturnType<Derived,OtherDerived>::Type
+ operator*(const MatrixBase<OtherDerived> &other) const
+ { return typename SparseDenseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived()); }
+
+ /** \returns an expression of P H P^-1 where H is the matrix represented by \c *this */
+ SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const
+ {
+ return SparseSymmetricPermutationProduct<Derived,Upper|Lower>(derived(), perm);
+ }
+
+ template<typename OtherDerived>
+ Derived& operator*=(const SparseMatrixBase<OtherDerived>& other);
+
+ #ifdef EIGEN2_SUPPORT
+ // deprecated
+ template<typename OtherDerived>
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type
+ solveTriangular(const MatrixBase<OtherDerived>& other) const;
+
+ // deprecated
+ template<typename OtherDerived>
+ void solveTriangularInPlace(MatrixBase<OtherDerived>& other) const;
+ #endif // EIGEN2_SUPPORT
+
+ template<int Mode>
+ inline const SparseTriangularView<Derived, Mode> triangularView() const;
+
+ template<unsigned int UpLo> inline const SparseSelfAdjointView<Derived, UpLo> selfadjointView() const;
+ template<unsigned int UpLo> inline SparseSelfAdjointView<Derived, UpLo> selfadjointView();
+
+ template<typename OtherDerived> Scalar dot(const MatrixBase<OtherDerived>& other) const;
+ template<typename OtherDerived> Scalar dot(const SparseMatrixBase<OtherDerived>& other) const;
+ RealScalar squaredNorm() const;
+ RealScalar norm() const;
+ RealScalar blueNorm() const;
+
+ Transpose<Derived> transpose() { return derived(); }
+ const Transpose<const Derived> transpose() const { return derived(); }
+ const AdjointReturnType adjoint() const { return transpose(); }
+
+ // inner-vector
+ typedef Block<Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true> InnerVectorReturnType;
+ typedef Block<const Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true> ConstInnerVectorReturnType;
+ InnerVectorReturnType innerVector(Index outer);
+ const ConstInnerVectorReturnType innerVector(Index outer) const;
+
+ // set of inner-vectors
+ typedef Block<Derived,Dynamic,Dynamic,true> InnerVectorsReturnType;
+ typedef Block<const Derived,Dynamic,Dynamic,true> ConstInnerVectorsReturnType;
+ InnerVectorsReturnType innerVectors(Index outerStart, Index outerSize);
+ const ConstInnerVectorsReturnType innerVectors(Index outerStart, Index outerSize) const;
+
+ /** \internal use operator= */
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& dst) const
+ {
+ dst.setZero();
+ for (Index j=0; j<outerSize(); ++j)
+ for (typename Derived::InnerIterator i(derived(),j); i; ++i)
+ dst.coeffRef(i.row(),i.col()) = i.value();
+ }
+
+ Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> toDense() const
+ {
+ return derived();
+ }
+
+ template<typename OtherDerived>
+ bool isApprox(const SparseMatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return toDense().isApprox(other.toDense(),prec); }
+
+ template<typename OtherDerived>
+ bool isApprox(const MatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return toDense().isApprox(other,prec); }
+
+ /** \returns the matrix or vector obtained by evaluating this expression.
+ *
+ * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+ * a const reference, in order to avoid a useless copy.
+ */
+ inline const typename internal::eval<Derived>::type eval() const
+ { return typename internal::eval<Derived>::type(derived()); }
+
+ Scalar sum() const;
+
+ protected:
+
+ bool m_isRValue;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEMATRIXBASE_H
diff --git a/Eigen/src/SparseCore/SparsePermutation.h b/Eigen/src/SparseCore/SparsePermutation.h
new file mode 100644
index 0000000..75e2100
--- /dev/null
+++ b/Eigen/src/SparseCore/SparsePermutation.h
@@ -0,0 +1,148 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_PERMUTATION_H
+#define EIGEN_SPARSE_PERMUTATION_H
+
+// This file implements sparse * permutation products
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct traits<permut_sparsematrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+ typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+ typedef typename MatrixTypeNestedCleaned::Scalar Scalar;
+ typedef typename MatrixTypeNestedCleaned::Index Index;
+ enum {
+ SrcStorageOrder = MatrixTypeNestedCleaned::Flags&RowMajorBit ? RowMajor : ColMajor,
+ MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight
+ };
+
+ typedef typename internal::conditional<MoveOuter,
+ SparseMatrix<Scalar,SrcStorageOrder,Index>,
+ SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,Index> >::type ReturnType;
+};
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct permut_sparsematrix_product_retval
+ : public ReturnByValue<permut_sparsematrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+ typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+ typedef typename MatrixTypeNestedCleaned::Scalar Scalar;
+ typedef typename MatrixTypeNestedCleaned::Index Index;
+
+ enum {
+ SrcStorageOrder = MatrixTypeNestedCleaned::Flags&RowMajorBit ? RowMajor : ColMajor,
+ MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight
+ };
+
+ permut_sparsematrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
+ : m_permutation(perm), m_matrix(matrix)
+ {}
+
+ inline int rows() const { return m_matrix.rows(); }
+ inline int cols() const { return m_matrix.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ if(MoveOuter)
+ {
+ SparseMatrix<Scalar,SrcStorageOrder,Index> tmp(m_matrix.rows(), m_matrix.cols());
+ Matrix<Index,Dynamic,1> sizes(m_matrix.outerSize());
+ for(Index j=0; j<m_matrix.outerSize(); ++j)
+ {
+ Index jp = m_permutation.indices().coeff(j);
+ sizes[((Side==OnTheLeft) ^ Transposed) ? jp : j] = m_matrix.innerVector(((Side==OnTheRight) ^ Transposed) ? jp : j).nonZeros();
+ }
+ tmp.reserve(sizes);
+ for(Index j=0; j<m_matrix.outerSize(); ++j)
+ {
+ Index jp = m_permutation.indices().coeff(j);
+ Index jsrc = ((Side==OnTheRight) ^ Transposed) ? jp : j;
+ Index jdst = ((Side==OnTheLeft) ^ Transposed) ? jp : j;
+ for(typename MatrixTypeNestedCleaned::InnerIterator it(m_matrix,jsrc); it; ++it)
+ tmp.insertByOuterInner(jdst,it.index()) = it.value();
+ }
+ dst = tmp;
+ }
+ else
+ {
+ SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,Index> tmp(m_matrix.rows(), m_matrix.cols());
+ Matrix<Index,Dynamic,1> sizes(tmp.outerSize());
+ sizes.setZero();
+ PermutationMatrix<Dynamic,Dynamic,Index> perm;
+ if((Side==OnTheLeft) ^ Transposed)
+ perm = m_permutation;
+ else
+ perm = m_permutation.transpose();
+
+ for(Index j=0; j<m_matrix.outerSize(); ++j)
+ for(typename MatrixTypeNestedCleaned::InnerIterator it(m_matrix,j); it; ++it)
+ sizes[perm.indices().coeff(it.index())]++;
+ tmp.reserve(sizes);
+ for(Index j=0; j<m_matrix.outerSize(); ++j)
+ for(typename MatrixTypeNestedCleaned::InnerIterator it(m_matrix,j); it; ++it)
+ tmp.insertByOuterInner(perm.indices().coeff(it.index()),j) = it.value();
+ dst = tmp;
+ }
+ }
+
+ protected:
+ const PermutationType& m_permutation;
+ typename MatrixType::Nested m_matrix;
+};
+
+}
+
+
+
+/** \returns the matrix with the permutation applied to the columns
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, false>
+operator*(const SparseMatrixBase<SparseDerived>& matrix, const PermutationBase<PermDerived>& perm)
+{
+ return internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, false>(perm, matrix.derived());
+}
+
+/** \returns the matrix with the permutation applied to the rows
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, false>
+operator*( const PermutationBase<PermDerived>& perm, const SparseMatrixBase<SparseDerived>& matrix)
+{
+ return internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, false>(perm, matrix.derived());
+}
+
+
+
+/** \returns the matrix with the inverse permutation applied to the columns.
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, true>
+operator*(const SparseMatrixBase<SparseDerived>& matrix, const Transpose<PermutationBase<PermDerived> >& tperm)
+{
+ return internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheRight, true>(tperm.nestedPermutation(), matrix.derived());
+}
+
+/** \returns the matrix with the inverse permutation applied to the rows.
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, true>
+operator*(const Transpose<PermutationBase<PermDerived> >& tperm, const SparseMatrixBase<SparseDerived>& matrix)
+{
+ return internal::permut_sparsematrix_product_retval<PermutationBase<PermDerived>, SparseDerived, OnTheLeft, true>(tperm.nestedPermutation(), matrix.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
diff --git a/Eigen/src/SparseCore/SparseProduct.h b/Eigen/src/SparseCore/SparseProduct.h
new file mode 100644
index 0000000..cf76630
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseProduct.h
@@ -0,0 +1,188 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEPRODUCT_H
+#define EIGEN_SPARSEPRODUCT_H
+
+namespace Eigen {
+
+template<typename Lhs, typename Rhs>
+struct SparseSparseProductReturnType
+{
+ typedef typename internal::traits<Lhs>::Scalar Scalar;
+ typedef typename internal::traits<Lhs>::Index Index;
+ enum {
+ LhsRowMajor = internal::traits<Lhs>::Flags & RowMajorBit,
+ RhsRowMajor = internal::traits<Rhs>::Flags & RowMajorBit,
+ TransposeRhs = (!LhsRowMajor) && RhsRowMajor,
+ TransposeLhs = LhsRowMajor && (!RhsRowMajor)
+ };
+
+ typedef typename internal::conditional<TransposeLhs,
+ SparseMatrix<Scalar,0,Index>,
+ typename internal::nested<Lhs,Rhs::RowsAtCompileTime>::type>::type LhsNested;
+
+ typedef typename internal::conditional<TransposeRhs,
+ SparseMatrix<Scalar,0,Index>,
+ typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type>::type RhsNested;
+
+ typedef SparseSparseProduct<LhsNested, RhsNested> Type;
+};
+
+namespace internal {
+template<typename LhsNested, typename RhsNested>
+struct traits<SparseSparseProduct<LhsNested, RhsNested> >
+{
+ typedef MatrixXpr XprKind;
+ // clean the nested types:
+ typedef typename remove_all<LhsNested>::type _LhsNested;
+ typedef typename remove_all<RhsNested>::type _RhsNested;
+ typedef typename _LhsNested::Scalar Scalar;
+ typedef typename promote_index_type<typename traits<_LhsNested>::Index,
+ typename traits<_RhsNested>::Index>::type Index;
+
+ enum {
+ LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+ RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+ LhsFlags = _LhsNested::Flags,
+ RhsFlags = _RhsNested::Flags,
+
+ RowsAtCompileTime = _LhsNested::RowsAtCompileTime,
+ ColsAtCompileTime = _RhsNested::ColsAtCompileTime,
+ MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,
+
+ InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime),
+
+ EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit),
+
+ RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
+
+ Flags = (int(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
+ | EvalBeforeAssigningBit
+ | EvalBeforeNestingBit,
+
+ CoeffReadCost = Dynamic
+ };
+
+ typedef Sparse StorageKind;
+};
+
+} // end namespace internal
+
+template<typename LhsNested, typename RhsNested>
+class SparseSparseProduct : internal::no_assignment_operator,
+ public SparseMatrixBase<SparseSparseProduct<LhsNested, RhsNested> >
+{
+ public:
+
+ typedef SparseMatrixBase<SparseSparseProduct> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(SparseSparseProduct)
+
+ private:
+
+ typedef typename internal::traits<SparseSparseProduct>::_LhsNested _LhsNested;
+ typedef typename internal::traits<SparseSparseProduct>::_RhsNested _RhsNested;
+
+ public:
+
+ template<typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE SparseSparseProduct(const Lhs& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs), m_tolerance(0), m_conservative(true)
+ {
+ init();
+ }
+
+ template<typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE SparseSparseProduct(const Lhs& lhs, const Rhs& rhs, const RealScalar& tolerance)
+ : m_lhs(lhs), m_rhs(rhs), m_tolerance(tolerance), m_conservative(false)
+ {
+ init();
+ }
+
+ SparseSparseProduct pruned(const Scalar& reference = 0, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision()) const
+ {
+ using std::abs;
+ return SparseSparseProduct(m_lhs,m_rhs,abs(reference)*epsilon);
+ }
+
+ template<typename Dest>
+ void evalTo(Dest& result) const
+ {
+ if(m_conservative)
+ internal::conservative_sparse_sparse_product_selector<_LhsNested, _RhsNested, Dest>::run(lhs(),rhs(),result);
+ else
+ internal::sparse_sparse_product_with_pruning_selector<_LhsNested, _RhsNested, Dest>::run(lhs(),rhs(),result,m_tolerance);
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return m_lhs.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return m_rhs.cols(); }
+
+ EIGEN_STRONG_INLINE const _LhsNested& lhs() const { return m_lhs; }
+ EIGEN_STRONG_INLINE const _RhsNested& rhs() const { return m_rhs; }
+
+ protected:
+ void init()
+ {
+ eigen_assert(m_lhs.cols() == m_rhs.rows());
+
+ enum {
+ ProductIsValid = _LhsNested::ColsAtCompileTime==Dynamic
+ || _RhsNested::RowsAtCompileTime==Dynamic
+ || int(_LhsNested::ColsAtCompileTime)==int(_RhsNested::RowsAtCompileTime),
+ AreVectors = _LhsNested::IsVectorAtCompileTime && _RhsNested::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(_LhsNested,_RhsNested)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwise()*v2
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+ }
+
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+ RealScalar m_tolerance;
+ bool m_conservative;
+};
+
+// sparse = sparse * sparse
+template<typename Derived>
+template<typename Lhs, typename Rhs>
+inline Derived& SparseMatrixBase<Derived>::operator=(const SparseSparseProduct<Lhs,Rhs>& product)
+{
+ product.evalTo(derived());
+ return derived();
+}
+
+/** \returns an expression of the product of two sparse matrices.
+ * By default a conservative product preserving the symbolic non zeros is performed.
+ * The automatic pruning of the small values can be achieved by calling the pruned() function
+ * in which case a totally different product algorithm is employed:
+ * \code
+ * C = (A*B).pruned(); // supress numerical zeros (exact)
+ * C = (A*B).pruned(ref);
+ * C = (A*B).pruned(ref,epsilon);
+ * \endcode
+ * where \c ref is a meaningful non zero reference value.
+ * */
+template<typename Derived>
+template<typename OtherDerived>
+inline const typename SparseSparseProductReturnType<Derived,OtherDerived>::Type
+SparseMatrixBase<Derived>::operator*(const SparseMatrixBase<OtherDerived> &other) const
+{
+ return typename SparseSparseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseRedux.h b/Eigen/src/SparseCore/SparseRedux.h
new file mode 100644
index 0000000..f3da93a
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseRedux.h
@@ -0,0 +1,45 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEREDUX_H
+#define EIGEN_SPARSEREDUX_H
+
+namespace Eigen {
+
+template<typename Derived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ Scalar res(0);
+ for (Index j=0; j<outerSize(); ++j)
+ for (typename Derived::InnerIterator iter(derived(),j); iter; ++iter)
+ res += iter.value();
+ return res;
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+typename internal::traits<SparseMatrix<_Scalar,_Options,_Index> >::Scalar
+SparseMatrix<_Scalar,_Options,_Index>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ return Matrix<Scalar,1,Dynamic>::Map(&m_data.value(0), m_data.size()).sum();
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+typename internal::traits<SparseVector<_Scalar,_Options, _Index> >::Scalar
+SparseVector<_Scalar,_Options,_Index>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ return Matrix<Scalar,1,Dynamic>::Map(&m_data.value(0), m_data.size()).sum();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEREDUX_H
diff --git a/Eigen/src/SparseCore/SparseSelfAdjointView.h b/Eigen/src/SparseCore/SparseSelfAdjointView.h
new file mode 100644
index 0000000..0eda96b
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseSelfAdjointView.h
@@ -0,0 +1,507 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_SELFADJOINTVIEW_H
+#define EIGEN_SPARSE_SELFADJOINTVIEW_H
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ * \class SparseSelfAdjointView
+ *
+ * \brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.
+ *
+ * \param MatrixType the type of the dense matrix storing the coefficients
+ * \param UpLo can be either \c #Lower or \c #Upper
+ *
+ * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
+ * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa SparseMatrixBase::selfadjointView()
+ */
+template<typename Lhs, typename Rhs, int UpLo>
+class SparseSelfAdjointTimeDenseProduct;
+
+template<typename Lhs, typename Rhs, int UpLo>
+class DenseTimeSparseSelfAdjointProduct;
+
+namespace internal {
+
+template<typename MatrixType, unsigned int UpLo>
+struct traits<SparseSelfAdjointView<MatrixType,UpLo> > : traits<MatrixType> {
+};
+
+template<int SrcUpLo,int DstUpLo,typename MatrixType,int DestOrder>
+void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
+
+template<int UpLo,typename MatrixType,int DestOrder>
+void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
+
+}
+
+template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView
+ : public EigenBase<SparseSelfAdjointView<MatrixType,UpLo> >
+{
+ public:
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Index,Dynamic,1> VectorI;
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+
+ inline SparseSelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
+ {
+ eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
+ }
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ /** \internal \returns a reference to the nested matrix */
+ const _MatrixTypeNested& matrix() const { return m_matrix; }
+ _MatrixTypeNested& matrix() { return m_matrix.const_cast_derived(); }
+
+ /** \returns an expression of the matrix product between a sparse self-adjoint matrix \c *this and a sparse matrix \a rhs.
+ *
+ * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
+ * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
+ */
+ template<typename OtherDerived>
+ SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>
+ operator*(const SparseMatrixBase<OtherDerived>& rhs) const
+ {
+ return SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>(*this, rhs.derived());
+ }
+
+ /** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
+ *
+ * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
+ * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
+ */
+ template<typename OtherDerived> friend
+ SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject >
+ operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
+ {
+ return SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject>(lhs.derived(), rhs);
+ }
+
+ /** Efficient sparse self-adjoint matrix times dense vector/matrix product */
+ template<typename OtherDerived>
+ SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>(m_matrix, rhs.derived());
+ }
+
+ /** Efficient dense vector/matrix times sparse self-adjoint matrix product */
+ template<typename OtherDerived> friend
+ DenseTimeSparseSelfAdjointProduct<OtherDerived,MatrixType,UpLo>
+ operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
+ {
+ return DenseTimeSparseSelfAdjointProduct<OtherDerived,_MatrixTypeNested,UpLo>(lhs.derived(), rhs.m_matrix);
+ }
+
+ /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
+ *
+ * \returns a reference to \c *this
+ *
+ * To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
+ * call this function with u.adjoint().
+ */
+ template<typename DerivedU>
+ SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
+
+ /** \internal triggered by sparse_matrix = SparseSelfadjointView; */
+ template<typename DestScalar,int StorageOrder> void evalTo(SparseMatrix<DestScalar,StorageOrder,Index>& _dest) const
+ {
+ internal::permute_symm_to_fullsymm<UpLo>(m_matrix, _dest);
+ }
+
+ template<typename DestScalar> void evalTo(DynamicSparseMatrix<DestScalar,ColMajor,Index>& _dest) const
+ {
+ // TODO directly evaluate into _dest;
+ SparseMatrix<DestScalar,ColMajor,Index> tmp(_dest.rows(),_dest.cols());
+ internal::permute_symm_to_fullsymm<UpLo>(m_matrix, tmp);
+ _dest = tmp;
+ }
+
+ /** \returns an expression of P H P^-1 */
+ SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const
+ {
+ return SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo>(m_matrix, perm);
+ }
+
+ template<typename SrcMatrixType,int SrcUpLo>
+ SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcUpLo>& permutedMatrix)
+ {
+ permutedMatrix.evalTo(*this);
+ return *this;
+ }
+
+
+ SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)
+ {
+ PermutationMatrix<Dynamic> pnull;
+ return *this = src.twistedBy(pnull);
+ }
+
+ template<typename SrcMatrixType,unsigned int SrcUpLo>
+ SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcUpLo>& src)
+ {
+ PermutationMatrix<Dynamic> pnull;
+ return *this = src.twistedBy(pnull);
+ }
+
+
+ // const SparseLLT<PlainObject, UpLo> llt() const;
+ // const SparseLDLT<PlainObject, UpLo> ldlt() const;
+
+ protected:
+
+ typename MatrixType::Nested m_matrix;
+ mutable VectorI m_countPerRow;
+ mutable VectorI m_countPerCol;
+};
+
+/***************************************************************************
+* Implementation of SparseMatrixBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<unsigned int UpLo>
+const SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView() const
+{
+ return derived();
+}
+
+template<typename Derived>
+template<unsigned int UpLo>
+SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView()
+{
+ return derived();
+}
+
+/***************************************************************************
+* Implementation of SparseSelfAdjointView methods
+***************************************************************************/
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename DerivedU>
+SparseSelfAdjointView<MatrixType,UpLo>&
+SparseSelfAdjointView<MatrixType,UpLo>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)
+{
+ SparseMatrix<Scalar,MatrixType::Flags&RowMajorBit?RowMajor:ColMajor> tmp = u * u.adjoint();
+ if(alpha==Scalar(0))
+ m_matrix.const_cast_derived() = tmp.template triangularView<UpLo>();
+ else
+ m_matrix.const_cast_derived() += alpha * tmp.template triangularView<UpLo>();
+
+ return *this;
+}
+
+/***************************************************************************
+* Implementation of sparse self-adjoint time dense matrix
+***************************************************************************/
+
+namespace internal {
+template<typename Lhs, typename Rhs, int UpLo>
+struct traits<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo> >
+ : traits<ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
+{
+ typedef Dense StorageKind;
+};
+}
+
+template<typename Lhs, typename Rhs, int UpLo>
+class SparseSelfAdjointTimeDenseProduct
+ : public ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(SparseSelfAdjointTimeDenseProduct)
+
+ SparseSelfAdjointTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(alpha);
+ // TODO use alpha
+ eigen_assert(alpha==Scalar(1) && "alpha != 1 is not implemented yet, sorry");
+ typedef typename internal::remove_all<Lhs>::type _Lhs;
+ typedef typename _Lhs::InnerIterator LhsInnerIterator;
+ enum {
+ LhsIsRowMajor = (_Lhs::Flags&RowMajorBit)==RowMajorBit,
+ ProcessFirstHalf =
+ ((UpLo&(Upper|Lower))==(Upper|Lower))
+ || ( (UpLo&Upper) && !LhsIsRowMajor)
+ || ( (UpLo&Lower) && LhsIsRowMajor),
+ ProcessSecondHalf = !ProcessFirstHalf
+ };
+ for (Index j=0; j<m_lhs.outerSize(); ++j)
+ {
+ LhsInnerIterator i(m_lhs,j);
+ if (ProcessSecondHalf)
+ {
+ while (i && i.index()<j) ++i;
+ if(i && i.index()==j)
+ {
+ dest.row(j) += i.value() * m_rhs.row(j);
+ ++i;
+ }
+ }
+ for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
+ {
+ Index a = LhsIsRowMajor ? j : i.index();
+ Index b = LhsIsRowMajor ? i.index() : j;
+ typename Lhs::Scalar v = i.value();
+ dest.row(a) += (v) * m_rhs.row(b);
+ dest.row(b) += numext::conj(v) * m_rhs.row(a);
+ }
+ if (ProcessFirstHalf && i && (i.index()==j))
+ dest.row(j) += i.value() * m_rhs.row(j);
+ }
+ }
+
+ private:
+ SparseSelfAdjointTimeDenseProduct& operator=(const SparseSelfAdjointTimeDenseProduct&);
+};
+
+namespace internal {
+template<typename Lhs, typename Rhs, int UpLo>
+struct traits<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo> >
+ : traits<ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
+{};
+}
+
+template<typename Lhs, typename Rhs, int UpLo>
+class DenseTimeSparseSelfAdjointProduct
+ : public ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(DenseTimeSparseSelfAdjointProduct)
+
+ DenseTimeSparseSelfAdjointProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& /*dest*/, const Scalar& /*alpha*/) const
+ {
+ // TODO
+ }
+
+ private:
+ DenseTimeSparseSelfAdjointProduct& operator=(const DenseTimeSparseSelfAdjointProduct&);
+};
+
+/***************************************************************************
+* Implementation of symmetric copies and permutations
+***************************************************************************/
+namespace internal {
+
+template<typename MatrixType, int UpLo>
+struct traits<SparseSymmetricPermutationProduct<MatrixType,UpLo> > : traits<MatrixType> {
+};
+
+template<int UpLo,typename MatrixType,int DestOrder>
+void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
+{
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef SparseMatrix<Scalar,DestOrder,Index> Dest;
+ typedef Matrix<Index,Dynamic,1> VectorI;
+
+ Dest& dest(_dest.derived());
+ enum {
+ StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)
+ };
+
+ Index size = mat.rows();
+ VectorI count;
+ count.resize(size);
+ count.setZero();
+ dest.resize(size,size);
+ for(Index j = 0; j<size; ++j)
+ {
+ Index jp = perm ? perm[j] : j;
+ for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
+ {
+ Index i = it.index();
+ Index r = it.row();
+ Index c = it.col();
+ Index ip = perm ? perm[i] : i;
+ if(UpLo==(Upper|Lower))
+ count[StorageOrderMatch ? jp : ip]++;
+ else if(r==c)
+ count[ip]++;
+ else if(( UpLo==Lower && r>c) || ( UpLo==Upper && r<c))
+ {
+ count[ip]++;
+ count[jp]++;
+ }
+ }
+ }
+ Index nnz = count.sum();
+
+ // reserve space
+ dest.resizeNonZeros(nnz);
+ dest.outerIndexPtr()[0] = 0;
+ for(Index j=0; j<size; ++j)
+ dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
+ for(Index j=0; j<size; ++j)
+ count[j] = dest.outerIndexPtr()[j];
+
+ // copy data
+ for(Index j = 0; j<size; ++j)
+ {
+ for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
+ {
+ Index i = it.index();
+ Index r = it.row();
+ Index c = it.col();
+
+ Index jp = perm ? perm[j] : j;
+ Index ip = perm ? perm[i] : i;
+
+ if(UpLo==(Upper|Lower))
+ {
+ Index k = count[StorageOrderMatch ? jp : ip]++;
+ dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;
+ dest.valuePtr()[k] = it.value();
+ }
+ else if(r==c)
+ {
+ Index k = count[ip]++;
+ dest.innerIndexPtr()[k] = ip;
+ dest.valuePtr()[k] = it.value();
+ }
+ else if(( (UpLo&Lower)==Lower && r>c) || ( (UpLo&Upper)==Upper && r<c))
+ {
+ if(!StorageOrderMatch)
+ std::swap(ip,jp);
+ Index k = count[jp]++;
+ dest.innerIndexPtr()[k] = ip;
+ dest.valuePtr()[k] = it.value();
+ k = count[ip]++;
+ dest.innerIndexPtr()[k] = jp;
+ dest.valuePtr()[k] = numext::conj(it.value());
+ }
+ }
+ }
+}
+
+template<int _SrcUpLo,int _DstUpLo,typename MatrixType,int DstOrder>
+void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
+{
+ typedef typename MatrixType::Index Index;
+ typedef typename MatrixType::Scalar Scalar;
+ SparseMatrix<Scalar,DstOrder,Index>& dest(_dest.derived());
+ typedef Matrix<Index,Dynamic,1> VectorI;
+ enum {
+ SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,
+ StorageOrderMatch = int(SrcOrder) == int(DstOrder),
+ DstUpLo = DstOrder==RowMajor ? (_DstUpLo==Upper ? Lower : Upper) : _DstUpLo,
+ SrcUpLo = SrcOrder==RowMajor ? (_SrcUpLo==Upper ? Lower : Upper) : _SrcUpLo
+ };
+
+ Index size = mat.rows();
+ VectorI count(size);
+ count.setZero();
+ dest.resize(size,size);
+ for(Index j = 0; j<size; ++j)
+ {
+ Index jp = perm ? perm[j] : j;
+ for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
+ {
+ Index i = it.index();
+ if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
+ continue;
+
+ Index ip = perm ? perm[i] : i;
+ count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
+ }
+ }
+ dest.outerIndexPtr()[0] = 0;
+ for(Index j=0; j<size; ++j)
+ dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
+ dest.resizeNonZeros(dest.outerIndexPtr()[size]);
+ for(Index j=0; j<size; ++j)
+ count[j] = dest.outerIndexPtr()[j];
+
+ for(Index j = 0; j<size; ++j)
+ {
+
+ for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
+ {
+ Index i = it.index();
+ if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
+ continue;
+
+ Index jp = perm ? perm[j] : j;
+ Index ip = perm? perm[i] : i;
+
+ Index k = count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
+ dest.innerIndexPtr()[k] = int(DstUpLo)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);
+
+ if(!StorageOrderMatch) std::swap(ip,jp);
+ if( ((int(DstUpLo)==int(Lower) && ip<jp) || (int(DstUpLo)==int(Upper) && ip>jp)))
+ dest.valuePtr()[k] = numext::conj(it.value());
+ else
+ dest.valuePtr()[k] = it.value();
+ }
+ }
+}
+
+}
+
+template<typename MatrixType,int UpLo>
+class SparseSymmetricPermutationProduct
+ : public EigenBase<SparseSymmetricPermutationProduct<MatrixType,UpLo> >
+{
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ protected:
+ typedef PermutationMatrix<Dynamic,Dynamic,Index> Perm;
+ public:
+ typedef Matrix<Index,Dynamic,1> VectorI;
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+
+ SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)
+ : m_matrix(mat), m_perm(perm)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ template<typename DestScalar, int Options, typename DstIndex>
+ void evalTo(SparseMatrix<DestScalar,Options,DstIndex>& _dest) const
+ {
+// internal::permute_symm_to_fullsymm<UpLo>(m_matrix,_dest,m_perm.indices().data());
+ SparseMatrix<DestScalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
+ internal::permute_symm_to_fullsymm<UpLo>(m_matrix,tmp,m_perm.indices().data());
+ _dest = tmp;
+ }
+
+ template<typename DestType,unsigned int DestUpLo> void evalTo(SparseSelfAdjointView<DestType,DestUpLo>& dest) const
+ {
+ internal::permute_symm_to_symm<UpLo,DestUpLo>(m_matrix,dest.matrix(),m_perm.indices().data());
+ }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const Perm& m_perm;
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
diff --git a/Eigen/src/SparseCore/SparseSparseProductWithPruning.h b/Eigen/src/SparseCore/SparseSparseProductWithPruning.h
new file mode 100644
index 0000000..fcc18f5
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseSparseProductWithPruning.h
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
+#define EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
+
+namespace Eigen {
+
+namespace internal {
+
+
+// perform a pseudo in-place sparse * sparse product assuming all matrices are col major
+template<typename Lhs, typename Rhs, typename ResultType>
+static void sparse_sparse_product_with_pruning_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, const typename ResultType::RealScalar& tolerance)
+{
+ // return sparse_sparse_product_with_pruning_impl2(lhs,rhs,res);
+
+ typedef typename remove_all<Lhs>::type::Scalar Scalar;
+ typedef typename remove_all<Lhs>::type::Index Index;
+
+ // make sure to call innerSize/outerSize since we fake the storage order.
+ Index rows = lhs.innerSize();
+ Index cols = rhs.outerSize();
+ //Index size = lhs.outerSize();
+ eigen_assert(lhs.outerSize() == rhs.innerSize());
+
+ // allocate a temporary buffer
+ AmbiVector<Scalar,Index> tempVector(rows);
+
+ // estimate the number of non zero entries
+ // given a rhs column containing Y non zeros, we assume that the respective Y columns
+ // of the lhs differs in average of one non zeros, thus the number of non zeros for
+ // the product of a rhs column with the lhs is X+Y where X is the average number of non zero
+ // per column of the lhs.
+ // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)
+ Index estimated_nnz_prod = lhs.nonZeros() + rhs.nonZeros();
+
+ // mimics a resizeByInnerOuter:
+ if(ResultType::IsRowMajor)
+ res.resize(cols, rows);
+ else
+ res.resize(rows, cols);
+
+ res.reserve(estimated_nnz_prod);
+ double ratioColRes = double(estimated_nnz_prod)/double(lhs.rows()*rhs.cols());
+ for (Index j=0; j<cols; ++j)
+ {
+ // FIXME:
+ //double ratioColRes = (double(rhs.innerVector(j).nonZeros()) + double(lhs.nonZeros())/double(lhs.cols()))/double(lhs.rows());
+ // let's do a more accurate determination of the nnz ratio for the current column j of res
+ tempVector.init(ratioColRes);
+ tempVector.setZero();
+ for (typename Rhs::InnerIterator rhsIt(rhs, j); rhsIt; ++rhsIt)
+ {
+ // FIXME should be written like this: tmp += rhsIt.value() * lhs.col(rhsIt.index())
+ tempVector.restart();
+ Scalar x = rhsIt.value();
+ for (typename Lhs::InnerIterator lhsIt(lhs, rhsIt.index()); lhsIt; ++lhsIt)
+ {
+ tempVector.coeffRef(lhsIt.index()) += lhsIt.value() * x;
+ }
+ }
+ res.startVec(j);
+ for (typename AmbiVector<Scalar,Index>::Iterator it(tempVector,tolerance); it; ++it)
+ res.insertBackByOuterInner(j,it.index()) = it.value();
+ }
+ res.finalize();
+}
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit,
+ int RhsStorageOrder = traits<Rhs>::Flags&RowMajorBit,
+ int ResStorageOrder = traits<ResultType>::Flags&RowMajorBit>
+struct sparse_sparse_product_with_pruning_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>
+{
+ typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar;
+ typedef typename ResultType::RealScalar RealScalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typename remove_all<ResultType>::type _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,ResultType>(lhs, rhs, _res, tolerance);
+ res.swap(_res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ // we need a col-major matrix to hold the result
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> SparseTemporaryType;
+ SparseTemporaryType _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,SparseTemporaryType>(lhs, rhs, _res, tolerance);
+ res = _res;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ // let's transpose the product to get a column x column product
+ typename remove_all<ResultType>::type _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Rhs,Lhs,ResultType>(rhs, lhs, _res, tolerance);
+ res.swap(_res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename Lhs::Index> ColMajorMatrixLhs;
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename Lhs::Index> ColMajorMatrixRhs;
+ ColMajorMatrixLhs colLhs(lhs);
+ ColMajorMatrixRhs colRhs(rhs);
+ internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,ColMajorMatrixRhs,ResultType>(colLhs, colRhs, res, tolerance);
+
+ // let's transpose the product to get a column x column product
+// typedef SparseMatrix<typename ResultType::Scalar> SparseTemporaryType;
+// SparseTemporaryType _res(res.cols(), res.rows());
+// sparse_sparse_product_with_pruning_impl<Rhs,Lhs,SparseTemporaryType>(rhs, lhs, _res);
+// res = _res.transpose();
+ }
+};
+
+// NOTE the 2 others cases (col row *) must never occur since they are caught
+// by ProductReturnType which transforms it to (col col *) by evaluating rhs.
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
diff --git a/Eigen/src/SparseCore/SparseTranspose.h b/Eigen/src/SparseCore/SparseTranspose.h
new file mode 100644
index 0000000..76d031d
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseTranspose.h
@@ -0,0 +1,63 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSETRANSPOSE_H
+#define EIGEN_SPARSETRANSPOSE_H
+
+namespace Eigen {
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>
+ : public SparseMatrixBase<Transpose<MatrixType> >
+{
+ typedef typename internal::remove_all<typename MatrixType::Nested>::type _MatrixTypeNested;
+ public:
+
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Transpose<MatrixType> )
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ inline Index nonZeros() const { return derived().nestedExpression().nonZeros(); }
+};
+
+// NOTE: VC10 and VC11 trigger an ICE if don't put typename TransposeImpl<MatrixType,Sparse>:: in front of Index,
+// a typedef typename TransposeImpl<MatrixType,Sparse>::Index Index;
+// does not fix the issue.
+// An alternative is to define the nested class in the parent class itself.
+template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>::InnerIterator
+ : public _MatrixTypeNested::InnerIterator
+{
+ typedef typename _MatrixTypeNested::InnerIterator Base;
+ typedef typename TransposeImpl::Index Index;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const TransposeImpl& trans, typename TransposeImpl<MatrixType,Sparse>::Index outer)
+ : Base(trans.derived().nestedExpression(), outer)
+ {}
+ typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
+ typename TransposeImpl<MatrixType,Sparse>::Index col() const { return Base::row(); }
+};
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>::ReverseInnerIterator
+ : public _MatrixTypeNested::ReverseInnerIterator
+{
+ typedef typename _MatrixTypeNested::ReverseInnerIterator Base;
+ typedef typename TransposeImpl::Index Index;
+ public:
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator(const TransposeImpl& xpr, typename TransposeImpl<MatrixType,Sparse>::Index outer)
+ : Base(xpr.derived().nestedExpression(), outer)
+ {}
+ typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
+ typename TransposeImpl<MatrixType,Sparse>::Index col() const { return Base::row(); }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSETRANSPOSE_H
diff --git a/Eigen/src/SparseCore/SparseTriangularView.h b/Eigen/src/SparseCore/SparseTriangularView.h
new file mode 100644
index 0000000..333127b
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseTriangularView.h
@@ -0,0 +1,179 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_TRIANGULARVIEW_H
+#define EIGEN_SPARSE_TRIANGULARVIEW_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, int Mode>
+struct traits<SparseTriangularView<MatrixType,Mode> >
+: public traits<MatrixType>
+{};
+
+} // namespace internal
+
+template<typename MatrixType, int Mode> class SparseTriangularView
+ : public SparseMatrixBase<SparseTriangularView<MatrixType,Mode> >
+{
+ enum { SkipFirst = ((Mode&Lower) && !(MatrixType::Flags&RowMajorBit))
+ || ((Mode&Upper) && (MatrixType::Flags&RowMajorBit)),
+ SkipLast = !SkipFirst,
+ SkipDiag = (Mode&ZeroDiag) ? 1 : 0,
+ HasUnitDiag = (Mode&UnitDiag) ? 1 : 0
+ };
+
+ public:
+
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseTriangularView)
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef typename internal::remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
+ typedef typename internal::remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+
+ inline SparseTriangularView(const MatrixType& matrix) : m_matrix(matrix) {}
+
+ /** \internal */
+ inline const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+
+ template<typename OtherDerived>
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type
+ solve(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived> void solveInPlace(MatrixBase<OtherDerived>& other) const;
+ template<typename OtherDerived> void solveInPlace(SparseMatrixBase<OtherDerived>& other) const;
+
+ protected:
+ MatrixTypeNested m_matrix;
+};
+
+template<typename MatrixType, int Mode>
+class SparseTriangularView<MatrixType,Mode>::InnerIterator : public MatrixTypeNestedCleaned::InnerIterator
+{
+ typedef typename MatrixTypeNestedCleaned::InnerIterator Base;
+ typedef typename SparseTriangularView::Index Index;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const SparseTriangularView& view, Index outer)
+ : Base(view.nestedExpression(), outer), m_returnOne(false)
+ {
+ if(SkipFirst)
+ {
+ while((*this) && ((HasUnitDiag||SkipDiag) ? this->index()<=outer : this->index()<outer))
+ Base::operator++();
+ if(HasUnitDiag)
+ m_returnOne = true;
+ }
+ else if(HasUnitDiag && ((!Base::operator bool()) || Base::index()>=Base::outer()))
+ {
+ if((!SkipFirst) && Base::operator bool())
+ Base::operator++();
+ m_returnOne = true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ if(HasUnitDiag && m_returnOne)
+ m_returnOne = false;
+ else
+ {
+ Base::operator++();
+ if(HasUnitDiag && (!SkipFirst) && ((!Base::operator bool()) || Base::index()>=Base::outer()))
+ {
+ if((!SkipFirst) && Base::operator bool())
+ Base::operator++();
+ m_returnOne = true;
+ }
+ }
+ return *this;
+ }
+
+ inline Index row() const { return (MatrixType::Flags&RowMajorBit ? Base::outer() : this->index()); }
+ inline Index col() const { return (MatrixType::Flags&RowMajorBit ? this->index() : Base::outer()); }
+ inline Index index() const
+ {
+ if(HasUnitDiag && m_returnOne) return Base::outer();
+ else return Base::index();
+ }
+ inline Scalar value() const
+ {
+ if(HasUnitDiag && m_returnOne) return Scalar(1);
+ else return Base::value();
+ }
+
+ EIGEN_STRONG_INLINE operator bool() const
+ {
+ if(HasUnitDiag && m_returnOne)
+ return true;
+ if(SkipFirst) return Base::operator bool();
+ else
+ {
+ if (SkipDiag) return (Base::operator bool() && this->index() < this->outer());
+ else return (Base::operator bool() && this->index() <= this->outer());
+ }
+ }
+ protected:
+ bool m_returnOne;
+};
+
+template<typename MatrixType, int Mode>
+class SparseTriangularView<MatrixType,Mode>::ReverseInnerIterator : public MatrixTypeNestedCleaned::ReverseInnerIterator
+{
+ typedef typename MatrixTypeNestedCleaned::ReverseInnerIterator Base;
+ typedef typename SparseTriangularView::Index Index;
+ public:
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator(const SparseTriangularView& view, Index outer)
+ : Base(view.nestedExpression(), outer)
+ {
+ eigen_assert((!HasUnitDiag) && "ReverseInnerIterator does not support yet triangular views with a unit diagonal");
+ if(SkipLast) {
+ while((*this) && (SkipDiag ? this->index()>=outer : this->index()>outer))
+ --(*this);
+ }
+ }
+
+ EIGEN_STRONG_INLINE ReverseInnerIterator& operator--()
+ { Base::operator--(); return *this; }
+
+ inline Index row() const { return Base::row(); }
+ inline Index col() const { return Base::col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const
+ {
+ if (SkipLast) return Base::operator bool() ;
+ else
+ {
+ if(SkipDiag) return (Base::operator bool() && this->index() > this->outer());
+ else return (Base::operator bool() && this->index() >= this->outer());
+ }
+ }
+};
+
+template<typename Derived>
+template<int Mode>
+inline const SparseTriangularView<Derived, Mode>
+SparseMatrixBase<Derived>::triangularView() const
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_TRIANGULARVIEW_H
diff --git a/Eigen/src/SparseCore/SparseUtil.h b/Eigen/src/SparseCore/SparseUtil.h
new file mode 100644
index 0000000..0ba4713
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseUtil.h
@@ -0,0 +1,173 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEUTIL_H
+#define EIGEN_SPARSEUTIL_H
+
+namespace Eigen {
+
+#ifdef NDEBUG
+#define EIGEN_DBG_SPARSE(X)
+#else
+#define EIGEN_DBG_SPARSE(X) X
+#endif
+
+#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SparseMatrixBase<OtherDerived>& other) \
+{ \
+ return Base::operator Op(other.derived()); \
+} \
+EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \
+{ \
+ return Base::operator Op(other); \
+}
+
+#define EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename Other> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \
+{ \
+ return Base::operator Op(scalar); \
+}
+
+#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \
+EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \
+EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \
+EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \
+EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=)
+
+#define _EIGEN_SPARSE_PUBLIC_INTERFACE(Derived, BaseClass) \
+ typedef BaseClass Base; \
+ typedef typename Eigen::internal::traits<Derived >::Scalar Scalar; \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \
+ typedef typename Eigen::internal::nested<Derived >::type Nested; \
+ typedef typename Eigen::internal::traits<Derived >::StorageKind StorageKind; \
+ typedef typename Eigen::internal::traits<Derived >::Index Index; \
+ enum { RowsAtCompileTime = Eigen::internal::traits<Derived >::RowsAtCompileTime, \
+ ColsAtCompileTime = Eigen::internal::traits<Derived >::ColsAtCompileTime, \
+ Flags = Eigen::internal::traits<Derived >::Flags, \
+ CoeffReadCost = Eigen::internal::traits<Derived >::CoeffReadCost, \
+ SizeAtCompileTime = Base::SizeAtCompileTime, \
+ IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
+ using Base::derived; \
+ using Base::const_cast_derived;
+
+#define EIGEN_SPARSE_PUBLIC_INTERFACE(Derived) \
+ _EIGEN_SPARSE_PUBLIC_INTERFACE(Derived, Eigen::SparseMatrixBase<Derived >)
+
+const int CoherentAccessPattern = 0x1;
+const int InnerRandomAccessPattern = 0x2 | CoherentAccessPattern;
+const int OuterRandomAccessPattern = 0x4 | CoherentAccessPattern;
+const int RandomAccessPattern = 0x8 | OuterRandomAccessPattern | InnerRandomAccessPattern;
+
+template<typename Derived> class SparseMatrixBase;
+template<typename _Scalar, int _Flags = 0, typename _Index = int> class SparseMatrix;
+template<typename _Scalar, int _Flags = 0, typename _Index = int> class DynamicSparseMatrix;
+template<typename _Scalar, int _Flags = 0, typename _Index = int> class SparseVector;
+template<typename _Scalar, int _Flags = 0, typename _Index = int> class MappedSparseMatrix;
+
+template<typename MatrixType, int Mode> class SparseTriangularView;
+template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView;
+template<typename Lhs, typename Rhs> class SparseDiagonalProduct;
+template<typename MatrixType> class SparseView;
+
+template<typename Lhs, typename Rhs> class SparseSparseProduct;
+template<typename Lhs, typename Rhs> class SparseTimeDenseProduct;
+template<typename Lhs, typename Rhs> class DenseTimeSparseProduct;
+template<typename Lhs, typename Rhs, bool Transpose> class SparseDenseOuterProduct;
+
+template<typename Lhs, typename Rhs> struct SparseSparseProductReturnType;
+template<typename Lhs, typename Rhs,
+ int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct DenseSparseProductReturnType;
+template<typename Lhs, typename Rhs,
+ int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct SparseDenseProductReturnType;
+template<typename MatrixType,int UpLo> class SparseSymmetricPermutationProduct;
+
+namespace internal {
+
+template<typename T,int Rows,int Cols> struct sparse_eval;
+
+template<typename T> struct eval<T,Sparse>
+ : public sparse_eval<T, traits<T>::RowsAtCompileTime,traits<T>::ColsAtCompileTime>
+{};
+
+template<typename T,int Cols> struct sparse_eval<T,1,Cols> {
+ typedef typename traits<T>::Scalar _Scalar;
+ typedef typename traits<T>::Index _Index;
+ public:
+ typedef SparseVector<_Scalar, RowMajor, _Index> type;
+};
+
+template<typename T,int Rows> struct sparse_eval<T,Rows,1> {
+ typedef typename traits<T>::Scalar _Scalar;
+ typedef typename traits<T>::Index _Index;
+ public:
+ typedef SparseVector<_Scalar, ColMajor, _Index> type;
+};
+
+template<typename T,int Rows,int Cols> struct sparse_eval {
+ typedef typename traits<T>::Scalar _Scalar;
+ typedef typename traits<T>::Index _Index;
+ enum { _Options = ((traits<T>::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };
+ public:
+ typedef SparseMatrix<_Scalar, _Options, _Index> type;
+};
+
+template<typename T> struct sparse_eval<T,1,1> {
+ typedef typename traits<T>::Scalar _Scalar;
+ public:
+ typedef Matrix<_Scalar, 1, 1> type;
+};
+
+template<typename T> struct plain_matrix_type<T,Sparse>
+{
+ typedef typename traits<T>::Scalar _Scalar;
+ typedef typename traits<T>::Index _Index;
+ enum { _Options = ((traits<T>::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };
+ public:
+ typedef SparseMatrix<_Scalar, _Options, _Index> type;
+};
+
+} // end namespace internal
+
+/** \ingroup SparseCore_Module
+ *
+ * \class Triplet
+ *
+ * \brief A small structure to hold a non zero as a triplet (i,j,value).
+ *
+ * \sa SparseMatrix::setFromTriplets()
+ */
+template<typename Scalar, typename Index=typename SparseMatrix<Scalar>::Index >
+class Triplet
+{
+public:
+ Triplet() : m_row(0), m_col(0), m_value(0) {}
+
+ Triplet(const Index& i, const Index& j, const Scalar& v = Scalar(0))
+ : m_row(i), m_col(j), m_value(v)
+ {}
+
+ /** \returns the row index of the element */
+ const Index& row() const { return m_row; }
+
+ /** \returns the column index of the element */
+ const Index& col() const { return m_col; }
+
+ /** \returns the value of the element */
+ const Scalar& value() const { return m_value; }
+protected:
+ Index m_row, m_col;
+ Scalar m_value;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEUTIL_H
diff --git a/Eigen/src/SparseCore/SparseVector.h b/Eigen/src/SparseCore/SparseVector.h
new file mode 100644
index 0000000..7e15c81
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseVector.h
@@ -0,0 +1,447 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEVECTOR_H
+#define EIGEN_SPARSEVECTOR_H
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ * \class SparseVector
+ *
+ * \brief a sparse vector class
+ *
+ * \tparam _Scalar the scalar type, i.e. the type of the coefficients
+ *
+ * See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_SPARSEVECTOR_PLUGIN.
+ */
+
+namespace internal {
+template<typename _Scalar, int _Options, typename _Index>
+struct traits<SparseVector<_Scalar, _Options, _Index> >
+{
+ typedef _Scalar Scalar;
+ typedef _Index Index;
+ typedef Sparse StorageKind;
+ typedef MatrixXpr XprKind;
+ enum {
+ IsColVector = (_Options & RowMajorBit) ? 0 : 1,
+
+ RowsAtCompileTime = IsColVector ? Dynamic : 1,
+ ColsAtCompileTime = IsColVector ? 1 : Dynamic,
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ Flags = _Options | NestByRefBit | LvalueBit | (IsColVector ? 0 : RowMajorBit),
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ SupportedAccessPatterns = InnerRandomAccessPattern
+ };
+};
+
+// Sparse-Vector-Assignment kinds:
+enum {
+ SVA_RuntimeSwitch,
+ SVA_Inner,
+ SVA_Outer
+};
+
+template< typename Dest, typename Src,
+ int AssignmentKind = !bool(Src::IsVectorAtCompileTime) ? SVA_RuntimeSwitch
+ : Src::InnerSizeAtCompileTime==1 ? SVA_Outer
+ : SVA_Inner>
+struct sparse_vector_assign_selector;
+
+}
+
+template<typename _Scalar, int _Options, typename _Index>
+class SparseVector
+ : public SparseMatrixBase<SparseVector<_Scalar, _Options, _Index> >
+{
+ typedef SparseMatrixBase<SparseVector> SparseBase;
+
+ public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseVector)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, +=)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, -=)
+
+ typedef internal::CompressedStorage<Scalar,Index> Storage;
+ enum { IsColVector = internal::traits<SparseVector>::IsColVector };
+
+ enum {
+ Options = _Options
+ };
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsColVector ? m_size : 1; }
+ EIGEN_STRONG_INLINE Index cols() const { return IsColVector ? 1 : m_size; }
+ EIGEN_STRONG_INLINE Index innerSize() const { return m_size; }
+ EIGEN_STRONG_INLINE Index outerSize() const { return 1; }
+
+ EIGEN_STRONG_INLINE const Scalar* valuePtr() const { return &m_data.value(0); }
+ EIGEN_STRONG_INLINE Scalar* valuePtr() { return &m_data.value(0); }
+
+ EIGEN_STRONG_INLINE const Index* innerIndexPtr() const { return &m_data.index(0); }
+ EIGEN_STRONG_INLINE Index* innerIndexPtr() { return &m_data.index(0); }
+
+ /** \internal */
+ inline Storage& data() { return m_data; }
+ /** \internal */
+ inline const Storage& data() const { return m_data; }
+
+ inline Scalar coeff(Index row, Index col) const
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+ return coeff(IsColVector ? row : col);
+ }
+ inline Scalar coeff(Index i) const
+ {
+ eigen_assert(i>=0 && i<m_size);
+ return m_data.at(i);
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+ return coeff(IsColVector ? row : col);
+ }
+
+ /** \returns a reference to the coefficient value at given index \a i
+ * This operation involes a log(rho*size) binary search. If the coefficient does not
+ * exist yet, then a sorted insertion into a sequential buffer is performed.
+ *
+ * This insertion might be very costly if the number of nonzeros above \a i is large.
+ */
+ inline Scalar& coeffRef(Index i)
+ {
+ eigen_assert(i>=0 && i<m_size);
+ return m_data.atWithInsertion(i);
+ }
+
+ public:
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ inline void setZero() { m_data.clear(); }
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const { return static_cast<Index>(m_data.size()); }
+
+ inline void startVec(Index outer)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ }
+
+ inline Scalar& insertBackByOuterInner(Index outer, Index inner)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ return insertBack(inner);
+ }
+ inline Scalar& insertBack(Index i)
+ {
+ m_data.append(0, i);
+ return m_data.value(m_data.size()-1);
+ }
+
+ inline Scalar& insert(Index row, Index col)
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+
+ Index inner = IsColVector ? row : col;
+ Index outer = IsColVector ? col : row;
+ eigen_assert(outer==0);
+ return insert(inner);
+ }
+ Scalar& insert(Index i)
+ {
+ eigen_assert(i>=0 && i<m_size);
+
+ Index startId = 0;
+ Index p = Index(m_data.size()) - 1;
+ // TODO smart realloc
+ m_data.resize(p+2,1);
+
+ while ( (p >= startId) && (m_data.index(p) > i) )
+ {
+ m_data.index(p+1) = m_data.index(p);
+ m_data.value(p+1) = m_data.value(p);
+ --p;
+ }
+ m_data.index(p+1) = i;
+ m_data.value(p+1) = 0;
+ return m_data.value(p+1);
+ }
+
+ /**
+ */
+ inline void reserve(Index reserveSize) { m_data.reserve(reserveSize); }
+
+
+ inline void finalize() {}
+
+ void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())
+ {
+ m_data.prune(reference,epsilon);
+ }
+
+ void resize(Index rows, Index cols)
+ {
+ eigen_assert(rows==1 || cols==1);
+ resize(IsColVector ? rows : cols);
+ }
+
+ void resize(Index newSize)
+ {
+ m_size = newSize;
+ m_data.clear();
+ }
+
+ void resizeNonZeros(Index size) { m_data.resize(size); }
+
+ inline SparseVector() : m_size(0) { check_template_parameters(); resize(0); }
+
+ inline SparseVector(Index size) : m_size(0) { check_template_parameters(); resize(size); }
+
+ inline SparseVector(Index rows, Index cols) : m_size(0) { check_template_parameters(); resize(rows,cols); }
+
+ template<typename OtherDerived>
+ inline SparseVector(const SparseMatrixBase<OtherDerived>& other)
+ : m_size(0)
+ {
+ check_template_parameters();
+ *this = other.derived();
+ }
+
+ inline SparseVector(const SparseVector& other)
+ : SparseBase(other), m_size(0)
+ {
+ check_template_parameters();
+ *this = other.derived();
+ }
+
+ /** Swaps the values of \c *this and \a other.
+ * Overloaded for performance: this version performs a \em shallow swap by swaping pointers and attributes only.
+ * \sa SparseMatrixBase::swap()
+ */
+ inline void swap(SparseVector& other)
+ {
+ std::swap(m_size, other.m_size);
+ m_data.swap(other.m_data);
+ }
+
+ inline SparseVector& operator=(const SparseVector& other)
+ {
+ if (other.isRValue())
+ {
+ swap(other.const_cast_derived());
+ }
+ else
+ {
+ resize(other.size());
+ m_data = other.m_data;
+ }
+ return *this;
+ }
+
+ template<typename OtherDerived>
+ inline SparseVector& operator=(const SparseMatrixBase<OtherDerived>& other)
+ {
+ SparseVector tmp(other.size());
+ internal::sparse_vector_assign_selector<SparseVector,OtherDerived>::run(tmp,other.derived());
+ this->swap(tmp);
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Lhs, typename Rhs>
+ inline SparseVector& operator=(const SparseSparseProduct<Lhs,Rhs>& product)
+ {
+ return Base::operator=(product);
+ }
+ #endif
+
+ friend std::ostream & operator << (std::ostream & s, const SparseVector& m)
+ {
+ for (Index i=0; i<m.nonZeros(); ++i)
+ s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
+ s << std::endl;
+ return s;
+ }
+
+ /** Destructor */
+ inline ~SparseVector() {}
+
+ /** Overloaded for performance */
+ Scalar sum() const;
+
+ public:
+
+ /** \internal \deprecated use setZero() and reserve() */
+ EIGEN_DEPRECATED void startFill(Index reserve)
+ {
+ setZero();
+ m_data.reserve(reserve);
+ }
+
+ /** \internal \deprecated use insertBack(Index,Index) */
+ EIGEN_DEPRECATED Scalar& fill(Index r, Index c)
+ {
+ eigen_assert(r==0 || c==0);
+ return fill(IsColVector ? r : c);
+ }
+
+ /** \internal \deprecated use insertBack(Index) */
+ EIGEN_DEPRECATED Scalar& fill(Index i)
+ {
+ m_data.append(0, i);
+ return m_data.value(m_data.size()-1);
+ }
+
+ /** \internal \deprecated use insert(Index,Index) */
+ EIGEN_DEPRECATED Scalar& fillrand(Index r, Index c)
+ {
+ eigen_assert(r==0 || c==0);
+ return fillrand(IsColVector ? r : c);
+ }
+
+ /** \internal \deprecated use insert(Index) */
+ EIGEN_DEPRECATED Scalar& fillrand(Index i)
+ {
+ return insert(i);
+ }
+
+ /** \internal \deprecated use finalize() */
+ EIGEN_DEPRECATED void endFill() {}
+
+ // These two functions were here in the 3.1 release, so let's keep them in case some code rely on them.
+ /** \internal \deprecated use data() */
+ EIGEN_DEPRECATED Storage& _data() { return m_data; }
+ /** \internal \deprecated use data() */
+ EIGEN_DEPRECATED const Storage& _data() const { return m_data; }
+
+# ifdef EIGEN_SPARSEVECTOR_PLUGIN
+# include EIGEN_SPARSEVECTOR_PLUGIN
+# endif
+
+protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT(NumTraits<Index>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);
+ EIGEN_STATIC_ASSERT((_Options&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS);
+ }
+
+ Storage m_data;
+ Index m_size;
+};
+
+template<typename Scalar, int _Options, typename _Index>
+class SparseVector<Scalar,_Options,_Index>::InnerIterator
+{
+ public:
+ InnerIterator(const SparseVector& vec, Index outer=0)
+ : m_data(vec.m_data), m_id(0), m_end(static_cast<Index>(m_data.size()))
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ }
+
+ InnerIterator(const internal::CompressedStorage<Scalar,Index>& data)
+ : m_data(data), m_id(0), m_end(static_cast<Index>(m_data.size()))
+ {}
+
+ inline InnerIterator& operator++() { m_id++; return *this; }
+
+ inline Scalar value() const { return m_data.value(m_id); }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_data.value(m_id)); }
+
+ inline Index index() const { return m_data.index(m_id); }
+ inline Index row() const { return IsColVector ? index() : 0; }
+ inline Index col() const { return IsColVector ? 0 : index(); }
+
+ inline operator bool() const { return (m_id < m_end); }
+
+ protected:
+ const internal::CompressedStorage<Scalar,Index>& m_data;
+ Index m_id;
+ const Index m_end;
+};
+
+template<typename Scalar, int _Options, typename _Index>
+class SparseVector<Scalar,_Options,_Index>::ReverseInnerIterator
+{
+ public:
+ ReverseInnerIterator(const SparseVector& vec, Index outer=0)
+ : m_data(vec.m_data), m_id(static_cast<Index>(m_data.size())), m_start(0)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ }
+
+ ReverseInnerIterator(const internal::CompressedStorage<Scalar,Index>& data)
+ : m_data(data), m_id(static_cast<Index>(m_data.size())), m_start(0)
+ {}
+
+ inline ReverseInnerIterator& operator--() { m_id--; return *this; }
+
+ inline Scalar value() const { return m_data.value(m_id-1); }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_data.value(m_id-1)); }
+
+ inline Index index() const { return m_data.index(m_id-1); }
+ inline Index row() const { return IsColVector ? index() : 0; }
+ inline Index col() const { return IsColVector ? 0 : index(); }
+
+ inline operator bool() const { return (m_id > m_start); }
+
+ protected:
+ const internal::CompressedStorage<Scalar,Index>& m_data;
+ Index m_id;
+ const Index m_start;
+};
+
+namespace internal {
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_Inner> {
+ static void run(Dest& dst, const Src& src) {
+ eigen_internal_assert(src.innerSize()==src.size());
+ for(typename Src::InnerIterator it(src, 0); it; ++it)
+ dst.insert(it.index()) = it.value();
+ }
+};
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_Outer> {
+ static void run(Dest& dst, const Src& src) {
+ eigen_internal_assert(src.outerSize()==src.size());
+ for(typename Dest::Index i=0; i<src.size(); ++i)
+ {
+ typename Src::InnerIterator it(src, i);
+ if(it)
+ dst.insert(i) = it.value();
+ }
+ }
+};
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_RuntimeSwitch> {
+ static void run(Dest& dst, const Src& src) {
+ if(src.outerSize()==1) sparse_vector_assign_selector<Dest,Src,SVA_Inner>::run(dst, src);
+ else sparse_vector_assign_selector<Dest,Src,SVA_Outer>::run(dst, src);
+ }
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEVECTOR_H
diff --git a/Eigen/src/SparseCore/SparseView.h b/Eigen/src/SparseCore/SparseView.h
new file mode 100644
index 0000000..fd84504
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseView.h
@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Daniel Lowengrub <lowdanie@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEVIEW_H
+#define EIGEN_SPARSEVIEW_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType>
+struct traits<SparseView<MatrixType> > : traits<MatrixType>
+{
+ typedef typename MatrixType::Index Index;
+ typedef Sparse StorageKind;
+ enum {
+ Flags = int(traits<MatrixType>::Flags) & (RowMajorBit)
+ };
+};
+
+} // end namespace internal
+
+template<typename MatrixType>
+class SparseView : public SparseMatrixBase<SparseView<MatrixType> >
+{
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseView)
+
+ SparseView(const MatrixType& mat, const Scalar& m_reference = Scalar(0),
+ typename NumTraits<Scalar>::Real m_epsilon = NumTraits<Scalar>::dummy_precision()) :
+ m_matrix(mat), m_reference(m_reference), m_epsilon(m_epsilon) {}
+
+ class InnerIterator;
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ inline Index innerSize() const { return m_matrix.innerSize(); }
+ inline Index outerSize() const { return m_matrix.outerSize(); }
+
+protected:
+ MatrixTypeNested m_matrix;
+ Scalar m_reference;
+ typename NumTraits<Scalar>::Real m_epsilon;
+};
+
+template<typename MatrixType>
+class SparseView<MatrixType>::InnerIterator : public _MatrixTypeNested::InnerIterator
+{
+ typedef typename SparseView::Index Index;
+public:
+ typedef typename _MatrixTypeNested::InnerIterator IterBase;
+ InnerIterator(const SparseView& view, Index outer) :
+ IterBase(view.m_matrix, outer), m_view(view)
+ {
+ incrementToNonZero();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ IterBase::operator++();
+ incrementToNonZero();
+ return *this;
+ }
+
+ using IterBase::value;
+
+protected:
+ const SparseView& m_view;
+
+private:
+ void incrementToNonZero()
+ {
+ while((bool(*this)) && internal::isMuchSmallerThan(value(), m_view.m_reference, m_view.m_epsilon))
+ {
+ IterBase::operator++();
+ }
+ }
+};
+
+template<typename Derived>
+const SparseView<Derived> MatrixBase<Derived>::sparseView(const Scalar& m_reference,
+ const typename NumTraits<Scalar>::Real& m_epsilon) const
+{
+ return SparseView<Derived>(derived(), m_reference, m_epsilon);
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseCore/TriangularSolver.h b/Eigen/src/SparseCore/TriangularSolver.h
new file mode 100644
index 0000000..ccc12af
--- /dev/null
+++ b/Eigen/src/SparseCore/TriangularSolver.h
@@ -0,0 +1,334 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSETRIANGULARSOLVER_H
+#define EIGEN_SPARSETRIANGULARSOLVER_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Mode,
+ int UpLo = (Mode & Lower)
+ ? Lower
+ : (Mode & Upper)
+ ? Upper
+ : -1,
+ int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit>
+struct sparse_solve_triangular_selector;
+
+// forward substitution, row-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int i=0; i<lhs.rows(); ++i)
+ {
+ Scalar tmp = other.coeff(i,col);
+ Scalar lastVal(0);
+ int lastIndex = 0;
+ for(typename Lhs::InnerIterator it(lhs, i); it; ++it)
+ {
+ lastVal = it.value();
+ lastIndex = it.index();
+ if(lastIndex==i)
+ break;
+ tmp -= lastVal * other.coeff(lastIndex,col);
+ }
+ if (Mode & UnitDiag)
+ other.coeffRef(i,col) = tmp;
+ else
+ {
+ eigen_assert(lastIndex==i);
+ other.coeffRef(i,col) = tmp/lastVal;
+ }
+ }
+ }
+ }
+};
+
+// backward substitution, row-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int i=lhs.rows()-1 ; i>=0 ; --i)
+ {
+ Scalar tmp = other.coeff(i,col);
+ Scalar l_ii(0);
+ typename Lhs::InnerIterator it(lhs, i);
+ while(it && it.index()<i)
+ ++it;
+ if(!(Mode & UnitDiag))
+ {
+ eigen_assert(it && it.index()==i);
+ l_ii = it.value();
+ ++it;
+ }
+ else if (it && it.index() == i)
+ ++it;
+ for(; it; ++it)
+ {
+ tmp -= it.value() * other.coeff(it.index(),col);
+ }
+
+ if (Mode & UnitDiag)
+ other.coeffRef(i,col) = tmp;
+ else
+ other.coeffRef(i,col) = tmp/l_ii;
+ }
+ }
+ }
+};
+
+// forward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int i=0; i<lhs.cols(); ++i)
+ {
+ Scalar& tmp = other.coeffRef(i,col);
+ if (tmp!=Scalar(0)) // optimization when other is actually sparse
+ {
+ typename Lhs::InnerIterator it(lhs, i);
+ while(it && it.index()<i)
+ ++it;
+ if(!(Mode & UnitDiag))
+ {
+ eigen_assert(it && it.index()==i);
+ tmp /= it.value();
+ }
+ if (it && it.index()==i)
+ ++it;
+ for(; it; ++it)
+ other.coeffRef(it.index(), col) -= tmp * it.value();
+ }
+ }
+ }
+ }
+};
+
+// backward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int i=lhs.cols()-1; i>=0; --i)
+ {
+ Scalar& tmp = other.coeffRef(i,col);
+ if (tmp!=Scalar(0)) // optimization when other is actually sparse
+ {
+ if(!(Mode & UnitDiag))
+ {
+ // TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements
+ typename Lhs::ReverseInnerIterator it(lhs, i);
+ while(it && it.index()!=i)
+ --it;
+ eigen_assert(it && it.index()==i);
+ other.coeffRef(i,col) /= it.value();
+ }
+ typename Lhs::InnerIterator it(lhs, i);
+ for(; it && it.index()<i; ++it)
+ other.coeffRef(it.index(), col) -= tmp * it.value();
+ }
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+template<typename ExpressionType,int Mode>
+template<typename OtherDerived>
+void SparseTriangularView<ExpressionType,Mode>::solveInPlace(MatrixBase<OtherDerived>& other) const
+{
+ eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());
+ eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+
+ enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
+
+ typedef typename internal::conditional<copy,
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
+ OtherCopy otherCopy(other.derived());
+
+ internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(m_matrix, otherCopy);
+
+ if (copy)
+ other = otherCopy;
+}
+
+template<typename ExpressionType,int Mode>
+template<typename OtherDerived>
+typename internal::plain_matrix_type_column_major<OtherDerived>::type
+SparseTriangularView<ExpressionType,Mode>::solve(const MatrixBase<OtherDerived>& other) const
+{
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type res(other);
+ solveInPlace(res);
+ return res;
+}
+
+// pure sparse path
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Mode,
+ int UpLo = (Mode & Lower)
+ ? Lower
+ : (Mode & Upper)
+ ? Upper
+ : -1,
+ int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>
+struct sparse_solve_triangular_sparse_selector;
+
+// forward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode, int UpLo>
+struct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef typename promote_index_type<typename traits<Lhs>::Index,
+ typename traits<Rhs>::Index>::type Index;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ const bool IsLower = (UpLo==Lower);
+ AmbiVector<Scalar,Index> tempVector(other.rows()*2);
+ tempVector.setBounds(0,other.rows());
+
+ Rhs res(other.rows(), other.cols());
+ res.reserve(other.nonZeros());
+
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ // FIXME estimate number of non zeros
+ tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);
+ tempVector.setZero();
+ tempVector.restart();
+ for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)
+ {
+ tempVector.coeffRef(rhsIt.index()) = rhsIt.value();
+ }
+
+ for(int i=IsLower?0:lhs.cols()-1;
+ IsLower?i<lhs.cols():i>=0;
+ i+=IsLower?1:-1)
+ {
+ tempVector.restart();
+ Scalar& ci = tempVector.coeffRef(i);
+ if (ci!=Scalar(0))
+ {
+ // find
+ typename Lhs::InnerIterator it(lhs, i);
+ if(!(Mode & UnitDiag))
+ {
+ if (IsLower)
+ {
+ eigen_assert(it.index()==i);
+ ci /= it.value();
+ }
+ else
+ ci /= lhs.coeff(i,i);
+ }
+ tempVector.restart();
+ if (IsLower)
+ {
+ if (it.index()==i)
+ ++it;
+ for(; it; ++it)
+ tempVector.coeffRef(it.index()) -= ci * it.value();
+ }
+ else
+ {
+ for(; it && it.index()<i; ++it)
+ tempVector.coeffRef(it.index()) -= ci * it.value();
+ }
+ }
+ }
+
+
+ int count = 0;
+ // FIXME compute a reference value to filter zeros
+ for (typename AmbiVector<Scalar,Index>::Iterator it(tempVector/*,1e-12*/); it; ++it)
+ {
+ ++ count;
+// std::cerr << "fill " << it.index() << ", " << col << "\n";
+// std::cout << it.value() << " ";
+ // FIXME use insertBack
+ res.insert(it.index(), col) = it.value();
+ }
+// std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";
+ }
+ res.finalize();
+ other = res.markAsRValue();
+ }
+};
+
+} // end namespace internal
+
+template<typename ExpressionType,int Mode>
+template<typename OtherDerived>
+void SparseTriangularView<ExpressionType,Mode>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const
+{
+ eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());
+ eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+
+// enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
+
+// typedef typename internal::conditional<copy,
+// typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
+// OtherCopy otherCopy(other.derived());
+
+ internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(m_matrix, other.derived());
+
+// if (copy)
+// other = otherCopy;
+}
+
+#ifdef EIGEN2_SUPPORT
+
+// deprecated stuff:
+
+/** \deprecated */
+template<typename Derived>
+template<typename OtherDerived>
+void SparseMatrixBase<Derived>::solveTriangularInPlace(MatrixBase<OtherDerived>& other) const
+{
+ this->template triangular<Flags&(Upper|Lower)>().solveInPlace(other);
+}
+
+/** \deprecated */
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::plain_matrix_type_column_major<OtherDerived>::type
+SparseMatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const
+{
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type res(other);
+ derived().solveTriangularInPlace(res);
+ return res;
+}
+#endif // EIGEN2_SUPPORT
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSETRIANGULARSOLVER_H
diff --git a/Eigen/src/SparseLU/CMakeLists.txt b/Eigen/src/SparseLU/CMakeLists.txt
new file mode 100644
index 0000000..69729ee
--- /dev/null
+++ b/Eigen/src/SparseLU/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SparseLU_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SparseLU_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseLU COMPONENT Devel
+ )
diff --git a/Eigen/src/SparseLU/SparseLU.h b/Eigen/src/SparseLU/SparseLU.h
new file mode 100644
index 0000000..4514cfd
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU.h
@@ -0,0 +1,806 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_SPARSE_LU_H
+#define EIGEN_SPARSE_LU_H
+
+namespace Eigen {
+
+template <typename _MatrixType, typename _OrderingType = COLAMDOrdering<typename _MatrixType::Index> > class SparseLU;
+template <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType;
+template <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType;
+
+/** \ingroup SparseLU_Module
+ * \class SparseLU
+ *
+ * \brief Sparse supernodal LU factorization for general matrices
+ *
+ * This class implements the supernodal LU factorization for general matrices.
+ * It uses the main techniques from the sequential SuperLU package
+ * (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real
+ * and complex arithmetics with single and double precision, depending on the
+ * scalar type of your input matrix.
+ * The code has been optimized to provide BLAS-3 operations during supernode-panel updates.
+ * It benefits directly from the built-in high-performant Eigen BLAS routines.
+ * Moreover, when the size of a supernode is very small, the BLAS calls are avoided to
+ * enable a better optimization from the compiler. For best performance,
+ * you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.
+ *
+ * An important parameter of this class is the ordering method. It is used to reorder the columns
+ * (and eventually the rows) of the matrix to reduce the number of new elements that are created during
+ * numerical factorization. The cheapest method available is COLAMD.
+ * See \link OrderingMethods_Module the OrderingMethods module \endlink for the list of
+ * built-in and external ordering methods.
+ *
+ * Simple example with key steps
+ * \code
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double, ColMajor> A;
+ * SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<Index> > solver;
+ * // fill A and b;
+ * // Compute the ordering permutation vector from the structural pattern of A
+ * solver.analyzePattern(A);
+ * // Compute the numerical factorization
+ * solver.factorize(A);
+ * //Use the factors to solve the linear system
+ * x = solver.solve(b);
+ * \endcode
+ *
+ * \warning The input matrix A should be in a \b compressed and \b column-major form.
+ * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
+ *
+ * \note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix.
+ * For badly scaled matrices, this step can be useful to reduce the pivoting during factorization.
+ * If this is the case for your matrices, you can try the basic scaling method at
+ * "unsupported/Eigen/src/IterativeSolvers/Scaling.h"
+ *
+ * \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<>
+ * \tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
+ *
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ * \sa \ref OrderingMethods_Module
+ */
+template <typename _MatrixType, typename _OrderingType>
+class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typename _MatrixType::Index>
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef _OrderingType OrderingType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> NCMatrix;
+ typedef internal::MappedSuperNodalMatrix<Scalar, Index> SCMatrix;
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ typedef Matrix<Index,Dynamic,1> IndexVector;
+ typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+ typedef internal::SparseLUImpl<Scalar, Index> Base;
+
+ public:
+ SparseLU():m_isInitialized(true),m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
+ {
+ initperfvalues();
+ }
+ SparseLU(const MatrixType& matrix):m_isInitialized(true),m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
+ {
+ initperfvalues();
+ compute(matrix);
+ }
+
+ ~SparseLU()
+ {
+ // Free all explicit dynamic pointers
+ }
+
+ void analyzePattern (const MatrixType& matrix);
+ void factorize (const MatrixType& matrix);
+ void simplicialfactorize(const MatrixType& matrix);
+
+ /**
+ * Compute the symbolic and numeric factorization of the input sparse matrix.
+ * The input matrix should be in column-major storage.
+ */
+ void compute (const MatrixType& matrix)
+ {
+ // Analyze
+ analyzePattern(matrix);
+ //Factorize
+ factorize(matrix);
+ }
+
+ inline Index rows() const { return m_mat.rows(); }
+ inline Index cols() const { return m_mat.cols(); }
+ /** Indicate that the pattern of the input matrix is symmetric */
+ void isSymmetric(bool sym)
+ {
+ m_symmetricmode = sym;
+ }
+
+ /** \returns an expression of the matrix L, internally stored as supernodes
+ * The only operation available with this expression is the triangular solve
+ * \code
+ * y = b; matrixL().solveInPlace(y);
+ * \endcode
+ */
+ SparseLUMatrixLReturnType<SCMatrix> matrixL() const
+ {
+ return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore);
+ }
+ /** \returns an expression of the matrix U,
+ * The only operation available with this expression is the triangular solve
+ * \code
+ * y = b; matrixU().solveInPlace(y);
+ * \endcode
+ */
+ SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,Index> > matrixU() const
+ {
+ return SparseLUMatrixUReturnType<SCMatrix, MappedSparseMatrix<Scalar,ColMajor,Index> >(m_Lstore, m_Ustore);
+ }
+
+ /**
+ * \returns a reference to the row matrix permutation \f$ P_r \f$ such that \f$P_r A P_c^T = L U\f$
+ * \sa colsPermutation()
+ */
+ inline const PermutationType& rowsPermutation() const
+ {
+ return m_perm_r;
+ }
+ /**
+ * \returns a reference to the column matrix permutation\f$ P_c^T \f$ such that \f$P_r A P_c^T = L U\f$
+ * \sa rowsPermutation()
+ */
+ inline const PermutationType& colsPermutation() const
+ {
+ return m_perm_c;
+ }
+ /** Set the threshold used for a diagonal entry to be an acceptable pivot. */
+ void setPivotThreshold(const RealScalar& thresh)
+ {
+ m_diagpivotthresh = thresh;
+ }
+
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \warning the destination matrix X in X = this->solve(B) must be colmun-major.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_factorizationIsOk && "SparseLU is not initialized.");
+ eigen_assert(rows()==B.rows()
+ && "SparseLU::solve(): invalid number of rows of the right hand side matrix B");
+ return internal::solve_retval<SparseLU, Rhs>(*this, B.derived());
+ }
+
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<SparseLU, Rhs> solve(const SparseMatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_factorizationIsOk && "SparseLU is not initialized.");
+ eigen_assert(rows()==B.rows()
+ && "SparseLU::solve(): invalid number of rows of the right hand side matrix B");
+ return internal::sparse_solve_retval<SparseLU, Rhs>(*this, B.derived());
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /**
+ * \returns A string describing the type of error
+ */
+ std::string lastErrorMessage() const
+ {
+ return m_lastError;
+ }
+
+ template<typename Rhs, typename Dest>
+ bool _solve(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const
+ {
+ Dest& X(X_base.derived());
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first");
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+
+ // Permute the right hand side to form X = Pr*B
+ // on return, X is overwritten by the computed solution
+ X.resize(B.rows(),B.cols());
+
+ // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
+ for(Index j = 0; j < B.cols(); ++j)
+ X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
+
+ //Forward substitution with L
+ this->matrixL().solveInPlace(X);
+ this->matrixU().solveInPlace(X);
+
+ // Permute back the solution
+ for (Index j = 0; j < B.cols(); ++j)
+ X.col(j) = colsPermutation().inverse() * X.col(j);
+
+ return true;
+ }
+
+ /**
+ * \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa logAbsDeterminant(), signDeterminant()
+ */
+ Scalar absDeterminant()
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Scalar det = Scalar(1.);
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ using std::abs;
+ det *= abs(it.value());
+ break;
+ }
+ }
+ }
+ return det;
+ }
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix
+ * of which **this is the QR decomposition
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's
+ * inherent to the determinant computation.
+ *
+ * \sa absDeterminant(), signDeterminant()
+ */
+ Scalar logAbsDeterminant() const
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ Scalar det = Scalar(0.);
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.row() < j) continue;
+ if(it.row() == j)
+ {
+ using std::log; using std::abs;
+ det += log(abs(it.value()));
+ break;
+ }
+ }
+ }
+ return det;
+ }
+
+ /** \returns A number representing the sign of the determinant
+ *
+ * \sa absDeterminant(), logAbsDeterminant()
+ */
+ Scalar signDeterminant()
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Index det = 1;
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ if(it.value()<0)
+ det = -det;
+ else if(it.value()==0)
+ return 0;
+ break;
+ }
+ }
+ }
+ return det * m_detPermR * m_detPermC;
+ }
+
+ /** \returns The determinant of the matrix.
+ *
+ * \sa absDeterminant(), logAbsDeterminant()
+ */
+ Scalar determinant()
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Scalar det = Scalar(1.);
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ det *= it.value();
+ break;
+ }
+ }
+ }
+ return det * Scalar(m_detPermR * m_detPermC);
+ }
+
+ protected:
+ // Functions
+ void initperfvalues()
+ {
+ m_perfv.panel_size = 16;
+ m_perfv.relax = 1;
+ m_perfv.maxsuper = 128;
+ m_perfv.rowblk = 16;
+ m_perfv.colblk = 8;
+ m_perfv.fillfactor = 20;
+ }
+
+ // Variables
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_factorizationIsOk;
+ bool m_analysisIsOk;
+ std::string m_lastError;
+ NCMatrix m_mat; // The input (permuted ) matrix
+ SCMatrix m_Lstore; // The lower triangular matrix (supernodal)
+ MappedSparseMatrix<Scalar,ColMajor,Index> m_Ustore; // The upper triangular matrix
+ PermutationType m_perm_c; // Column permutation
+ PermutationType m_perm_r ; // Row permutation
+ IndexVector m_etree; // Column elimination tree
+
+ typename Base::GlobalLU_t m_glu;
+
+ // SparseLU options
+ bool m_symmetricmode;
+ // values for performance
+ internal::perfvalues<Index> m_perfv;
+ RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
+ Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
+ Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
+ private:
+ // Disable copy constructor
+ SparseLU (const SparseLU& );
+
+}; // End class SparseLU
+
+
+
+// Functions needed by the anaysis phase
+/**
+ * Compute the column permutation to minimize the fill-in
+ *
+ * - Apply this permutation to the input matrix -
+ *
+ * - Compute the column elimination tree on the permuted matrix
+ *
+ * - Postorder the elimination tree and the column permutation
+ *
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat)
+{
+
+ //TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.
+
+ OrderingType ord;
+ ord(mat,m_perm_c);
+
+ // Apply the permutation to the column of the input matrix
+ //First copy the whole input matrix.
+ m_mat = mat;
+ if (m_perm_c.size()) {
+ m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used.
+ //Then, permute only the column pointers
+ const Index * outerIndexPtr;
+ if (mat.isCompressed()) outerIndexPtr = mat.outerIndexPtr();
+ else
+ {
+ Index *outerIndexPtr_t = new Index[mat.cols()+1];
+ for(Index i = 0; i <= mat.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
+ outerIndexPtr = outerIndexPtr_t;
+ }
+ for (Index i = 0; i < mat.cols(); i++)
+ {
+ m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
+ m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
+ }
+ if(!mat.isCompressed()) delete[] outerIndexPtr;
+ }
+ // Compute the column elimination tree of the permuted matrix
+ IndexVector firstRowElt;
+ internal::coletree(m_mat, m_etree,firstRowElt);
+
+ // In symmetric mode, do not do postorder here
+ if (!m_symmetricmode) {
+ IndexVector post, iwork;
+ // Post order etree
+ internal::treePostorder(m_mat.cols(), m_etree, post);
+
+
+ // Renumber etree in postorder
+ Index m = m_mat.cols();
+ iwork.resize(m+1);
+ for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));
+ m_etree = iwork;
+
+ // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree
+ PermutationType post_perm(m);
+ for (Index i = 0; i < m; i++)
+ post_perm.indices()(i) = post(i);
+
+ // Combine the two permutations : postorder the permutation for future use
+ if(m_perm_c.size()) {
+ m_perm_c = post_perm * m_perm_c;
+ }
+
+ } // end postordering
+
+ m_analysisIsOk = true;
+}
+
+// Functions needed by the numerical factorization phase
+
+
+/**
+ * - Numerical factorization
+ * - Interleaved with the symbolic factorization
+ * On exit, info is
+ *
+ * = 0: successful factorization
+ *
+ * > 0: if info = i, and i is
+ *
+ * <= A->ncol: U(i,i) is exactly zero. The factorization has
+ * been completed, but the factor U is exactly singular,
+ * and division by zero will occur if it is used to solve a
+ * system of equations.
+ *
+ * > A->ncol: number of bytes allocated when memory allocation
+ * failure occurred, plus A->ncol. If lwork = -1, it is
+ * the estimated amount of space needed, plus A->ncol.
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
+{
+ using internal::emptyIdxLU;
+ eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
+ eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices");
+
+ typedef typename IndexVector::Scalar Index;
+
+
+ // Apply the column permutation computed in analyzepattern()
+ // m_mat = matrix * m_perm_c.inverse();
+ m_mat = matrix;
+ if (m_perm_c.size())
+ {
+ m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers.
+ //Then, permute only the column pointers
+ const Index * outerIndexPtr;
+ if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr();
+ else
+ {
+ Index* outerIndexPtr_t = new Index[matrix.cols()+1];
+ for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
+ outerIndexPtr = outerIndexPtr_t;
+ }
+ for (Index i = 0; i < matrix.cols(); i++)
+ {
+ m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
+ m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
+ }
+ if(!matrix.isCompressed()) delete[] outerIndexPtr;
+ }
+ else
+ { //FIXME This should not be needed if the empty permutation is handled transparently
+ m_perm_c.resize(matrix.cols());
+ for(Index i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;
+ }
+
+ Index m = m_mat.rows();
+ Index n = m_mat.cols();
+ Index nnz = m_mat.nonZeros();
+ Index maxpanel = m_perfv.panel_size * m;
+ // Allocate working storage common to the factor routines
+ Index lwork = 0;
+ Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu);
+ if (info)
+ {
+ m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ;
+ m_factorizationIsOk = false;
+ return ;
+ }
+
+ // Set up pointers for integer working arrays
+ IndexVector segrep(m); segrep.setZero();
+ IndexVector parent(m); parent.setZero();
+ IndexVector xplore(m); xplore.setZero();
+ IndexVector repfnz(maxpanel);
+ IndexVector panel_lsub(maxpanel);
+ IndexVector xprune(n); xprune.setZero();
+ IndexVector marker(m*internal::LUNoMarker); marker.setZero();
+
+ repfnz.setConstant(-1);
+ panel_lsub.setConstant(-1);
+
+ // Set up pointers for scalar working arrays
+ ScalarVector dense;
+ dense.setZero(maxpanel);
+ ScalarVector tempv;
+ tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) );
+
+ // Compute the inverse of perm_c
+ PermutationType iperm_c(m_perm_c.inverse());
+
+ // Identify initial relaxed snodes
+ IndexVector relax_end(n);
+ if ( m_symmetricmode == true )
+ Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
+ else
+ Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
+
+
+ m_perm_r.resize(m);
+ m_perm_r.indices().setConstant(-1);
+ marker.setConstant(-1);
+ m_detPermR = 1; // Record the determinant of the row permutation
+
+ m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0);
+ m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);
+
+ // Work on one 'panel' at a time. A panel is one of the following :
+ // (a) a relaxed supernode at the bottom of the etree, or
+ // (b) panel_size contiguous columns, <panel_size> defined by the user
+ Index jcol;
+ IndexVector panel_histo(n);
+ Index pivrow; // Pivotal row number in the original row matrix
+ Index nseg1; // Number of segments in U-column above panel row jcol
+ Index nseg; // Number of segments in each U-column
+ Index irep;
+ Index i, k, jj;
+ for (jcol = 0; jcol < n; )
+ {
+ // Adjust panel size so that a panel won't overlap with the next relaxed snode.
+ Index panel_size = m_perfv.panel_size; // upper bound on panel width
+ for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)
+ {
+ if (relax_end(k) != emptyIdxLU)
+ {
+ panel_size = k - jcol;
+ break;
+ }
+ }
+ if (k == n)
+ panel_size = n - jcol;
+
+ // Symbolic outer factorization on a panel of columns
+ Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu);
+
+ // Numeric sup-panel updates in topological order
+ Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu);
+
+ // Sparse LU within the panel, and below the panel diagonal
+ for ( jj = jcol; jj< jcol + panel_size; jj++)
+ {
+ k = (jj - jcol) * m; // Column index for w-wide arrays
+
+ nseg = nseg1; // begin after all the panel segments
+ //Depth-first-search for the current column
+ VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);
+ VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
+ info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+ // Numeric updates to this column
+ VectorBlock<ScalarVector> dense_k(dense, k, m);
+ VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1);
+ info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Copy the U-segments to ucol(*)
+ info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Form the L-segment
+ info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);
+ if ( info )
+ {
+ m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT ";
+ std::ostringstream returnInfo;
+ returnInfo << info;
+ m_lastError += returnInfo.str();
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Update the determinant of the row permutation matrix
+ // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
+ if (pivrow != jj) m_detPermR = -m_detPermR;
+
+ // Prune columns (0:jj-1) using column jj
+ Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu);
+
+ // Reset repfnz for this column
+ for (i = 0; i < nseg; i++)
+ {
+ irep = segrep(i);
+ repfnz_k(irep) = emptyIdxLU;
+ }
+ } // end SparseLU within the panel
+ jcol += panel_size; // Move to the next panel
+ } // end for -- end elimination
+
+ m_detPermR = m_perm_r.determinant();
+ m_detPermC = m_perm_c.determinant();
+
+ // Count the number of nonzeros in factors
+ Base::countnz(n, m_nnzL, m_nnzU, m_glu);
+ // Apply permutation to the L subscripts
+ Base::fixupL(n, m_perm_r.indices(), m_glu);
+
+ // Create supernode matrix L
+ m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup);
+ // Create the column major upper sparse matrix U;
+ new (&m_Ustore) MappedSparseMatrix<Scalar, ColMajor, Index> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() );
+
+ m_info = Success;
+ m_factorizationIsOk = true;
+}
+
+template<typename MappedSupernodalType>
+struct SparseLUMatrixLReturnType : internal::no_assignment_operator
+{
+ typedef typename MappedSupernodalType::Index Index;
+ typedef typename MappedSupernodalType::Scalar Scalar;
+ SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL)
+ { }
+ Index rows() { return m_mapL.rows(); }
+ Index cols() { return m_mapL.cols(); }
+ template<typename Dest>
+ void solveInPlace( MatrixBase<Dest> &X) const
+ {
+ m_mapL.solveInPlace(X);
+ }
+ const MappedSupernodalType& m_mapL;
+};
+
+template<typename MatrixLType, typename MatrixUType>
+struct SparseLUMatrixUReturnType : internal::no_assignment_operator
+{
+ typedef typename MatrixLType::Index Index;
+ typedef typename MatrixLType::Scalar Scalar;
+ SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU)
+ : m_mapL(mapL),m_mapU(mapU)
+ { }
+ Index rows() { return m_mapL.rows(); }
+ Index cols() { return m_mapL.cols(); }
+
+ template<typename Dest> void solveInPlace(MatrixBase<Dest> &X) const
+ {
+ Index nrhs = X.cols();
+ Index n = X.rows();
+ // Backward solve with U
+ for (Index k = m_mapL.nsuper(); k >= 0; k--)
+ {
+ Index fsupc = m_mapL.supToCol()[k];
+ Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension
+ Index nsupc = m_mapL.supToCol()[k+1] - fsupc;
+ Index luptr = m_mapL.colIndexPtr()[fsupc];
+
+ if (nsupc == 1)
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ X(fsupc, j) /= m_mapL.valuePtr()[luptr];
+ }
+ }
+ else
+ {
+ Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ U = A.template triangularView<Upper>().solve(U);
+ }
+
+ for (Index j = 0; j < nrhs; ++j)
+ {
+ for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)
+ {
+ typename MatrixUType::InnerIterator it(m_mapU, jcol);
+ for ( ; it; ++it)
+ {
+ Index irow = it.index();
+ X(irow, j) -= X(jcol, j) * it.value();
+ }
+ }
+ }
+ } // End For U-solve
+ }
+ const MatrixLType& m_mapL;
+ const MatrixUType& m_mapU;
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Derived, typename Rhs>
+struct solve_retval<SparseLU<_MatrixType,Derived>, Rhs>
+ : solve_retval_base<SparseLU<_MatrixType,Derived>, Rhs>
+{
+ typedef SparseLU<_MatrixType,Derived> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+template<typename _MatrixType, typename Derived, typename Rhs>
+struct sparse_solve_retval<SparseLU<_MatrixType,Derived>, Rhs>
+ : sparse_solve_retval_base<SparseLU<_MatrixType,Derived>, Rhs>
+{
+ typedef SparseLU<_MatrixType,Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+} // end namespace internal
+
+} // End namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLUImpl.h b/Eigen/src/SparseLU/SparseLUImpl.h
new file mode 100644
index 0000000..14d7089
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLUImpl.h
@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef SPARSELU_IMPL_H
+#define SPARSELU_IMPL_H
+
+namespace Eigen {
+namespace internal {
+
+/** \ingroup SparseLU_Module
+ * \class SparseLUImpl
+ * Base class for sparseLU
+ */
+template <typename Scalar, typename Index>
+class SparseLUImpl
+{
+ public:
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ typedef Matrix<Index,Dynamic,1> IndexVector;
+ typedef typename ScalarVector::RealScalar RealScalar;
+ typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;
+ typedef Ref<Matrix<Index,Dynamic,1> > BlockIndexVector;
+ typedef LU_GlobalLU_t<IndexVector, ScalarVector> GlobalLU_t;
+ typedef SparseMatrix<Scalar,ColMajor,Index> MatrixType;
+
+ protected:
+ template <typename VectorType>
+ Index expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions);
+ Index memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu);
+ template <typename VectorType>
+ Index memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions);
+ void heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
+ void relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
+ Index snode_dfs(const Index jcol, const Index kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, GlobalLU_t& glu);
+ Index snode_bmod (const Index jcol, const Index fsupc, ScalarVector& dense, GlobalLU_t& glu);
+ Index pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu);
+ template <typename Traits>
+ void dfs_kernel(const Index jj, IndexVector& perm_r,
+ Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
+ Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
+ IndexVector& xplore, GlobalLU_t& glu, Index& nextl_col, Index krow, Traits& traits);
+ void panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
+
+ void panel_bmod(const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu);
+ Index column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg, BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
+ Index column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu);
+ Index copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep, BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu);
+ void pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg, const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu);
+ void countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu);
+ void fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu);
+
+ template<typename , typename >
+ friend struct column_dfs_traits;
+};
+
+} // end namespace internal
+} // namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLU_Memory.h b/Eigen/src/SparseLU/SparseLU_Memory.h
new file mode 100644
index 0000000..1ffa7d5
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Memory.h
@@ -0,0 +1,227 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]memory.c files in SuperLU
+
+ * -- SuperLU routine (version 3.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * August 1, 2008
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef EIGEN_SPARSELU_MEMORY
+#define EIGEN_SPARSELU_MEMORY
+
+namespace Eigen {
+namespace internal {
+
+enum { LUNoMarker = 3 };
+enum {emptyIdxLU = -1};
+template<typename Index>
+inline Index LUnumTempV(Index& m, Index& w, Index& t, Index& b)
+{
+ return (std::max)(m, (t+b)*w);
+}
+
+template< typename Scalar, typename Index>
+inline Index LUTempSpace(Index&m, Index& w)
+{
+ return (2*w + 4 + LUNoMarker) * m * sizeof(Index) + (w + 1) * m * sizeof(Scalar);
+}
+
+
+
+
+/**
+ * Expand the existing storage to accomodate more fill-ins
+ * \param vec Valid pointer to the vector to allocate or expand
+ * \param[in,out] length At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector
+ * \param[in] nbElts Current number of elements in the factors
+ * \param keep_prev 1: use length and do not expand the vector; 0: compute new_len and expand
+ * \param[in,out] num_expansions Number of times the memory has been expanded
+ */
+template <typename Scalar, typename Index>
+template <typename VectorType>
+Index SparseLUImpl<Scalar,Index>::expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions)
+{
+
+ float alpha = 1.5; // Ratio of the memory increase
+ Index new_len; // New size of the allocated memory
+
+ if(num_expansions == 0 || keep_prev)
+ new_len = length ; // First time allocate requested
+ else
+ new_len = (std::max)(length+1,Index(alpha * length));
+
+ VectorType old_vec; // Temporary vector to hold the previous values
+ if (nbElts > 0 )
+ old_vec = vec.segment(0,nbElts);
+
+ //Allocate or expand the current vector
+#ifdef EIGEN_EXCEPTIONS
+ try
+#endif
+ {
+ vec.resize(new_len);
+ }
+#ifdef EIGEN_EXCEPTIONS
+ catch(std::bad_alloc& )
+#else
+ if(!vec.size())
+#endif
+ {
+ if (!num_expansions)
+ {
+ // First time to allocate from LUMemInit()
+ // Let LUMemInit() deals with it.
+ return -1;
+ }
+ if (keep_prev)
+ {
+ // In this case, the memory length should not not be reduced
+ return new_len;
+ }
+ else
+ {
+ // Reduce the size and increase again
+ Index tries = 0; // Number of attempts
+ do
+ {
+ alpha = (alpha + 1)/2;
+ new_len = (std::max)(length+1,Index(alpha * length));
+#ifdef EIGEN_EXCEPTIONS
+ try
+#endif
+ {
+ vec.resize(new_len);
+ }
+#ifdef EIGEN_EXCEPTIONS
+ catch(std::bad_alloc& )
+#else
+ if (!vec.size())
+#endif
+ {
+ tries += 1;
+ if ( tries > 10) return new_len;
+ }
+ } while (!vec.size());
+ }
+ }
+ //Copy the previous values to the newly allocated space
+ if (nbElts > 0)
+ vec.segment(0, nbElts) = old_vec;
+
+
+ length = new_len;
+ if(num_expansions) ++num_expansions;
+ return 0;
+}
+
+/**
+ * \brief Allocate various working space for the numerical factorization phase.
+ * \param m number of rows of the input matrix
+ * \param n number of columns
+ * \param annz number of initial nonzeros in the matrix
+ * \param lwork if lwork=-1, this routine returns an estimated size of the required memory
+ * \param glu persistent data to facilitate multiple factors : will be deleted later ??
+ * \param fillratio estimated ratio of fill in the factors
+ * \param panel_size Size of a panel
+ * \return an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success
+ * \note Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation
+ */
+template <typename Scalar, typename Index>
+Index SparseLUImpl<Scalar,Index>::memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu)
+{
+ Index& num_expansions = glu.num_expansions; //No memory expansions so far
+ num_expansions = 0;
+ glu.nzumax = glu.nzlumax = (std::min)(fillratio * annz / n, m) * n; // estimated number of nonzeros in U
+ glu.nzlmax = (std::max)(Index(4), fillratio) * annz / 4; // estimated nnz in L factor
+ // Return the estimated size to the user if necessary
+ Index tempSpace;
+ tempSpace = (2*panel_size + 4 + LUNoMarker) * m * sizeof(Index) + (panel_size + 1) * m * sizeof(Scalar);
+ if (lwork == emptyIdxLU)
+ {
+ Index estimated_size;
+ estimated_size = (5 * n + 5) * sizeof(Index) + tempSpace
+ + (glu.nzlmax + glu.nzumax) * sizeof(Index) + (glu.nzlumax+glu.nzumax) * sizeof(Scalar) + n;
+ return estimated_size;
+ }
+
+ // Setup the required space
+
+ // First allocate Integer pointers for L\U factors
+ glu.xsup.resize(n+1);
+ glu.supno.resize(n+1);
+ glu.xlsub.resize(n+1);
+ glu.xlusup.resize(n+1);
+ glu.xusub.resize(n+1);
+
+ // Reserve memory for L/U factors
+ do
+ {
+ if( (expand<ScalarVector>(glu.lusup, glu.nzlumax, 0, 0, num_expansions)<0)
+ || (expand<ScalarVector>(glu.ucol, glu.nzumax, 0, 0, num_expansions)<0)
+ || (expand<IndexVector> (glu.lsub, glu.nzlmax, 0, 0, num_expansions)<0)
+ || (expand<IndexVector> (glu.usub, glu.nzumax, 0, 1, num_expansions)<0) )
+ {
+ //Reduce the estimated size and retry
+ glu.nzlumax /= 2;
+ glu.nzumax /= 2;
+ glu.nzlmax /= 2;
+ if (glu.nzlumax < annz ) return glu.nzlumax;
+ }
+ } while (!glu.lusup.size() || !glu.ucol.size() || !glu.lsub.size() || !glu.usub.size());
+
+ ++num_expansions;
+ return 0;
+
+} // end LuMemInit
+
+/**
+ * \brief Expand the existing storage
+ * \param vec vector to expand
+ * \param[in,out] maxlen On input, previous size of vec (Number of elements to copy ). on output, new size
+ * \param nbElts current number of elements in the vector.
+ * \param memtype Type of the element to expand
+ * \param num_expansions Number of expansions
+ * \return 0 on success, > 0 size of the memory allocated so far
+ */
+template <typename Scalar, typename Index>
+template <typename VectorType>
+Index SparseLUImpl<Scalar,Index>::memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions)
+{
+ Index failed_size;
+ if (memtype == USUB)
+ failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 1, num_expansions);
+ else
+ failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 0, num_expansions);
+
+ if (failed_size)
+ return failed_size;
+
+ return 0 ;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_SPARSELU_MEMORY
diff --git a/Eigen/src/SparseLU/SparseLU_Structs.h b/Eigen/src/SparseLU/SparseLU_Structs.h
new file mode 100644
index 0000000..24d6bf1
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Structs.h
@@ -0,0 +1,111 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+ * NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h
+ * -- SuperLU routine (version 4.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November, 2010
+ *
+ * Global data structures used in LU factorization -
+ *
+ * nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].
+ * (xsup,supno): supno[i] is the supernode no to which i belongs;
+ * xsup(s) points to the beginning of the s-th supernode.
+ * e.g. supno 0 1 2 2 3 3 3 4 4 4 4 4 (n=12)
+ * xsup 0 1 2 4 7 12
+ * Note: dfs will be performed on supernode rep. relative to the new
+ * row pivoting ordering
+ *
+ * (xlsub,lsub): lsub[*] contains the compressed subscript of
+ * rectangular supernodes; xlsub[j] points to the starting
+ * location of the j-th column in lsub[*]. Note that xlsub
+ * is indexed by column.
+ * Storage: original row subscripts
+ *
+ * During the course of sparse LU factorization, we also use
+ * (xlsub,lsub) for the purpose of symmetric pruning. For each
+ * supernode {s,s+1,...,t=s+r} with first column s and last
+ * column t, the subscript set
+ * lsub[j], j=xlsub[s], .., xlsub[s+1]-1
+ * is the structure of column s (i.e. structure of this supernode).
+ * It is used for the storage of numerical values.
+ * Furthermore,
+ * lsub[j], j=xlsub[t], .., xlsub[t+1]-1
+ * is the structure of the last column t of this supernode.
+ * It is for the purpose of symmetric pruning. Therefore, the
+ * structural subscripts can be rearranged without making physical
+ * interchanges among the numerical values.
+ *
+ * However, if the supernode has only one column, then we
+ * only keep one set of subscripts. For any subscript interchange
+ * performed, similar interchange must be done on the numerical
+ * values.
+ *
+ * The last column structures (for pruning) will be removed
+ * after the numercial LU factorization phase.
+ *
+ * (xlusup,lusup): lusup[*] contains the numerical values of the
+ * rectangular supernodes; xlusup[j] points to the starting
+ * location of the j-th column in storage vector lusup[*]
+ * Note: xlusup is indexed by column.
+ * Each rectangular supernode is stored by column-major
+ * scheme, consistent with Fortran 2-dim array storage.
+ *
+ * (xusub,ucol,usub): ucol[*] stores the numerical values of
+ * U-columns outside the rectangular supernodes. The row
+ * subscript of nonzero ucol[k] is stored in usub[k].
+ * xusub[i] points to the starting location of column i in ucol.
+ * Storage: new row subscripts; that is subscripts of PA.
+ */
+
+#ifndef EIGEN_LU_STRUCTS
+#define EIGEN_LU_STRUCTS
+namespace Eigen {
+namespace internal {
+
+typedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} MemType;
+
+template <typename IndexVector, typename ScalarVector>
+struct LU_GlobalLU_t {
+ typedef typename IndexVector::Scalar Index;
+ IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode
+ IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)
+ ScalarVector lusup; // nonzero values of L ordered by columns
+ IndexVector lsub; // Compressed row indices of L rectangular supernodes.
+ IndexVector xlusup; // pointers to the beginning of each column in lusup
+ IndexVector xlsub; // pointers to the beginning of each column in lsub
+ Index nzlmax; // Current max size of lsub
+ Index nzlumax; // Current max size of lusup
+ ScalarVector ucol; // nonzero values of U ordered by columns
+ IndexVector usub; // row indices of U columns in ucol
+ IndexVector xusub; // Pointers to the beginning of each column of U in ucol
+ Index nzumax; // Current max size of ucol
+ Index n; // Number of columns in the matrix
+ Index num_expansions;
+};
+
+// Values to set for performance
+template <typename Index>
+struct perfvalues {
+ Index panel_size; // a panel consists of at most <panel_size> consecutive columns
+ Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
+ // in a subtree of the elimination tree is less than relax, this subtree is considered
+ // as one supernode regardless of the row structures of those columns
+ Index maxsuper; // The maximum size for a supernode in complete LU
+ Index rowblk; // The minimum row dimension for 2-D blocking to be used;
+ Index colblk; // The minimum column dimension for 2-D blocking to be used;
+ Index fillfactor; // The estimated fills factors for L and U, compared with A
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_LU_STRUCTS
diff --git a/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h b/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
new file mode 100644
index 0000000..b16afd6
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
@@ -0,0 +1,298 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
+#define EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
+
+namespace Eigen {
+namespace internal {
+
+/** \ingroup SparseLU_Module
+ * \brief a class to manipulate the L supernodal factor from the SparseLU factorization
+ *
+ * This class contain the data to easily store
+ * and manipulate the supernodes during the factorization and solution phase of Sparse LU.
+ * Only the lower triangular matrix has supernodes.
+ *
+ * NOTE : This class corresponds to the SCformat structure in SuperLU
+ *
+ */
+/* TODO
+ * InnerIterator as for sparsematrix
+ * SuperInnerIterator to iterate through all supernodes
+ * Function for triangular solve
+ */
+template <typename _Scalar, typename _Index>
+class MappedSuperNodalMatrix
+{
+ public:
+ typedef _Scalar Scalar;
+ typedef _Index Index;
+ typedef Matrix<Index,Dynamic,1> IndexVector;
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ public:
+ MappedSuperNodalMatrix()
+ {
+
+ }
+ MappedSuperNodalMatrix(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
+ IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
+ {
+ setInfos(m, n, nzval, nzval_colptr, rowind, rowind_colptr, col_to_sup, sup_to_col);
+ }
+
+ ~MappedSuperNodalMatrix()
+ {
+
+ }
+ /**
+ * Set appropriate pointers for the lower triangular supernodal matrix
+ * These infos are available at the end of the numerical factorization
+ * FIXME This class will be modified such that it can be use in the course
+ * of the factorization.
+ */
+ void setInfos(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
+ IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
+ {
+ m_row = m;
+ m_col = n;
+ m_nzval = nzval.data();
+ m_nzval_colptr = nzval_colptr.data();
+ m_rowind = rowind.data();
+ m_rowind_colptr = rowind_colptr.data();
+ m_nsuper = col_to_sup(n);
+ m_col_to_sup = col_to_sup.data();
+ m_sup_to_col = sup_to_col.data();
+ }
+
+ /**
+ * Number of rows
+ */
+ Index rows() { return m_row; }
+
+ /**
+ * Number of columns
+ */
+ Index cols() { return m_col; }
+
+ /**
+ * Return the array of nonzero values packed by column
+ *
+ * The size is nnz
+ */
+ Scalar* valuePtr() { return m_nzval; }
+
+ const Scalar* valuePtr() const
+ {
+ return m_nzval;
+ }
+ /**
+ * Return the pointers to the beginning of each column in \ref valuePtr()
+ */
+ Index* colIndexPtr()
+ {
+ return m_nzval_colptr;
+ }
+
+ const Index* colIndexPtr() const
+ {
+ return m_nzval_colptr;
+ }
+
+ /**
+ * Return the array of compressed row indices of all supernodes
+ */
+ Index* rowIndex() { return m_rowind; }
+
+ const Index* rowIndex() const
+ {
+ return m_rowind;
+ }
+
+ /**
+ * Return the location in \em rowvaluePtr() which starts each column
+ */
+ Index* rowIndexPtr() { return m_rowind_colptr; }
+
+ const Index* rowIndexPtr() const
+ {
+ return m_rowind_colptr;
+ }
+
+ /**
+ * Return the array of column-to-supernode mapping
+ */
+ Index* colToSup() { return m_col_to_sup; }
+
+ const Index* colToSup() const
+ {
+ return m_col_to_sup;
+ }
+ /**
+ * Return the array of supernode-to-column mapping
+ */
+ Index* supToCol() { return m_sup_to_col; }
+
+ const Index* supToCol() const
+ {
+ return m_sup_to_col;
+ }
+
+ /**
+ * Return the number of supernodes
+ */
+ Index nsuper() const
+ {
+ return m_nsuper;
+ }
+
+ class InnerIterator;
+ template<typename Dest>
+ void solveInPlace( MatrixBase<Dest>&X) const;
+
+
+
+
+ protected:
+ Index m_row; // Number of rows
+ Index m_col; // Number of columns
+ Index m_nsuper; // Number of supernodes
+ Scalar* m_nzval; //array of nonzero values packed by column
+ Index* m_nzval_colptr; //nzval_colptr[j] Stores the location in nzval[] which starts column j
+ Index* m_rowind; // Array of compressed row indices of rectangular supernodes
+ Index* m_rowind_colptr; //rowind_colptr[j] stores the location in rowind[] which starts column j
+ Index* m_col_to_sup; // col_to_sup[j] is the supernode number to which column j belongs
+ Index* m_sup_to_col; //sup_to_col[s] points to the starting column of the s-th supernode
+
+ private :
+};
+
+/**
+ * \brief InnerIterator class to iterate over nonzero values of the current column in the supernodal matrix L
+ *
+ */
+template<typename Scalar, typename Index>
+class MappedSuperNodalMatrix<Scalar,Index>::InnerIterator
+{
+ public:
+ InnerIterator(const MappedSuperNodalMatrix& mat, Index outer)
+ : m_matrix(mat),
+ m_outer(outer),
+ m_supno(mat.colToSup()[outer]),
+ m_idval(mat.colIndexPtr()[outer]),
+ m_startidval(m_idval),
+ m_endidval(mat.colIndexPtr()[outer+1]),
+ m_idrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]]),
+ m_endidrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]+1])
+ {}
+ inline InnerIterator& operator++()
+ {
+ m_idval++;
+ m_idrow++;
+ return *this;
+ }
+ inline Scalar value() const { return m_matrix.valuePtr()[m_idval]; }
+
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_idval]); }
+
+ inline Index index() const { return m_matrix.rowIndex()[m_idrow]; }
+ inline Index row() const { return index(); }
+ inline Index col() const { return m_outer; }
+
+ inline Index supIndex() const { return m_supno; }
+
+ inline operator bool() const
+ {
+ return ( (m_idval < m_endidval) && (m_idval >= m_startidval)
+ && (m_idrow < m_endidrow) );
+ }
+
+ protected:
+ const MappedSuperNodalMatrix& m_matrix; // Supernodal lower triangular matrix
+ const Index m_outer; // Current column
+ const Index m_supno; // Current SuperNode number
+ Index m_idval; // Index to browse the values in the current column
+ const Index m_startidval; // Start of the column value
+ const Index m_endidval; // End of the column value
+ Index m_idrow; // Index to browse the row indices
+ Index m_endidrow; // End index of row indices of the current column
+};
+
+/**
+ * \brief Solve with the supernode triangular matrix
+ *
+ */
+template<typename Scalar, typename Index>
+template<typename Dest>
+void MappedSuperNodalMatrix<Scalar,Index>::solveInPlace( MatrixBase<Dest>&X) const
+{
+ Index n = X.rows();
+ Index nrhs = X.cols();
+ const Scalar * Lval = valuePtr(); // Nonzero values
+ Matrix<Scalar,Dynamic,Dynamic> work(n, nrhs); // working vector
+ work.setZero();
+ for (Index k = 0; k <= nsuper(); k ++)
+ {
+ Index fsupc = supToCol()[k]; // First column of the current supernode
+ Index istart = rowIndexPtr()[fsupc]; // Pointer index to the subscript of the current column
+ Index nsupr = rowIndexPtr()[fsupc+1] - istart; // Number of rows in the current supernode
+ Index nsupc = supToCol()[k+1] - fsupc; // Number of columns in the current supernode
+ Index nrow = nsupr - nsupc; // Number of rows in the non-diagonal part of the supernode
+ Index irow; //Current index row
+
+ if (nsupc == 1 )
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ InnerIterator it(*this, fsupc);
+ ++it; // Skip the diagonal element
+ for (; it; ++it)
+ {
+ irow = it.row();
+ X(irow, j) -= X(fsupc, j) * it.value();
+ }
+ }
+ }
+ else
+ {
+ // The supernode has more than one column
+ Index luptr = colIndexPtr()[fsupc];
+ Index lda = colIndexPtr()[fsupc+1] - luptr;
+
+ // Triangular solve
+ Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ U = A.template triangularView<UnitLower>().solve(U);
+
+ // Matrix-vector product
+ new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
+ work.block(0, 0, nrow, nrhs) = A * U;
+
+ //Begin Scatter
+ for (Index j = 0; j < nrhs; j++)
+ {
+ Index iptr = istart + nsupc;
+ for (Index i = 0; i < nrow; i++)
+ {
+ irow = rowIndex()[iptr];
+ X(irow, j) -= work(i, j); // Scatter operation
+ work(i, j) = Scalar(0);
+ iptr++;
+ }
+ }
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSELU_MATRIX_H
diff --git a/Eigen/src/SparseLU/SparseLU_Utils.h b/Eigen/src/SparseLU/SparseLU_Utils.h
new file mode 100644
index 0000000..15352ac
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Utils.h
@@ -0,0 +1,80 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_SPARSELU_UTILS_H
+#define EIGEN_SPARSELU_UTILS_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Count Nonzero elements in the factors
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu)
+{
+ nnzL = 0;
+ nnzU = (glu.xusub)(n);
+ Index nsuper = (glu.supno)(n);
+ Index jlen;
+ Index i, j, fsupc;
+ if (n <= 0 ) return;
+ // For each supernode
+ for (i = 0; i <= nsuper; i++)
+ {
+ fsupc = glu.xsup(i);
+ jlen = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+
+ for (j = fsupc; j < glu.xsup(i+1); j++)
+ {
+ nnzL += jlen;
+ nnzU += j - fsupc + 1;
+ jlen--;
+ }
+ }
+}
+
+/**
+ * \brief Fix up the data storage lsub for L-subscripts.
+ *
+ * It removes the subscripts sets for structural pruning,
+ * and applies permutation to the remaining subscripts
+ *
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu)
+{
+ Index fsupc, i, j, k, jstart;
+
+ Index nextl = 0;
+ Index nsuper = (glu.supno)(n);
+
+ // For each supernode
+ for (i = 0; i <= nsuper; i++)
+ {
+ fsupc = glu.xsup(i);
+ jstart = glu.xlsub(fsupc);
+ glu.xlsub(fsupc) = nextl;
+ for (j = jstart; j < glu.xlsub(fsupc + 1); j++)
+ {
+ glu.lsub(nextl) = perm_r(glu.lsub(j)); // Now indexed into P*A
+ nextl++;
+ }
+ for (k = fsupc+1; k < glu.xsup(i+1); k++)
+ glu.xlsub(k) = nextl; // other columns in supernode i
+ }
+
+ glu.xlsub(n) = nextl;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_SPARSELU_UTILS_H
diff --git a/Eigen/src/SparseLU/SparseLU_column_bmod.h b/Eigen/src/SparseLU/SparseLU_column_bmod.h
new file mode 100644
index 0000000..f24bd87
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_column_bmod.h
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COLUMN_BMOD_H
+#define SPARSELU_COLUMN_BMOD_H
+
+namespace Eigen {
+
+namespace internal {
+/**
+ * \brief Performs numeric block updates (sup-col) in topological order
+ *
+ * \param jcol current column to update
+ * \param nseg Number of segments in the U part
+ * \param dense Store the full representation of the column
+ * \param tempv working array
+ * \param segrep segment representative ...
+ * \param repfnz ??? First nonzero column in each row ??? ...
+ * \param fpanelc First column in the current panel
+ * \param glu Global LU data.
+ * \return 0 - successful return
+ * > 0 - number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename Index>
+Index SparseLUImpl<Scalar,Index>::column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)
+{
+ Index jsupno, k, ksub, krep, ksupno;
+ Index lptr, nrow, isub, irow, nextlu, new_next, ufirst;
+ Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros;
+ /* krep = representative of current k-th supernode
+ * fsupc = first supernodal column
+ * nsupc = number of columns in a supernode
+ * nsupr = number of rows in a supernode
+ * luptr = location of supernodal LU-block in storage
+ * kfnz = first nonz in the k-th supernodal segment
+ * no_zeros = no lf leading zeros in a supernodal U-segment
+ */
+
+ jsupno = glu.supno(jcol);
+ // For each nonzero supernode segment of U[*,j] in topological order
+ k = nseg - 1;
+ Index d_fsupc; // distance between the first column of the current panel and the
+ // first column of the current snode
+ Index fst_col; // First column within small LU update
+ Index segsize;
+ for (ksub = 0; ksub < nseg; ksub++)
+ {
+ krep = segrep(k); k--;
+ ksupno = glu.supno(krep);
+ if (jsupno != ksupno )
+ {
+ // outside the rectangular supernode
+ fsupc = glu.xsup(ksupno);
+ fst_col = (std::max)(fsupc, fpanelc);
+
+ // Distance from the current supernode to the current panel;
+ // d_fsupc = 0 if fsupc > fpanelc
+ d_fsupc = fst_col - fsupc;
+
+ luptr = glu.xlusup(fst_col) + d_fsupc;
+ lptr = glu.xlsub(fsupc) + d_fsupc;
+
+ kfnz = repfnz(krep);
+ kfnz = (std::max)(kfnz, fpanelc);
+
+ segsize = krep - kfnz + 1;
+ nsupc = krep - fst_col + 1;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+ nrow = nsupr - d_fsupc - nsupc;
+ Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);
+
+
+ // Perform a triangular solver and block update,
+ // then scatter the result of sup-col update to dense
+ no_zeros = kfnz - fst_col;
+ if(segsize==1)
+ LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else
+ LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ } // end if jsupno
+ } // end for each segment
+
+ // Process the supernodal portion of L\U[*,j]
+ nextlu = glu.xlusup(jcol);
+ fsupc = glu.xsup(jsupno);
+
+ // copy the SPA dense into L\U[*,j]
+ Index mem;
+ new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
+ Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;
+ if(offset)
+ new_next += offset;
+ while (new_next > glu.nzlumax )
+ {
+ mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);
+ if (mem) return mem;
+ }
+
+ for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)
+ {
+ irow = glu.lsub(isub);
+ glu.lusup(nextlu) = dense(irow);
+ dense(irow) = Scalar(0.0);
+ ++nextlu;
+ }
+
+ if(offset)
+ {
+ glu.lusup.segment(nextlu,offset).setZero();
+ nextlu += offset;
+ }
+ glu.xlusup(jcol + 1) = nextlu; // close L\U(*,jcol);
+
+ /* For more updates within the panel (also within the current supernode),
+ * should start from the first column of the panel, or the first column
+ * of the supernode, whichever is bigger. There are two cases:
+ * 1) fsupc < fpanelc, then fst_col <-- fpanelc
+ * 2) fsupc >= fpanelc, then fst_col <-- fsupc
+ */
+ fst_col = (std::max)(fsupc, fpanelc);
+
+ if (fst_col < jcol)
+ {
+ // Distance between the current supernode and the current panel
+ // d_fsupc = 0 if fsupc >= fpanelc
+ d_fsupc = fst_col - fsupc;
+
+ lptr = glu.xlsub(fsupc) + d_fsupc;
+ luptr = glu.xlusup(fst_col) + d_fsupc;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension
+ nsupc = jcol - fst_col; // excluding jcol
+ nrow = nsupr - d_fsupc - nsupc;
+
+ // points to the beginning of jcol in snode L\U(jsupno)
+ ufirst = glu.xlusup(jcol) + d_fsupc;
+ Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
+ Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
+ u = A.template triangularView<UnitLower>().solve(u);
+
+ new (&A) Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
+ VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
+ l.noalias() -= A * u;
+
+ } // End if fst_col
+ return 0;
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_COLUMN_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_column_dfs.h b/Eigen/src/SparseLU/SparseLU_column_dfs.h
new file mode 100644
index 0000000..4c04b0e
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_column_dfs.h
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COLUMN_DFS_H
+#define SPARSELU_COLUMN_DFS_H
+
+template <typename Scalar, typename Index> class SparseLUImpl;
+namespace Eigen {
+
+namespace internal {
+
+template<typename IndexVector, typename ScalarVector>
+struct column_dfs_traits : no_assignment_operator
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ typedef typename IndexVector::Scalar Index;
+ column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, Index>::GlobalLU_t& glu, SparseLUImpl<Scalar, Index>& luImpl)
+ : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)
+ {}
+ bool update_segrep(Index /*krep*/, Index /*jj*/)
+ {
+ return true;
+ }
+ void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)
+ {
+ if (nextl >= m_glu.nzlmax)
+ m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
+ if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;
+ }
+ enum { ExpandMem = true };
+
+ Index m_jcol;
+ Index& m_jsuper_ref;
+ typename SparseLUImpl<Scalar, Index>::GlobalLU_t& m_glu;
+ SparseLUImpl<Scalar, Index>& m_luImpl;
+};
+
+
+/**
+ * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
+ *
+ * A supernode representative is the last column of a supernode.
+ * The nonzeros in U[*,j] are segments that end at supernodes representatives.
+ * The routine returns a list of the supernodal representatives
+ * in topological order of the dfs that generates them.
+ * The location of the first nonzero in each supernodal segment
+ * (supernodal entry location) is also returned.
+ *
+ * \param m number of rows in the matrix
+ * \param jcol Current column
+ * \param perm_r Row permutation
+ * \param maxsuper Maximum number of column allowed in a supernode
+ * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
+ * \param lsub_col defines the rhs vector to start the dfs
+ * \param [in,out] segrep Segment representatives - new segments appended
+ * \param repfnz First nonzero location in each row
+ * \param xprune
+ * \param marker marker[i] == jj, if i was visited during dfs of current column jj;
+ * \param parent
+ * \param xplore working array
+ * \param glu global LU data
+ * \return 0 success
+ * > 0 number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename Index>
+Index SparseLUImpl<Scalar,Index>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg, BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
+{
+
+ Index jsuper = glu.supno(jcol);
+ Index nextl = glu.xlsub(jcol);
+ VectorBlock<IndexVector> marker2(marker, 2*m, m);
+
+
+ column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);
+
+ // For each nonzero in A(*,jcol) do dfs
+ for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)
+ {
+ Index krow = lsub_col(k);
+ lsub_col(k) = emptyIdxLU;
+ Index kmark = marker2(krow);
+
+ // krow was visited before, go to the next nonz;
+ if (kmark == jcol) continue;
+
+ dfs_kernel(jcol, perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,
+ xplore, glu, nextl, krow, traits);
+ } // for each nonzero ...
+
+ Index fsupc, jptr, jm1ptr, ito, ifrom, istop;
+ Index nsuper = glu.supno(jcol);
+ Index jcolp1 = jcol + 1;
+ Index jcolm1 = jcol - 1;
+
+ // check to see if j belongs in the same supernode as j-1
+ if ( jcol == 0 )
+ { // Do nothing for column 0
+ nsuper = glu.supno(0) = 0 ;
+ }
+ else
+ {
+ fsupc = glu.xsup(nsuper);
+ jptr = glu.xlsub(jcol); // Not yet compressed
+ jm1ptr = glu.xlsub(jcolm1);
+
+ // Use supernodes of type T2 : see SuperLU paper
+ if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;
+
+ // Make sure the number of columns in a supernode doesn't
+ // exceed threshold
+ if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;
+
+ /* If jcol starts a new supernode, reclaim storage space in
+ * glu.lsub from previous supernode. Note we only store
+ * the subscript set of the first and last columns of
+ * a supernode. (first for num values, last for pruning)
+ */
+ if (jsuper == emptyIdxLU)
+ { // starts a new supernode
+ if ( (fsupc < jcolm1-1) )
+ { // >= 3 columns in nsuper
+ ito = glu.xlsub(fsupc+1);
+ glu.xlsub(jcolm1) = ito;
+ istop = ito + jptr - jm1ptr;
+ xprune(jcolm1) = istop; // intialize xprune(jcol-1)
+ glu.xlsub(jcol) = istop;
+
+ for (ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
+ glu.lsub(ito) = glu.lsub(ifrom);
+ nextl = ito; // = istop + length(jcol)
+ }
+ nsuper++;
+ glu.supno(jcol) = nsuper;
+ } // if a new supernode
+ } // end else: jcol > 0
+
+ // Tidy up the pointers before exit
+ glu.xsup(nsuper+1) = jcolp1;
+ glu.supno(jcolp1) = nsuper;
+ xprune(jcol) = nextl; // Intialize upper bound for pruning
+ glu.xlsub(jcolp1) = nextl;
+
+ return 0;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
new file mode 100644
index 0000000..170610d
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
@@ -0,0 +1,106 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]copy_to_ucol.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COPY_TO_UCOL_H
+#define SPARSELU_COPY_TO_UCOL_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs numeric block updates (sup-col) in topological order
+ *
+ * \param jcol current column to update
+ * \param nseg Number of segments in the U part
+ * \param segrep segment representative ...
+ * \param repfnz First nonzero column in each row ...
+ * \param perm_r Row permutation
+ * \param dense Store the full representation of the column
+ * \param glu Global LU data.
+ * \return 0 - successful return
+ * > 0 - number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename Index>
+Index SparseLUImpl<Scalar,Index>::copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep, BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu)
+{
+ Index ksub, krep, ksupno;
+
+ Index jsupno = glu.supno(jcol);
+
+ // For each nonzero supernode segment of U[*,j] in topological order
+ Index k = nseg - 1, i;
+ Index nextu = glu.xusub(jcol);
+ Index kfnz, isub, segsize;
+ Index new_next,irow;
+ Index fsupc, mem;
+ for (ksub = 0; ksub < nseg; ksub++)
+ {
+ krep = segrep(k); k--;
+ ksupno = glu.supno(krep);
+ if (jsupno != ksupno ) // should go into ucol();
+ {
+ kfnz = repfnz(krep);
+ if (kfnz != emptyIdxLU)
+ { // Nonzero U-segment
+ fsupc = glu.xsup(ksupno);
+ isub = glu.xlsub(fsupc) + kfnz - fsupc;
+ segsize = krep - kfnz + 1;
+ new_next = nextu + segsize;
+ while (new_next > glu.nzumax)
+ {
+ mem = memXpand<ScalarVector>(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions);
+ if (mem) return mem;
+ mem = memXpand<IndexVector>(glu.usub, glu.nzumax, nextu, USUB, glu.num_expansions);
+ if (mem) return mem;
+
+ }
+
+ for (i = 0; i < segsize; i++)
+ {
+ irow = glu.lsub(isub);
+ glu.usub(nextu) = perm_r(irow); // Unlike the L part, the U part is stored in its final order
+ glu.ucol(nextu) = dense(irow);
+ dense(irow) = Scalar(0.0);
+ nextu++;
+ isub++;
+ }
+
+ } // end nonzero U-segment
+
+ } // end if jsupno
+
+ } // end for each segment
+ glu.xusub(jcol + 1) = nextu; // close U(*,jcol)
+ return 0;
+}
+
+} // namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_COPY_TO_UCOL_H
diff --git a/Eigen/src/SparseLU/SparseLU_gemm_kernel.h b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
new file mode 100644
index 0000000..9e4e3e7
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
@@ -0,0 +1,279 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
+#define EIGEN_SPARSELU_GEMM_KERNEL_H
+
+namespace Eigen {
+
+namespace internal {
+
+
+/** \internal
+ * A general matrix-matrix product kernel optimized for the SparseLU factorization.
+ * - A, B, and C must be column major
+ * - lda and ldc must be multiples of the respective packet size
+ * - C must have the same alignment as A
+ */
+template<typename Scalar,typename Index>
+EIGEN_DONT_INLINE
+void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
+{
+ using namespace Eigen::internal;
+
+ typedef typename packet_traits<Scalar>::type Packet;
+ enum {
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ PacketSize = packet_traits<Scalar>::size,
+ PM = 8, // peeling in M
+ RN = 2, // register blocking
+ RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
+ BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
+ SM = PM*PacketSize // step along M
+ };
+ Index d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
+ Index n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
+ Index i0 = internal::first_aligned(A,m);
+
+ eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_aligned(C,m)));
+
+ // handle the non aligned rows of A and C without any optimization:
+ for(Index i=0; i<i0; ++i)
+ {
+ for(Index j=0; j<n; ++j)
+ {
+ Scalar c = C[i+j*ldc];
+ for(Index k=0; k<d; ++k)
+ c += B[k+j*ldb] * A[i+k*lda];
+ C[i+j*ldc] = c;
+ }
+ }
+ // process the remaining rows per chunk of BM rows
+ for(Index ib=i0; ib<m; ib+=BM)
+ {
+ Index actual_b = std::min<Index>(BM, m-ib); // actual number of rows
+ Index actual_b_end1 = (actual_b/SM)*SM; // actual number of rows suitable for peeling
+ Index actual_b_end2 = (actual_b/PacketSize)*PacketSize; // actual number of rows suitable for vectorization
+
+ // Let's process two columns of B-C at once
+ for(Index j=0; j<n_end; j+=RN)
+ {
+ const Scalar* Bc0 = B+(j+0)*ldb;
+ const Scalar* Bc1 = B+(j+1)*ldb;
+
+ for(Index k=0; k<d_end; k+=RK)
+ {
+
+ // load and expand a RN x RK block of B
+ Packet b00, b10, b20, b30, b01, b11, b21, b31;
+ b00 = pset1<Packet>(Bc0[0]);
+ b10 = pset1<Packet>(Bc0[1]);
+ if(RK==4) b20 = pset1<Packet>(Bc0[2]);
+ if(RK==4) b30 = pset1<Packet>(Bc0[3]);
+ b01 = pset1<Packet>(Bc1[0]);
+ b11 = pset1<Packet>(Bc1[1]);
+ if(RK==4) b21 = pset1<Packet>(Bc1[2]);
+ if(RK==4) b31 = pset1<Packet>(Bc1[3]);
+
+ Packet a0, a1, a2, a3, c0, c1, t0, t1;
+
+ const Scalar* A0 = A+ib+(k+0)*lda;
+ const Scalar* A1 = A+ib+(k+1)*lda;
+ const Scalar* A2 = A+ib+(k+2)*lda;
+ const Scalar* A3 = A+ib+(k+3)*lda;
+
+ Scalar* C0 = C+ib+(j+0)*ldc;
+ Scalar* C1 = C+ib+(j+1)*ldc;
+
+ a0 = pload<Packet>(A0);
+ a1 = pload<Packet>(A1);
+ if(RK==4)
+ {
+ a2 = pload<Packet>(A2);
+ a3 = pload<Packet>(A3);
+ }
+ else
+ {
+ // workaround "may be used uninitialized in this function" warning
+ a2 = a3 = a0;
+ }
+
+#define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
+#define WORK(I) \
+ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
+ c1 = pload<Packet>(C1+i+(I)*PacketSize); \
+ KMADD(c0, a0, b00, t0) \
+ KMADD(c1, a0, b01, t1) \
+ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
+ KMADD(c0, a1, b10, t0) \
+ KMADD(c1, a1, b11, t1) \
+ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
+ if(RK==4) KMADD(c0, a2, b20, t0) \
+ if(RK==4) KMADD(c1, a2, b21, t1) \
+ if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
+ if(RK==4) KMADD(c0, a3, b30, t0) \
+ if(RK==4) KMADD(c1, a3, b31, t1) \
+ if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
+ pstore(C0+i+(I)*PacketSize, c0); \
+ pstore(C1+i+(I)*PacketSize, c1)
+
+ // process rows of A' - C' with aggressive vectorization and peeling
+ for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
+ {
+ EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
+ prefetch((A0+i+(5)*PacketSize));
+ prefetch((A1+i+(5)*PacketSize));
+ if(RK==4) prefetch((A2+i+(5)*PacketSize));
+ if(RK==4) prefetch((A3+i+(5)*PacketSize));
+ WORK(0);
+ WORK(1);
+ WORK(2);
+ WORK(3);
+ WORK(4);
+ WORK(5);
+ WORK(6);
+ WORK(7);
+ }
+ // process the remaining rows with vectorization only
+ for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
+ {
+ WORK(0);
+ }
+#undef WORK
+ // process the remaining rows without vectorization
+ for(Index i=actual_b_end2; i<actual_b; ++i)
+ {
+ if(RK==4)
+ {
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
+ C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
+ }
+ else
+ {
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
+ C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
+ }
+ }
+
+ Bc0 += RK;
+ Bc1 += RK;
+ } // peeled loop on k
+ } // peeled loop on the columns j
+ // process the last column (we now perform a matrux-vector product)
+ if((n-n_end)>0)
+ {
+ const Scalar* Bc0 = B+(n-1)*ldb;
+
+ for(Index k=0; k<d_end; k+=RK)
+ {
+
+ // load and expand a 1 x RK block of B
+ Packet b00, b10, b20, b30;
+ b00 = pset1<Packet>(Bc0[0]);
+ b10 = pset1<Packet>(Bc0[1]);
+ if(RK==4) b20 = pset1<Packet>(Bc0[2]);
+ if(RK==4) b30 = pset1<Packet>(Bc0[3]);
+
+ Packet a0, a1, a2, a3, c0, t0/*, t1*/;
+
+ const Scalar* A0 = A+ib+(k+0)*lda;
+ const Scalar* A1 = A+ib+(k+1)*lda;
+ const Scalar* A2 = A+ib+(k+2)*lda;
+ const Scalar* A3 = A+ib+(k+3)*lda;
+
+ Scalar* C0 = C+ib+(n_end)*ldc;
+
+ a0 = pload<Packet>(A0);
+ a1 = pload<Packet>(A1);
+ if(RK==4)
+ {
+ a2 = pload<Packet>(A2);
+ a3 = pload<Packet>(A3);
+ }
+ else
+ {
+ // workaround "may be used uninitialized in this function" warning
+ a2 = a3 = a0;
+ }
+
+#define WORK(I) \
+ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
+ KMADD(c0, a0, b00, t0) \
+ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
+ KMADD(c0, a1, b10, t0) \
+ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
+ if(RK==4) KMADD(c0, a2, b20, t0) \
+ if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
+ if(RK==4) KMADD(c0, a3, b30, t0) \
+ if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
+ pstore(C0+i+(I)*PacketSize, c0);
+
+ // agressive vectorization and peeling
+ for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
+ {
+ EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
+ WORK(0);
+ WORK(1);
+ WORK(2);
+ WORK(3);
+ WORK(4);
+ WORK(5);
+ WORK(6);
+ WORK(7);
+ }
+ // vectorization only
+ for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
+ {
+ WORK(0);
+ }
+ // remaining scalars
+ for(Index i=actual_b_end2; i<actual_b; ++i)
+ {
+ if(RK==4)
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
+ else
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
+ }
+
+ Bc0 += RK;
+#undef WORK
+ }
+ }
+
+ // process the last columns of A, corresponding to the last rows of B
+ Index rd = d-d_end;
+ if(rd>0)
+ {
+ for(Index j=0; j<n; ++j)
+ {
+ enum {
+ Alignment = PacketSize>1 ? Aligned : 0
+ };
+ typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
+ typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
+ if(rd==1) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);
+
+ else if(rd==2) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
+ + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
+
+ else MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
+ + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
+ + B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
+ }
+ }
+
+ } // blocking on the rows of A and C
+}
+#undef KMADD
+
+} // namespace internal
+
+} // namespace Eigen
+
+#endif // EIGEN_SPARSELU_GEMM_KERNEL_H
diff --git a/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
new file mode 100644
index 0000000..7a4e430
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
@@ -0,0 +1,127 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* This file is a modified version of heap_relax_snode.c file in SuperLU
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef SPARSELU_HEAP_RELAX_SNODE_H
+#define SPARSELU_HEAP_RELAX_SNODE_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Identify the initial relaxed supernodes
+ *
+ * This routine applied to a symmetric elimination tree.
+ * It assumes that the matrix has been reordered according to the postorder of the etree
+ * \param n The number of columns
+ * \param et elimination tree
+ * \param relax_columns Maximum number of columns allowed in a relaxed snode
+ * \param descendants Number of descendants of each node in the etree
+ * \param relax_end last column in a supernode
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
+{
+
+ // The etree may not be postordered, but its heap ordered
+ IndexVector post;
+ internal::treePostorder(n, et, post); // Post order etree
+ IndexVector inv_post(n+1);
+ Index i;
+ for (i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()???
+
+ // Renumber etree in postorder
+ IndexVector iwork(n);
+ IndexVector et_save(n+1);
+ for (i = 0; i < n; ++i)
+ {
+ iwork(post(i)) = post(et(i));
+ }
+ et_save = et; // Save the original etree
+ et = iwork;
+
+ // compute the number of descendants of each node in the etree
+ relax_end.setConstant(emptyIdxLU);
+ Index j, parent;
+ descendants.setZero();
+ for (j = 0; j < n; j++)
+ {
+ parent = et(j);
+ if (parent != n) // not the dummy root
+ descendants(parent) += descendants(j) + 1;
+ }
+ // Identify the relaxed supernodes by postorder traversal of the etree
+ Index snode_start; // beginning of a snode
+ Index k;
+ Index nsuper_et_post = 0; // Number of relaxed snodes in postordered etree
+ Index nsuper_et = 0; // Number of relaxed snodes in the original etree
+ Index l;
+ for (j = 0; j < n; )
+ {
+ parent = et(j);
+ snode_start = j;
+ while ( parent != n && descendants(parent) < relax_columns )
+ {
+ j = parent;
+ parent = et(j);
+ }
+ // Found a supernode in postordered etree, j is the last column
+ ++nsuper_et_post;
+ k = n;
+ for (i = snode_start; i <= j; ++i)
+ k = (std::min)(k, inv_post(i));
+ l = inv_post(j);
+ if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode
+ {
+ // This is also a supernode in the original etree
+ relax_end(k) = l; // Record last column
+ ++nsuper_et;
+ }
+ else
+ {
+ for (i = snode_start; i <= j; ++i)
+ {
+ l = inv_post(i);
+ if (descendants(i) == 0)
+ {
+ relax_end(l) = l;
+ ++nsuper_et;
+ }
+ }
+ }
+ j++;
+ // Search for a new leaf
+ while (descendants(j) != 0 && j < n) j++;
+ } // End postorder traversal of the etree
+
+ // Recover the original etree
+ et = et_save;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // SPARSELU_HEAP_RELAX_SNODE_H
diff --git a/Eigen/src/SparseLU/SparseLU_kernel_bmod.h b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
new file mode 100644
index 0000000..0d0283b
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SPARSELU_KERNEL_BMOD_H
+#define SPARSELU_KERNEL_BMOD_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs numeric block updates from a given supernode to a single column
+ *
+ * \param segsize Size of the segment (and blocks ) to use for updates
+ * \param[in,out] dense Packed values of the original matrix
+ * \param tempv temporary vector to use for updates
+ * \param lusup array containing the supernodes
+ * \param lda Leading dimension in the supernode
+ * \param nrow Number of rows in the rectangular part of the supernode
+ * \param lsub compressed row subscripts of supernodes
+ * \param lptr pointer to the first column of the current supernode in lsub
+ * \param no_zeros Number of nonzeros elements before the diagonal part of the supernode
+ * \return 0 on success
+ */
+template <int SegSizeAtCompileTime> struct LU_kernel_bmod
+{
+ template <typename BlockScalarVector, typename ScalarVector, typename IndexVector, typename Index>
+ static EIGEN_DONT_INLINE void run(const int segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
+ const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
+};
+
+template <int SegSizeAtCompileTime>
+template <typename BlockScalarVector, typename ScalarVector, typename IndexVector, typename Index>
+EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const int segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
+ const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ // First, copy U[*,j] segment from dense(*) to tempv(*)
+ // The result of triangular solve is in tempv[*];
+ // The result of matric-vector update is in dense[*]
+ Index isub = lptr + no_zeros;
+ int i;
+ Index irow;
+ for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
+ {
+ irow = lsub(isub);
+ tempv(i) = dense(irow);
+ ++isub;
+ }
+ // Dense triangular solve -- start effective triangle
+ luptr += lda * no_zeros + no_zeros;
+ // Form Eigen matrix and vector
+ Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );
+ Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);
+
+ u = A.template triangularView<UnitLower>().solve(u);
+
+ // Dense matrix-vector product y <-- B*x
+ luptr += segsize;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+ Index ldl = internal::first_multiple(nrow, PacketSize);
+ Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
+ Index aligned_offset = internal::first_aligned(tempv.data()+segsize, PacketSize);
+ Index aligned_with_B_offset = (PacketSize-internal::first_aligned(B.data(), PacketSize))%PacketSize;
+ Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );
+
+ l.setZero();
+ internal::sparselu_gemm<Scalar>(l.rows(), l.cols(), B.cols(), B.data(), B.outerStride(), u.data(), u.outerStride(), l.data(), l.outerStride());
+
+ // Scatter tempv[] into SPA dense[] as a temporary storage
+ isub = lptr + no_zeros;
+ for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
+ {
+ irow = lsub(isub++);
+ dense(irow) = tempv(i);
+ }
+
+ // Scatter l into SPA dense[]
+ for (i = 0; i < nrow; i++)
+ {
+ irow = lsub(isub++);
+ dense(irow) -= l(i);
+ }
+}
+
+template <> struct LU_kernel_bmod<1>
+{
+ template <typename BlockScalarVector, typename ScalarVector, typename IndexVector, typename Index>
+ static EIGEN_DONT_INLINE void run(const int /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
+ const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
+};
+
+
+template <typename BlockScalarVector, typename ScalarVector, typename IndexVector, typename Index>
+EIGEN_DONT_INLINE void LU_kernel_bmod<1>::run(const int /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
+ const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ Scalar f = dense(lsub(lptr + no_zeros));
+ luptr += lda * no_zeros + no_zeros + 1;
+ const Scalar* a(lusup.data() + luptr);
+ const /*typename IndexVector::Scalar*/Index* irow(lsub.data()+lptr + no_zeros + 1);
+ Index i = 0;
+ for (; i+1 < nrow; i+=2)
+ {
+ Index i0 = *(irow++);
+ Index i1 = *(irow++);
+ Scalar a0 = *(a++);
+ Scalar a1 = *(a++);
+ Scalar d0 = dense.coeff(i0);
+ Scalar d1 = dense.coeff(i1);
+ d0 -= f*a0;
+ d1 -= f*a1;
+ dense.coeffRef(i0) = d0;
+ dense.coeffRef(i1) = d1;
+ }
+ if(i<nrow)
+ dense.coeffRef(*(irow++)) -= f * *(a++);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // SPARSELU_KERNEL_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_panel_bmod.h b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
new file mode 100644
index 0000000..da0e0fc
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
@@ -0,0 +1,223 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]panel_bmod.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PANEL_BMOD_H
+#define SPARSELU_PANEL_BMOD_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs numeric block updates (sup-panel) in topological order.
+ *
+ * Before entering this routine, the original nonzeros in the panel
+ * were already copied i nto the spa[m,w]
+ *
+ * \param m number of rows in the matrix
+ * \param w Panel size
+ * \param jcol Starting column of the panel
+ * \param nseg Number of segments in the U part
+ * \param dense Store the full representation of the panel
+ * \param tempv working array
+ * \param segrep segment representative... first row in the segment
+ * \param repfnz First nonzero rows
+ * \param glu Global LU data.
+ *
+ *
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::panel_bmod(const Index m, const Index w, const Index jcol,
+ const Index nseg, ScalarVector& dense, ScalarVector& tempv,
+ IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu)
+{
+
+ Index ksub,jj,nextl_col;
+ Index fsupc, nsupc, nsupr, nrow;
+ Index krep, kfnz;
+ Index lptr; // points to the row subscripts of a supernode
+ Index luptr; // ...
+ Index segsize,no_zeros ;
+ // For each nonz supernode segment of U[*,j] in topological order
+ Index k = nseg - 1;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+
+ for (ksub = 0; ksub < nseg; ksub++)
+ { // For each updating supernode
+ /* krep = representative of current k-th supernode
+ * fsupc = first supernodal column
+ * nsupc = number of columns in a supernode
+ * nsupr = number of rows in a supernode
+ */
+ krep = segrep(k); k--;
+ fsupc = glu.xsup(glu.supno(krep));
+ nsupc = krep - fsupc + 1;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+ nrow = nsupr - nsupc;
+ lptr = glu.xlsub(fsupc);
+
+ // loop over the panel columns to detect the actual number of columns and rows
+ Index u_rows = 0;
+ Index u_cols = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ u_cols++;
+ u_rows = (std::max)(segsize,u_rows);
+ }
+
+ if(nsupc >= 2)
+ {
+ Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);
+ Map<Matrix<Scalar,Dynamic,Dynamic>, Aligned, OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));
+
+ // gather U
+ Index u_col = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ luptr = glu.xlusup(fsupc);
+ no_zeros = kfnz - fsupc;
+
+ Index isub = lptr + no_zeros;
+ Index off = u_rows-segsize;
+ for (Index i = 0; i < off; i++) U(i,u_col) = 0;
+ for (Index i = 0; i < segsize; i++)
+ {
+ Index irow = glu.lsub(isub);
+ U(i+off,u_col) = dense_col(irow);
+ ++isub;
+ }
+ u_col++;
+ }
+ // solve U = A^-1 U
+ luptr = glu.xlusup(fsupc);
+ Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc);
+ no_zeros = (krep - u_rows + 1) - fsupc;
+ luptr += lda * no_zeros + no_zeros;
+ Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(lda) );
+ U = A.template triangularView<UnitLower>().solve(U);
+
+ // update
+ luptr += u_rows;
+ Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(lda) );
+ eigen_assert(tempv.size()>w*ldu + nrow*w + 1);
+
+ Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
+ Index offset = (PacketSize-internal::first_aligned(B.data(), PacketSize)) % PacketSize;
+ Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
+
+ L.setZero();
+ internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());
+
+ // scatter U and L
+ u_col = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ no_zeros = kfnz - fsupc;
+ Index isub = lptr + no_zeros;
+
+ Index off = u_rows-segsize;
+ for (Index i = 0; i < segsize; i++)
+ {
+ Index irow = glu.lsub(isub++);
+ dense_col(irow) = U.coeff(i+off,u_col);
+ U.coeffRef(i+off,u_col) = 0;
+ }
+
+ // Scatter l into SPA dense[]
+ for (Index i = 0; i < nrow; i++)
+ {
+ Index irow = glu.lsub(isub++);
+ dense_col(irow) -= L.coeff(i,u_col);
+ L.coeffRef(i,u_col) = 0;
+ }
+ u_col++;
+ }
+ }
+ else // level 2 only
+ {
+ // Sequence through each column in the panel
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ luptr = glu.xlusup(fsupc);
+
+ Index lda = glu.xlusup(fsupc+1)-glu.xlusup(fsupc);// nsupr
+
+ // Perform a trianglar solve and block update,
+ // then scatter the result of sup-col update to dense[]
+ no_zeros = kfnz - fsupc;
+ if(segsize==1) LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else if(segsize==2) LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else if(segsize==3) LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ } // End for each column in the panel
+ }
+
+ } // End for each updating supernode
+} // end panel bmod
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // SPARSELU_PANEL_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_panel_dfs.h b/Eigen/src/SparseLU/SparseLU_panel_dfs.h
new file mode 100644
index 0000000..dc0054e
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_panel_dfs.h
@@ -0,0 +1,258 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PANEL_DFS_H
+#define SPARSELU_PANEL_DFS_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename IndexVector>
+struct panel_dfs_traits
+{
+ typedef typename IndexVector::Scalar Index;
+ panel_dfs_traits(Index jcol, Index* marker)
+ : m_jcol(jcol), m_marker(marker)
+ {}
+ bool update_segrep(Index krep, Index jj)
+ {
+ if(m_marker[krep]<m_jcol)
+ {
+ m_marker[krep] = jj;
+ return true;
+ }
+ return false;
+ }
+ void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}
+ enum { ExpandMem = false };
+ Index m_jcol;
+ Index* m_marker;
+};
+
+
+template <typename Scalar, typename Index>
+template <typename Traits>
+void SparseLUImpl<Scalar,Index>::dfs_kernel(const Index jj, IndexVector& perm_r,
+ Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
+ Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
+ IndexVector& xplore, GlobalLU_t& glu,
+ Index& nextl_col, Index krow, Traits& traits
+ )
+{
+
+ Index kmark = marker(krow);
+
+ // For each unmarked krow of jj
+ marker(krow) = jj;
+ Index kperm = perm_r(krow);
+ if (kperm == emptyIdxLU ) {
+ // krow is in L : place it in structure of L(*, jj)
+ panel_lsub(nextl_col++) = krow; // krow is indexed into A
+
+ traits.mem_expand(panel_lsub, nextl_col, kmark);
+ }
+ else
+ {
+ // krow is in U : if its supernode-representative krep
+ // has been explored, update repfnz(*)
+ // krep = supernode representative of the current row
+ Index krep = glu.xsup(glu.supno(kperm)+1) - 1;
+ // First nonzero element in the current column:
+ Index myfnz = repfnz_col(krep);
+
+ if (myfnz != emptyIdxLU )
+ {
+ // Representative visited before
+ if (myfnz > kperm ) repfnz_col(krep) = kperm;
+
+ }
+ else
+ {
+ // Otherwise, perform dfs starting at krep
+ Index oldrep = emptyIdxLU;
+ parent(krep) = oldrep;
+ repfnz_col(krep) = kperm;
+ Index xdfs = glu.xlsub(krep);
+ Index maxdfs = xprune(krep);
+
+ Index kpar;
+ do
+ {
+ // For each unmarked kchild of krep
+ while (xdfs < maxdfs)
+ {
+ Index kchild = glu.lsub(xdfs);
+ xdfs++;
+ Index chmark = marker(kchild);
+
+ if (chmark != jj )
+ {
+ marker(kchild) = jj;
+ Index chperm = perm_r(kchild);
+
+ if (chperm == emptyIdxLU)
+ {
+ // case kchild is in L: place it in L(*, j)
+ panel_lsub(nextl_col++) = kchild;
+ traits.mem_expand(panel_lsub, nextl_col, chmark);
+ }
+ else
+ {
+ // case kchild is in U :
+ // chrep = its supernode-rep. If its rep has been explored,
+ // update its repfnz(*)
+ Index chrep = glu.xsup(glu.supno(chperm)+1) - 1;
+ myfnz = repfnz_col(chrep);
+
+ if (myfnz != emptyIdxLU)
+ { // Visited before
+ if (myfnz > chperm)
+ repfnz_col(chrep) = chperm;
+ }
+ else
+ { // Cont. dfs at snode-rep of kchild
+ xplore(krep) = xdfs;
+ oldrep = krep;
+ krep = chrep; // Go deeper down G(L)
+ parent(krep) = oldrep;
+ repfnz_col(krep) = chperm;
+ xdfs = glu.xlsub(krep);
+ maxdfs = xprune(krep);
+
+ } // end if myfnz != -1
+ } // end if chperm == -1
+
+ } // end if chmark !=jj
+ } // end while xdfs < maxdfs
+
+ // krow has no more unexplored nbrs :
+ // Place snode-rep krep in postorder DFS, if this
+ // segment is seen for the first time. (Note that
+ // "repfnz(krep)" may change later.)
+ // Baktrack dfs to its parent
+ if(traits.update_segrep(krep,jj))
+ //if (marker1(krep) < jcol )
+ {
+ segrep(nseg) = krep;
+ ++nseg;
+ //marker1(krep) = jj;
+ }
+
+ kpar = parent(krep); // Pop recursion, mimic recursion
+ if (kpar == emptyIdxLU)
+ break; // dfs done
+ krep = kpar;
+ xdfs = xplore(krep);
+ maxdfs = xprune(krep);
+
+ } while (kpar != emptyIdxLU); // Do until empty stack
+
+ } // end if (myfnz = -1)
+
+ } // end if (kperm == -1)
+}
+
+/**
+ * \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)
+ *
+ * A supernode representative is the last column of a supernode.
+ * The nonzeros in U[*,j] are segments that end at supernodes representatives
+ *
+ * The routine returns a list of the supernodal representatives
+ * in topological order of the dfs that generates them. This list is
+ * a superset of the topological order of each individual column within
+ * the panel.
+ * The location of the first nonzero in each supernodal segment
+ * (supernodal entry location) is also returned. Each column has
+ * a separate list for this purpose.
+ *
+ * Two markers arrays are used for dfs :
+ * marker[i] == jj, if i was visited during dfs of current column jj;
+ * marker1[i] >= jcol, if i was visited by earlier columns in this panel;
+ *
+ * \param[in] m number of rows in the matrix
+ * \param[in] w Panel size
+ * \param[in] jcol Starting column of the panel
+ * \param[in] A Input matrix in column-major storage
+ * \param[in] perm_r Row permutation
+ * \param[out] nseg Number of U segments
+ * \param[out] dense Accumulate the column vectors of the panel
+ * \param[out] panel_lsub Subscripts of the row in the panel
+ * \param[out] segrep Segment representative i.e first nonzero row of each segment
+ * \param[out] repfnz First nonzero location in each row
+ * \param[out] xprune The pruned elimination tree
+ * \param[out] marker work vector
+ * \param parent The elimination tree
+ * \param xplore work vector
+ * \param glu The global data structure
+ *
+ */
+
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
+{
+ Index nextl_col; // Next available position in panel_lsub[*,jj]
+
+ // Initialize pointers
+ VectorBlock<IndexVector> marker1(marker, m, m);
+ nseg = 0;
+
+ panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
+
+ // For each column in the panel
+ for (Index jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj - jcol) * m;
+
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
+ VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
+
+
+ // For each nnz in A[*, jj] do depth first search
+ for (typename MatrixType::InnerIterator it(A, jj); it; ++it)
+ {
+ Index krow = it.row();
+ dense_col(krow) = it.value();
+
+ Index kmark = marker(krow);
+ if (kmark == jj)
+ continue; // krow visited before, go to the next nonzero
+
+ dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,
+ xplore, glu, nextl_col, krow, traits);
+ }// end for nonzeros in column jj
+
+ } // end for column jj
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PANEL_DFS_H
diff --git a/Eigen/src/SparseLU/SparseLU_pivotL.h b/Eigen/src/SparseLU/SparseLU_pivotL.h
new file mode 100644
index 0000000..457789c
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_pivotL.h
@@ -0,0 +1,136 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of xpivotL.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PIVOTL_H
+#define SPARSELU_PIVOTL_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
+ *
+ * Pivot policy :
+ * (1) Compute thresh = u * max_(i>=j) abs(A_ij);
+ * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
+ * pivot row = k;
+ * ELSE IF abs(A_jj) >= thresh THEN
+ * pivot row = j;
+ * ELSE
+ * pivot row = m;
+ *
+ * Note: If you absolutely want to use a given pivot order, then set u=0.0.
+ *
+ * \param jcol The current column of L
+ * \param diagpivotthresh diagonal pivoting threshold
+ * \param[in,out] perm_r Row permutation (threshold pivoting)
+ * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
+ * \param[out] pivrow The pivot row
+ * \param glu Global LU data
+ * \return 0 if success, i > 0 if U(i,i) is exactly zero
+ *
+ */
+template <typename Scalar, typename Index>
+Index SparseLUImpl<Scalar,Index>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)
+{
+
+ Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
+ Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
+ Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
+ Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode
+ Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension
+ Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
+ Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode
+ Index* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode
+
+ // Determine the largest abs numerical value for partial pivoting
+ Index diagind = iperm_c(jcol); // diagonal index
+ RealScalar pivmax = 0.0;
+ Index pivptr = nsupc;
+ Index diag = emptyIdxLU;
+ RealScalar rtemp;
+ Index isub, icol, itemp, k;
+ for (isub = nsupc; isub < nsupr; ++isub) {
+ using std::abs;
+ rtemp = abs(lu_col_ptr[isub]);
+ if (rtemp > pivmax) {
+ pivmax = rtemp;
+ pivptr = isub;
+ }
+ if (lsub_ptr[isub] == diagind) diag = isub;
+ }
+
+ // Test for singularity
+ if ( pivmax == 0.0 ) {
+ pivrow = lsub_ptr[pivptr];
+ perm_r(pivrow) = jcol;
+ return (jcol+1);
+ }
+
+ RealScalar thresh = diagpivotthresh * pivmax;
+
+ // Choose appropriate pivotal element
+
+ {
+ // Test if the diagonal element can be used as a pivot (given the threshold value)
+ if (diag >= 0 )
+ {
+ // Diagonal element exists
+ using std::abs;
+ rtemp = abs(lu_col_ptr[diag]);
+ if (rtemp != 0.0 && rtemp >= thresh) pivptr = diag;
+ }
+ pivrow = lsub_ptr[pivptr];
+ }
+
+ // Record pivot row
+ perm_r(pivrow) = jcol;
+ // Interchange row subscripts
+ if (pivptr != nsupc )
+ {
+ std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
+ // Interchange numerical values as well, for the two rows in the whole snode
+ // such that L is indexed the same way as A
+ for (icol = 0; icol <= nsupc; icol++)
+ {
+ itemp = pivptr + icol * lda;
+ std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
+ }
+ }
+ // cdiv operations
+ Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
+ for (k = nsupc+1; k < nsupr; k++)
+ lu_col_ptr[k] *= temp;
+ return 0;
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PIVOTL_H
diff --git a/Eigen/src/SparseLU/SparseLU_pruneL.h b/Eigen/src/SparseLU/SparseLU_pruneL.h
new file mode 100644
index 0000000..66460d1
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_pruneL.h
@@ -0,0 +1,135 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]pruneL.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PRUNEL_H
+#define SPARSELU_PRUNEL_H
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Prunes the L-structure.
+ *
+ * It prunes the L-structure of supernodes whose L-structure contains the current pivot row "pivrow"
+ *
+ *
+ * \param jcol The current column of L
+ * \param[in] perm_r Row permutation
+ * \param[out] pivrow The pivot row
+ * \param nseg Number of segments
+ * \param segrep
+ * \param repfnz
+ * \param[out] xprune
+ * \param glu Global LU data
+ *
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg, const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu)
+{
+ // For each supernode-rep irep in U(*,j]
+ Index jsupno = glu.supno(jcol);
+ Index i,irep,irep1;
+ bool movnum, do_prune = false;
+ Index kmin = 0, kmax = 0, minloc, maxloc,krow;
+ for (i = 0; i < nseg; i++)
+ {
+ irep = segrep(i);
+ irep1 = irep + 1;
+ do_prune = false;
+
+ // Don't prune with a zero U-segment
+ if (repfnz(irep) == emptyIdxLU) continue;
+
+ // If a snode overlaps with the next panel, then the U-segment
+ // is fragmented into two parts -- irep and irep1. We should let
+ // pruning occur at the rep-column in irep1s snode.
+ if (glu.supno(irep) == glu.supno(irep1) ) continue; // don't prune
+
+ // If it has not been pruned & it has a nonz in row L(pivrow,i)
+ if (glu.supno(irep) != jsupno )
+ {
+ if ( xprune (irep) >= glu.xlsub(irep1) )
+ {
+ kmin = glu.xlsub(irep);
+ kmax = glu.xlsub(irep1) - 1;
+ for (krow = kmin; krow <= kmax; krow++)
+ {
+ if (glu.lsub(krow) == pivrow)
+ {
+ do_prune = true;
+ break;
+ }
+ }
+ }
+
+ if (do_prune)
+ {
+ // do a quicksort-type partition
+ // movnum=true means that the num values have to be exchanged
+ movnum = false;
+ if (irep == glu.xsup(glu.supno(irep)) ) // Snode of size 1
+ movnum = true;
+
+ while (kmin <= kmax)
+ {
+ if (perm_r(glu.lsub(kmax)) == emptyIdxLU)
+ kmax--;
+ else if ( perm_r(glu.lsub(kmin)) != emptyIdxLU)
+ kmin++;
+ else
+ {
+ // kmin below pivrow (not yet pivoted), and kmax
+ // above pivrow: interchange the two suscripts
+ std::swap(glu.lsub(kmin), glu.lsub(kmax));
+
+ // If the supernode has only one column, then we
+ // only keep one set of subscripts. For any subscript
+ // intercnahge performed, similar interchange must be
+ // done on the numerical values.
+ if (movnum)
+ {
+ minloc = glu.xlusup(irep) + ( kmin - glu.xlsub(irep) );
+ maxloc = glu.xlusup(irep) + ( kmax - glu.xlsub(irep) );
+ std::swap(glu.lusup(minloc), glu.lusup(maxloc));
+ }
+ kmin++;
+ kmax--;
+ }
+ } // end while
+
+ xprune(irep) = kmin; //Pruning
+ } // end if do_prune
+ } // end pruning
+ } // End for each U-segment
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PRUNEL_H
diff --git a/Eigen/src/SparseLU/SparseLU_relax_snode.h b/Eigen/src/SparseLU/SparseLU_relax_snode.h
new file mode 100644
index 0000000..58ec32e
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_relax_snode.h
@@ -0,0 +1,83 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* This file is a modified version of heap_relax_snode.c file in SuperLU
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef SPARSELU_RELAX_SNODE_H
+#define SPARSELU_RELAX_SNODE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/**
+ * \brief Identify the initial relaxed supernodes
+ *
+ * This routine is applied to a column elimination tree.
+ * It assumes that the matrix has been reordered according to the postorder of the etree
+ * \param n the number of columns
+ * \param et elimination tree
+ * \param relax_columns Maximum number of columns allowed in a relaxed snode
+ * \param descendants Number of descendants of each node in the etree
+ * \param relax_end last column in a supernode
+ */
+template <typename Scalar, typename Index>
+void SparseLUImpl<Scalar,Index>::relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
+{
+
+ // compute the number of descendants of each node in the etree
+ Index j, parent;
+ relax_end.setConstant(emptyIdxLU);
+ descendants.setZero();
+ for (j = 0; j < n; j++)
+ {
+ parent = et(j);
+ if (parent != n) // not the dummy root
+ descendants(parent) += descendants(j) + 1;
+ }
+ // Identify the relaxed supernodes by postorder traversal of the etree
+ Index snode_start; // beginning of a snode
+ for (j = 0; j < n; )
+ {
+ parent = et(j);
+ snode_start = j;
+ while ( parent != n && descendants(parent) < relax_columns )
+ {
+ j = parent;
+ parent = et(j);
+ }
+ // Found a supernode in postordered etree, j is the last column
+ relax_end(snode_start) = j; // Record last column
+ j++;
+ // Search for a new leaf
+ while (descendants(j) != 0 && j < n) j++;
+ } // End postorder traversal of the etree
+
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif
diff --git a/Eigen/src/SparseQR/CMakeLists.txt b/Eigen/src/SparseQR/CMakeLists.txt
new file mode 100644
index 0000000..f9ddf2b
--- /dev/null
+++ b/Eigen/src/SparseQR/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SparseQR_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SparseQR_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseQR/ COMPONENT Devel
+ )
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
new file mode 100644
index 0000000..a00bd5d
--- /dev/null
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -0,0 +1,714 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012-2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_QR_H
+#define EIGEN_SPARSE_QR_H
+
+namespace Eigen {
+
+template<typename MatrixType, typename OrderingType> class SparseQR;
+template<typename SparseQRType> struct SparseQRMatrixQReturnType;
+template<typename SparseQRType> struct SparseQRMatrixQTransposeReturnType;
+template<typename SparseQRType, typename Derived> struct SparseQR_QProduct;
+namespace internal {
+ template <typename SparseQRType> struct traits<SparseQRMatrixQReturnType<SparseQRType> >
+ {
+ typedef typename SparseQRType::MatrixType ReturnType;
+ typedef typename ReturnType::Index Index;
+ typedef typename ReturnType::StorageKind StorageKind;
+ };
+ template <typename SparseQRType> struct traits<SparseQRMatrixQTransposeReturnType<SparseQRType> >
+ {
+ typedef typename SparseQRType::MatrixType ReturnType;
+ };
+ template <typename SparseQRType, typename Derived> struct traits<SparseQR_QProduct<SparseQRType, Derived> >
+ {
+ typedef typename Derived::PlainObject ReturnType;
+ };
+} // End namespace internal
+
+/**
+ * \ingroup SparseQR_Module
+ * \class SparseQR
+ * \brief Sparse left-looking rank-revealing QR factorization
+ *
+ * This class implements a left-looking rank-revealing QR decomposition
+ * of sparse matrices. When a column has a norm less than a given tolerance
+ * it is implicitly permuted to the end. The QR factorization thus obtained is
+ * given by A*P = Q*R where R is upper triangular or trapezoidal.
+ *
+ * P is the column permutation which is the product of the fill-reducing and the
+ * rank-revealing permutations. Use colsPermutation() to get it.
+ *
+ * Q is the orthogonal matrix represented as products of Householder reflectors.
+ * Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose.
+ * You can then apply it to a vector.
+ *
+ * R is the sparse triangular or trapezoidal matrix. The later occurs when A is rank-deficient.
+ * matrixR().topLeftCorner(rank(), rank()) always returns a triangular factor of full rank.
+ *
+ * \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>
+ * \tparam _OrderingType The fill-reducing ordering method. See the \link OrderingMethods_Module
+ * OrderingMethods \endlink module for the list of built-in and external ordering methods.
+ *
+ * \warning The input sparse matrix A must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ */
+template<typename _MatrixType, typename _OrderingType>
+class SparseQR
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef _OrderingType OrderingType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef SparseMatrix<Scalar,ColMajor,Index> QRMatrixType;
+ typedef Matrix<Index, Dynamic, 1> IndexVector;
+ typedef Matrix<Scalar, Dynamic, 1> ScalarVector;
+ typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+ public:
+ SparseQR () : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
+ { }
+
+ /** Construct a QR factorization of the matrix \a mat.
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * \sa compute()
+ */
+ SparseQR(const MatrixType& mat) : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
+ {
+ compute(mat);
+ }
+
+ /** Computes the QR factorization of the sparse matrix \a mat.
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * \sa analyzePattern(), factorize()
+ */
+ void compute(const MatrixType& mat)
+ {
+ analyzePattern(mat);
+ factorize(mat);
+ }
+ void analyzePattern(const MatrixType& mat);
+ void factorize(const MatrixType& mat);
+
+ /** \returns the number of rows of the represented matrix.
+ */
+ inline Index rows() const { return m_pmat.rows(); }
+
+ /** \returns the number of columns of the represented matrix.
+ */
+ inline Index cols() const { return m_pmat.cols();}
+
+ /** \returns a const reference to the \b sparse upper triangular matrix R of the QR factorization.
+ */
+ const QRMatrixType& matrixR() const { return m_R; }
+
+ /** \returns the number of non linearly dependent columns as determined by the pivoting threshold.
+ *
+ * \sa setPivotThreshold()
+ */
+ Index rank() const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ return m_nonzeropivots;
+ }
+
+ /** \returns an expression of the matrix Q as products of sparse Householder reflectors.
+ * The common usage of this function is to apply it to a dense matrix or vector
+ * \code
+ * VectorXd B1, B2;
+ * // Initialize B1
+ * B2 = matrixQ() * B1;
+ * \endcode
+ *
+ * To get a plain SparseMatrix representation of Q:
+ * \code
+ * SparseMatrix<double> Q;
+ * Q = SparseQR<SparseMatrix<double> >(A).matrixQ();
+ * \endcode
+ * Internally, this call simply performs a sparse product between the matrix Q
+ * and a sparse identity matrix. However, due to the fact that the sparse
+ * reflectors are stored unsorted, two transpositions are needed to sort
+ * them before performing the product.
+ */
+ SparseQRMatrixQReturnType<SparseQR> matrixQ() const
+ { return SparseQRMatrixQReturnType<SparseQR>(*this); }
+
+ /** \returns a const reference to the column permutation P that was applied to A such that A*P = Q*R
+ * It is the combination of the fill-in reducing permutation and numerical column pivoting.
+ */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_outputPerm_c;
+ }
+
+ /** \returns A string describing the type of error.
+ * This method is provided to ease debugging, not to handle errors.
+ */
+ std::string lastErrorMessage() const { return m_lastError; }
+
+ /** \internal */
+ template<typename Rhs, typename Dest>
+ bool _solve(const MatrixBase<Rhs> &B, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+
+ Index rank = this->rank();
+
+ // Compute Q^T * b;
+ typename Dest::PlainObject y, b;
+ y = this->matrixQ().transpose() * B;
+ b = y;
+
+ // Solve with the triangular matrix R
+ y.resize((std::max)(cols(),Index(y.rows())),y.cols());
+ y.topRows(rank) = this->matrixR().topLeftCorner(rank, rank).template triangularView<Upper>().solve(b.topRows(rank));
+ y.bottomRows(y.rows()-rank).setZero();
+
+ // Apply the column permutation
+ if (m_perm_c.size()) dest = colsPermutation() * y.topRows(cols());
+ else dest = y.topRows(cols());
+
+ m_info = Success;
+ return true;
+ }
+
+
+ /** Sets the threshold that is used to determine linearly dependent columns during the factorization.
+ *
+ * In practice, if during the factorization the norm of the column that has to be eliminated is below
+ * this threshold, then the entire column is treated as zero, and it is moved at the end.
+ */
+ void setPivotThreshold(const RealScalar& threshold)
+ {
+ m_useDefaultThreshold = false;
+ m_threshold = threshold;
+ }
+
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<SparseQR, Rhs> solve(const MatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+ return internal::solve_retval<SparseQR, Rhs>(*this, B.derived());
+ }
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<SparseQR, Rhs> solve(const SparseMatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+ return internal::sparse_solve_retval<SparseQR, Rhs>(*this, B.derived());
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the QR factorization reports a numerical problem
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ protected:
+ inline void sort_matrix_Q()
+ {
+ if(this->m_isQSorted) return;
+ // The matrix Q is sorted during the transposition
+ SparseMatrix<Scalar, RowMajor, Index> mQrm(this->m_Q);
+ this->m_Q = mQrm;
+ this->m_isQSorted = true;
+ }
+
+
+ protected:
+ bool m_isInitialized;
+ bool m_analysisIsok;
+ bool m_factorizationIsok;
+ mutable ComputationInfo m_info;
+ std::string m_lastError;
+ QRMatrixType m_pmat; // Temporary matrix
+ QRMatrixType m_R; // The triangular factor matrix
+ QRMatrixType m_Q; // The orthogonal reflectors
+ ScalarVector m_hcoeffs; // The Householder coefficients
+ PermutationType m_perm_c; // Fill-reducing Column permutation
+ PermutationType m_pivotperm; // The permutation for rank revealing
+ PermutationType m_outputPerm_c; // The final column permutation
+ RealScalar m_threshold; // Threshold to determine null Householder reflections
+ bool m_useDefaultThreshold; // Use default threshold
+ Index m_nonzeropivots; // Number of non zero pivots found
+ IndexVector m_etree; // Column elimination tree
+ IndexVector m_firstRowElt; // First element in each row
+ bool m_isQSorted; // whether Q is sorted or not
+ bool m_isEtreeOk; // whether the elimination tree match the initial input matrix
+
+ template <typename, typename > friend struct SparseQR_QProduct;
+ template <typename > friend struct SparseQRMatrixQReturnType;
+
+};
+
+/** \brief Preprocessing step of a QR factorization
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * In this step, the fill-reducing permutation is computed and applied to the columns of A
+ * and the column elimination tree is computed as well. Only the sparsity pattern of \a mat is exploited.
+ *
+ * \note In this step it is assumed that there is no empty row in the matrix \a mat.
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseQR<MatrixType,OrderingType>::analyzePattern(const MatrixType& mat)
+{
+ eigen_assert(mat.isCompressed() && "SparseQR requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to SparseQR");
+ // Copy to a column major matrix if the input is rowmajor
+ typename internal::conditional<MatrixType::IsRowMajor,QRMatrixType,const MatrixType&>::type matCpy(mat);
+ // Compute the column fill reducing ordering
+ OrderingType ord;
+ ord(matCpy, m_perm_c);
+ Index n = mat.cols();
+ Index m = mat.rows();
+ Index diagSize = (std::min)(m,n);
+
+ if (!m_perm_c.size())
+ {
+ m_perm_c.resize(n);
+ m_perm_c.indices().setLinSpaced(n, 0,n-1);
+ }
+
+ // Compute the column elimination tree of the permuted matrix
+ m_outputPerm_c = m_perm_c.inverse();
+ internal::coletree(matCpy, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+ m_isEtreeOk = true;
+
+ m_R.resize(m, n);
+ m_Q.resize(m, diagSize);
+
+ // Allocate space for nonzero elements : rough estimation
+ m_R.reserve(2*mat.nonZeros()); //FIXME Get a more accurate estimation through symbolic factorization with the etree
+ m_Q.reserve(2*mat.nonZeros());
+ m_hcoeffs.resize(diagSize);
+ m_analysisIsok = true;
+}
+
+/** \brief Performs the numerical QR factorization of the input matrix
+ *
+ * The function SparseQR::analyzePattern(const MatrixType&) must have been called beforehand with
+ * a matrix having the same sparsity pattern than \a mat.
+ *
+ * \param mat The sparse column-major matrix
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
+{
+ using std::abs;
+ using std::max;
+
+ eigen_assert(m_analysisIsok && "analyzePattern() should be called before this step");
+ Index m = mat.rows();
+ Index n = mat.cols();
+ Index diagSize = (std::min)(m,n);
+ IndexVector mark((std::max)(m,n)); mark.setConstant(-1); // Record the visited nodes
+ IndexVector Ridx(n), Qidx(m); // Store temporarily the row indexes for the current column of R and Q
+ Index nzcolR, nzcolQ; // Number of nonzero for the current column of R and Q
+ ScalarVector tval(m); // The dense vector used to compute the current column
+ RealScalar pivotThreshold = m_threshold;
+
+ m_R.setZero();
+ m_Q.setZero();
+ m_pmat = mat;
+ if(!m_isEtreeOk)
+ {
+ m_outputPerm_c = m_perm_c.inverse();
+ internal::coletree(m_pmat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+ m_isEtreeOk = true;
+ }
+
+ m_pmat.uncompress(); // To have the innerNonZeroPtr allocated
+
+ // Apply the fill-in reducing permutation lazily:
+ {
+ // If the input is row major, copy the original column indices,
+ // otherwise directly use the input matrix
+ //
+ IndexVector originalOuterIndicesCpy;
+ const Index *originalOuterIndices = mat.outerIndexPtr();
+ if(MatrixType::IsRowMajor)
+ {
+ originalOuterIndicesCpy = IndexVector::Map(m_pmat.outerIndexPtr(),n+1);
+ originalOuterIndices = originalOuterIndicesCpy.data();
+ }
+
+ for (int i = 0; i < n; i++)
+ {
+ Index p = m_perm_c.size() ? m_perm_c.indices()(i) : i;
+ m_pmat.outerIndexPtr()[p] = originalOuterIndices[i];
+ m_pmat.innerNonZeroPtr()[p] = originalOuterIndices[i+1] - originalOuterIndices[i];
+ }
+ }
+
+ /* Compute the default threshold as in MatLab, see:
+ * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+ * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
+ */
+ if(m_useDefaultThreshold)
+ {
+ RealScalar max2Norm = 0.0;
+ for (int j = 0; j < n; j++) max2Norm = (max)(max2Norm, m_pmat.col(j).norm());
+ if(max2Norm==RealScalar(0))
+ max2Norm = RealScalar(1);
+ pivotThreshold = 20 * (m + n) * max2Norm * NumTraits<RealScalar>::epsilon();
+ }
+
+ // Initialize the numerical permutation
+ m_pivotperm.setIdentity(n);
+
+ Index nonzeroCol = 0; // Record the number of valid pivots
+ m_Q.startVec(0);
+
+ // Left looking rank-revealing QR factorization: compute a column of R and Q at a time
+ for (Index col = 0; col < n; ++col)
+ {
+ mark.setConstant(-1);
+ m_R.startVec(col);
+ mark(nonzeroCol) = col;
+ Qidx(0) = nonzeroCol;
+ nzcolR = 0; nzcolQ = 1;
+ bool found_diag = nonzeroCol>=m;
+ tval.setZero();
+
+ // Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,
+ // all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.
+ // Note: if the diagonal entry does not exist, then its contribution must be explicitly added,
+ // thus the trick with found_diag that permits to do one more iteration on the diagonal element if this one has not been found.
+ for (typename QRMatrixType::InnerIterator itp(m_pmat, col); itp || !found_diag; ++itp)
+ {
+ Index curIdx = nonzeroCol;
+ if(itp) curIdx = itp.row();
+ if(curIdx == nonzeroCol) found_diag = true;
+
+ // Get the nonzeros indexes of the current column of R
+ Index st = m_firstRowElt(curIdx); // The traversal of the etree starts here
+ if (st < 0 )
+ {
+ m_lastError = "Empty row found during numerical factorization";
+ m_info = InvalidInput;
+ return;
+ }
+
+ // Traverse the etree
+ Index bi = nzcolR;
+ for (; mark(st) != col; st = m_etree(st))
+ {
+ Ridx(nzcolR) = st; // Add this row to the list,
+ mark(st) = col; // and mark this row as visited
+ nzcolR++;
+ }
+
+ // Reverse the list to get the topological ordering
+ Index nt = nzcolR-bi;
+ for(Index i = 0; i < nt/2; i++) std::swap(Ridx(bi+i), Ridx(nzcolR-i-1));
+
+ // Copy the current (curIdx,pcol) value of the input matrix
+ if(itp) tval(curIdx) = itp.value();
+ else tval(curIdx) = Scalar(0);
+
+ // Compute the pattern of Q(:,k)
+ if(curIdx > nonzeroCol && mark(curIdx) != col )
+ {
+ Qidx(nzcolQ) = curIdx; // Add this row to the pattern of Q,
+ mark(curIdx) = col; // and mark it as visited
+ nzcolQ++;
+ }
+ }
+
+ // Browse all the indexes of R(:,col) in reverse order
+ for (Index i = nzcolR-1; i >= 0; i--)
+ {
+ Index curIdx = Ridx(i);
+
+ // Apply the curIdx-th householder vector to the current column (temporarily stored into tval)
+ Scalar tdot(0);
+
+ // First compute q' * tval
+ tdot = m_Q.col(curIdx).dot(tval);
+
+ tdot *= m_hcoeffs(curIdx);
+
+ // Then update tval = tval - q * tau
+ // FIXME: tval -= tdot * m_Q.col(curIdx) should amount to the same (need to check/add support for efficient "dense ?= sparse")
+ for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)
+ tval(itq.row()) -= itq.value() * tdot;
+
+ // Detect fill-in for the current column of Q
+ if(m_etree(Ridx(i)) == nonzeroCol)
+ {
+ for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)
+ {
+ Index iQ = itq.row();
+ if (mark(iQ) != col)
+ {
+ Qidx(nzcolQ++) = iQ; // Add this row to the pattern of Q,
+ mark(iQ) = col; // and mark it as visited
+ }
+ }
+ }
+ } // End update current column
+
+ Scalar tau = 0;
+ RealScalar beta = 0;
+
+ if(nonzeroCol < diagSize)
+ {
+ // Compute the Householder reflection that eliminate the current column
+ // FIXME this step should call the Householder module.
+ Scalar c0 = nzcolQ ? tval(Qidx(0)) : Scalar(0);
+
+ // First, the squared norm of Q((col+1):m, col)
+ RealScalar sqrNorm = 0.;
+ for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));
+ if(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))
+ {
+ beta = numext::real(c0);
+ tval(Qidx(0)) = 1;
+ }
+ else
+ {
+ using std::sqrt;
+ beta = sqrt(numext::abs2(c0) + sqrNorm);
+ if(numext::real(c0) >= RealScalar(0))
+ beta = -beta;
+ tval(Qidx(0)) = 1;
+ for (Index itq = 1; itq < nzcolQ; ++itq)
+ tval(Qidx(itq)) /= (c0 - beta);
+ tau = numext::conj((beta-c0) / beta);
+
+ }
+ }
+
+ // Insert values in R
+ for (Index i = nzcolR-1; i >= 0; i--)
+ {
+ Index curIdx = Ridx(i);
+ if(curIdx < nonzeroCol)
+ {
+ m_R.insertBackByOuterInnerUnordered(col, curIdx) = tval(curIdx);
+ tval(curIdx) = Scalar(0.);
+ }
+ }
+
+ if(nonzeroCol < diagSize && abs(beta) >= pivotThreshold)
+ {
+ m_R.insertBackByOuterInner(col, nonzeroCol) = beta;
+ // The householder coefficient
+ m_hcoeffs(nonzeroCol) = tau;
+ // Record the householder reflections
+ for (Index itq = 0; itq < nzcolQ; ++itq)
+ {
+ Index iQ = Qidx(itq);
+ m_Q.insertBackByOuterInnerUnordered(nonzeroCol,iQ) = tval(iQ);
+ tval(iQ) = Scalar(0.);
+ }
+ nonzeroCol++;
+ if(nonzeroCol<diagSize)
+ m_Q.startVec(nonzeroCol);
+ }
+ else
+ {
+ // Zero pivot found: move implicitly this column to the end
+ for (Index j = nonzeroCol; j < n-1; j++)
+ std::swap(m_pivotperm.indices()(j), m_pivotperm.indices()[j+1]);
+
+ // Recompute the column elimination tree
+ internal::coletree(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());
+ m_isEtreeOk = false;
+ }
+ }
+
+ m_hcoeffs.tail(diagSize-nonzeroCol).setZero();
+
+ // Finalize the column pointers of the sparse matrices R and Q
+ m_Q.finalize();
+ m_Q.makeCompressed();
+ m_R.finalize();
+ m_R.makeCompressed();
+ m_isQSorted = false;
+
+ m_nonzeropivots = nonzeroCol;
+
+ if(nonzeroCol<n)
+ {
+ // Permute the triangular factor to put the 'dead' columns to the end
+ QRMatrixType tempR(m_R);
+ m_R = tempR * m_pivotperm;
+
+ // Update the column permutation
+ m_outputPerm_c = m_outputPerm_c * m_pivotperm;
+ }
+
+ m_isInitialized = true;
+ m_factorizationIsok = true;
+ m_info = Success;
+}
+
+namespace internal {
+
+template<typename _MatrixType, typename OrderingType, typename Rhs>
+struct solve_retval<SparseQR<_MatrixType,OrderingType>, Rhs>
+ : solve_retval_base<SparseQR<_MatrixType,OrderingType>, Rhs>
+{
+ typedef SparseQR<_MatrixType,OrderingType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+template<typename _MatrixType, typename OrderingType, typename Rhs>
+struct sparse_solve_retval<SparseQR<_MatrixType, OrderingType>, Rhs>
+ : sparse_solve_retval_base<SparseQR<_MatrixType, OrderingType>, Rhs>
+{
+ typedef SparseQR<_MatrixType, OrderingType> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec, Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+} // end namespace internal
+
+template <typename SparseQRType, typename Derived>
+struct SparseQR_QProduct : ReturnByValue<SparseQR_QProduct<SparseQRType, Derived> >
+{
+ typedef typename SparseQRType::QRMatrixType MatrixType;
+ typedef typename SparseQRType::Scalar Scalar;
+ typedef typename SparseQRType::Index Index;
+ // Get the references
+ SparseQR_QProduct(const SparseQRType& qr, const Derived& other, bool transpose) :
+ m_qr(qr),m_other(other),m_transpose(transpose) {}
+ inline Index rows() const { return m_transpose ? m_qr.rows() : m_qr.cols(); }
+ inline Index cols() const { return m_other.cols(); }
+
+ // Assign to a vector
+ template<typename DesType>
+ void evalTo(DesType& res) const
+ {
+ Index m = m_qr.rows();
+ Index n = m_qr.cols();
+ Index diagSize = (std::min)(m,n);
+ res = m_other;
+ if (m_transpose)
+ {
+ eigen_assert(m_qr.m_Q.rows() == m_other.rows() && "Non conforming object sizes");
+ //Compute res = Q' * other column by column
+ for(Index j = 0; j < res.cols(); j++){
+ for (Index k = 0; k < diagSize; k++)
+ {
+ Scalar tau = Scalar(0);
+ tau = m_qr.m_Q.col(k).dot(res.col(j));
+ if(tau==Scalar(0)) continue;
+ tau = tau * m_qr.m_hcoeffs(k);
+ res.col(j) -= tau * m_qr.m_Q.col(k);
+ }
+ }
+ }
+ else
+ {
+ eigen_assert(m_qr.m_Q.rows() == m_other.rows() && "Non conforming object sizes");
+ // Compute res = Q * other column by column
+ for(Index j = 0; j < res.cols(); j++)
+ {
+ for (Index k = diagSize-1; k >=0; k--)
+ {
+ Scalar tau = Scalar(0);
+ tau = m_qr.m_Q.col(k).dot(res.col(j));
+ if(tau==Scalar(0)) continue;
+ tau = tau * m_qr.m_hcoeffs(k);
+ res.col(j) -= tau * m_qr.m_Q.col(k);
+ }
+ }
+ }
+ }
+
+ const SparseQRType& m_qr;
+ const Derived& m_other;
+ bool m_transpose;
+};
+
+template<typename SparseQRType>
+struct SparseQRMatrixQReturnType : public EigenBase<SparseQRMatrixQReturnType<SparseQRType> >
+{
+ typedef typename SparseQRType::Index Index;
+ typedef typename SparseQRType::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ SparseQRMatrixQReturnType(const SparseQRType& qr) : m_qr(qr) {}
+ template<typename Derived>
+ SparseQR_QProduct<SparseQRType, Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(),false);
+ }
+ SparseQRMatrixQTransposeReturnType<SparseQRType> adjoint() const
+ {
+ return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);
+ }
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return (std::min)(m_qr.rows(),m_qr.cols()); }
+ // To use for operations with the transpose of Q
+ SparseQRMatrixQTransposeReturnType<SparseQRType> transpose() const
+ {
+ return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);
+ }
+ template<typename Dest> void evalTo(MatrixBase<Dest>& dest) const
+ {
+ dest.derived() = m_qr.matrixQ() * Dest::Identity(m_qr.rows(), m_qr.rows());
+ }
+ template<typename Dest> void evalTo(SparseMatrixBase<Dest>& dest) const
+ {
+ Dest idMat(m_qr.rows(), m_qr.rows());
+ idMat.setIdentity();
+ // Sort the sparse householder reflectors if needed
+ const_cast<SparseQRType *>(&m_qr)->sort_matrix_Q();
+ dest.derived() = SparseQR_QProduct<SparseQRType, Dest>(m_qr, idMat, false);
+ }
+
+ const SparseQRType& m_qr;
+};
+
+template<typename SparseQRType>
+struct SparseQRMatrixQTransposeReturnType
+{
+ SparseQRMatrixQTransposeReturnType(const SparseQRType& qr) : m_qr(qr) {}
+ template<typename Derived>
+ SparseQR_QProduct<SparseQRType,Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(), true);
+ }
+ const SparseQRType& m_qr;
+};
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/StlSupport/CMakeLists.txt b/Eigen/src/StlSupport/CMakeLists.txt
new file mode 100644
index 0000000..0f094f6
--- /dev/null
+++ b/Eigen/src/StlSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_StlSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_StlSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/StlSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/StlSupport/StdDeque.h b/Eigen/src/StlSupport/StdDeque.h
new file mode 100644
index 0000000..aaf6633
--- /dev/null
+++ b/Eigen/src/StlSupport/StdDeque.h
@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDDEQUE_H
+#define EIGEN_STDDEQUE_H
+
+#include "details.h"
+
+// Define the explicit instantiation (e.g. necessary for the Intel compiler)
+#if defined(__INTEL_COMPILER) || defined(__GNUC__)
+ #define EIGEN_EXPLICIT_STL_DEQUE_INSTANTIATION(...) template class std::deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> >;
+#else
+ #define EIGEN_EXPLICIT_STL_DEQUE_INSTANTIATION(...)
+#endif
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::deque such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...) \
+EIGEN_EXPLICIT_STL_DEQUE_INSTANTIATION(__VA_ARGS__) \
+namespace std \
+{ \
+ template<typename _Ay> \
+ class deque<__VA_ARGS__, _Ay> \
+ : public deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > deque_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef typename deque_base::allocator_type allocator_type; \
+ typedef typename deque_base::size_type size_type; \
+ typedef typename deque_base::iterator iterator; \
+ explicit deque(const allocator_type& a = allocator_type()) : deque_base(a) {} \
+ template<typename InputIterator> \
+ deque(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : deque_base(first, last, a) {} \
+ deque(const deque& c) : deque_base(c) {} \
+ explicit deque(size_type num, const value_type& val = value_type()) : deque_base(num, val) {} \
+ deque(iterator start, iterator end) : deque_base(start, end) {} \
+ deque& operator=(const deque& x) { \
+ deque_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+// check whether we really need the std::deque specialization
+#if !(defined(_GLIBCXX_DEQUE) && (!EIGEN_GNUC_AT_LEAST(4,1))) /* Note that before gcc-4.1 we already have: std::deque::resize(size_type,const T&). */
+
+namespace std {
+
+#define EIGEN_STD_DEQUE_SPECIALIZATION_BODY \
+ public: \
+ typedef T value_type; \
+ typedef typename deque_base::allocator_type allocator_type; \
+ typedef typename deque_base::size_type size_type; \
+ typedef typename deque_base::iterator iterator; \
+ typedef typename deque_base::const_iterator const_iterator; \
+ explicit deque(const allocator_type& a = allocator_type()) : deque_base(a) {} \
+ template<typename InputIterator> \
+ deque(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \
+ : deque_base(first, last, a) {} \
+ deque(const deque& c) : deque_base(c) {} \
+ explicit deque(size_type num, const value_type& val = value_type()) : deque_base(num, val) {} \
+ deque(iterator start, iterator end) : deque_base(start, end) {} \
+ deque& operator=(const deque& x) { \
+ deque_base::operator=(x); \
+ return *this; \
+ }
+
+ template<typename T>
+ class deque<T,EIGEN_ALIGNED_ALLOCATOR<T> >
+ : public deque<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >
+{
+ typedef deque<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > deque_base;
+ EIGEN_STD_DEQUE_SPECIALIZATION_BODY
+
+ void resize(size_type new_size)
+ { resize(new_size, T()); }
+
+#if defined(_DEQUE_)
+ // workaround MSVC std::deque implementation
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (deque_base::size() < new_size)
+ deque_base::_Insert_n(deque_base::end(), new_size - deque_base::size(), x);
+ else if (new_size < deque_base::size())
+ deque_base::erase(deque_base::begin() + new_size, deque_base::end());
+ }
+ void push_back(const value_type& x)
+ { deque_base::push_back(x); }
+ void push_front(const value_type& x)
+ { deque_base::push_front(x); }
+ using deque_base::insert;
+ iterator insert(const_iterator position, const value_type& x)
+ { return deque_base::insert(position,x); }
+ void insert(const_iterator position, size_type new_size, const value_type& x)
+ { deque_base::insert(position, new_size, x); }
+#elif defined(_GLIBCXX_DEQUE) && EIGEN_GNUC_AT_LEAST(4,2)
+ // workaround GCC std::deque implementation
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (new_size < deque_base::size())
+ deque_base::_M_erase_at_end(this->_M_impl._M_start + new_size);
+ else
+ deque_base::insert(deque_base::end(), new_size - deque_base::size(), x);
+ }
+#else
+ // either GCC 4.1 or non-GCC
+ // default implementation which should always work.
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (new_size < deque_base::size())
+ deque_base::erase(deque_base::begin() + new_size, deque_base::end());
+ else if (new_size > deque_base::size())
+ deque_base::insert(deque_base::end(), new_size - deque_base::size(), x);
+ }
+#endif
+ };
+}
+
+#endif // check whether specialization is actually required
+
+#endif // EIGEN_STDDEQUE_H
diff --git a/Eigen/src/StlSupport/StdList.h b/Eigen/src/StlSupport/StdList.h
new file mode 100644
index 0000000..3c74243
--- /dev/null
+++ b/Eigen/src/StlSupport/StdList.h
@@ -0,0 +1,114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDLIST_H
+#define EIGEN_STDLIST_H
+
+#include "details.h"
+
+// Define the explicit instantiation (e.g. necessary for the Intel compiler)
+#if defined(__INTEL_COMPILER) || defined(__GNUC__)
+ #define EIGEN_EXPLICIT_STL_LIST_INSTANTIATION(...) template class std::list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> >;
+#else
+ #define EIGEN_EXPLICIT_STL_LIST_INSTANTIATION(...)
+#endif
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::list such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...) \
+EIGEN_EXPLICIT_STL_LIST_INSTANTIATION(__VA_ARGS__) \
+namespace std \
+{ \
+ template<typename _Ay> \
+ class list<__VA_ARGS__, _Ay> \
+ : public list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > list_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef typename list_base::allocator_type allocator_type; \
+ typedef typename list_base::size_type size_type; \
+ typedef typename list_base::iterator iterator; \
+ explicit list(const allocator_type& a = allocator_type()) : list_base(a) {} \
+ template<typename InputIterator> \
+ list(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : list_base(first, last, a) {} \
+ list(const list& c) : list_base(c) {} \
+ explicit list(size_type num, const value_type& val = value_type()) : list_base(num, val) {} \
+ list(iterator start, iterator end) : list_base(start, end) {} \
+ list& operator=(const list& x) { \
+ list_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+// check whether we really need the std::vector specialization
+#if !(defined(_GLIBCXX_VECTOR) && (!EIGEN_GNUC_AT_LEAST(4,1))) /* Note that before gcc-4.1 we already have: std::list::resize(size_type,const T&). */
+
+namespace std
+{
+
+#define EIGEN_STD_LIST_SPECIALIZATION_BODY \
+ public: \
+ typedef T value_type; \
+ typedef typename list_base::allocator_type allocator_type; \
+ typedef typename list_base::size_type size_type; \
+ typedef typename list_base::iterator iterator; \
+ typedef typename list_base::const_iterator const_iterator; \
+ explicit list(const allocator_type& a = allocator_type()) : list_base(a) {} \
+ template<typename InputIterator> \
+ list(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \
+ : list_base(first, last, a) {} \
+ list(const list& c) : list_base(c) {} \
+ explicit list(size_type num, const value_type& val = value_type()) : list_base(num, val) {} \
+ list(iterator start, iterator end) : list_base(start, end) {} \
+ list& operator=(const list& x) { \
+ list_base::operator=(x); \
+ return *this; \
+ }
+
+ template<typename T>
+ class list<T,EIGEN_ALIGNED_ALLOCATOR<T> >
+ : public list<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >
+ {
+ typedef list<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > list_base;
+ EIGEN_STD_LIST_SPECIALIZATION_BODY
+
+ void resize(size_type new_size)
+ { resize(new_size, T()); }
+
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (list_base::size() < new_size)
+ list_base::insert(list_base::end(), new_size - list_base::size(), x);
+ else
+ while (new_size < list_base::size()) list_base::pop_back();
+ }
+
+#if defined(_LIST_)
+ // workaround MSVC std::list implementation
+ void push_back(const value_type& x)
+ { list_base::push_back(x); }
+ using list_base::insert;
+ iterator insert(const_iterator position, const value_type& x)
+ { return list_base::insert(position,x); }
+ void insert(const_iterator position, size_type new_size, const value_type& x)
+ { list_base::insert(position, new_size, x); }
+#endif
+ };
+}
+
+#endif // check whether specialization is actually required
+
+#endif // EIGEN_STDLIST_H
diff --git a/Eigen/src/StlSupport/StdVector.h b/Eigen/src/StlSupport/StdVector.h
new file mode 100644
index 0000000..611664a
--- /dev/null
+++ b/Eigen/src/StlSupport/StdVector.h
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDVECTOR_H
+#define EIGEN_STDVECTOR_H
+
+#include "details.h"
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::vector such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...) \
+namespace std \
+{ \
+ template<> \
+ class vector<__VA_ARGS__, std::allocator<__VA_ARGS__> > \
+ : public vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > vector_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef vector_base::allocator_type allocator_type; \
+ typedef vector_base::size_type size_type; \
+ typedef vector_base::iterator iterator; \
+ explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {} \
+ template<typename InputIterator> \
+ vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : vector_base(first, last, a) {} \
+ vector(const vector& c) : vector_base(c) {} \
+ explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \
+ vector(iterator start, iterator end) : vector_base(start, end) {} \
+ vector& operator=(const vector& x) { \
+ vector_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+namespace std {
+
+#define EIGEN_STD_VECTOR_SPECIALIZATION_BODY \
+ public: \
+ typedef T value_type; \
+ typedef typename vector_base::allocator_type allocator_type; \
+ typedef typename vector_base::size_type size_type; \
+ typedef typename vector_base::iterator iterator; \
+ typedef typename vector_base::const_iterator const_iterator; \
+ explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {} \
+ template<typename InputIterator> \
+ vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \
+ : vector_base(first, last, a) {} \
+ vector(const vector& c) : vector_base(c) {} \
+ explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \
+ vector(iterator start, iterator end) : vector_base(start, end) {} \
+ vector& operator=(const vector& x) { \
+ vector_base::operator=(x); \
+ return *this; \
+ }
+
+ template<typename T>
+ class vector<T,EIGEN_ALIGNED_ALLOCATOR<T> >
+ : public vector<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >
+{
+ typedef vector<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),
+ Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > vector_base;
+ EIGEN_STD_VECTOR_SPECIALIZATION_BODY
+
+ void resize(size_type new_size)
+ { resize(new_size, T()); }
+
+#if defined(_VECTOR_)
+ // workaround MSVC std::vector implementation
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (vector_base::size() < new_size)
+ vector_base::_Insert_n(vector_base::end(), new_size - vector_base::size(), x);
+ else if (new_size < vector_base::size())
+ vector_base::erase(vector_base::begin() + new_size, vector_base::end());
+ }
+ void push_back(const value_type& x)
+ { vector_base::push_back(x); }
+ using vector_base::insert;
+ iterator insert(const_iterator position, const value_type& x)
+ { return vector_base::insert(position,x); }
+ void insert(const_iterator position, size_type new_size, const value_type& x)
+ { vector_base::insert(position, new_size, x); }
+#elif defined(_GLIBCXX_VECTOR) && (!(EIGEN_GNUC_AT_LEAST(4,1)))
+ /* Note that before gcc-4.1 we already have: std::vector::resize(size_type,const T&).
+ * However, this specialization is still needed to make the above EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION trick to work. */
+ void resize(size_type new_size, const value_type& x)
+ {
+ vector_base::resize(new_size,x);
+ }
+#elif defined(_GLIBCXX_VECTOR) && EIGEN_GNUC_AT_LEAST(4,2)
+ // workaround GCC std::vector implementation
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (new_size < vector_base::size())
+ vector_base::_M_erase_at_end(this->_M_impl._M_start + new_size);
+ else
+ vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);
+ }
+#else
+ // either GCC 4.1 or non-GCC
+ // default implementation which should always work.
+ void resize(size_type new_size, const value_type& x)
+ {
+ if (new_size < vector_base::size())
+ vector_base::erase(vector_base::begin() + new_size, vector_base::end());
+ else if (new_size > vector_base::size())
+ vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);
+ }
+#endif
+ };
+}
+
+#endif // EIGEN_STDVECTOR_H
diff --git a/Eigen/src/StlSupport/details.h b/Eigen/src/StlSupport/details.h
new file mode 100644
index 0000000..d8debc7
--- /dev/null
+++ b/Eigen/src/StlSupport/details.h
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STL_DETAILS_H
+#define EIGEN_STL_DETAILS_H
+
+#ifndef EIGEN_ALIGNED_ALLOCATOR
+ #define EIGEN_ALIGNED_ALLOCATOR Eigen::aligned_allocator
+#endif
+
+namespace Eigen {
+
+ // This one is needed to prevent reimplementing the whole std::vector.
+ template <class T>
+ class aligned_allocator_indirection : public EIGEN_ALIGNED_ALLOCATOR<T>
+ {
+ public:
+ typedef size_t size_type;
+ typedef ptrdiff_t difference_type;
+ typedef T* pointer;
+ typedef const T* const_pointer;
+ typedef T& reference;
+ typedef const T& const_reference;
+ typedef T value_type;
+
+ template<class U>
+ struct rebind
+ {
+ typedef aligned_allocator_indirection<U> other;
+ };
+
+ aligned_allocator_indirection() {}
+ aligned_allocator_indirection(const aligned_allocator_indirection& ) : EIGEN_ALIGNED_ALLOCATOR<T>() {}
+ aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<T>& ) {}
+ template<class U>
+ aligned_allocator_indirection(const aligned_allocator_indirection<U>& ) {}
+ template<class U>
+ aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<U>& ) {}
+ ~aligned_allocator_indirection() {}
+ };
+
+#ifdef _MSC_VER
+
+ // sometimes, MSVC detects, at compile time, that the argument x
+ // in std::vector::resize(size_t s,T x) won't be aligned and generate an error
+ // even if this function is never called. Whence this little wrapper.
+#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) \
+ typename Eigen::internal::conditional< \
+ Eigen::internal::is_arithmetic<T>::value, \
+ T, \
+ Eigen::internal::workaround_msvc_stl_support<T> \
+ >::type
+
+ namespace internal {
+ template<typename T> struct workaround_msvc_stl_support : public T
+ {
+ inline workaround_msvc_stl_support() : T() {}
+ inline workaround_msvc_stl_support(const T& other) : T(other) {}
+ inline operator T& () { return *static_cast<T*>(this); }
+ inline operator const T& () const { return *static_cast<const T*>(this); }
+ template<typename OtherT>
+ inline T& operator=(const OtherT& other)
+ { T::operator=(other); return *this; }
+ inline workaround_msvc_stl_support& operator=(const workaround_msvc_stl_support& other)
+ { T::operator=(other); return *this; }
+ };
+ }
+
+#else
+
+#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) T
+
+#endif
+
+}
+
+#endif // EIGEN_STL_DETAILS_H
diff --git a/Eigen/src/SuperLUSupport/CMakeLists.txt b/Eigen/src/SuperLUSupport/CMakeLists.txt
new file mode 100644
index 0000000..b28ebe5
--- /dev/null
+++ b/Eigen/src/SuperLUSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SuperLUSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_SuperLUSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SuperLUSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/SuperLUSupport/SuperLUSupport.h b/Eigen/src/SuperLUSupport/SuperLUSupport.h
new file mode 100644
index 0000000..bcb3557
--- /dev/null
+++ b/Eigen/src/SuperLUSupport/SuperLUSupport.h
@@ -0,0 +1,1026 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SUPERLUSUPPORT_H
+#define EIGEN_SUPERLUSUPPORT_H
+
+namespace Eigen {
+
+#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
+ extern "C" { \
+ typedef struct { FLOATTYPE for_lu; FLOATTYPE total_needed; int expansions; } PREFIX##mem_usage_t; \
+ extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
+ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
+ void *, int, SuperMatrix *, SuperMatrix *, \
+ FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
+ PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \
+ } \
+ inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
+ int *perm_c, int *perm_r, int *etree, char *equed, \
+ FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
+ SuperMatrix *U, void *work, int lwork, \
+ SuperMatrix *B, SuperMatrix *X, \
+ FLOATTYPE *recip_pivot_growth, \
+ FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
+ SuperLUStat_t *stats, int *info, KEYTYPE) { \
+ PREFIX##mem_usage_t mem_usage; \
+ PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
+ U, work, lwork, B, X, recip_pivot_growth, rcond, \
+ ferr, berr, &mem_usage, stats, info); \
+ return mem_usage.for_lu; /* bytes used by the factor storage */ \
+ }
+
+DECL_GSSVX(s,float,float)
+DECL_GSSVX(c,float,std::complex<float>)
+DECL_GSSVX(d,double,double)
+DECL_GSSVX(z,double,std::complex<double>)
+
+#ifdef MILU_ALPHA
+#define EIGEN_SUPERLU_HAS_ILU
+#endif
+
+#ifdef EIGEN_SUPERLU_HAS_ILU
+
+// similarly for the incomplete factorization using gsisx
+#define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE) \
+ extern "C" { \
+ extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
+ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
+ void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *, \
+ PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \
+ } \
+ inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A, \
+ int *perm_c, int *perm_r, int *etree, char *equed, \
+ FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
+ SuperMatrix *U, void *work, int lwork, \
+ SuperMatrix *B, SuperMatrix *X, \
+ FLOATTYPE *recip_pivot_growth, \
+ FLOATTYPE *rcond, \
+ SuperLUStat_t *stats, int *info, KEYTYPE) { \
+ PREFIX##mem_usage_t mem_usage; \
+ PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
+ U, work, lwork, B, X, recip_pivot_growth, rcond, \
+ &mem_usage, stats, info); \
+ return mem_usage.for_lu; /* bytes used by the factor storage */ \
+ }
+
+DECL_GSISX(s,float,float)
+DECL_GSISX(c,float,std::complex<float>)
+DECL_GSISX(d,double,double)
+DECL_GSISX(z,double,std::complex<double>)
+
+#endif
+
+template<typename MatrixType>
+struct SluMatrixMapHelper;
+
+/** \internal
+ *
+ * A wrapper class for SuperLU matrices. It supports only compressed sparse matrices
+ * and dense matrices. Supernodal and other fancy format are not supported by this wrapper.
+ *
+ * This wrapper class mainly aims to avoids the need of dynamic allocation of the storage structure.
+ */
+struct SluMatrix : SuperMatrix
+{
+ SluMatrix()
+ {
+ Store = &storage;
+ }
+
+ SluMatrix(const SluMatrix& other)
+ : SuperMatrix(other)
+ {
+ Store = &storage;
+ storage = other.storage;
+ }
+
+ SluMatrix& operator=(const SluMatrix& other)
+ {
+ SuperMatrix::operator=(static_cast<const SuperMatrix&>(other));
+ Store = &storage;
+ storage = other.storage;
+ return *this;
+ }
+
+ struct
+ {
+ union {int nnz;int lda;};
+ void *values;
+ int *innerInd;
+ int *outerInd;
+ } storage;
+
+ void setStorageType(Stype_t t)
+ {
+ Stype = t;
+ if (t==SLU_NC || t==SLU_NR || t==SLU_DN)
+ Store = &storage;
+ else
+ {
+ eigen_assert(false && "storage type not supported");
+ Store = 0;
+ }
+ }
+
+ template<typename Scalar>
+ void setScalarType()
+ {
+ if (internal::is_same<Scalar,float>::value)
+ Dtype = SLU_S;
+ else if (internal::is_same<Scalar,double>::value)
+ Dtype = SLU_D;
+ else if (internal::is_same<Scalar,std::complex<float> >::value)
+ Dtype = SLU_C;
+ else if (internal::is_same<Scalar,std::complex<double> >::value)
+ Dtype = SLU_Z;
+ else
+ {
+ eigen_assert(false && "Scalar type not supported by SuperLU");
+ }
+ }
+
+ template<typename MatrixType>
+ static SluMatrix Map(MatrixBase<MatrixType>& _mat)
+ {
+ MatrixType& mat(_mat.derived());
+ eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && "row-major dense matrices are not supported by SuperLU");
+ SluMatrix res;
+ res.setStorageType(SLU_DN);
+ res.setScalarType<typename MatrixType::Scalar>();
+ res.Mtype = SLU_GE;
+
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+
+ res.storage.lda = MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride();
+ res.storage.values = (void*)(mat.data());
+ return res;
+ }
+
+ template<typename MatrixType>
+ static SluMatrix Map(SparseMatrixBase<MatrixType>& mat)
+ {
+ SluMatrix res;
+ if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
+ {
+ res.setStorageType(SLU_NR);
+ res.nrow = mat.cols();
+ res.ncol = mat.rows();
+ }
+ else
+ {
+ res.setStorageType(SLU_NC);
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ }
+
+ res.Mtype = SLU_GE;
+
+ res.storage.nnz = mat.nonZeros();
+ res.storage.values = mat.derived().valuePtr();
+ res.storage.innerInd = mat.derived().innerIndexPtr();
+ res.storage.outerInd = mat.derived().outerIndexPtr();
+
+ res.setScalarType<typename MatrixType::Scalar>();
+
+ // FIXME the following is not very accurate
+ if (MatrixType::Flags & Upper)
+ res.Mtype = SLU_TRU;
+ if (MatrixType::Flags & Lower)
+ res.Mtype = SLU_TRL;
+
+ eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
+
+ return res;
+ }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols>
+struct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> >
+{
+ typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType;
+ static void run(MatrixType& mat, SluMatrix& res)
+ {
+ eigen_assert( ((Options&RowMajor)!=RowMajor) && "row-major dense matrices is not supported by SuperLU");
+ res.setStorageType(SLU_DN);
+ res.setScalarType<Scalar>();
+ res.Mtype = SLU_GE;
+
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+
+ res.storage.lda = mat.outerStride();
+ res.storage.values = mat.data();
+ }
+};
+
+template<typename Derived>
+struct SluMatrixMapHelper<SparseMatrixBase<Derived> >
+{
+ typedef Derived MatrixType;
+ static void run(MatrixType& mat, SluMatrix& res)
+ {
+ if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
+ {
+ res.setStorageType(SLU_NR);
+ res.nrow = mat.cols();
+ res.ncol = mat.rows();
+ }
+ else
+ {
+ res.setStorageType(SLU_NC);
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ }
+
+ res.Mtype = SLU_GE;
+
+ res.storage.nnz = mat.nonZeros();
+ res.storage.values = mat.valuePtr();
+ res.storage.innerInd = mat.innerIndexPtr();
+ res.storage.outerInd = mat.outerIndexPtr();
+
+ res.setScalarType<typename MatrixType::Scalar>();
+
+ // FIXME the following is not very accurate
+ if (MatrixType::Flags & Upper)
+ res.Mtype = SLU_TRU;
+ if (MatrixType::Flags & Lower)
+ res.Mtype = SLU_TRL;
+
+ eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
+ }
+};
+
+namespace internal {
+
+template<typename MatrixType>
+SluMatrix asSluMatrix(MatrixType& mat)
+{
+ return SluMatrix::Map(mat);
+}
+
+/** View a Super LU matrix as an Eigen expression */
+template<typename Scalar, int Flags, typename Index>
+MappedSparseMatrix<Scalar,Flags,Index> map_superlu(SluMatrix& sluMat)
+{
+ eigen_assert((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR
+ || (Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC);
+
+ Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow;
+
+ return MappedSparseMatrix<Scalar,Flags,Index>(
+ sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize],
+ sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) );
+}
+
+} // end namespace internal
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperLUBase
+ * \brief The base class for the direct and incomplete LU factorization of SuperLU
+ */
+template<typename _MatrixType, typename Derived>
+class SuperLUBase : internal::noncopyable
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef SparseMatrix<Scalar> LUMatrixType;
+
+ public:
+
+ SuperLUBase() {}
+
+ ~SuperLUBase()
+ {
+ clearFactors();
+ }
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ /** \returns a reference to the Super LU option object to configure the Super LU algorithms. */
+ inline superlu_options_t& options() { return m_sluOptions; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ void compute(const MatrixType& matrix)
+ {
+ derived().analyzePattern(matrix);
+ derived().factorize(matrix);
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<SuperLUBase, Rhs> solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "SuperLU is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "SuperLU::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<SuperLUBase, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<SuperLUBase, Rhs> solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "SuperLU is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "SuperLU::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<SuperLUBase, Rhs>(*this, b.derived());
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& /*matrix*/)
+ {
+ m_isInitialized = true;
+ m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ }
+
+ template<typename Stream>
+ void dumpMemory(Stream& /*s*/)
+ {}
+
+ protected:
+
+ void initFactorization(const MatrixType& a)
+ {
+ set_default_options(&this->m_sluOptions);
+
+ const int size = a.rows();
+ m_matrix = a;
+
+ m_sluA = internal::asSluMatrix(m_matrix);
+ clearFactors();
+
+ m_p.resize(size);
+ m_q.resize(size);
+ m_sluRscale.resize(size);
+ m_sluCscale.resize(size);
+ m_sluEtree.resize(size);
+
+ // set empty B and X
+ m_sluB.setStorageType(SLU_DN);
+ m_sluB.setScalarType<Scalar>();
+ m_sluB.Mtype = SLU_GE;
+ m_sluB.storage.values = 0;
+ m_sluB.nrow = 0;
+ m_sluB.ncol = 0;
+ m_sluB.storage.lda = size;
+ m_sluX = m_sluB;
+
+ m_extractedDataAreDirty = true;
+ }
+
+ void init()
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ m_sluL.Store = 0;
+ m_sluU.Store = 0;
+ }
+
+ void extractData() const;
+
+ void clearFactors()
+ {
+ if(m_sluL.Store)
+ Destroy_SuperNode_Matrix(&m_sluL);
+ if(m_sluU.Store)
+ Destroy_CompCol_Matrix(&m_sluU);
+
+ m_sluL.Store = 0;
+ m_sluU.Store = 0;
+
+ memset(&m_sluL,0,sizeof m_sluL);
+ memset(&m_sluU,0,sizeof m_sluU);
+ }
+
+ // cached data to reduce reallocation, etc.
+ mutable LUMatrixType m_l;
+ mutable LUMatrixType m_u;
+ mutable IntColVectorType m_p;
+ mutable IntRowVectorType m_q;
+
+ mutable LUMatrixType m_matrix; // copy of the factorized matrix
+ mutable SluMatrix m_sluA;
+ mutable SuperMatrix m_sluL, m_sluU;
+ mutable SluMatrix m_sluB, m_sluX;
+ mutable SuperLUStat_t m_sluStat;
+ mutable superlu_options_t m_sluOptions;
+ mutable std::vector<int> m_sluEtree;
+ mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale;
+ mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr;
+ mutable char m_sluEqued;
+
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+ mutable bool m_extractedDataAreDirty;
+
+ private:
+ SuperLUBase(SuperLUBase& ) { }
+};
+
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperLU
+ * \brief A sparse direct LU factorization and solver based on the SuperLU library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
+ * using the SuperLU library. The sparse matrix A must be squared and invertible. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType>
+class SuperLU : public SuperLUBase<_MatrixType,SuperLU<_MatrixType> >
+{
+ public:
+ typedef SuperLUBase<_MatrixType,SuperLU> Base;
+ typedef _MatrixType MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::Index Index;
+ typedef typename Base::IntRowVectorType IntRowVectorType;
+ typedef typename Base::IntColVectorType IntColVectorType;
+ typedef typename Base::LUMatrixType LUMatrixType;
+ typedef TriangularView<LUMatrixType, Lower|UnitDiag> LMatrixType;
+ typedef TriangularView<LUMatrixType, Upper> UMatrixType;
+
+ public:
+
+ SuperLU() : Base() { init(); }
+
+ SuperLU(const MatrixType& matrix) : Base()
+ {
+ init();
+ Base::compute(matrix);
+ }
+
+ ~SuperLU()
+ {
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ Base::analyzePattern(matrix);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix);
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+ inline const LMatrixType& matrixL() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_l;
+ }
+
+ inline const UMatrixType& matrixU() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_u;
+ }
+
+ inline const IntColVectorType& permutationP() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_p;
+ }
+
+ inline const IntRowVectorType& permutationQ() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_q;
+ }
+
+ Scalar determinant() const;
+
+ protected:
+
+ using Base::m_matrix;
+ using Base::m_sluOptions;
+ using Base::m_sluA;
+ using Base::m_sluB;
+ using Base::m_sluX;
+ using Base::m_p;
+ using Base::m_q;
+ using Base::m_sluEtree;
+ using Base::m_sluEqued;
+ using Base::m_sluRscale;
+ using Base::m_sluCscale;
+ using Base::m_sluL;
+ using Base::m_sluU;
+ using Base::m_sluStat;
+ using Base::m_sluFerr;
+ using Base::m_sluBerr;
+ using Base::m_l;
+ using Base::m_u;
+
+ using Base::m_analysisIsOk;
+ using Base::m_factorizationIsOk;
+ using Base::m_extractedDataAreDirty;
+ using Base::m_isInitialized;
+ using Base::m_info;
+
+ void init()
+ {
+ Base::init();
+
+ set_default_options(&this->m_sluOptions);
+ m_sluOptions.PrintStat = NO;
+ m_sluOptions.ConditionNumber = NO;
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.ColPerm = COLAMD;
+ }
+
+
+ private:
+ SuperLU(SuperLU& ) { }
+};
+
+template<typename MatrixType>
+void SuperLU<MatrixType>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ if(!m_analysisIsOk)
+ {
+ m_info = InvalidInput;
+ return;
+ }
+
+ this->initFactorization(a);
+
+ m_sluOptions.ColPerm = COLAMD;
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+ RealScalar ferr, berr;
+
+ StatInit(&m_sluStat);
+ SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
+ &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &ferr, &berr,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ m_extractedDataAreDirty = true;
+
+ // FIXME how to better check for errors ???
+ m_info = info == 0 ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+template<typename MatrixType>
+template<typename Rhs,typename Dest>
+void SuperLU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
+
+ const int size = m_matrix.rows();
+ const int rhsCols = b.cols();
+ eigen_assert(size==b.rows());
+
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.Fact = FACTORED;
+ m_sluOptions.IterRefine = NOREFINE;
+
+
+ m_sluFerr.resize(rhsCols);
+ m_sluBerr.resize(rhsCols);
+ m_sluB = SluMatrix::Map(b.const_cast_derived());
+ m_sluX = SluMatrix::Map(x.derived());
+
+ typename Rhs::PlainObject b_cpy;
+ if(m_sluEqued!='N')
+ {
+ b_cpy = b;
+ m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
+ }
+
+ StatInit(&m_sluStat);
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+ SuperLU_gssvx(&m_sluOptions, &m_sluA,
+ m_q.data(), m_p.data(),
+ &m_sluEtree[0], &m_sluEqued,
+ &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluFerr[0], &m_sluBerr[0],
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+ m_info = info==0 ? Success : NumericalIssue;
+}
+
+// the code of this extractData() function has been adapted from the SuperLU's Matlab support code,
+//
+// Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+//
+// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+//
+template<typename MatrixType, typename Derived>
+void SuperLUBase<MatrixType,Derived>::extractData() const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()");
+ if (m_extractedDataAreDirty)
+ {
+ int upper;
+ int fsupc, istart, nsupr;
+ int lastl = 0, lastu = 0;
+ SCformat *Lstore = static_cast<SCformat*>(m_sluL.Store);
+ NCformat *Ustore = static_cast<NCformat*>(m_sluU.Store);
+ Scalar *SNptr;
+
+ const int size = m_matrix.rows();
+ m_l.resize(size,size);
+ m_l.resizeNonZeros(Lstore->nnz);
+ m_u.resize(size,size);
+ m_u.resizeNonZeros(Ustore->nnz);
+
+ int* Lcol = m_l.outerIndexPtr();
+ int* Lrow = m_l.innerIndexPtr();
+ Scalar* Lval = m_l.valuePtr();
+
+ int* Ucol = m_u.outerIndexPtr();
+ int* Urow = m_u.innerIndexPtr();
+ Scalar* Uval = m_u.valuePtr();
+
+ Ucol[0] = 0;
+ Ucol[0] = 0;
+
+ /* for each supernode */
+ for (int k = 0; k <= Lstore->nsuper; ++k)
+ {
+ fsupc = L_FST_SUPC(k);
+ istart = L_SUB_START(fsupc);
+ nsupr = L_SUB_START(fsupc+1) - istart;
+ upper = 1;
+
+ /* for each column in the supernode */
+ for (int j = fsupc; j < L_FST_SUPC(k+1); ++j)
+ {
+ SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)];
+
+ /* Extract U */
+ for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i)
+ {
+ Uval[lastu] = ((Scalar*)Ustore->nzval)[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Uval[lastu] != 0.0)
+ Urow[lastu++] = U_SUB(i);
+ }
+ for (int i = 0; i < upper; ++i)
+ {
+ /* upper triangle in the supernode */
+ Uval[lastu] = SNptr[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Uval[lastu] != 0.0)
+ Urow[lastu++] = L_SUB(istart+i);
+ }
+ Ucol[j+1] = lastu;
+
+ /* Extract L */
+ Lval[lastl] = 1.0; /* unit diagonal */
+ Lrow[lastl++] = L_SUB(istart + upper - 1);
+ for (int i = upper; i < nsupr; ++i)
+ {
+ Lval[lastl] = SNptr[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Lval[lastl] != 0.0)
+ Lrow[lastl++] = L_SUB(istart+i);
+ }
+ Lcol[j+1] = lastl;
+
+ ++upper;
+ } /* for j ... */
+
+ } /* for k ... */
+
+ // squeeze the matrices :
+ m_l.resizeNonZeros(lastl);
+ m_u.resizeNonZeros(lastu);
+
+ m_extractedDataAreDirty = false;
+ }
+}
+
+template<typename MatrixType>
+typename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()");
+
+ if (m_extractedDataAreDirty)
+ this->extractData();
+
+ Scalar det = Scalar(1);
+ for (int j=0; j<m_u.cols(); ++j)
+ {
+ if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0)
+ {
+ int lastId = m_u.outerIndexPtr()[j+1]-1;
+ eigen_assert(m_u.innerIndexPtr()[lastId]<=j);
+ if (m_u.innerIndexPtr()[lastId]==j)
+ det *= m_u.valuePtr()[lastId];
+ }
+ }
+ if(m_sluEqued!='N')
+ return det/m_sluRscale.prod()/m_sluCscale.prod();
+ else
+ return det;
+}
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+#define EIGEN_SUPERLU_HAS_ILU
+#endif
+
+#ifdef EIGEN_SUPERLU_HAS_ILU
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperILU
+ * \brief A sparse direct \b incomplete LU factorization and solver based on the SuperLU library
+ *
+ * This class allows to solve for an approximate solution of A.X = B sparse linear problems via an incomplete LU factorization
+ * using the SuperLU library. This class is aimed to be used as a preconditioner of the iterative linear solvers.
+ *
+ * \warning This class requires SuperLU 4 or later.
+ *
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseDirectSolvers, class ConjugateGradient, class BiCGSTAB
+ */
+
+template<typename _MatrixType>
+class SuperILU : public SuperLUBase<_MatrixType,SuperILU<_MatrixType> >
+{
+ public:
+ typedef SuperLUBase<_MatrixType,SuperILU> Base;
+ typedef _MatrixType MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::Index Index;
+
+ public:
+
+ SuperILU() : Base() { init(); }
+
+ SuperILU(const MatrixType& matrix) : Base()
+ {
+ init();
+ Base::compute(matrix);
+ }
+
+ ~SuperILU()
+ {
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ Base::analyzePattern(matrix);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix);
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+ protected:
+
+ using Base::m_matrix;
+ using Base::m_sluOptions;
+ using Base::m_sluA;
+ using Base::m_sluB;
+ using Base::m_sluX;
+ using Base::m_p;
+ using Base::m_q;
+ using Base::m_sluEtree;
+ using Base::m_sluEqued;
+ using Base::m_sluRscale;
+ using Base::m_sluCscale;
+ using Base::m_sluL;
+ using Base::m_sluU;
+ using Base::m_sluStat;
+ using Base::m_sluFerr;
+ using Base::m_sluBerr;
+ using Base::m_l;
+ using Base::m_u;
+
+ using Base::m_analysisIsOk;
+ using Base::m_factorizationIsOk;
+ using Base::m_extractedDataAreDirty;
+ using Base::m_isInitialized;
+ using Base::m_info;
+
+ void init()
+ {
+ Base::init();
+
+ ilu_set_default_options(&m_sluOptions);
+ m_sluOptions.PrintStat = NO;
+ m_sluOptions.ConditionNumber = NO;
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.ColPerm = MMD_AT_PLUS_A;
+
+ // no attempt to preserve column sum
+ m_sluOptions.ILU_MILU = SILU;
+ // only basic ILU(k) support -- no direct control over memory consumption
+ // better to use ILU_DropRule = DROP_BASIC | DROP_AREA
+ // and set ILU_FillFactor to max memory growth
+ m_sluOptions.ILU_DropRule = DROP_BASIC;
+ m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10;
+ }
+
+ private:
+ SuperILU(SuperILU& ) { }
+};
+
+template<typename MatrixType>
+void SuperILU<MatrixType>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ if(!m_analysisIsOk)
+ {
+ m_info = InvalidInput;
+ return;
+ }
+
+ this->initFactorization(a);
+
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+
+ StatInit(&m_sluStat);
+ SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
+ &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ // FIXME how to better check for errors ???
+ m_info = info == 0 ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+template<typename MatrixType>
+template<typename Rhs,typename Dest>
+void SuperILU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
+
+ const int size = m_matrix.rows();
+ const int rhsCols = b.cols();
+ eigen_assert(size==b.rows());
+
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.Fact = FACTORED;
+ m_sluOptions.IterRefine = NOREFINE;
+
+ m_sluFerr.resize(rhsCols);
+ m_sluBerr.resize(rhsCols);
+ m_sluB = SluMatrix::Map(b.const_cast_derived());
+ m_sluX = SluMatrix::Map(x.derived());
+
+ typename Rhs::PlainObject b_cpy;
+ if(m_sluEqued!='N')
+ {
+ b_cpy = b;
+ m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
+ }
+
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+
+ StatInit(&m_sluStat);
+ SuperLU_gsisx(&m_sluOptions, &m_sluA,
+ m_q.data(), m_p.data(),
+ &m_sluEtree[0], &m_sluEqued,
+ &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ m_info = info==0 ? Success : NumericalIssue;
+}
+#endif
+
+namespace internal {
+
+template<typename _MatrixType, typename Derived, typename Rhs>
+struct solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs>
+ : solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs>
+{
+ typedef SuperLUBase<_MatrixType,Derived> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec().derived()._solve(rhs(),dst);
+ }
+};
+
+template<typename _MatrixType, typename Derived, typename Rhs>
+struct sparse_solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs>
+ : sparse_solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs>
+{
+ typedef SuperLUBase<_MatrixType,Derived> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SUPERLUSUPPORT_H
diff --git a/Eigen/src/UmfPackSupport/CMakeLists.txt b/Eigen/src/UmfPackSupport/CMakeLists.txt
new file mode 100644
index 0000000..a57de00
--- /dev/null
+++ b/Eigen/src/UmfPackSupport/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_UmfPackSupport_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_UmfPackSupport_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/UmfPackSupport COMPONENT Devel
+ )
diff --git a/Eigen/src/UmfPackSupport/UmfPackSupport.h b/Eigen/src/UmfPackSupport/UmfPackSupport.h
new file mode 100644
index 0000000..29c60c3
--- /dev/null
+++ b/Eigen/src/UmfPackSupport/UmfPackSupport.h
@@ -0,0 +1,474 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UMFPACKSUPPORT_H
+#define EIGEN_UMFPACKSUPPORT_H
+
+namespace Eigen {
+
+/* TODO extract L, extract U, compute det, etc... */
+
+// generic double/complex<double> wrapper functions:
+
+inline void umfpack_free_numeric(void **Numeric, double)
+{ umfpack_di_free_numeric(Numeric); *Numeric = 0; }
+
+inline void umfpack_free_numeric(void **Numeric, std::complex<double>)
+{ umfpack_zi_free_numeric(Numeric); *Numeric = 0; }
+
+inline void umfpack_free_symbolic(void **Symbolic, double)
+{ umfpack_di_free_symbolic(Symbolic); *Symbolic = 0; }
+
+inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>)
+{ umfpack_zi_free_symbolic(Symbolic); *Symbolic = 0; }
+
+inline int umfpack_symbolic(int n_row,int n_col,
+ const int Ap[], const int Ai[], const double Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
+}
+
+inline int umfpack_symbolic(int n_row,int n_col,
+ const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
+}
+
+inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
+}
+
+inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
+}
+
+inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
+ double X[], const double B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
+}
+
+inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],
+ std::complex<double> X[], const std::complex<double> B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
+}
+
+inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
+{
+ return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)
+{
+ return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],
+ int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)
+{
+ return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
+}
+
+inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
+ int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
+{
+ double& lx0_real = numext::real_ref(Lx[0]);
+ double& ux0_real = numext::real_ref(Ux[0]);
+ double& dx0_real = numext::real_ref(Dx[0]);
+ return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
+ Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
+}
+
+inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
+{
+ return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);
+}
+
+inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
+{
+ double& mx_real = numext::real_ref(*Mx);
+ return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
+}
+
+namespace internal {
+ template<typename T> struct umfpack_helper_is_sparse_plain : false_type {};
+ template<typename Scalar, int Options, typename StorageIndex>
+ struct umfpack_helper_is_sparse_plain<SparseMatrix<Scalar,Options,StorageIndex> >
+ : true_type {};
+ template<typename Scalar, int Options, typename StorageIndex>
+ struct umfpack_helper_is_sparse_plain<MappedSparseMatrix<Scalar,Options,StorageIndex> >
+ : true_type {};
+}
+
+/** \ingroup UmfPackSupport_Module
+ * \brief A sparse LU factorization and solver based on UmfPack
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LU factorization
+ * using the UmfPack library. The sparse matrix A must be squared and full rank.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \warning The input matrix A should be in a \b compressed and \b column-major form.
+ * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
+ * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseDirectSolvers
+ */
+template<typename _MatrixType>
+class UmfPackLU : internal::noncopyable
+{
+ public:
+ typedef _MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef SparseMatrix<Scalar> LUMatrixType;
+ typedef SparseMatrix<Scalar,ColMajor,int> UmfpackMatrixType;
+
+ public:
+
+ UmfPackLU() { init(); }
+
+ UmfPackLU(const MatrixType& matrix)
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~UmfPackLU()
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
+ }
+
+ inline Index rows() const { return m_copyMatrix.rows(); }
+ inline Index cols() const { return m_copyMatrix.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was succesful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ inline const LUMatrixType& matrixL() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_l;
+ }
+
+ inline const LUMatrixType& matrixU() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_u;
+ }
+
+ inline const IntColVectorType& permutationP() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_p;
+ }
+
+ inline const IntRowVectorType& permutationQ() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_q;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix
+ * Note that the matrix should be column-major, and in compressed format for best performance.
+ * \sa SparseMatrix::makeCompressed().
+ */
+ template<typename InputMatrixType>
+ void compute(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
+ grapInput(matrix.derived());
+ analyzePattern_impl();
+ factorize_impl();
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::solve_retval<UmfPackLU, Rhs> solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::solve_retval<UmfPackLU, Rhs>(*this, b.derived());
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const internal::sparse_solve_retval<UmfPackLU, Rhs> solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
+ eigen_assert(rows()==b.rows()
+ && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
+ return internal::sparse_solve_retval<UmfPackLU, Rhs>(*this, b.derived());
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize(), compute()
+ */
+ template<typename InputMatrixType>
+ void analyzePattern(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
+
+ grapInput(matrix.derived());
+
+ analyzePattern_impl();
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
+ *
+ * \sa analyzePattern(), compute()
+ */
+ template<typename InputMatrixType>
+ void factorize(const InputMatrixType& matrix)
+ {
+ eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
+ if(m_numeric)
+ umfpack_free_numeric(&m_numeric,Scalar());
+
+ grapInput(matrix.derived());
+
+ factorize_impl();
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename BDerived,typename XDerived>
+ bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;
+ #endif
+
+ Scalar determinant() const;
+
+ void extractData() const;
+
+ protected:
+
+ void init()
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ m_numeric = 0;
+ m_symbolic = 0;
+ m_outerIndexPtr = 0;
+ m_innerIndexPtr = 0;
+ m_valuePtr = 0;
+ m_extractedDataAreDirty = true;
+ }
+
+ template<typename InputMatrixType>
+ void grapInput_impl(const InputMatrixType& mat, internal::true_type)
+ {
+ m_copyMatrix.resize(mat.rows(), mat.cols());
+ if( ((MatrixType::Flags&RowMajorBit)==RowMajorBit) || sizeof(typename MatrixType::Index)!=sizeof(int) || !mat.isCompressed() )
+ {
+ // non supported input -> copy
+ m_copyMatrix = mat;
+ m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
+ m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
+ m_valuePtr = m_copyMatrix.valuePtr();
+ }
+ else
+ {
+ m_outerIndexPtr = mat.outerIndexPtr();
+ m_innerIndexPtr = mat.innerIndexPtr();
+ m_valuePtr = mat.valuePtr();
+ }
+ }
+
+ template<typename InputMatrixType>
+ void grapInput_impl(const InputMatrixType& mat, internal::false_type)
+ {
+ m_copyMatrix = mat;
+ m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
+ m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
+ m_valuePtr = m_copyMatrix.valuePtr();
+ }
+
+ template<typename InputMatrixType>
+ void grapInput(const InputMatrixType& mat)
+ {
+ grapInput_impl(mat, internal::umfpack_helper_is_sparse_plain<InputMatrixType>());
+ }
+
+ void analyzePattern_impl()
+ {
+ int errorCode = 0;
+ errorCode = umfpack_symbolic(m_copyMatrix.rows(), m_copyMatrix.cols(), m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
+ &m_symbolic, 0, 0);
+
+ m_isInitialized = true;
+ m_info = errorCode ? InvalidInput : Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_extractedDataAreDirty = true;
+ }
+
+ void factorize_impl()
+ {
+ int errorCode;
+ errorCode = umfpack_numeric(m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
+ m_symbolic, &m_numeric, 0, 0);
+
+ m_info = errorCode ? NumericalIssue : Success;
+ m_factorizationIsOk = true;
+ m_extractedDataAreDirty = true;
+ }
+
+ // cached data to reduce reallocation, etc.
+ mutable LUMatrixType m_l;
+ mutable LUMatrixType m_u;
+ mutable IntColVectorType m_p;
+ mutable IntRowVectorType m_q;
+
+ UmfpackMatrixType m_copyMatrix;
+ const Scalar* m_valuePtr;
+ const int* m_outerIndexPtr;
+ const int* m_innerIndexPtr;
+ void* m_numeric;
+ void* m_symbolic;
+
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+ mutable bool m_extractedDataAreDirty;
+
+ private:
+ UmfPackLU(UmfPackLU& ) { }
+};
+
+
+template<typename MatrixType>
+void UmfPackLU<MatrixType>::extractData() const
+{
+ if (m_extractedDataAreDirty)
+ {
+ // get size of the data
+ int lnz, unz, rows, cols, nz_udiag;
+ umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
+
+ // allocate data
+ m_l.resize(rows,(std::min)(rows,cols));
+ m_l.resizeNonZeros(lnz);
+
+ m_u.resize((std::min)(rows,cols),cols);
+ m_u.resizeNonZeros(unz);
+
+ m_p.resize(rows);
+ m_q.resize(cols);
+
+ // extract
+ umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
+ m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
+ m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
+
+ m_extractedDataAreDirty = false;
+ }
+}
+
+template<typename MatrixType>
+typename UmfPackLU<MatrixType>::Scalar UmfPackLU<MatrixType>::determinant() const
+{
+ Scalar det;
+ umfpack_get_determinant(&det, 0, m_numeric, 0);
+ return det;
+}
+
+template<typename MatrixType>
+template<typename BDerived,typename XDerived>
+bool UmfPackLU<MatrixType>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const
+{
+ const int rhsCols = b.cols();
+ eigen_assert((BDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major rhs yet");
+ eigen_assert((XDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major result yet");
+ eigen_assert(b.derived().data() != x.derived().data() && " Umfpack does not support inplace solve");
+
+ int errorCode;
+ for (int j=0; j<rhsCols; ++j)
+ {
+ errorCode = umfpack_solve(UMFPACK_A,
+ m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
+ &x.col(j).coeffRef(0), &b.const_cast_derived().col(j).coeffRef(0), m_numeric, 0, 0);
+ if (errorCode!=0)
+ return false;
+ }
+
+ return true;
+}
+
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<UmfPackLU<_MatrixType>, Rhs>
+ : solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
+{
+ typedef UmfPackLU<_MatrixType> Dec;
+ EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ dec()._solve(rhs(),dst);
+ }
+};
+
+template<typename _MatrixType, typename Rhs>
+struct sparse_solve_retval<UmfPackLU<_MatrixType>, Rhs>
+ : sparse_solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
+{
+ typedef UmfPackLU<_MatrixType> Dec;
+ EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ this->defaultEvalTo(dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_UMFPACKSUPPORT_H
diff --git a/Eigen/src/misc/CMakeLists.txt b/Eigen/src/misc/CMakeLists.txt
new file mode 100644
index 0000000..a58ffb7
--- /dev/null
+++ b/Eigen/src/misc/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_misc_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_misc_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/misc COMPONENT Devel
+ )
diff --git a/Eigen/src/misc/Image.h b/Eigen/src/misc/Image.h
new file mode 100644
index 0000000..75c5f43
--- /dev/null
+++ b/Eigen/src/misc/Image.h
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_IMAGE_H
+#define EIGEN_MISC_IMAGE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \class image_retval_base
+ *
+ */
+template<typename DecompositionType>
+struct traits<image_retval_base<DecompositionType> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<
+ typename MatrixType::Scalar,
+ MatrixType::RowsAtCompileTime, // the image is a subspace of the destination space, whose
+ // dimension is the number of rows of the original matrix
+ Dynamic, // we don't know at compile time the dimension of the image (the rank)
+ MatrixType::Options,
+ MatrixType::MaxRowsAtCompileTime, // the image matrix will consist of columns from the original matrix,
+ MatrixType::MaxColsAtCompileTime // so it has the same number of rows and at most as many columns.
+ > ReturnType;
+};
+
+template<typename _DecompositionType> struct image_retval_base
+ : public ReturnByValue<image_retval_base<_DecompositionType> >
+{
+ typedef _DecompositionType DecompositionType;
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef ReturnByValue<image_retval_base> Base;
+ typedef typename Base::Index Index;
+
+ image_retval_base(const DecompositionType& dec, const MatrixType& originalMatrix)
+ : m_dec(dec), m_rank(dec.rank()),
+ m_cols(m_rank == 0 ? 1 : m_rank),
+ m_originalMatrix(originalMatrix)
+ {}
+
+ inline Index rows() const { return m_dec.rows(); }
+ inline Index cols() const { return m_cols; }
+ inline Index rank() const { return m_rank; }
+ inline const DecompositionType& dec() const { return m_dec; }
+ inline const MatrixType& originalMatrix() const { return m_originalMatrix; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const image_retval<DecompositionType>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ Index m_rank, m_cols;
+ const MatrixType& m_originalMatrix;
+};
+
+} // end namespace internal
+
+#define EIGEN_MAKE_IMAGE_HELPERS(DecompositionType) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef typename MatrixType::Index Index; \
+ typedef Eigen::internal::image_retval_base<DecompositionType> Base; \
+ using Base::dec; \
+ using Base::originalMatrix; \
+ using Base::rank; \
+ using Base::rows; \
+ using Base::cols; \
+ image_retval(const DecompositionType& dec, const MatrixType& originalMatrix) \
+ : Base(dec, originalMatrix) {}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MISC_IMAGE_H
diff --git a/Eigen/src/misc/Kernel.h b/Eigen/src/misc/Kernel.h
new file mode 100644
index 0000000..b9e1518
--- /dev/null
+++ b/Eigen/src/misc/Kernel.h
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_KERNEL_H
+#define EIGEN_MISC_KERNEL_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \class kernel_retval_base
+ *
+ */
+template<typename DecompositionType>
+struct traits<kernel_retval_base<DecompositionType> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<
+ typename MatrixType::Scalar,
+ MatrixType::ColsAtCompileTime, // the number of rows in the "kernel matrix"
+ // is the number of cols of the original matrix
+ // so that the product "matrix * kernel = zero" makes sense
+ Dynamic, // we don't know at compile-time the dimension of the kernel
+ MatrixType::Options,
+ MatrixType::MaxColsAtCompileTime, // see explanation for 2nd template parameter
+ MatrixType::MaxColsAtCompileTime // the kernel is a subspace of the domain space,
+ // whose dimension is the number of columns of the original matrix
+ > ReturnType;
+};
+
+template<typename _DecompositionType> struct kernel_retval_base
+ : public ReturnByValue<kernel_retval_base<_DecompositionType> >
+{
+ typedef _DecompositionType DecompositionType;
+ typedef ReturnByValue<kernel_retval_base> Base;
+ typedef typename Base::Index Index;
+
+ kernel_retval_base(const DecompositionType& dec)
+ : m_dec(dec),
+ m_rank(dec.rank()),
+ m_cols(m_rank==dec.cols() ? 1 : dec.cols() - m_rank)
+ {}
+
+ inline Index rows() const { return m_dec.cols(); }
+ inline Index cols() const { return m_cols; }
+ inline Index rank() const { return m_rank; }
+ inline const DecompositionType& dec() const { return m_dec; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const kernel_retval<DecompositionType>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ Index m_rank, m_cols;
+};
+
+} // end namespace internal
+
+#define EIGEN_MAKE_KERNEL_HELPERS(DecompositionType) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef typename MatrixType::Index Index; \
+ typedef Eigen::internal::kernel_retval_base<DecompositionType> Base; \
+ using Base::dec; \
+ using Base::rank; \
+ using Base::rows; \
+ using Base::cols; \
+ kernel_retval(const DecompositionType& dec) : Base(dec) {}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MISC_KERNEL_H
diff --git a/Eigen/src/misc/Solve.h b/Eigen/src/misc/Solve.h
new file mode 100644
index 0000000..7f70d60
--- /dev/null
+++ b/Eigen/src/misc/Solve.h
@@ -0,0 +1,76 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_SOLVE_H
+#define EIGEN_MISC_SOLVE_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \class solve_retval_base
+ *
+ */
+template<typename DecompositionType, typename Rhs>
+struct traits<solve_retval_base<DecompositionType, Rhs> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<typename Rhs::Scalar,
+ MatrixType::ColsAtCompileTime,
+ Rhs::ColsAtCompileTime,
+ Rhs::PlainObject::Options,
+ MatrixType::MaxColsAtCompileTime,
+ Rhs::MaxColsAtCompileTime> ReturnType;
+};
+
+template<typename _DecompositionType, typename Rhs> struct solve_retval_base
+ : public ReturnByValue<solve_retval_base<_DecompositionType, Rhs> >
+{
+ typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
+ typedef _DecompositionType DecompositionType;
+ typedef ReturnByValue<solve_retval_base> Base;
+ typedef typename Base::Index Index;
+
+ solve_retval_base(const DecompositionType& dec, const Rhs& rhs)
+ : m_dec(dec), m_rhs(rhs)
+ {}
+
+ inline Index rows() const { return m_dec.cols(); }
+ inline Index cols() const { return m_rhs.cols(); }
+ inline const DecompositionType& dec() const { return m_dec; }
+ inline const RhsNestedCleaned& rhs() const { return m_rhs; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const solve_retval<DecompositionType,Rhs>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ typename Rhs::Nested m_rhs;
+};
+
+} // end namespace internal
+
+#define EIGEN_MAKE_SOLVE_HELPERS(DecompositionType,Rhs) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef typename MatrixType::Index Index; \
+ typedef Eigen::internal::solve_retval_base<DecompositionType,Rhs> Base; \
+ using Base::dec; \
+ using Base::rhs; \
+ using Base::rows; \
+ using Base::cols; \
+ solve_retval(const DecompositionType& dec, const Rhs& rhs) \
+ : Base(dec, rhs) {}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MISC_SOLVE_H
diff --git a/Eigen/src/misc/SparseSolve.h b/Eigen/src/misc/SparseSolve.h
new file mode 100644
index 0000000..244bb8e
--- /dev/null
+++ b/Eigen/src/misc/SparseSolve.h
@@ -0,0 +1,128 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_SOLVE_H
+#define EIGEN_SPARSE_SOLVE_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename _DecompositionType, typename Rhs> struct sparse_solve_retval_base;
+template<typename _DecompositionType, typename Rhs> struct sparse_solve_retval;
+
+template<typename DecompositionType, typename Rhs>
+struct traits<sparse_solve_retval_base<DecompositionType, Rhs> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef SparseMatrix<typename Rhs::Scalar, Rhs::Options, typename Rhs::Index> ReturnType;
+};
+
+template<typename _DecompositionType, typename Rhs> struct sparse_solve_retval_base
+ : public ReturnByValue<sparse_solve_retval_base<_DecompositionType, Rhs> >
+{
+ typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
+ typedef _DecompositionType DecompositionType;
+ typedef ReturnByValue<sparse_solve_retval_base> Base;
+ typedef typename Base::Index Index;
+
+ sparse_solve_retval_base(const DecompositionType& dec, const Rhs& rhs)
+ : m_dec(dec), m_rhs(rhs)
+ {}
+
+ inline Index rows() const { return m_dec.cols(); }
+ inline Index cols() const { return m_rhs.cols(); }
+ inline const DecompositionType& dec() const { return m_dec; }
+ inline const RhsNestedCleaned& rhs() const { return m_rhs; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const sparse_solve_retval<DecompositionType,Rhs>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ template<typename DestScalar, int DestOptions, typename DestIndex>
+ inline void defaultEvalTo(SparseMatrix<DestScalar,DestOptions,DestIndex>& dst) const
+ {
+ // we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix.
+ static const int NbColsAtOnce = 4;
+ int rhsCols = m_rhs.cols();
+ int size = m_rhs.rows();
+ Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmp(size,rhsCols);
+ Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmpX(size,rhsCols);
+ for(int k=0; k<rhsCols; k+=NbColsAtOnce)
+ {
+ int actualCols = std::min<int>(rhsCols-k, NbColsAtOnce);
+ tmp.leftCols(actualCols) = m_rhs.middleCols(k,actualCols);
+ tmpX.leftCols(actualCols) = m_dec.solve(tmp.leftCols(actualCols));
+ dst.middleCols(k,actualCols) = tmpX.leftCols(actualCols).sparseView();
+ }
+ }
+ const DecompositionType& m_dec;
+ typename Rhs::Nested m_rhs;
+};
+
+#define EIGEN_MAKE_SPARSE_SOLVE_HELPERS(DecompositionType,Rhs) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef typename MatrixType::Index Index; \
+ typedef Eigen::internal::sparse_solve_retval_base<DecompositionType,Rhs> Base; \
+ using Base::dec; \
+ using Base::rhs; \
+ using Base::rows; \
+ using Base::cols; \
+ sparse_solve_retval(const DecompositionType& dec, const Rhs& rhs) \
+ : Base(dec, rhs) {}
+
+
+
+template<typename DecompositionType, typename Rhs, typename Guess> struct solve_retval_with_guess;
+
+template<typename DecompositionType, typename Rhs, typename Guess>
+struct traits<solve_retval_with_guess<DecompositionType, Rhs, Guess> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<typename Rhs::Scalar,
+ MatrixType::ColsAtCompileTime,
+ Rhs::ColsAtCompileTime,
+ Rhs::PlainObject::Options,
+ MatrixType::MaxColsAtCompileTime,
+ Rhs::MaxColsAtCompileTime> ReturnType;
+};
+
+template<typename DecompositionType, typename Rhs, typename Guess> struct solve_retval_with_guess
+ : public ReturnByValue<solve_retval_with_guess<DecompositionType, Rhs, Guess> >
+{
+ typedef typename DecompositionType::Index Index;
+
+ solve_retval_with_guess(const DecompositionType& dec, const Rhs& rhs, const Guess& guess)
+ : m_dec(dec), m_rhs(rhs), m_guess(guess)
+ {}
+
+ inline Index rows() const { return m_dec.cols(); }
+ inline Index cols() const { return m_rhs.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ dst = m_guess;
+ m_dec._solveWithGuess(m_rhs,dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ const typename Rhs::Nested m_rhs;
+ const typename Guess::Nested m_guess;
+};
+
+} // namepsace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_SOLVE_H
diff --git a/Eigen/src/misc/blas.h b/Eigen/src/misc/blas.h
new file mode 100644
index 0000000..6fce99e
--- /dev/null
+++ b/Eigen/src/misc/blas.h
@@ -0,0 +1,658 @@
+#ifndef BLAS_H
+#define BLAS_H
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+#define BLASFUNC(FUNC) FUNC##_
+
+#ifdef __WIN64__
+typedef long long BLASLONG;
+typedef unsigned long long BLASULONG;
+#else
+typedef long BLASLONG;
+typedef unsigned long BLASULONG;
+#endif
+
+int BLASFUNC(xerbla)(const char *, int *info, int);
+
+float BLASFUNC(sdot) (int *, float *, int *, float *, int *);
+float BLASFUNC(sdsdot)(int *, float *, float *, int *, float *, int *);
+
+double BLASFUNC(dsdot) (int *, float *, int *, float *, int *);
+double BLASFUNC(ddot) (int *, double *, int *, double *, int *);
+double BLASFUNC(qdot) (int *, double *, int *, double *, int *);
+
+int BLASFUNC(cdotuw) (int *, float *, int *, float *, int *, float*);
+int BLASFUNC(cdotcw) (int *, float *, int *, float *, int *, float*);
+int BLASFUNC(zdotuw) (int *, double *, int *, double *, int *, double*);
+int BLASFUNC(zdotcw) (int *, double *, int *, double *, int *, double*);
+
+int BLASFUNC(saxpy) (int *, float *, float *, int *, float *, int *);
+int BLASFUNC(daxpy) (int *, double *, double *, int *, double *, int *);
+int BLASFUNC(qaxpy) (int *, double *, double *, int *, double *, int *);
+int BLASFUNC(caxpy) (int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zaxpy) (int *, double *, double *, int *, double *, int *);
+int BLASFUNC(xaxpy) (int *, double *, double *, int *, double *, int *);
+int BLASFUNC(caxpyc)(int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zaxpyc)(int *, double *, double *, int *, double *, int *);
+int BLASFUNC(xaxpyc)(int *, double *, double *, int *, double *, int *);
+
+int BLASFUNC(scopy) (int *, float *, int *, float *, int *);
+int BLASFUNC(dcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(qcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(ccopy) (int *, float *, int *, float *, int *);
+int BLASFUNC(zcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(xcopy) (int *, double *, int *, double *, int *);
+
+int BLASFUNC(sswap) (int *, float *, int *, float *, int *);
+int BLASFUNC(dswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(qswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(cswap) (int *, float *, int *, float *, int *);
+int BLASFUNC(zswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(xswap) (int *, double *, int *, double *, int *);
+
+float BLASFUNC(sasum) (int *, float *, int *);
+float BLASFUNC(scasum)(int *, float *, int *);
+double BLASFUNC(dasum) (int *, double *, int *);
+double BLASFUNC(qasum) (int *, double *, int *);
+double BLASFUNC(dzasum)(int *, double *, int *);
+double BLASFUNC(qxasum)(int *, double *, int *);
+
+int BLASFUNC(isamax)(int *, float *, int *);
+int BLASFUNC(idamax)(int *, double *, int *);
+int BLASFUNC(iqamax)(int *, double *, int *);
+int BLASFUNC(icamax)(int *, float *, int *);
+int BLASFUNC(izamax)(int *, double *, int *);
+int BLASFUNC(ixamax)(int *, double *, int *);
+
+int BLASFUNC(ismax) (int *, float *, int *);
+int BLASFUNC(idmax) (int *, double *, int *);
+int BLASFUNC(iqmax) (int *, double *, int *);
+int BLASFUNC(icmax) (int *, float *, int *);
+int BLASFUNC(izmax) (int *, double *, int *);
+int BLASFUNC(ixmax) (int *, double *, int *);
+
+int BLASFUNC(isamin)(int *, float *, int *);
+int BLASFUNC(idamin)(int *, double *, int *);
+int BLASFUNC(iqamin)(int *, double *, int *);
+int BLASFUNC(icamin)(int *, float *, int *);
+int BLASFUNC(izamin)(int *, double *, int *);
+int BLASFUNC(ixamin)(int *, double *, int *);
+
+int BLASFUNC(ismin)(int *, float *, int *);
+int BLASFUNC(idmin)(int *, double *, int *);
+int BLASFUNC(iqmin)(int *, double *, int *);
+int BLASFUNC(icmin)(int *, float *, int *);
+int BLASFUNC(izmin)(int *, double *, int *);
+int BLASFUNC(ixmin)(int *, double *, int *);
+
+float BLASFUNC(samax) (int *, float *, int *);
+double BLASFUNC(damax) (int *, double *, int *);
+double BLASFUNC(qamax) (int *, double *, int *);
+float BLASFUNC(scamax)(int *, float *, int *);
+double BLASFUNC(dzamax)(int *, double *, int *);
+double BLASFUNC(qxamax)(int *, double *, int *);
+
+float BLASFUNC(samin) (int *, float *, int *);
+double BLASFUNC(damin) (int *, double *, int *);
+double BLASFUNC(qamin) (int *, double *, int *);
+float BLASFUNC(scamin)(int *, float *, int *);
+double BLASFUNC(dzamin)(int *, double *, int *);
+double BLASFUNC(qxamin)(int *, double *, int *);
+
+float BLASFUNC(smax) (int *, float *, int *);
+double BLASFUNC(dmax) (int *, double *, int *);
+double BLASFUNC(qmax) (int *, double *, int *);
+float BLASFUNC(scmax) (int *, float *, int *);
+double BLASFUNC(dzmax) (int *, double *, int *);
+double BLASFUNC(qxmax) (int *, double *, int *);
+
+float BLASFUNC(smin) (int *, float *, int *);
+double BLASFUNC(dmin) (int *, double *, int *);
+double BLASFUNC(qmin) (int *, double *, int *);
+float BLASFUNC(scmin) (int *, float *, int *);
+double BLASFUNC(dzmin) (int *, double *, int *);
+double BLASFUNC(qxmin) (int *, double *, int *);
+
+int BLASFUNC(sscal) (int *, float *, float *, int *);
+int BLASFUNC(dscal) (int *, double *, double *, int *);
+int BLASFUNC(qscal) (int *, double *, double *, int *);
+int BLASFUNC(cscal) (int *, float *, float *, int *);
+int BLASFUNC(zscal) (int *, double *, double *, int *);
+int BLASFUNC(xscal) (int *, double *, double *, int *);
+int BLASFUNC(csscal)(int *, float *, float *, int *);
+int BLASFUNC(zdscal)(int *, double *, double *, int *);
+int BLASFUNC(xqscal)(int *, double *, double *, int *);
+
+float BLASFUNC(snrm2) (int *, float *, int *);
+float BLASFUNC(scnrm2)(int *, float *, int *);
+
+double BLASFUNC(dnrm2) (int *, double *, int *);
+double BLASFUNC(qnrm2) (int *, double *, int *);
+double BLASFUNC(dznrm2)(int *, double *, int *);
+double BLASFUNC(qxnrm2)(int *, double *, int *);
+
+int BLASFUNC(srot) (int *, float *, int *, float *, int *, float *, float *);
+int BLASFUNC(drot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(qrot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(csrot) (int *, float *, int *, float *, int *, float *, float *);
+int BLASFUNC(zdrot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(xqrot) (int *, double *, int *, double *, int *, double *, double *);
+
+int BLASFUNC(srotg) (float *, float *, float *, float *);
+int BLASFUNC(drotg) (double *, double *, double *, double *);
+int BLASFUNC(qrotg) (double *, double *, double *, double *);
+int BLASFUNC(crotg) (float *, float *, float *, float *);
+int BLASFUNC(zrotg) (double *, double *, double *, double *);
+int BLASFUNC(xrotg) (double *, double *, double *, double *);
+
+int BLASFUNC(srotmg)(float *, float *, float *, float *, float *);
+int BLASFUNC(drotmg)(double *, double *, double *, double *, double *);
+
+int BLASFUNC(srotm) (int *, float *, int *, float *, int *, float *);
+int BLASFUNC(drotm) (int *, double *, int *, double *, int *, double *);
+int BLASFUNC(qrotm) (int *, double *, int *, double *, int *, double *);
+
+/* Level 2 routines */
+
+int BLASFUNC(sger)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(dger)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(qger)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(cgeru)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(cgerc)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(zgeru)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(zgerc)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(xgeru)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(xgerc)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+
+int BLASFUNC(sgemv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dgemv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qgemv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(cgemv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zgemv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xgemv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(strsv) (char *, char *, char *, int *, float *, int *,
+ float *, int *);
+int BLASFUNC(dtrsv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(qtrsv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(ctrsv) (char *, char *, char *, int *, float *, int *,
+ float *, int *);
+int BLASFUNC(ztrsv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(xtrsv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(stpsv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(dtpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(qtpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(ctpsv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(ztpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(xtpsv) (char *, char *, char *, int *, double *, double *, int *);
+
+int BLASFUNC(strmv) (char *, char *, char *, int *, float *, int *,
+ float *, int *);
+int BLASFUNC(dtrmv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(qtrmv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(ctrmv) (char *, char *, char *, int *, float *, int *,
+ float *, int *);
+int BLASFUNC(ztrmv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+int BLASFUNC(xtrmv) (char *, char *, char *, int *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(stpmv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(dtpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(qtpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(ctpmv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(ztpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(xtpmv) (char *, char *, char *, int *, double *, double *, int *);
+
+int BLASFUNC(stbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(dtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(qtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(ctbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(ztbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(xtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(stbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(dtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(qtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(ctbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(ztbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(xtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(ssymv) (char *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dsymv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qsymv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(csymv) (char *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsymv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xsymv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(sspmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(cspmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssyr) (char *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(dsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(qsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(csyr) (char *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(xsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(ssyr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *, int *);
+int BLASFUNC(dsyr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+int BLASFUNC(qsyr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+int BLASFUNC(csyr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *, int *);
+int BLASFUNC(zsyr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+int BLASFUNC(xsyr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(sspr) (char *, int *, float *, float *, int *,
+ float *);
+int BLASFUNC(dspr) (char *, int *, double *, double *, int *,
+ double *);
+int BLASFUNC(qspr) (char *, int *, double *, double *, int *,
+ double *);
+int BLASFUNC(cspr) (char *, int *, float *, float *, int *,
+ float *);
+int BLASFUNC(zspr) (char *, int *, double *, double *, int *,
+ double *);
+int BLASFUNC(xspr) (char *, int *, double *, double *, int *,
+ double *);
+
+int BLASFUNC(sspr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(dspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(qspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(cspr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(zspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(xspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+
+int BLASFUNC(cher) (char *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zher) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(xher) (char *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(chpr) (char *, int *, float *, float *, int *, float *);
+int BLASFUNC(zhpr) (char *, int *, double *, double *, int *, double *);
+int BLASFUNC(xhpr) (char *, int *, double *, double *, int *, double *);
+
+int BLASFUNC(cher2) (char *, int *, float *,
+ float *, int *, float *, int *, float *, int *);
+int BLASFUNC(zher2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+int BLASFUNC(xher2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(chpr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(zhpr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(xhpr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+
+int BLASFUNC(chemv) (char *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhemv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhemv) (char *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(chpmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhpmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhpmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(snorm)(char *, int *, int *, float *, int *);
+int BLASFUNC(dnorm)(char *, int *, int *, double *, int *);
+int BLASFUNC(cnorm)(char *, int *, int *, float *, int *);
+int BLASFUNC(znorm)(char *, int *, int *, double *, int *);
+
+int BLASFUNC(sgbmv)(char *, int *, int *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(cgbmv)(char *, int *, int *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(csbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(chbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+/* Level 3 routines */
+
+int BLASFUNC(sgemm)(char *, char *, int *, int *, int *, float *,
+ float *, int *, float *, int *, float *, float *, int *);
+int BLASFUNC(dgemm)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(qgemm)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(cgemm)(char *, char *, int *, int *, int *, float *,
+ float *, int *, float *, int *, float *, float *, int *);
+int BLASFUNC(zgemm)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(xgemm)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+
+int BLASFUNC(cgemm3m)(char *, char *, int *, int *, int *, float *,
+ float *, int *, float *, int *, float *, float *, int *);
+int BLASFUNC(zgemm3m)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(xgemm3m)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+
+int BLASFUNC(sge2mm)(char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(dge2mm)(char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(cge2mm)(char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(zge2mm)(char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *,
+ double *, double *, int *);
+
+int BLASFUNC(strsm)(char *, char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *);
+int BLASFUNC(dtrsm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(qtrsm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(ctrsm)(char *, char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *);
+int BLASFUNC(ztrsm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(xtrsm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+
+int BLASFUNC(strmm)(char *, char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *);
+int BLASFUNC(dtrmm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(qtrmm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(ctrmm)(char *, char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *);
+int BLASFUNC(ztrmm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+int BLASFUNC(xtrmm)(char *, char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *);
+
+int BLASFUNC(ssymm)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dsymm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qsymm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(csymm)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsymm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xsymm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(csymm3m)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsymm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xsymm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssyrk)(char *, char *, int *, int *, float *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(dsyrk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(qsyrk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(csyrk)(char *, char *, int *, int *, float *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(zsyrk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(xsyrk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+
+int BLASFUNC(ssyr2k)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dsyr2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(qsyr2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(csyr2k)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsyr2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(xsyr2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+
+int BLASFUNC(chemm)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhemm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhemm)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(chemm3m)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhemm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhemm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(cherk)(char *, char *, int *, int *, float *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(zherk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(xherk)(char *, char *, int *, int *, double *, double *, int *,
+ double *, double *, int *);
+
+int BLASFUNC(cher2k)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zher2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(xher2k)(char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(cher2m)(char *, char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zher2m)(char *, char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+int BLASFUNC(xher2m)(char *, char *, char *, int *, int *, double *, double *, int *,
+ double*, int *, double *, double *, int *);
+
+int BLASFUNC(sgemt)(char *, int *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(dgemt)(char *, int *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(cgemt)(char *, int *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zgemt)(char *, int *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(sgema)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(dgema)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+int BLASFUNC(cgema)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zgema)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+
+int BLASFUNC(sgems)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(dgems)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+int BLASFUNC(cgems)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zgems)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+
+int BLASFUNC(sgetf2)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(dgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(qgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(cgetf2)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(zgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(xgetf2)(int *, int *, double *, int *, int *, int *);
+
+int BLASFUNC(sgetrf)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(dgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(qgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(cgetrf)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(zgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(xgetrf)(int *, int *, double *, int *, int *, int *);
+
+int BLASFUNC(slaswp)(int *, float *, int *, int *, int *, int *, int *);
+int BLASFUNC(dlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(qlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(claswp)(int *, float *, int *, int *, int *, int *, int *);
+int BLASFUNC(zlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(xlaswp)(int *, double *, int *, int *, int *, int *, int *);
+
+int BLASFUNC(sgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(dgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(qgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(cgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(zgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(xgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+
+int BLASFUNC(sgesv)(int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(dgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(qgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(cgesv)(int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(zgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(xgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+
+int BLASFUNC(spotf2)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotf2)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotf2)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(spotrf)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotrf)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotrf)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(slauu2)(char *, int *, float *, int *, int *);
+int BLASFUNC(dlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(qlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(clauu2)(char *, int *, float *, int *, int *);
+int BLASFUNC(zlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(xlauu2)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(slauum)(char *, int *, float *, int *, int *);
+int BLASFUNC(dlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(qlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(clauum)(char *, int *, float *, int *, int *);
+int BLASFUNC(zlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(xlauum)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(strti2)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(dtrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(qtrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(ctrti2)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(ztrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(xtrti2)(char *, char *, int *, double *, int *, int *);
+
+int BLASFUNC(strtri)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(dtrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(qtrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(ctrtri)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(ztrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(xtrtri)(char *, char *, int *, double *, int *, int *);
+
+int BLASFUNC(spotri)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotri)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotri)(char *, int *, double *, int *, int *);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
new file mode 100644
index 0000000..1951286
--- /dev/null
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -0,0 +1,253 @@
+/** \returns an expression of the coefficient wise product of \c *this and \a other
+ *
+ * \sa MatrixBase::cwiseProduct
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)
+operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient wise quotient of \c *this and \a other
+ *
+ * \sa MatrixBase::cwiseQuotient
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>
+operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of \c *this and \a other
+ *
+ * Example: \include Cwise_min.cpp
+ * Output: \verbinclude Cwise_min.out
+ *
+ * \sa max()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(min,internal::scalar_min_op)
+
+/** \returns an expression of the coefficient-wise min of \c *this and scalar \a other
+ *
+ * \sa max()
+ */
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+min
+#else
+(min)
+#endif
+(const Scalar &other) const
+{
+ return (min)(Derived::PlainObject::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise max of \c *this and \a other
+ *
+ * Example: \include Cwise_max.cpp
+ * Output: \verbinclude Cwise_max.out
+ *
+ * \sa min()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(max,internal::scalar_max_op)
+
+/** \returns an expression of the coefficient-wise max of \c *this and scalar \a other
+ *
+ * \sa min()
+ */
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+max
+#else
+(max)
+#endif
+(const Scalar &other) const
+{
+ return (max)(Derived::PlainObject::Constant(rows(), cols(), other));
+}
+
+
+#define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
+OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+{ \
+ return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
+}\
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
+EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \
+OP(const Scalar& s) const { \
+ return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \
+} \
+friend EIGEN_STRONG_INLINE const RCmp ## COMPARATOR ## ReturnType \
+OP(const Scalar& s, const Derived& d) { \
+ return Derived::PlainObject::Constant(d.rows(), d.cols(), s).OP(d); \
+}
+
+#define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
+OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+{ \
+ return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
+} \
+\
+inline const RCmp ## RCOMPARATOR ## ReturnType \
+OP(const Scalar& s) const { \
+ return Derived::PlainObject::Constant(rows(), cols(), s).R_OP(*this); \
+} \
+friend inline const Cmp ## RCOMPARATOR ## ReturnType \
+OP(const Scalar& s, const Derived& d) { \
+ return d.R_OP(Derived::PlainObject::Constant(d.rows(), d.cols(), s)); \
+}
+
+
+/** \returns an expression of the coefficient-wise \< operator of *this and \a other
+ *
+ * Example: \include Cwise_less.cpp
+ * Output: \verbinclude Cwise_less.out
+ *
+ * \sa all(), any(), operator>(), operator<=()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator<, LT)
+
+/** \returns an expression of the coefficient-wise \<= operator of *this and \a other
+ *
+ * Example: \include Cwise_less_equal.cpp
+ * Output: \verbinclude Cwise_less_equal.out
+ *
+ * \sa all(), any(), operator>=(), operator<()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator<=, LE)
+
+/** \returns an expression of the coefficient-wise \> operator of *this and \a other
+ *
+ * Example: \include Cwise_greater.cpp
+ * Output: \verbinclude Cwise_greater.out
+ *
+ * \sa all(), any(), operator>=(), operator<()
+ */
+EIGEN_MAKE_CWISE_COMP_R_OP(operator>, operator<, LT)
+
+/** \returns an expression of the coefficient-wise \>= operator of *this and \a other
+ *
+ * Example: \include Cwise_greater_equal.cpp
+ * Output: \verbinclude Cwise_greater_equal.out
+ *
+ * \sa all(), any(), operator>(), operator<=()
+ */
+EIGEN_MAKE_CWISE_COMP_R_OP(operator>=, operator<=, LE)
+
+/** \returns an expression of the coefficient-wise == operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include Cwise_equal_equal.cpp
+ * Output: \verbinclude Cwise_equal_equal.out
+ *
+ * \sa all(), any(), isApprox(), isMuchSmallerThan()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator==, EQ)
+
+/** \returns an expression of the coefficient-wise != operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include Cwise_not_equal.cpp
+ * Output: \verbinclude Cwise_not_equal.out
+ *
+ * \sa all(), any(), isApprox(), isMuchSmallerThan()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)
+
+#undef EIGEN_MAKE_CWISE_COMP_OP
+#undef EIGEN_MAKE_CWISE_COMP_R_OP
+
+// scalar addition
+
+/** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
+ *
+ * Example: \include Cwise_plus.cpp
+ * Output: \verbinclude Cwise_plus.out
+ *
+ * \sa operator+=(), operator-()
+ */
+inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
+operator+(const Scalar& scalar) const
+{
+ return CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>(derived(), internal::scalar_add_op<Scalar>(scalar));
+}
+
+friend inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
+operator+(const Scalar& scalar,const EIGEN_CURRENT_STORAGE_BASE_CLASS<Derived>& other)
+{
+ return other + scalar;
+}
+
+/** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
+ *
+ * Example: \include Cwise_minus.cpp
+ * Output: \verbinclude Cwise_minus.out
+ *
+ * \sa operator+(), operator-=()
+ */
+inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
+operator-(const Scalar& scalar) const
+{
+ return *this + (-scalar);
+}
+
+friend inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> >
+operator-(const Scalar& scalar,const EIGEN_CURRENT_STORAGE_BASE_CLASS<Derived>& other)
+{
+ return (-other) + scalar;
+}
+
+/** \returns an expression of the coefficient-wise && operator of *this and \a other
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_and.cpp
+ * Output: \verbinclude Cwise_boolean_and.out
+ *
+ * \sa operator||(), select()
+ */
+template<typename OtherDerived>
+inline const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>
+operator&&(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>(derived(),other.derived());
+}
+
+/** \returns an expression of the coefficient-wise || operator of *this and \a other
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_or.cpp
+ * Output: \verbinclude Cwise_boolean_or.out
+ *
+ * \sa operator&&(), select()
+ */
+template<typename OtherDerived>
+inline const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>
+operator||(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>(derived(),other.derived());
+}
+
+
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
new file mode 100644
index 0000000..1c3ed3f
--- /dev/null
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -0,0 +1,187 @@
+
+
+/** \returns an expression of the coefficient-wise absolute value of \c *this
+ *
+ * Example: \include Cwise_abs.cpp
+ * Output: \verbinclude Cwise_abs.out
+ *
+ * \sa abs2()
+ */
+EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived>
+abs() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise squared absolute value of \c *this
+ *
+ * Example: \include Cwise_abs2.cpp
+ * Output: \verbinclude Cwise_abs2.out
+ *
+ * \sa abs(), square()
+ */
+EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived>
+abs2() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise exponential of *this.
+ *
+ * Example: \include Cwise_exp.cpp
+ * Output: \verbinclude Cwise_exp.out
+ *
+ * \sa pow(), log(), sin(), cos()
+ */
+inline const CwiseUnaryOp<internal::scalar_exp_op<Scalar>, const Derived>
+exp() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise logarithm of *this.
+ *
+ * Example: \include Cwise_log.cpp
+ * Output: \verbinclude Cwise_log.out
+ *
+ * \sa exp()
+ */
+inline const CwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived>
+log() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise square root of *this.
+ *
+ * Example: \include Cwise_sqrt.cpp
+ * Output: \verbinclude Cwise_sqrt.out
+ *
+ * \sa pow(), square()
+ */
+inline const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived>
+sqrt() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise cosine of *this.
+ *
+ * Example: \include Cwise_cos.cpp
+ * Output: \verbinclude Cwise_cos.out
+ *
+ * \sa sin(), acos()
+ */
+inline const CwiseUnaryOp<internal::scalar_cos_op<Scalar>, const Derived>
+cos() const
+{
+ return derived();
+}
+
+
+/** \returns an expression of the coefficient-wise sine of *this.
+ *
+ * Example: \include Cwise_sin.cpp
+ * Output: \verbinclude Cwise_sin.out
+ *
+ * \sa cos(), asin()
+ */
+inline const CwiseUnaryOp<internal::scalar_sin_op<Scalar>, const Derived>
+sin() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise arc cosine of *this.
+ *
+ * Example: \include Cwise_acos.cpp
+ * Output: \verbinclude Cwise_acos.out
+ *
+ * \sa cos(), asin()
+ */
+inline const CwiseUnaryOp<internal::scalar_acos_op<Scalar>, const Derived>
+acos() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise arc sine of *this.
+ *
+ * Example: \include Cwise_asin.cpp
+ * Output: \verbinclude Cwise_asin.out
+ *
+ * \sa sin(), acos()
+ */
+inline const CwiseUnaryOp<internal::scalar_asin_op<Scalar>, const Derived>
+asin() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise tan of *this.
+ *
+ * Example: \include Cwise_tan.cpp
+ * Output: \verbinclude Cwise_tan.out
+ *
+ * \sa cos(), sin()
+ */
+inline const CwiseUnaryOp<internal::scalar_tan_op<Scalar>, Derived>
+tan() const
+{
+ return derived();
+}
+
+
+/** \returns an expression of the coefficient-wise power of *this to the given exponent.
+ *
+ * Example: \include Cwise_pow.cpp
+ * Output: \verbinclude Cwise_pow.out
+ *
+ * \sa exp(), log()
+ */
+inline const CwiseUnaryOp<internal::scalar_pow_op<Scalar>, const Derived>
+pow(const Scalar& exponent) const
+{
+ return CwiseUnaryOp<internal::scalar_pow_op<Scalar>, const Derived>
+ (derived(), internal::scalar_pow_op<Scalar>(exponent));
+}
+
+
+/** \returns an expression of the coefficient-wise inverse of *this.
+ *
+ * Example: \include Cwise_inverse.cpp
+ * Output: \verbinclude Cwise_inverse.out
+ *
+ * \sa operator/(), operator*()
+ */
+inline const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived>
+inverse() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise square of *this.
+ *
+ * Example: \include Cwise_square.cpp
+ * Output: \verbinclude Cwise_square.out
+ *
+ * \sa operator/(), operator*(), abs2()
+ */
+inline const CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived>
+square() const
+{
+ return derived();
+}
+
+/** \returns an expression of the coefficient-wise cube of *this.
+ *
+ * Example: \include Cwise_cube.cpp
+ * Output: \verbinclude Cwise_cube.out
+ *
+ * \sa square(), pow()
+ */
+inline const CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived>
+cube() const
+{
+ return derived();
+}
diff --git a/Eigen/src/plugins/BlockMethods.h b/Eigen/src/plugins/BlockMethods.h
new file mode 100644
index 0000000..2788251
--- /dev/null
+++ b/Eigen/src/plugins/BlockMethods.h
@@ -0,0 +1,935 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+/** \internal expression type of a column */
+typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ColXpr;
+typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ConstColXpr;
+/** \internal expression type of a row */
+typedef Block<Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowXpr;
+typedef const Block<const Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowXpr;
+/** \internal expression type of a block of whole columns */
+typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ColsBlockXpr;
+typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ConstColsBlockXpr;
+/** \internal expression type of a block of whole rows */
+typedef Block<Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowsBlockXpr;
+typedef const Block<const Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowsBlockXpr;
+/** \internal expression type of a block of whole columns */
+template<int N> struct NColsBlockXpr { typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
+template<int N> struct ConstNColsBlockXpr { typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
+/** \internal expression type of a block of whole rows */
+template<int N> struct NRowsBlockXpr { typedef Block<Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
+template<int N> struct ConstNRowsBlockXpr { typedef const Block<const Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
+
+typedef VectorBlock<Derived> SegmentReturnType;
+typedef const VectorBlock<const Derived> ConstSegmentReturnType;
+template<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };
+template<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+/** \returns a dynamic-size expression of a block in *this.
+ *
+ * \param startRow the first row in the block
+ * \param startCol the first column in the block
+ * \param blockRows the number of rows in the block
+ * \param blockCols the number of columns in the block
+ *
+ * Example: \include MatrixBase_block_int_int_int_int.cpp
+ * Output: \verbinclude MatrixBase_block_int_int_int_int.out
+ *
+ * \note Even though the returned expression has dynamic size, in the case
+ * when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
+ * which means that evaluating it does not cause a dynamic memory allocation.
+ *
+ * \sa class Block, block(Index,Index)
+ */
+inline Block<Derived> block(Index startRow, Index startCol, Index blockRows, Index blockCols)
+{
+ return Block<Derived>(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/** This is the const version of block(Index,Index,Index,Index). */
+inline const Block<const Derived> block(Index startRow, Index startCol, Index blockRows, Index blockCols) const
+{
+ return Block<const Derived>(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+
+
+
+/** \returns a dynamic-size expression of a top-right corner of *this.
+ *
+ * \param cRows the number of rows in the corner
+ * \param cCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_topRightCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_topRightCorner_int_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline Block<Derived> topRightCorner(Index cRows, Index cCols)
+{
+ return Block<Derived>(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+/** This is the const version of topRightCorner(Index, Index).*/
+inline const Block<const Derived> topRightCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived>(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+/** \returns an expression of a fixed-size top-right corner of *this.
+ *
+ * \tparam CRows the number of rows in the corner
+ * \tparam CCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_template_int_int_topRightCorner.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_topRightCorner.out
+ *
+ * \sa class Block, block<int,int>(Index,Index)
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> topRightCorner()
+{
+ return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+}
+
+/** This is the const version of topRightCorner<int, int>().*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> topRightCorner() const
+{
+ return Block<const Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+}
+
+/** \returns an expression of a top-right corner of *this.
+ *
+ * \tparam CRows number of rows in corner as specified at compile-time
+ * \tparam CCols number of columns in corner as specified at compile-time
+ * \param cRows number of rows in corner as specified at run-time
+ * \param cCols number of columns in corner as specified at run-time
+ *
+ * This function is mainly useful for corners where the number of rows is specified at compile-time
+ * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+ * information should not contradict. In other words, \a cRows should equal \a CRows unless
+ * \a CRows is \a Dynamic, and the same for the number of columns.
+ *
+ * Example: \include MatrixBase_template_int_int_topRightCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_topRightCorner_int_int.out
+ *
+ * \sa class Block
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> topRightCorner(Index cRows, Index cCols)
+{
+ return Block<Derived, CRows, CCols>(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+/** This is the const version of topRightCorner<int, int>(Index, Index).*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> topRightCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived, CRows, CCols>(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+
+
+/** \returns a dynamic-size expression of a top-left corner of *this.
+ *
+ * \param cRows the number of rows in the corner
+ * \param cCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_topLeftCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_topLeftCorner_int_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline Block<Derived> topLeftCorner(Index cRows, Index cCols)
+{
+ return Block<Derived>(derived(), 0, 0, cRows, cCols);
+}
+
+/** This is the const version of topLeftCorner(Index, Index).*/
+inline const Block<const Derived> topLeftCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived>(derived(), 0, 0, cRows, cCols);
+}
+
+/** \returns an expression of a fixed-size top-left corner of *this.
+ *
+ * The template parameters CRows and CCols are the number of rows and columns in the corner.
+ *
+ * Example: \include MatrixBase_template_int_int_topLeftCorner.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_topLeftCorner.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> topLeftCorner()
+{
+ return Block<Derived, CRows, CCols>(derived(), 0, 0);
+}
+
+/** This is the const version of topLeftCorner<int, int>().*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> topLeftCorner() const
+{
+ return Block<const Derived, CRows, CCols>(derived(), 0, 0);
+}
+
+/** \returns an expression of a top-left corner of *this.
+ *
+ * \tparam CRows number of rows in corner as specified at compile-time
+ * \tparam CCols number of columns in corner as specified at compile-time
+ * \param cRows number of rows in corner as specified at run-time
+ * \param cCols number of columns in corner as specified at run-time
+ *
+ * This function is mainly useful for corners where the number of rows is specified at compile-time
+ * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+ * information should not contradict. In other words, \a cRows should equal \a CRows unless
+ * \a CRows is \a Dynamic, and the same for the number of columns.
+ *
+ * Example: \include MatrixBase_template_int_int_topLeftCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_topLeftCorner_int_int.out
+ *
+ * \sa class Block
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> topLeftCorner(Index cRows, Index cCols)
+{
+ return Block<Derived, CRows, CCols>(derived(), 0, 0, cRows, cCols);
+}
+
+/** This is the const version of topLeftCorner<int, int>(Index, Index).*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> topLeftCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived, CRows, CCols>(derived(), 0, 0, cRows, cCols);
+}
+
+
+
+/** \returns a dynamic-size expression of a bottom-right corner of *this.
+ *
+ * \param cRows the number of rows in the corner
+ * \param cCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_bottomRightCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_bottomRightCorner_int_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline Block<Derived> bottomRightCorner(Index cRows, Index cCols)
+{
+ return Block<Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+/** This is the const version of bottomRightCorner(Index, Index).*/
+inline const Block<const Derived> bottomRightCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+/** \returns an expression of a fixed-size bottom-right corner of *this.
+ *
+ * The template parameters CRows and CCols are the number of rows and columns in the corner.
+ *
+ * Example: \include MatrixBase_template_int_int_bottomRightCorner.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> bottomRightCorner()
+{
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+}
+
+/** This is the const version of bottomRightCorner<int, int>().*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> bottomRightCorner() const
+{
+ return Block<const Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+}
+
+/** \returns an expression of a bottom-right corner of *this.
+ *
+ * \tparam CRows number of rows in corner as specified at compile-time
+ * \tparam CCols number of columns in corner as specified at compile-time
+ * \param cRows number of rows in corner as specified at run-time
+ * \param cCols number of columns in corner as specified at run-time
+ *
+ * This function is mainly useful for corners where the number of rows is specified at compile-time
+ * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+ * information should not contradict. In other words, \a cRows should equal \a CRows unless
+ * \a CRows is \a Dynamic, and the same for the number of columns.
+ *
+ * Example: \include MatrixBase_template_int_int_bottomRightCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner_int_int.out
+ *
+ * \sa class Block
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> bottomRightCorner(Index cRows, Index cCols)
+{
+ return Block<Derived, CRows, CCols>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+/** This is the const version of bottomRightCorner<int, int>(Index, Index).*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> bottomRightCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived, CRows, CCols>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+
+
+/** \returns a dynamic-size expression of a bottom-left corner of *this.
+ *
+ * \param cRows the number of rows in the corner
+ * \param cCols the number of columns in the corner
+ *
+ * Example: \include MatrixBase_bottomLeftCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_bottomLeftCorner_int_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline Block<Derived> bottomLeftCorner(Index cRows, Index cCols)
+{
+ return Block<Derived>(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+/** This is the const version of bottomLeftCorner(Index, Index).*/
+inline const Block<const Derived> bottomLeftCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived>(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+/** \returns an expression of a fixed-size bottom-left corner of *this.
+ *
+ * The template parameters CRows and CCols are the number of rows and columns in the corner.
+ *
+ * Example: \include MatrixBase_template_int_int_bottomLeftCorner.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> bottomLeftCorner()
+{
+ return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+}
+
+/** This is the const version of bottomLeftCorner<int, int>().*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> bottomLeftCorner() const
+{
+ return Block<const Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+}
+
+/** \returns an expression of a bottom-left corner of *this.
+ *
+ * \tparam CRows number of rows in corner as specified at compile-time
+ * \tparam CCols number of columns in corner as specified at compile-time
+ * \param cRows number of rows in corner as specified at run-time
+ * \param cCols number of columns in corner as specified at run-time
+ *
+ * This function is mainly useful for corners where the number of rows is specified at compile-time
+ * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+ * information should not contradict. In other words, \a cRows should equal \a CRows unless
+ * \a CRows is \a Dynamic, and the same for the number of columns.
+ *
+ * Example: \include MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner_int_int.out
+ *
+ * \sa class Block
+ */
+template<int CRows, int CCols>
+inline Block<Derived, CRows, CCols> bottomLeftCorner(Index cRows, Index cCols)
+{
+ return Block<Derived, CRows, CCols>(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+/** This is the const version of bottomLeftCorner<int, int>(Index, Index).*/
+template<int CRows, int CCols>
+inline const Block<const Derived, CRows, CCols> bottomLeftCorner(Index cRows, Index cCols) const
+{
+ return Block<const Derived, CRows, CCols>(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+
+
+/** \returns a block consisting of the top rows of *this.
+ *
+ * \param n the number of rows in the block
+ *
+ * Example: \include MatrixBase_topRows_int.cpp
+ * Output: \verbinclude MatrixBase_topRows_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline RowsBlockXpr topRows(Index n)
+{
+ return RowsBlockXpr(derived(), 0, 0, n, cols());
+}
+
+/** This is the const version of topRows(Index).*/
+inline ConstRowsBlockXpr topRows(Index n) const
+{
+ return ConstRowsBlockXpr(derived(), 0, 0, n, cols());
+}
+
+/** \returns a block consisting of the top rows of *this.
+ *
+ * \tparam N the number of rows in the block as specified at compile-time
+ * \param n the number of rows in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_topRows.cpp
+ * Output: \verbinclude MatrixBase_template_int_topRows.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NRowsBlockXpr<N>::Type topRows(Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
+}
+
+/** This is the const version of topRows<int>().*/
+template<int N>
+inline typename ConstNRowsBlockXpr<N>::Type topRows(Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
+}
+
+
+
+/** \returns a block consisting of the bottom rows of *this.
+ *
+ * \param n the number of rows in the block
+ *
+ * Example: \include MatrixBase_bottomRows_int.cpp
+ * Output: \verbinclude MatrixBase_bottomRows_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline RowsBlockXpr bottomRows(Index n)
+{
+ return RowsBlockXpr(derived(), rows() - n, 0, n, cols());
+}
+
+/** This is the const version of bottomRows(Index).*/
+inline ConstRowsBlockXpr bottomRows(Index n) const
+{
+ return ConstRowsBlockXpr(derived(), rows() - n, 0, n, cols());
+}
+
+/** \returns a block consisting of the bottom rows of *this.
+ *
+ * \tparam N the number of rows in the block as specified at compile-time
+ * \param n the number of rows in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_bottomRows.cpp
+ * Output: \verbinclude MatrixBase_template_int_bottomRows.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NRowsBlockXpr<N>::Type bottomRows(Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
+}
+
+/** This is the const version of bottomRows<int>().*/
+template<int N>
+inline typename ConstNRowsBlockXpr<N>::Type bottomRows(Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
+}
+
+
+
+/** \returns a block consisting of a range of rows of *this.
+ *
+ * \param startRow the index of the first row in the block
+ * \param n the number of rows in the block
+ *
+ * Example: \include DenseBase_middleRows_int.cpp
+ * Output: \verbinclude DenseBase_middleRows_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline RowsBlockXpr middleRows(Index startRow, Index n)
+{
+ return RowsBlockXpr(derived(), startRow, 0, n, cols());
+}
+
+/** This is the const version of middleRows(Index,Index).*/
+inline ConstRowsBlockXpr middleRows(Index startRow, Index n) const
+{
+ return ConstRowsBlockXpr(derived(), startRow, 0, n, cols());
+}
+
+/** \returns a block consisting of a range of rows of *this.
+ *
+ * \tparam N the number of rows in the block as specified at compile-time
+ * \param startRow the index of the first row in the block
+ * \param n the number of rows in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include DenseBase_template_int_middleRows.cpp
+ * Output: \verbinclude DenseBase_template_int_middleRows.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
+}
+
+/** This is the const version of middleRows<int>().*/
+template<int N>
+inline typename ConstNRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
+}
+
+
+
+/** \returns a block consisting of the left columns of *this.
+ *
+ * \param n the number of columns in the block
+ *
+ * Example: \include MatrixBase_leftCols_int.cpp
+ * Output: \verbinclude MatrixBase_leftCols_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline ColsBlockXpr leftCols(Index n)
+{
+ return ColsBlockXpr(derived(), 0, 0, rows(), n);
+}
+
+/** This is the const version of leftCols(Index).*/
+inline ConstColsBlockXpr leftCols(Index n) const
+{
+ return ConstColsBlockXpr(derived(), 0, 0, rows(), n);
+}
+
+/** \returns a block consisting of the left columns of *this.
+ *
+ * \tparam N the number of columns in the block as specified at compile-time
+ * \param n the number of columns in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_leftCols.cpp
+ * Output: \verbinclude MatrixBase_template_int_leftCols.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NColsBlockXpr<N>::Type leftCols(Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
+}
+
+/** This is the const version of leftCols<int>().*/
+template<int N>
+inline typename ConstNColsBlockXpr<N>::Type leftCols(Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
+}
+
+
+
+/** \returns a block consisting of the right columns of *this.
+ *
+ * \param n the number of columns in the block
+ *
+ * Example: \include MatrixBase_rightCols_int.cpp
+ * Output: \verbinclude MatrixBase_rightCols_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline ColsBlockXpr rightCols(Index n)
+{
+ return ColsBlockXpr(derived(), 0, cols() - n, rows(), n);
+}
+
+/** This is the const version of rightCols(Index).*/
+inline ConstColsBlockXpr rightCols(Index n) const
+{
+ return ConstColsBlockXpr(derived(), 0, cols() - n, rows(), n);
+}
+
+/** \returns a block consisting of the right columns of *this.
+ *
+ * \tparam N the number of columns in the block as specified at compile-time
+ * \param n the number of columns in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_rightCols.cpp
+ * Output: \verbinclude MatrixBase_template_int_rightCols.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NColsBlockXpr<N>::Type rightCols(Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
+}
+
+/** This is the const version of rightCols<int>().*/
+template<int N>
+inline typename ConstNColsBlockXpr<N>::Type rightCols(Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
+}
+
+
+
+/** \returns a block consisting of a range of columns of *this.
+ *
+ * \param startCol the index of the first column in the block
+ * \param numCols the number of columns in the block
+ *
+ * Example: \include DenseBase_middleCols_int.cpp
+ * Output: \verbinclude DenseBase_middleCols_int.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+inline ColsBlockXpr middleCols(Index startCol, Index numCols)
+{
+ return ColsBlockXpr(derived(), 0, startCol, rows(), numCols);
+}
+
+/** This is the const version of middleCols(Index,Index).*/
+inline ConstColsBlockXpr middleCols(Index startCol, Index numCols) const
+{
+ return ConstColsBlockXpr(derived(), 0, startCol, rows(), numCols);
+}
+
+/** \returns a block consisting of a range of columns of *this.
+ *
+ * \tparam N the number of columns in the block as specified at compile-time
+ * \param startCol the index of the first column in the block
+ * \param n the number of columns in the block as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include DenseBase_template_int_middleCols.cpp
+ * Output: \verbinclude DenseBase_template_int_middleCols.out
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int N>
+inline typename NColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
+}
+
+/** This is the const version of middleCols<int>().*/
+template<int N>
+inline typename ConstNColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
+}
+
+
+
+/** \returns a fixed-size expression of a block in *this.
+ *
+ * The template parameters \a BlockRows and \a BlockCols are the number of
+ * rows and columns in the block.
+ *
+ * \param startRow the first row in the block
+ * \param startCol the first column in the block
+ *
+ * Example: \include MatrixBase_block_int_int.cpp
+ * Output: \verbinclude MatrixBase_block_int_int.out
+ *
+ * \note since block is a templated member, the keyword template has to be used
+ * if the matrix type is also a template parameter: \code m.template block<3,3>(1,1); \endcode
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int BlockRows, int BlockCols>
+inline Block<Derived, BlockRows, BlockCols> block(Index startRow, Index startCol)
+{
+ return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
+}
+
+/** This is the const version of block<>(Index, Index). */
+template<int BlockRows, int BlockCols>
+inline const Block<const Derived, BlockRows, BlockCols> block(Index startRow, Index startCol) const
+{
+ return Block<const Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
+}
+
+/** \returns an expression of a block in *this.
+ *
+ * \tparam BlockRows number of rows in block as specified at compile-time
+ * \tparam BlockCols number of columns in block as specified at compile-time
+ * \param startRow the first row in the block
+ * \param startCol the first column in the block
+ * \param blockRows number of rows in block as specified at run-time
+ * \param blockCols number of columns in block as specified at run-time
+ *
+ * This function is mainly useful for blocks where the number of rows is specified at compile-time
+ * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+ * information should not contradict. In other words, \a blockRows should equal \a BlockRows unless
+ * \a BlockRows is \a Dynamic, and the same for the number of columns.
+ *
+ * Example: \include MatrixBase_template_int_int_block_int_int_int_int.cpp
+ * Output: \verbinclude MatrixBase_template_int_int_block_int_int_int_int.cpp
+ *
+ * \sa class Block, block(Index,Index,Index,Index)
+ */
+template<int BlockRows, int BlockCols>
+inline Block<Derived, BlockRows, BlockCols> block(Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+{
+ return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/** This is the const version of block<>(Index, Index, Index, Index). */
+template<int BlockRows, int BlockCols>
+inline const Block<const Derived, BlockRows, BlockCols> block(Index startRow, Index startCol,
+ Index blockRows, Index blockCols) const
+{
+ return Block<const Derived, BlockRows, BlockCols>(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/** \returns an expression of the \a i-th column of *this. Note that the numbering starts at 0.
+ *
+ * Example: \include MatrixBase_col.cpp
+ * Output: \verbinclude MatrixBase_col.out
+ *
+ * \sa row(), class Block */
+inline ColXpr col(Index i)
+{
+ return ColXpr(derived(), i);
+}
+
+/** This is the const version of col(). */
+inline ConstColXpr col(Index i) const
+{
+ return ConstColXpr(derived(), i);
+}
+
+/** \returns an expression of the \a i-th row of *this. Note that the numbering starts at 0.
+ *
+ * Example: \include MatrixBase_row.cpp
+ * Output: \verbinclude MatrixBase_row.out
+ *
+ * \sa col(), class Block */
+inline RowXpr row(Index i)
+{
+ return RowXpr(derived(), i);
+}
+
+/** This is the const version of row(). */
+inline ConstRowXpr row(Index i) const
+{
+ return ConstRowXpr(derived(), i);
+}
+
+/** \returns a dynamic-size expression of a segment (i.e. a vector block) in *this.
+ *
+ * \only_for_vectors
+ *
+ * \param start the first coefficient in the segment
+ * \param n the number of coefficients in the segment
+ *
+ * Example: \include MatrixBase_segment_int_int.cpp
+ * Output: \verbinclude MatrixBase_segment_int_int.out
+ *
+ * \note Even though the returned expression has dynamic size, in the case
+ * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+ * which means that evaluating it does not cause a dynamic memory allocation.
+ *
+ * \sa class Block, segment(Index)
+ */
+inline SegmentReturnType segment(Index start, Index n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return SegmentReturnType(derived(), start, n);
+}
+
+
+/** This is the const version of segment(Index,Index).*/
+inline ConstSegmentReturnType segment(Index start, Index n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return ConstSegmentReturnType(derived(), start, n);
+}
+
+/** \returns a dynamic-size expression of the first coefficients of *this.
+ *
+ * \only_for_vectors
+ *
+ * \param n the number of coefficients in the segment
+ *
+ * Example: \include MatrixBase_start_int.cpp
+ * Output: \verbinclude MatrixBase_start_int.out
+ *
+ * \note Even though the returned expression has dynamic size, in the case
+ * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+ * which means that evaluating it does not cause a dynamic memory allocation.
+ *
+ * \sa class Block, block(Index,Index)
+ */
+inline SegmentReturnType head(Index n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return SegmentReturnType(derived(), 0, n);
+}
+
+/** This is the const version of head(Index).*/
+inline ConstSegmentReturnType head(Index n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return ConstSegmentReturnType(derived(), 0, n);
+}
+
+/** \returns a dynamic-size expression of the last coefficients of *this.
+ *
+ * \only_for_vectors
+ *
+ * \param n the number of coefficients in the segment
+ *
+ * Example: \include MatrixBase_end_int.cpp
+ * Output: \verbinclude MatrixBase_end_int.out
+ *
+ * \note Even though the returned expression has dynamic size, in the case
+ * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+ * which means that evaluating it does not cause a dynamic memory allocation.
+ *
+ * \sa class Block, block(Index,Index)
+ */
+inline SegmentReturnType tail(Index n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return SegmentReturnType(derived(), this->size() - n, n);
+}
+
+/** This is the const version of tail(Index).*/
+inline ConstSegmentReturnType tail(Index n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return ConstSegmentReturnType(derived(), this->size() - n, n);
+}
+
+/** \returns a fixed-size expression of a segment (i.e. a vector block) in \c *this
+ *
+ * \only_for_vectors
+ *
+ * \tparam N the number of coefficients in the segment as specified at compile-time
+ * \param start the index of the first element in the segment
+ * \param n the number of coefficients in the segment as specified at compile-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_segment.cpp
+ * Output: \verbinclude MatrixBase_template_int_segment.out
+ *
+ * \sa class Block
+ */
+template<int N>
+inline typename FixedSegmentReturnType<N>::Type segment(Index start, Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), start, n);
+}
+
+/** This is the const version of segment<int>(Index).*/
+template<int N>
+inline typename ConstFixedSegmentReturnType<N>::Type segment(Index start, Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), start, n);
+}
+
+/** \returns a fixed-size expression of the first coefficients of *this.
+ *
+ * \only_for_vectors
+ *
+ * \tparam N the number of coefficients in the segment as specified at compile-time
+ * \param n the number of coefficients in the segment as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_start.cpp
+ * Output: \verbinclude MatrixBase_template_int_start.out
+ *
+ * \sa class Block
+ */
+template<int N>
+inline typename FixedSegmentReturnType<N>::Type head(Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), 0, n);
+}
+
+/** This is the const version of head<int>().*/
+template<int N>
+inline typename ConstFixedSegmentReturnType<N>::Type head(Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), 0, n);
+}
+
+/** \returns a fixed-size expression of the last coefficients of *this.
+ *
+ * \only_for_vectors
+ *
+ * \tparam N the number of coefficients in the segment as specified at compile-time
+ * \param n the number of coefficients in the segment as specified at run-time
+ *
+ * The compile-time and run-time information should not contradict. In other words,
+ * \a n should equal \a N unless \a N is \a Dynamic.
+ *
+ * Example: \include MatrixBase_template_int_end.cpp
+ * Output: \verbinclude MatrixBase_template_int_end.out
+ *
+ * \sa class Block
+ */
+template<int N>
+inline typename FixedSegmentReturnType<N>::Type tail(Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), size() - n);
+}
+
+/** This is the const version of tail<int>.*/
+template<int N>
+inline typename ConstFixedSegmentReturnType<N>::Type tail(Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), size() - n);
+}
diff --git a/Eigen/src/plugins/CMakeLists.txt b/Eigen/src/plugins/CMakeLists.txt
new file mode 100644
index 0000000..1a1d3ff
--- /dev/null
+++ b/Eigen/src/plugins/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_plugins_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_plugins_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/plugins COMPONENT Devel
+ )
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
new file mode 100644
index 0000000..688d224
--- /dev/null
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -0,0 +1,46 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing common coefficient wise functions.
+
+/** \returns an expression of the difference of \c *this and \a other
+ *
+ * \note If you want to substract a given scalar from all coefficients, see Cwise::operator-().
+ *
+ * \sa class CwiseBinaryOp, operator-=()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(operator-,internal::scalar_difference_op)
+
+/** \returns an expression of the sum of \c *this and \a other
+ *
+ * \note If you want to add a given scalar to all coefficients, see Cwise::operator+().
+ *
+ * \sa class CwiseBinaryOp, operator+=()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(operator+,internal::scalar_sum_op)
+
+/** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
+ *
+ * The template parameter \a CustomBinaryOp is the type of the functor
+ * of the custom operator (see class CwiseBinaryOp for an example)
+ *
+ * Here is an example illustrating the use of custom functors:
+ * \include class_CwiseBinaryOp.cpp
+ * Output: \verbinclude class_CwiseBinaryOp.out
+ *
+ * \sa class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
+ */
+template<typename CustomBinaryOp, typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>
+binaryExpr(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const
+{
+ return CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other.derived(), func);
+}
+
diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h
new file mode 100644
index 0000000..08e931a
--- /dev/null
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@@ -0,0 +1,172 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing common coefficient wise functions.
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+/** \internal Represents a scalar multiple of an expression */
+typedef CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived> ScalarMultipleReturnType;
+/** \internal Represents a quotient of an expression by a scalar*/
+typedef CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived> ScalarQuotient1ReturnType;
+/** \internal the return type of conjugate() */
+typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ const CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>,
+ const Derived&
+ >::type ConjugateReturnType;
+/** \internal the return type of real() const */
+typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ const CwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>,
+ const Derived&
+ >::type RealReturnType;
+/** \internal the return type of real() */
+typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryView<internal::scalar_real_ref_op<Scalar>, Derived>,
+ Derived&
+ >::type NonConstRealReturnType;
+/** \internal the return type of imag() const */
+typedef CwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived> ImagReturnType;
+/** \internal the return type of imag() */
+typedef CwiseUnaryView<internal::scalar_imag_ref_op<Scalar>, Derived> NonConstImagReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+/** \returns an expression of the opposite of \c *this
+ */
+inline const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived>
+operator-() const { return derived(); }
+
+
+/** \returns an expression of \c *this scaled by the scalar factor \a scalar */
+inline const ScalarMultipleReturnType
+operator*(const Scalar& scalar) const
+{
+ return CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived>
+ (derived(), internal::scalar_multiple_op<Scalar>(scalar));
+}
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+const ScalarMultipleReturnType operator*(const RealScalar& scalar) const;
+#endif
+
+/** \returns an expression of \c *this divided by the scalar value \a scalar */
+inline const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived>
+operator/(const Scalar& scalar) const
+{
+ return CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived>
+ (derived(), internal::scalar_quotient1_op<Scalar>(scalar));
+}
+
+/** Overloaded for efficient real matrix times complex scalar value */
+inline const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived>
+operator*(const std::complex<Scalar>& scalar) const
+{
+ return CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived>
+ (*static_cast<const Derived*>(this), internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >(scalar));
+}
+
+inline friend const ScalarMultipleReturnType
+operator*(const Scalar& scalar, const StorageBaseType& matrix)
+{ return matrix*scalar; }
+
+inline friend const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived>
+operator*(const std::complex<Scalar>& scalar, const StorageBaseType& matrix)
+{ return matrix*scalar; }
+
+/** \returns an expression of *this with the \a Scalar type casted to
+ * \a NewScalar.
+ *
+ * The template parameter \a NewScalar is the type we are casting the scalars to.
+ *
+ * \sa class CwiseUnaryOp
+ */
+template<typename NewType>
+typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type
+cast() const
+{
+ return derived();
+}
+
+/** \returns an expression of the complex conjugate of \c *this.
+ *
+ * \sa adjoint() */
+inline ConjugateReturnType
+conjugate() const
+{
+ return ConjugateReturnType(derived());
+}
+
+/** \returns a read-only expression of the real part of \c *this.
+ *
+ * \sa imag() */
+inline RealReturnType
+real() const { return derived(); }
+
+/** \returns an read-only expression of the imaginary part of \c *this.
+ *
+ * \sa real() */
+inline const ImagReturnType
+imag() const { return derived(); }
+
+/** \brief Apply a unary operator coefficient-wise
+ * \param[in] func Functor implementing the unary operator
+ * \tparam CustomUnaryOp Type of \a func
+ * \returns An expression of a custom coefficient-wise unary operator \a func of *this
+ *
+ * The function \c ptr_fun() from the C++ standard library can be used to make functors out of normal functions.
+ *
+ * Example:
+ * \include class_CwiseUnaryOp_ptrfun.cpp
+ * Output: \verbinclude class_CwiseUnaryOp_ptrfun.out
+ *
+ * Genuine functors allow for more possibilities, for instance it may contain a state.
+ *
+ * Example:
+ * \include class_CwiseUnaryOp.cpp
+ * Output: \verbinclude class_CwiseUnaryOp.out
+ *
+ * \sa class CwiseUnaryOp, class CwiseBinaryOp
+ */
+template<typename CustomUnaryOp>
+inline const CwiseUnaryOp<CustomUnaryOp, const Derived>
+unaryExpr(const CustomUnaryOp& func = CustomUnaryOp()) const
+{
+ return CwiseUnaryOp<CustomUnaryOp, const Derived>(derived(), func);
+}
+
+/** \returns an expression of a custom coefficient-wise unary operator \a func of *this
+ *
+ * The template parameter \a CustomUnaryOp is the type of the functor
+ * of the custom unary operator.
+ *
+ * Example:
+ * \include class_CwiseUnaryOp.cpp
+ * Output: \verbinclude class_CwiseUnaryOp.out
+ *
+ * \sa class CwiseUnaryOp, class CwiseBinaryOp
+ */
+template<typename CustomViewOp>
+inline const CwiseUnaryView<CustomViewOp, const Derived>
+unaryViewExpr(const CustomViewOp& func = CustomViewOp()) const
+{
+ return CwiseUnaryView<CustomViewOp, const Derived>(derived(), func);
+}
+
+/** \returns a non const expression of the real part of \c *this.
+ *
+ * \sa imag() */
+inline NonConstRealReturnType
+real() { return derived(); }
+
+/** \returns a non const expression of the imaginary part of \c *this.
+ *
+ * \sa real() */
+inline NonConstImagReturnType
+imag() { return derived(); }
diff --git a/Eigen/src/plugins/MatrixCwiseBinaryOps.h b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
new file mode 100644
index 0000000..c4a042b
--- /dev/null
+++ b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
@@ -0,0 +1,143 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing matrix specifics coefficient wise functions.
+
+/** \returns an expression of the Schur product (coefficient wise product) of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseProduct.cpp
+ * Output: \verbinclude MatrixBase_cwiseProduct.out
+ *
+ * \sa class CwiseBinaryOp, cwiseAbs2
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)
+cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise == operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include MatrixBase_cwiseEqual.cpp
+ * Output: \verbinclude MatrixBase_cwiseEqual.out
+ *
+ * \sa cwiseNotEqual(), isApprox(), isMuchSmallerThan()
+ */
+template<typename OtherDerived>
+inline const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived>
+cwiseEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise != operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include MatrixBase_cwiseNotEqual.cpp
+ * Output: \verbinclude MatrixBase_cwiseNotEqual.out
+ *
+ * \sa cwiseEqual(), isApprox(), isMuchSmallerThan()
+ */
+template<typename OtherDerived>
+inline const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived>
+cwiseNotEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseMin.cpp
+ * Output: \verbinclude MatrixBase_cwiseMin.out
+ *
+ * \sa class CwiseBinaryOp, max()
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived>
+cwiseMin(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of *this and scalar \a other
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType>
+cwiseMin(const Scalar &other) const
+{
+ return cwiseMin(Derived::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise max of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseMax.cpp
+ * Output: \verbinclude MatrixBase_cwiseMax.out
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived>
+cwiseMax(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise max of *this and scalar \a other
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType>
+cwiseMax(const Scalar &other) const
+{
+ return cwiseMax(Derived::Constant(rows(), cols(), other));
+}
+
+
+/** \returns an expression of the coefficient-wise quotient of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseQuotient.cpp
+ * Output: \verbinclude MatrixBase_cwiseQuotient.out
+ *
+ * \sa class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
+ */
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>
+cwiseQuotient(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> CwiseScalarEqualReturnType;
+
+/** \returns an expression of the coefficient-wise == operator of \c *this and a scalar \a s
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * \sa cwiseEqual(const MatrixBase<OtherDerived> &) const
+ */
+inline const CwiseScalarEqualReturnType
+cwiseEqual(const Scalar& s) const
+{
+ return CwiseScalarEqualReturnType(derived(), Derived::Constant(rows(), cols(), s), internal::scalar_cmp_op<Scalar,internal::cmp_EQ>());
+}
diff --git a/Eigen/src/plugins/MatrixCwiseUnaryOps.h b/Eigen/src/plugins/MatrixCwiseUnaryOps.h
new file mode 100644
index 0000000..8de1093
--- /dev/null
+++ b/Eigen/src/plugins/MatrixCwiseUnaryOps.h
@@ -0,0 +1,52 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing matrix specifics coefficient wise functions.
+
+/** \returns an expression of the coefficient-wise absolute value of \c *this
+ *
+ * Example: \include MatrixBase_cwiseAbs.cpp
+ * Output: \verbinclude MatrixBase_cwiseAbs.out
+ *
+ * \sa cwiseAbs2()
+ */
+EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived>
+cwiseAbs() const { return derived(); }
+
+/** \returns an expression of the coefficient-wise squared absolute value of \c *this
+ *
+ * Example: \include MatrixBase_cwiseAbs2.cpp
+ * Output: \verbinclude MatrixBase_cwiseAbs2.out
+ *
+ * \sa cwiseAbs()
+ */
+EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived>
+cwiseAbs2() const { return derived(); }
+
+/** \returns an expression of the coefficient-wise square root of *this.
+ *
+ * Example: \include MatrixBase_cwiseSqrt.cpp
+ * Output: \verbinclude MatrixBase_cwiseSqrt.out
+ *
+ * \sa cwisePow(), cwiseSquare()
+ */
+inline const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived>
+cwiseSqrt() const { return derived(); }
+
+/** \returns an expression of the coefficient-wise inverse of *this.
+ *
+ * Example: \include MatrixBase_cwiseInverse.cpp
+ * Output: \verbinclude MatrixBase_cwiseInverse.out
+ *
+ * \sa cwiseProduct()
+ */
+inline const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived>
+cwiseInverse() const { return derived(); }
+