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/LU/Inverse.h b/Eigen/src/LU/Inverse.h
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+++ b/Eigen/src/LU/Inverse.h
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+// 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