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/SVD/UpperBidiagonalization.h b/Eigen/src/SVD/UpperBidiagonalization.h
new file mode 100644
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+++ b/Eigen/src/SVD/UpperBidiagonalization.h
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+// 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