diff options
Diffstat (limited to 'third_party/eigen3/Eigen/src/QR')
| -rw-r--r-- | third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR.h | 582 | ||||
| -rw-r--r-- | third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR_MKL.h | 99 | ||||
| -rw-r--r-- | third_party/eigen3/Eigen/src/QR/FullPivHouseholderQR.h | 616 | ||||
| -rw-r--r-- | third_party/eigen3/Eigen/src/QR/HouseholderQR.h | 382 | ||||
| -rw-r--r-- | third_party/eigen3/Eigen/src/QR/HouseholderQR_MKL.h | 71 |
5 files changed, 0 insertions, 1750 deletions
diff --git a/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR.h b/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR.h deleted file mode 100644 index 4824880f51..0000000000 --- a/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR.h +++ /dev/null @@ -1,582 +0,0 @@ -// 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: - 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) -{ - 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; - - // if the current biggest column is smaller than epsilon times the initial biggest column, - // terminate to avoid generating nan/inf values. - // Note that here, if we test instead for "biggest == 0", we get a failure every 1000 (or so) - // repetitions of the unit test, with the result of solve() filled with large values of the order - // of 1/(size*epsilon). - if(biggest_col_sq_norm < threshold_helper * RealScalar(rows-k)) - { - m_nonzero_pivots = k; - m_hCoeffs.tail(size-k).setZero(); - m_qr.bottomRightCorner(rows-k,cols-k) - .template triangularView<StrictlyLower>() - .setZero(); - break; - } - - // 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 < 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 */ -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()).setLength(m_nonzero_pivots); -} - -#ifndef __CUDACC__ -/** \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()); -} -#endif // __CUDACC__ - -} // end namespace Eigen - -#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H diff --git a/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR_MKL.h b/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR_MKL.h deleted file mode 100644 index b5b1983265..0000000000 --- a/third_party/eigen3/Eigen/src/QR/ColPivHouseholderQR_MKL.h +++ /dev/null @@ -1,99 +0,0 @@ -/* - 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/third_party/eigen3/Eigen/src/QR/FullPivHouseholderQR.h b/third_party/eigen3/Eigen/src/QR/FullPivHouseholderQR.h deleted file mode 100644 index a7b0fc16f3..0000000000 --- a/third_party/eigen3/Eigen/src/QR/FullPivHouseholderQR.h +++ /dev/null @@ -1,616 +0,0 @@ -// 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 P', \b Q and \b R - * such that - * \f[ - * \mathbf{P} \, \mathbf{A} \, \mathbf{P}' = \mathbf{Q} \, \mathbf{R} - * \f] - * by using Householder transformations. Here, \b P and \b P' are permutation matrices, \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: - 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) -{ - 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); -} - -#ifndef __CUDACC__ -/** \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()); -} -#endif // __CUDACC__ - -} // end namespace Eigen - -#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H diff --git a/third_party/eigen3/Eigen/src/QR/HouseholderQR.h b/third_party/eigen3/Eigen/src/QR/HouseholderQR.h deleted file mode 100644 index 352dbf3f0e..0000000000 --- a/third_party/eigen3/Eigen/src/QR/HouseholderQR.h +++ /dev/null @@ -1,382 +0,0 @@ -// 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: - 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) -{ - 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; -} - -#ifndef __CUDACC__ -/** \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()); -} -#endif // __CUDACC__ - -} // end namespace Eigen - -#endif // EIGEN_QR_H diff --git a/third_party/eigen3/Eigen/src/QR/HouseholderQR_MKL.h b/third_party/eigen3/Eigen/src/QR/HouseholderQR_MKL.h deleted file mode 100644 index 8a3a7e4063..0000000000 --- a/third_party/eigen3/Eigen/src/QR/HouseholderQR_MKL.h +++ /dev/null @@ -1,71 +0,0 @@ -/* - 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 |