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Diffstat (limited to 'third_party/eigen3/Eigen/src/QR/HouseholderQR.h')
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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 |