HouseholderSequence.h revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba
1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com> 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN_HOUSEHOLDER_SEQUENCE_H 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen { 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup Householder_Module 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \householder_module 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \class HouseholderSequence 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief Sequence of Householder reflections acting on subspaces with decreasing size 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \tparam VectorsType type of matrix containing the Householder vectors 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \tparam CoeffsType type of vector containing the Householder coefficients 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \tparam Side either OnTheLeft (the default) or OnTheRight 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This class represents a product sequence of Householder reflections where the first Householder reflection 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(), 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence. 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * More precisely, the class %HouseholderSequence represents an \f$ n \times n \f$ matrix \f$ H \f$ of the 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * form \f$ H = \prod_{i=0}^{n-1} H_i \f$ where the i-th Householder reflection is \f$ H_i = I - h_i v_i 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * v_i^* \f$. The i-th Householder coefficient \f$ h_i \f$ is a scalar and the i-th Householder vector \f$ 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * v_i \f$ is a vector of the form 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \f[ 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \f] 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector. 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Typical usages are listed below, where H is a HouseholderSequence: 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \code 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * A.applyOnTheRight(H); // A = A * H 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * A.applyOnTheLeft(H); // A = H * A 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * A.applyOnTheRight(H.adjoint()); // A = A * H^* 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * A.applyOnTheLeft(H.adjoint()); // A = H^* * A 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * MatrixXd Q = H; // conversion to a dense matrix 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \endcode 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate operators. 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example. 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace internal { 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType, int Side> 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct traits<HouseholderSequence<VectorsType,CoeffsType,Side> > 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::Scalar Scalar; 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::Index Index; 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::StorageKind StorageKind; 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : traits<VectorsType>::ColsAtCompileTime, 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColsAtCompileTime = RowsAtCompileTime, 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : traits<VectorsType>::MaxColsAtCompileTime, 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MaxColsAtCompileTime = MaxRowsAtCompileTime, 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Flags = 0 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType, int Side> 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct hseq_side_dependent_impl 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType; 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType; 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::Index Index; 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index start = k+1+h.m_shift; 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1); 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType> 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight> 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType; 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType; 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::Index Index; 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index start = k+1+h.m_shift; 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose(); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename scalar_product_traits<OtherScalarType, typename MatrixType::Scalar>::ReturnType 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ResultScalar; 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type; 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace internal 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> > 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 1157faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType; 1167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez public: 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime, 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime, 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime, 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename internal::traits<HouseholderSequence>::Scalar Scalar; 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename VectorsType::Index Index; 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef HouseholderSequence< 1287faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez typename internal::conditional<NumTraits<Scalar>::IsComplex, 1297faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type, 1307faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VectorsType>::type, 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::conditional<NumTraits<Scalar>::IsComplex, 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type, 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CoeffsType>::type, 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Side 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath > ConjugateReturnType; 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Constructor. 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] v %Matrix containing the essential parts of the Householder vectors 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] h Vector containing the Householder coefficients 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Constructs the Householder sequence with coefficients given by \p h and vectors given by \p v. The 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * i-th Householder coefficient \f$ h_i \f$ is given by \p h(i) and the essential part of the i-th 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Householder vector \f$ v_i \f$ is given by \p v(k,i) with \p k > \p i (the subdiagonal part of the 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * i-th column). If \p v has fewer columns than rows, then the Householder sequence contains as many 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Householder reflections as there are columns. 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \note The %HouseholderSequence object stores \p v and \p h by reference. 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Example: \include HouseholderSequence_HouseholderSequence.cpp 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Output: \verbinclude HouseholderSequence_HouseholderSequence.out 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa setLength(), setShift() 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence(const VectorsType& v, const CoeffsType& h) 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : m_vectors(v), m_coeffs(h), m_trans(false), m_length(v.diagonalSize()), 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_shift(0) 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Copy constructor. */ 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence(const HouseholderSequence& other) 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : m_vectors(other.m_vectors), 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_coeffs(other.m_coeffs), 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_trans(other.m_trans), 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_length(other.m_length), 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_shift(other.m_shift) 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Number of rows of transformation viewed as a matrix. 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns Number of rows 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \details This equals the dimension of the space that the transformation acts on. 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows() const { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); } 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Number of columns of transformation viewed as a matrix. 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns Number of columns 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \details This equals the dimension of the space that the transformation acts on. 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols() const { return rows(); } 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Essential part of a Householder vector. 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] k Index of Householder reflection 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns Vector containing non-trivial entries of k-th Householder vector 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This function returns the essential part of the Householder vector \f$ v_i \f$. This is a vector of 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * length \f$ n-i \f$ containing the last \f$ n-i \f$ entries of the vector 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \f[ 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \f] 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * The index \f$ i \f$ equals \p k + shift(), corresponding to the k-th column of the matrix \p v 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * passed to the constructor. 193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa setShift(), shift() 195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const EssentialVectorType essentialVector(Index k) const 197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(k >= 0 && k < m_length); 199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k); 200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief %Transpose of the Householder sequence. */ 203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence transpose() const 204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return HouseholderSequence(*this).setTrans(!m_trans); 206c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Complex conjugate of the Householder sequence. */ 209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ConjugateReturnType conjugate() const 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 2117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate()) 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .setTrans(m_trans) 213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .setLength(m_length) 214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .setShift(m_shift); 215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Adjoint (conjugate transpose) of the Householder sequence. */ 218c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ConjugateReturnType adjoint() const 219c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return conjugate().setTrans(!m_trans); 221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Inverse of the Householder sequence (equals the adjoint). */ 224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ConjugateReturnType inverse() const { return adjoint(); } 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename DestType> inline void evalTo(DestType& dst) const 228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar, DestType::RowsAtCompileTime, 1, 230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows()); 231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath evalTo(dst, workspace); 232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest, typename Workspace> 236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath void evalTo(Dest& dst, Workspace& workspace) const 237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath workspace.resize(rows()); 239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index vecs = m_length; 240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( internal::is_same<typename internal::remove_all<VectorsType>::type,Dest>::value 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath && internal::extract_data(dst) == internal::extract_data(m_vectors)) 242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // in-place 244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.diagonal().setOnes(); 245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.template triangularView<StrictlyUpper>().setZero(); 246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(Index k = vecs-1; k >= 0; --k) 247c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 248c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cornerSize = rows() - k - m_shift; 249c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(m_trans) 250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.bottomRightCorner(cornerSize, cornerSize) 251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data()); 252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.bottomRightCorner(cornerSize, cornerSize) 254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data()); 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // clear the off diagonal vector 257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.col(k).tail(rows()-k-1).setZero(); 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // clear the remaining columns if needed 260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(Index k = 0; k<cols()-vecs ; ++k) 261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.col(k).tail(rows()-k-1).setZero(); 262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 265c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.setIdentity(rows(), rows()); 266c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(Index k = vecs-1; k >= 0; --k) 267c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cornerSize = rows() - k - m_shift; 269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(m_trans) 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.bottomRightCorner(cornerSize, cornerSize) 271c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0)); 272c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.bottomRightCorner(cornerSize, cornerSize) 274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0)); 275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 276c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 280c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const 281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows()); 283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath applyThisOnTheRight(dst, workspace); 284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest, typename Workspace> 288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const 289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 290c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath workspace.resize(dst.rows()); 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(Index k = 0; k < m_length; ++k) 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index actual_k = m_trans ? m_length-k-1 : k; 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.rightCols(rows()-m_shift-actual_k) 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data()); 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace(dst.cols()); 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath applyThisOnTheLeft(dst, workspace); 304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \internal */ 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest, typename Workspace> 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace) const 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath workspace.resize(dst.cols()); 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(Index k = 0; k < m_length; ++k) 312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index actual_k = m_trans ? k : m_length-k-1; 314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dst.bottomRows(rows()-m_shift-actual_k) 315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data()); 316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 317c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 318c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Computes the product of a Householder sequence with a matrix. 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] other %Matrix being multiplied. 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns Expression object representing the product. 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This function computes \f$ HM \f$ where \f$ H \f$ is the Householder sequence represented by \p *this 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * and \f$ M \f$ is the matrix \p other. 325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename OtherDerived> 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>()); 331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath applyThisOnTheLeft(res); 332c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return res; 333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl; 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Sets the length of the Householder sequence. 338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param [in] length New value for the length. 339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * By default, the length \f$ n \f$ of the Householder sequence \f$ H = H_0 H_1 \ldots H_{n-1} \f$ is set 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * to the number of columns of the matrix \p v passed to the constructor, or the number of rows if that 342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * is smaller. After this function is called, the length equals \p length. 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa length() 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence& setLength(Index length) 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_length = length; 349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Sets the shift of the Householder sequence. 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param [in] shift New value for the shift. 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * By default, a %HouseholderSequence object represents \f$ H = H_0 H_1 \ldots H_{n-1} \f$ and the i-th 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * column of the matrix \p v passed to the constructor corresponds to the i-th Householder 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * reflection. After this function is called, the object represents \f$ H = H_{\mathrm{shift}} 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * H_{\mathrm{shift}+1} \ldots H_{n-1} \f$ and the i-th column of \p v corresponds to the (shift+i)-th 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Householder reflection. 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa shift() 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence& setShift(Index shift) 364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_shift = shift; 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index length() const { return m_length; } /**< \brief Returns the length of the Householder sequence. */ 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index shift() const { return m_shift; } /**< \brief Returns the shift of the Householder sequence. */ 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* Necessary for .adjoint() and .conjugate() */ 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence; 374c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath protected: 376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 377c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Sets the transpose flag. 378c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param [in] trans New value of the transpose flag. 379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * By default, the transpose flag is not set. If the transpose flag is set, then this object represents 381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \f$ H^T = H_{n-1}^T \ldots H_1^T H_0^T \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$. 382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa trans() 384c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 385c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence& setTrans(bool trans) 386c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 387c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_trans = trans; 388c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 389c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 390c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool trans() const { return m_trans; } /**< \brief Returns the transpose flag. */ 392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename VectorsType::Nested m_vectors; 394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename CoeffsType::Nested m_coeffs; 395c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool m_trans; 396c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index m_length; 397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index m_shift; 398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \brief Computes the product of a matrix with a Householder sequence. 401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] other %Matrix being multiplied. 402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] h %HouseholderSequence being multiplied. 403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns Expression object representing the product. 404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 405c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This function computes \f$ MH \f$ where \f$ M \f$ is the matrix \p other and \f$ H \f$ is the 406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Householder sequence represented by \p h. 407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side> 409c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtypename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h) 410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type 412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>()); 413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath h.applyThisOnTheRight(res); 414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return res; 415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup Householder_Module \householder_module 418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief Convenience function for constructing a Householder sequence. 419c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns A HouseholderSequence constructed from the specified arguments. 420c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 421c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType> 422c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathHouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h) 423c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h); 425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup Householder_Module \householder_module 428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief Convenience function for constructing a Householder sequence. 429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns A HouseholderSequence constructed from the specified arguments. 430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \details This function differs from householderSequence() in that the template argument \p OnTheSide of 431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft. 432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 433c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename VectorsType, typename CoeffsType> 434c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathHouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h) 435c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 436c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h); 437c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 438c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 439c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace Eigen 440c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 441c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H 442