1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 5 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud (at) inria.fr> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_HOUSEHOLDER_H 12 #define EIGEN_HOUSEHOLDER_H 13 14 namespace Eigen { 15 16 namespace internal { 17 template<int n> struct decrement_size 18 { 19 enum { 20 ret = n==Dynamic ? n : n-1 21 }; 22 }; 23 } 24 25 /** Computes the elementary reflector H such that: 26 * \f$ H *this = [ beta 0 ... 0]^T \f$ 27 * where the transformation H is: 28 * \f$ H = I - tau v v^*\f$ 29 * and the vector v is: 30 * \f$ v^T = [1 essential^T] \f$ 31 * 32 * The essential part of the vector \c v is stored in *this. 33 * 34 * On output: 35 * \param tau the scaling factor of the Householder transformation 36 * \param beta the result of H * \c *this 37 * 38 * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), 39 * MatrixBase::applyHouseholderOnTheRight() 40 */ 41 template<typename Derived> 42 void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta) 43 { 44 VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1); 45 makeHouseholder(essentialPart, tau, beta); 46 } 47 48 /** Computes the elementary reflector H such that: 49 * \f$ H *this = [ beta 0 ... 0]^T \f$ 50 * where the transformation H is: 51 * \f$ H = I - tau v v^*\f$ 52 * and the vector v is: 53 * \f$ v^T = [1 essential^T] \f$ 54 * 55 * On output: 56 * \param essential the essential part of the vector \c v 57 * \param tau the scaling factor of the Householder transformation 58 * \param beta the result of H * \c *this 59 * 60 * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), 61 * MatrixBase::applyHouseholderOnTheRight() 62 */ 63 template<typename Derived> 64 template<typename EssentialPart> 65 void MatrixBase<Derived>::makeHouseholder( 66 EssentialPart& essential, 67 Scalar& tau, 68 RealScalar& beta) const 69 { 70 EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart) 71 VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1); 72 73 RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm(); 74 Scalar c0 = coeff(0); 75 76 if(tailSqNorm == RealScalar(0) && internal::imag(c0)==RealScalar(0)) 77 { 78 tau = RealScalar(0); 79 beta = internal::real(c0); 80 essential.setZero(); 81 } 82 else 83 { 84 beta = internal::sqrt(internal::abs2(c0) + tailSqNorm); 85 if (internal::real(c0)>=RealScalar(0)) 86 beta = -beta; 87 essential = tail / (c0 - beta); 88 tau = internal::conj((beta - c0) / beta); 89 } 90 } 91 92 /** Apply the elementary reflector H given by 93 * \f$ H = I - tau v v^*\f$ 94 * with 95 * \f$ v^T = [1 essential^T] \f$ 96 * from the left to a vector or matrix. 97 * 98 * On input: 99 * \param essential the essential part of the vector \c v 100 * \param tau the scaling factor of the Householder transformation 101 * \param workspace a pointer to working space with at least 102 * this->cols() * essential.size() entries 103 * 104 * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 105 * MatrixBase::applyHouseholderOnTheRight() 106 */ 107 template<typename Derived> 108 template<typename EssentialPart> 109 void MatrixBase<Derived>::applyHouseholderOnTheLeft( 110 const EssentialPart& essential, 111 const Scalar& tau, 112 Scalar* workspace) 113 { 114 if(rows() == 1) 115 { 116 *this *= Scalar(1)-tau; 117 } 118 else 119 { 120 Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols()); 121 Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols()); 122 tmp.noalias() = essential.adjoint() * bottom; 123 tmp += this->row(0); 124 this->row(0) -= tau * tmp; 125 bottom.noalias() -= tau * essential * tmp; 126 } 127 } 128 129 /** Apply the elementary reflector H given by 130 * \f$ H = I - tau v v^*\f$ 131 * with 132 * \f$ v^T = [1 essential^T] \f$ 133 * from the right to a vector or matrix. 134 * 135 * On input: 136 * \param essential the essential part of the vector \c v 137 * \param tau the scaling factor of the Householder transformation 138 * \param workspace a pointer to working space with at least 139 * this->cols() * essential.size() entries 140 * 141 * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 142 * MatrixBase::applyHouseholderOnTheLeft() 143 */ 144 template<typename Derived> 145 template<typename EssentialPart> 146 void MatrixBase<Derived>::applyHouseholderOnTheRight( 147 const EssentialPart& essential, 148 const Scalar& tau, 149 Scalar* workspace) 150 { 151 if(cols() == 1) 152 { 153 *this *= Scalar(1)-tau; 154 } 155 else 156 { 157 Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows()); 158 Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1); 159 tmp.noalias() = right * essential.conjugate(); 160 tmp += this->col(0); 161 this->col(0) -= tau * tmp; 162 right.noalias() -= tau * tmp * essential.transpose(); 163 } 164 } 165 166 } // end namespace Eigen 167 168 #endif // EIGEN_HOUSEHOLDER_H 169
