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 using std::sqrt; 71 using numext::conj; 72 73 EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart) 74 VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1); 75 76 RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm(); 77 Scalar c0 = coeff(0); 78 const RealScalar tol = (std::numeric_limits<RealScalar>::min)(); 79 80 if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol) 81 { 82 tau = RealScalar(0); 83 beta = numext::real(c0); 84 essential.setZero(); 85 } 86 else 87 { 88 beta = sqrt(numext::abs2(c0) + tailSqNorm); 89 if (numext::real(c0)>=RealScalar(0)) 90 beta = -beta; 91 essential = tail / (c0 - beta); 92 tau = conj((beta - c0) / beta); 93 } 94 } 95 96 /** Apply the elementary reflector H given by 97 * \f$ H = I - tau v v^*\f$ 98 * with 99 * \f$ v^T = [1 essential^T] \f$ 100 * from the left to a vector or matrix. 101 * 102 * On input: 103 * \param essential the essential part of the vector \c v 104 * \param tau the scaling factor of the Householder transformation 105 * \param workspace a pointer to working space with at least 106 * this->cols() * essential.size() entries 107 * 108 * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 109 * MatrixBase::applyHouseholderOnTheRight() 110 */ 111 template<typename Derived> 112 template<typename EssentialPart> 113 void MatrixBase<Derived>::applyHouseholderOnTheLeft( 114 const EssentialPart& essential, 115 const Scalar& tau, 116 Scalar* workspace) 117 { 118 if(rows() == 1) 119 { 120 *this *= Scalar(1)-tau; 121 } 122 else if(tau!=Scalar(0)) 123 { 124 Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols()); 125 Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols()); 126 tmp.noalias() = essential.adjoint() * bottom; 127 tmp += this->row(0); 128 this->row(0) -= tau * tmp; 129 bottom.noalias() -= tau * essential * tmp; 130 } 131 } 132 133 /** Apply the elementary reflector H given by 134 * \f$ H = I - tau v v^*\f$ 135 * with 136 * \f$ v^T = [1 essential^T] \f$ 137 * from the right to a vector or matrix. 138 * 139 * On input: 140 * \param essential the essential part of the vector \c v 141 * \param tau the scaling factor of the Householder transformation 142 * \param workspace a pointer to working space with at least 143 * this->cols() * essential.size() entries 144 * 145 * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 146 * MatrixBase::applyHouseholderOnTheLeft() 147 */ 148 template<typename Derived> 149 template<typename EssentialPart> 150 void MatrixBase<Derived>::applyHouseholderOnTheRight( 151 const EssentialPart& essential, 152 const Scalar& tau, 153 Scalar* workspace) 154 { 155 if(cols() == 1) 156 { 157 *this *= Scalar(1)-tau; 158 } 159 else if(tau!=Scalar(0)) 160 { 161 Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows()); 162 Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1); 163 tmp.noalias() = right * essential.conjugate(); 164 tmp += this->col(0); 165 this->col(0) -= tau * tmp; 166 right.noalias() -= tau * tmp * essential.transpose(); 167 } 168 } 169 170 } // end namespace Eigen 171 172 #endif // EIGEN_HOUSEHOLDER_H 173
