1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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6 | //
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7 | // This Source Code Form is subject to the terms of the Mozilla
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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10 |
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11 | #ifndef EIGEN_HOUSEHOLDER_H
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12 | #define EIGEN_HOUSEHOLDER_H
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13 |
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14 | namespace Eigen {
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15 |
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16 | namespace internal {
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17 | template<int n> struct decrement_size
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18 | {
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19 | enum {
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20 | ret = n==Dynamic ? n : n-1
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21 | };
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22 | };
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23 | }
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24 |
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25 | /** Computes the elementary reflector H such that:
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26 | * \f$ H *this = [ beta 0 ... 0]^T \f$
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27 | * where the transformation H is:
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28 | * \f$ H = I - tau v v^*\f$
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29 | * and the vector v is:
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30 | * \f$ v^T = [1 essential^T] \f$
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31 | *
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32 | * The essential part of the vector \c v is stored in *this.
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33 | *
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34 | * On output:
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35 | * \param tau the scaling factor of the Householder transformation
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36 | * \param beta the result of H * \c *this
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37 | *
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38 | * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
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39 | * MatrixBase::applyHouseholderOnTheRight()
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40 | */
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41 | template<typename Derived>
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42 | void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
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43 | {
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44 | VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
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45 | makeHouseholder(essentialPart, tau, beta);
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46 | }
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47 |
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48 | /** Computes the elementary reflector H such that:
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49 | * \f$ H *this = [ beta 0 ... 0]^T \f$
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50 | * where the transformation H is:
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51 | * \f$ H = I - tau v v^*\f$
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52 | * and the vector v is:
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53 | * \f$ v^T = [1 essential^T] \f$
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54 | *
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55 | * On output:
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56 | * \param essential the essential part of the vector \c v
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57 | * \param tau the scaling factor of the Householder transformation
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58 | * \param beta the result of H * \c *this
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59 | *
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60 | * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
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61 | * MatrixBase::applyHouseholderOnTheRight()
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62 | */
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63 | template<typename Derived>
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64 | template<typename EssentialPart>
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65 | void MatrixBase<Derived>::makeHouseholder(
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66 | EssentialPart& essential,
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67 | Scalar& tau,
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68 | RealScalar& beta) const
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69 | {
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70 | using std::sqrt;
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71 | using numext::conj;
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72 |
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73 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
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74 | VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
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75 |
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76 | RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
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77 | Scalar c0 = coeff(0);
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78 | const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
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79 |
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80 | if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
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81 | {
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82 | tau = RealScalar(0);
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83 | beta = numext::real(c0);
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84 | essential.setZero();
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85 | }
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86 | else
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87 | {
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88 | beta = sqrt(numext::abs2(c0) + tailSqNorm);
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89 | if (numext::real(c0)>=RealScalar(0))
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90 | beta = -beta;
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91 | essential = tail / (c0 - beta);
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92 | tau = conj((beta - c0) / beta);
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93 | }
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94 | }
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95 |
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96 | /** Apply the elementary reflector H given by
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97 | * \f$ H = I - tau v v^*\f$
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98 | * with
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99 | * \f$ v^T = [1 essential^T] \f$
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100 | * from the left to a vector or matrix.
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101 | *
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102 | * On input:
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103 | * \param essential the essential part of the vector \c v
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104 | * \param tau the scaling factor of the Householder transformation
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105 | * \param workspace a pointer to working space with at least
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106 | * this->cols() * essential.size() entries
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107 | *
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108 | * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
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109 | * MatrixBase::applyHouseholderOnTheRight()
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110 | */
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111 | template<typename Derived>
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112 | template<typename EssentialPart>
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113 | void MatrixBase<Derived>::applyHouseholderOnTheLeft(
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114 | const EssentialPart& essential,
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115 | const Scalar& tau,
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116 | Scalar* workspace)
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117 | {
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118 | if(rows() == 1)
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119 | {
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120 | *this *= Scalar(1)-tau;
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121 | }
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122 | else
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123 | {
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124 | Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
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125 | Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
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126 | tmp.noalias() = essential.adjoint() * bottom;
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127 | tmp += this->row(0);
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128 | this->row(0) -= tau * tmp;
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129 | bottom.noalias() -= tau * essential * tmp;
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130 | }
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131 | }
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132 |
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133 | /** Apply the elementary reflector H given by
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134 | * \f$ H = I - tau v v^*\f$
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135 | * with
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136 | * \f$ v^T = [1 essential^T] \f$
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137 | * from the right to a vector or matrix.
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138 | *
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139 | * On input:
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140 | * \param essential the essential part of the vector \c v
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141 | * \param tau the scaling factor of the Householder transformation
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142 | * \param workspace a pointer to working space with at least
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143 | * this->cols() * essential.size() entries
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144 | *
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145 | * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
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146 | * MatrixBase::applyHouseholderOnTheLeft()
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147 | */
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148 | template<typename Derived>
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149 | template<typename EssentialPart>
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150 | void MatrixBase<Derived>::applyHouseholderOnTheRight(
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151 | const EssentialPart& essential,
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152 | const Scalar& tau,
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153 | Scalar* workspace)
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154 | {
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155 | if(cols() == 1)
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156 | {
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157 | *this *= Scalar(1)-tau;
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158 | }
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159 | else
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160 | {
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161 | Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
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162 | Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
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163 | tmp.noalias() = right * essential.conjugate();
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164 | tmp += this->col(0);
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165 | this->col(0) -= tau * tmp;
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166 | right.noalias() -= tau * tmp * essential.transpose();
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167 | }
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168 | }
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169 |
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170 | } // end namespace Eigen
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171 |
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172 | #endif // EIGEN_HOUSEHOLDER_H
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