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) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_BASIC_PRECONDITIONERS_H
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11 | #define EIGEN_BASIC_PRECONDITIONERS_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /** \ingroup IterativeLinearSolvers_Module
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16 | * \brief A preconditioner based on the digonal entries
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17 | *
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18 | * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
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19 | * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
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20 | * \code
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21 | * A.diagonal().asDiagonal() . x = b
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22 | * \endcode
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23 | *
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24 | * \tparam _Scalar the type of the scalar.
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25 | *
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26 | * This preconditioner is suitable for both selfadjoint and general problems.
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27 | * The diagonal entries are pre-inverted and stored into a dense vector.
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28 | *
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29 | * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
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30 | *
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31 | */
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32 | template <typename _Scalar>
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33 | class DiagonalPreconditioner
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34 | {
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35 | typedef _Scalar Scalar;
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36 | typedef Matrix<Scalar,Dynamic,1> Vector;
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37 | typedef typename Vector::Index Index;
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38 |
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39 | public:
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40 | // this typedef is only to export the scalar type and compile-time dimensions to solve_retval
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41 | typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
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42 |
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43 | DiagonalPreconditioner() : m_isInitialized(false) {}
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44 |
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45 | template<typename MatType>
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46 | DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols())
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47 | {
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48 | compute(mat);
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49 | }
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50 |
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51 | Index rows() const { return m_invdiag.size(); }
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52 | Index cols() const { return m_invdiag.size(); }
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53 |
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54 | template<typename MatType>
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55 | DiagonalPreconditioner& analyzePattern(const MatType& )
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56 | {
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57 | return *this;
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58 | }
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59 |
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60 | template<typename MatType>
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61 | DiagonalPreconditioner& factorize(const MatType& mat)
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62 | {
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63 | m_invdiag.resize(mat.cols());
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64 | for(int j=0; j<mat.outerSize(); ++j)
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65 | {
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66 | typename MatType::InnerIterator it(mat,j);
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67 | while(it && it.index()!=j) ++it;
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68 | if(it && it.index()==j && it.value()!=Scalar(0))
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69 | m_invdiag(j) = Scalar(1)/it.value();
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70 | else
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71 | m_invdiag(j) = Scalar(1);
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72 | }
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73 | m_isInitialized = true;
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74 | return *this;
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75 | }
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76 |
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77 | template<typename MatType>
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78 | DiagonalPreconditioner& compute(const MatType& mat)
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79 | {
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80 | return factorize(mat);
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81 | }
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82 |
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83 | template<typename Rhs, typename Dest>
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84 | void _solve(const Rhs& b, Dest& x) const
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85 | {
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86 | x = m_invdiag.array() * b.array() ;
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87 | }
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88 |
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89 | template<typename Rhs> inline const internal::solve_retval<DiagonalPreconditioner, Rhs>
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90 | solve(const MatrixBase<Rhs>& b) const
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91 | {
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92 | eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
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93 | eigen_assert(m_invdiag.size()==b.rows()
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94 | && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
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95 | return internal::solve_retval<DiagonalPreconditioner, Rhs>(*this, b.derived());
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96 | }
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97 |
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98 | protected:
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99 | Vector m_invdiag;
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100 | bool m_isInitialized;
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101 | };
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102 |
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103 | namespace internal {
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104 |
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105 | template<typename _MatrixType, typename Rhs>
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106 | struct solve_retval<DiagonalPreconditioner<_MatrixType>, Rhs>
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107 | : solve_retval_base<DiagonalPreconditioner<_MatrixType>, Rhs>
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108 | {
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109 | typedef DiagonalPreconditioner<_MatrixType> Dec;
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110 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
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111 |
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112 | template<typename Dest> void evalTo(Dest& dst) const
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113 | {
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114 | dec()._solve(rhs(),dst);
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115 | }
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116 | };
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117 |
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118 | }
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119 |
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120 | /** \ingroup IterativeLinearSolvers_Module
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121 | * \brief A naive preconditioner which approximates any matrix as the identity matrix
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122 | *
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123 | * \sa class DiagonalPreconditioner
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124 | */
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125 | class IdentityPreconditioner
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126 | {
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127 | public:
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128 |
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129 | IdentityPreconditioner() {}
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130 |
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131 | template<typename MatrixType>
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132 | IdentityPreconditioner(const MatrixType& ) {}
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133 |
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134 | template<typename MatrixType>
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135 | IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }
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136 |
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137 | template<typename MatrixType>
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138 | IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }
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139 |
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140 | template<typename MatrixType>
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141 | IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
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142 |
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143 | template<typename Rhs>
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144 | inline const Rhs& solve(const Rhs& b) const { return b; }
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145 | };
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146 |
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147 | } // end namespace Eigen
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148 |
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149 | #endif // EIGEN_BASIC_PRECONDITIONERS_H
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