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) 2010-2011 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_TRANSPOSITIONS_H |
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11 | #define EIGEN_TRANSPOSITIONS_H |
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12 | |
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13 | namespace Eigen { |
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14 | |
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15 | /** \class Transpositions |
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16 | * \ingroup Core_Module |
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17 | * |
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18 | * \brief Represents a sequence of transpositions (row/column interchange) |
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19 | * |
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20 | * \param SizeAtCompileTime the number of transpositions, or Dynamic |
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21 | * \param MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it. |
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22 | * |
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23 | * This class represents a permutation transformation as a sequence of \em n transpositions |
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24 | * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices. |
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25 | * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges |
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26 | * the rows \c i and \c indices[i] of the matrix \c M. |
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27 | * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange. |
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28 | * |
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29 | * Compared to the class PermutationMatrix, such a sequence of transpositions is what is |
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30 | * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place. |
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31 | * |
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32 | * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example: |
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33 | * \code |
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34 | * Transpositions tr; |
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35 | * MatrixXf mat; |
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36 | * mat = tr * mat; |
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37 | * \endcode |
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38 | * In this example, we detect that the matrix appears on both side, and so the transpositions |
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39 | * are applied in-place without any temporary or extra copy. |
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40 | * |
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41 | * \sa class PermutationMatrix |
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42 | */ |
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43 | |
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44 | namespace internal { |
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45 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed=false> struct transposition_matrix_product_retval; |
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46 | } |
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47 | |
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48 | template<typename Derived> |
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49 | class TranspositionsBase |
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50 | { |
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51 | typedef internal::traits<Derived> Traits; |
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52 | |
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53 | public: |
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54 | |
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55 | typedef typename Traits::IndicesType IndicesType; |
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56 | typedef typename IndicesType::Scalar Index; |
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57 | |
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58 | Derived& derived() { return *static_cast<Derived*>(this); } |
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59 | const Derived& derived() const { return *static_cast<const Derived*>(this); } |
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60 | |
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61 | /** Copies the \a other transpositions into \c *this */ |
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62 | template<typename OtherDerived> |
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63 | Derived& operator=(const TranspositionsBase<OtherDerived>& other) |
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64 | { |
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65 | indices() = other.indices(); |
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66 | return derived(); |
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67 | } |
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68 | |
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69 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
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70 | /** This is a special case of the templated operator=. Its purpose is to |
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71 | * prevent a default operator= from hiding the templated operator=. |
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72 | */ |
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73 | Derived& operator=(const TranspositionsBase& other) |
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74 | { |
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75 | indices() = other.indices(); |
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76 | return derived(); |
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77 | } |
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78 | #endif |
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79 | |
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80 | /** \returns the number of transpositions */ |
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81 | inline Index size() const { return indices().size(); } |
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82 | |
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83 | /** Direct access to the underlying index vector */ |
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84 | inline const Index& coeff(Index i) const { return indices().coeff(i); } |
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85 | /** Direct access to the underlying index vector */ |
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86 | inline Index& coeffRef(Index i) { return indices().coeffRef(i); } |
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87 | /** Direct access to the underlying index vector */ |
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88 | inline const Index& operator()(Index i) const { return indices()(i); } |
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89 | /** Direct access to the underlying index vector */ |
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90 | inline Index& operator()(Index i) { return indices()(i); } |
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91 | /** Direct access to the underlying index vector */ |
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92 | inline const Index& operator[](Index i) const { return indices()(i); } |
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93 | /** Direct access to the underlying index vector */ |
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94 | inline Index& operator[](Index i) { return indices()(i); } |
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95 | |
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96 | /** const version of indices(). */ |
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97 | const IndicesType& indices() const { return derived().indices(); } |
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98 | /** \returns a reference to the stored array representing the transpositions. */ |
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99 | IndicesType& indices() { return derived().indices(); } |
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100 | |
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101 | /** Resizes to given size. */ |
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102 | inline void resize(int size) |
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103 | { |
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104 | indices().resize(size); |
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105 | } |
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106 | |
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107 | /** Sets \c *this to represents an identity transformation */ |
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108 | void setIdentity() |
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109 | { |
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110 | for(int i = 0; i < indices().size(); ++i) |
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111 | coeffRef(i) = i; |
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112 | } |
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113 | |
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114 | // FIXME: do we want such methods ? |
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115 | // might be usefull when the target matrix expression is complex, e.g.: |
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116 | // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..); |
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117 | /* |
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118 | template<typename MatrixType> |
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119 | void applyForwardToRows(MatrixType& mat) const |
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120 | { |
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121 | for(Index k=0 ; k<size() ; ++k) |
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122 | if(m_indices(k)!=k) |
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123 | mat.row(k).swap(mat.row(m_indices(k))); |
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124 | } |
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125 | |
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126 | template<typename MatrixType> |
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127 | void applyBackwardToRows(MatrixType& mat) const |
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128 | { |
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129 | for(Index k=size()-1 ; k>=0 ; --k) |
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130 | if(m_indices(k)!=k) |
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131 | mat.row(k).swap(mat.row(m_indices(k))); |
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132 | } |
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133 | */ |
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134 | |
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135 | /** \returns the inverse transformation */ |
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136 | inline Transpose<TranspositionsBase> inverse() const |
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137 | { return Transpose<TranspositionsBase>(derived()); } |
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138 | |
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139 | /** \returns the tranpose transformation */ |
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140 | inline Transpose<TranspositionsBase> transpose() const |
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141 | { return Transpose<TranspositionsBase>(derived()); } |
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142 | |
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143 | protected: |
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144 | }; |
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145 | |
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146 | namespace internal { |
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147 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType> |
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148 | struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> > |
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149 | { |
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150 | typedef IndexType Index; |
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151 | typedef Matrix<Index, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType; |
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152 | }; |
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153 | } |
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154 | |
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155 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType> |
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156 | class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> > |
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157 | { |
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158 | typedef internal::traits<Transpositions> Traits; |
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159 | public: |
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160 | |
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161 | typedef TranspositionsBase<Transpositions> Base; |
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162 | typedef typename Traits::IndicesType IndicesType; |
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163 | typedef typename IndicesType::Scalar Index; |
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164 | |
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165 | inline Transpositions() {} |
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166 | |
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167 | /** Copy constructor. */ |
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168 | template<typename OtherDerived> |
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169 | inline Transpositions(const TranspositionsBase<OtherDerived>& other) |
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170 | : m_indices(other.indices()) {} |
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171 | |
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172 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
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173 | /** Standard copy constructor. Defined only to prevent a default copy constructor |
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174 | * from hiding the other templated constructor */ |
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175 | inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {} |
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176 | #endif |
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177 | |
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178 | /** Generic constructor from expression of the transposition indices. */ |
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179 | template<typename Other> |
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180 | explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices) |
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181 | {} |
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182 | |
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183 | /** Copies the \a other transpositions into \c *this */ |
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184 | template<typename OtherDerived> |
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185 | Transpositions& operator=(const TranspositionsBase<OtherDerived>& other) |
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186 | { |
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187 | return Base::operator=(other); |
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188 | } |
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189 | |
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190 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
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191 | /** This is a special case of the templated operator=. Its purpose is to |
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192 | * prevent a default operator= from hiding the templated operator=. |
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193 | */ |
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194 | Transpositions& operator=(const Transpositions& other) |
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195 | { |
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196 | m_indices = other.m_indices; |
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197 | return *this; |
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198 | } |
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199 | #endif |
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200 | |
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201 | /** Constructs an uninitialized permutation matrix of given size. |
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202 | */ |
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203 | inline Transpositions(Index size) : m_indices(size) |
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204 | {} |
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205 | |
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206 | /** const version of indices(). */ |
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207 | const IndicesType& indices() const { return m_indices; } |
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208 | /** \returns a reference to the stored array representing the transpositions. */ |
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209 | IndicesType& indices() { return m_indices; } |
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210 | |
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211 | protected: |
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212 | |
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213 | IndicesType m_indices; |
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214 | }; |
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215 | |
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216 | |
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217 | namespace internal { |
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218 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess> |
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219 | struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,_PacketAccess> > |
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220 | { |
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221 | typedef IndexType Index; |
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222 | typedef Map<const Matrix<Index,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType; |
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223 | }; |
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224 | } |
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225 | |
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226 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int PacketAccess> |
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227 | class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess> |
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228 | : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess> > |
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229 | { |
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230 | typedef internal::traits<Map> Traits; |
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231 | public: |
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232 | |
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233 | typedef TranspositionsBase<Map> Base; |
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234 | typedef typename Traits::IndicesType IndicesType; |
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235 | typedef typename IndicesType::Scalar Index; |
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236 | |
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237 | inline Map(const Index* indices) |
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238 | : m_indices(indices) |
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239 | {} |
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240 | |
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241 | inline Map(const Index* indices, Index size) |
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242 | : m_indices(indices,size) |
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243 | {} |
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244 | |
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245 | /** Copies the \a other transpositions into \c *this */ |
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246 | template<typename OtherDerived> |
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247 | Map& operator=(const TranspositionsBase<OtherDerived>& other) |
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248 | { |
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249 | return Base::operator=(other); |
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250 | } |
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251 | |
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252 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
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253 | /** This is a special case of the templated operator=. Its purpose is to |
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254 | * prevent a default operator= from hiding the templated operator=. |
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255 | */ |
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256 | Map& operator=(const Map& other) |
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257 | { |
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258 | m_indices = other.m_indices; |
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259 | return *this; |
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260 | } |
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261 | #endif |
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262 | |
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263 | /** const version of indices(). */ |
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264 | const IndicesType& indices() const { return m_indices; } |
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265 | |
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266 | /** \returns a reference to the stored array representing the transpositions. */ |
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267 | IndicesType& indices() { return m_indices; } |
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268 | |
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269 | protected: |
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270 | |
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271 | IndicesType m_indices; |
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272 | }; |
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273 | |
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274 | namespace internal { |
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275 | template<typename _IndicesType> |
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276 | struct traits<TranspositionsWrapper<_IndicesType> > |
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277 | { |
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278 | typedef typename _IndicesType::Scalar Index; |
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279 | typedef _IndicesType IndicesType; |
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280 | }; |
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281 | } |
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282 | |
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283 | template<typename _IndicesType> |
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284 | class TranspositionsWrapper |
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285 | : public TranspositionsBase<TranspositionsWrapper<_IndicesType> > |
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286 | { |
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287 | typedef internal::traits<TranspositionsWrapper> Traits; |
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288 | public: |
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289 | |
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290 | typedef TranspositionsBase<TranspositionsWrapper> Base; |
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291 | typedef typename Traits::IndicesType IndicesType; |
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292 | typedef typename IndicesType::Scalar Index; |
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293 | |
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294 | inline TranspositionsWrapper(IndicesType& indices) |
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295 | : m_indices(indices) |
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296 | {} |
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297 | |
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298 | /** Copies the \a other transpositions into \c *this */ |
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299 | template<typename OtherDerived> |
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300 | TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other) |
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301 | { |
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302 | return Base::operator=(other); |
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303 | } |
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304 | |
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305 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
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306 | /** This is a special case of the templated operator=. Its purpose is to |
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307 | * prevent a default operator= from hiding the templated operator=. |
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308 | */ |
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309 | TranspositionsWrapper& operator=(const TranspositionsWrapper& other) |
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310 | { |
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311 | m_indices = other.m_indices; |
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312 | return *this; |
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313 | } |
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314 | #endif |
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315 | |
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316 | /** const version of indices(). */ |
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317 | const IndicesType& indices() const { return m_indices; } |
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318 | |
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319 | /** \returns a reference to the stored array representing the transpositions. */ |
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320 | IndicesType& indices() { return m_indices; } |
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321 | |
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322 | protected: |
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323 | |
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324 | const typename IndicesType::Nested m_indices; |
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325 | }; |
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326 | |
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327 | /** \returns the \a matrix with the \a transpositions applied to the columns. |
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328 | */ |
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329 | template<typename Derived, typename TranspositionsDerived> |
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330 | inline const internal::transposition_matrix_product_retval<TranspositionsDerived, Derived, OnTheRight> |
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331 | operator*(const MatrixBase<Derived>& matrix, |
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332 | const TranspositionsBase<TranspositionsDerived> &transpositions) |
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333 | { |
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334 | return internal::transposition_matrix_product_retval |
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335 | <TranspositionsDerived, Derived, OnTheRight> |
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336 | (transpositions.derived(), matrix.derived()); |
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337 | } |
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338 | |
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339 | /** \returns the \a matrix with the \a transpositions applied to the rows. |
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340 | */ |
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341 | template<typename Derived, typename TranspositionDerived> |
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342 | inline const internal::transposition_matrix_product_retval |
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343 | <TranspositionDerived, Derived, OnTheLeft> |
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344 | operator*(const TranspositionsBase<TranspositionDerived> &transpositions, |
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345 | const MatrixBase<Derived>& matrix) |
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346 | { |
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347 | return internal::transposition_matrix_product_retval |
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348 | <TranspositionDerived, Derived, OnTheLeft> |
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349 | (transpositions.derived(), matrix.derived()); |
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350 | } |
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351 | |
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352 | namespace internal { |
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353 | |
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354 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed> |
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355 | struct traits<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> > |
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356 | { |
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357 | typedef typename MatrixType::PlainObject ReturnType; |
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358 | }; |
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359 | |
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360 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed> |
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361 | struct transposition_matrix_product_retval |
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362 | : public ReturnByValue<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> > |
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363 | { |
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364 | typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned; |
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365 | typedef typename TranspositionType::Index Index; |
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366 | |
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367 | transposition_matrix_product_retval(const TranspositionType& tr, const MatrixType& matrix) |
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368 | : m_transpositions(tr), m_matrix(matrix) |
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369 | {} |
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370 | |
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371 | inline int rows() const { return m_matrix.rows(); } |
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372 | inline int cols() const { return m_matrix.cols(); } |
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373 | |
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374 | template<typename Dest> inline void evalTo(Dest& dst) const |
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375 | { |
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376 | const int size = m_transpositions.size(); |
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377 | Index j = 0; |
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378 | |
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379 | if(!(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))) |
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380 | dst = m_matrix; |
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381 | |
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382 | for(int k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k) |
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383 | if((j=m_transpositions.coeff(k))!=k) |
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384 | { |
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385 | if(Side==OnTheLeft) |
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386 | dst.row(k).swap(dst.row(j)); |
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387 | else if(Side==OnTheRight) |
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388 | dst.col(k).swap(dst.col(j)); |
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389 | } |
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390 | } |
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391 | |
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392 | protected: |
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393 | const TranspositionType& m_transpositions; |
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394 | typename MatrixType::Nested m_matrix; |
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395 | }; |
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396 | |
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397 | } // end namespace internal |
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398 | |
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399 | /* Template partial specialization for transposed/inverse transpositions */ |
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400 | |
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401 | template<typename TranspositionsDerived> |
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402 | class Transpose<TranspositionsBase<TranspositionsDerived> > |
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403 | { |
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404 | typedef TranspositionsDerived TranspositionType; |
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405 | typedef typename TranspositionType::IndicesType IndicesType; |
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406 | public: |
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407 | |
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408 | Transpose(const TranspositionType& t) : m_transpositions(t) {} |
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409 | |
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410 | inline int size() const { return m_transpositions.size(); } |
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411 | |
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412 | /** \returns the \a matrix with the inverse transpositions applied to the columns. |
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413 | */ |
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414 | template<typename Derived> friend |
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415 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true> |
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416 | operator*(const MatrixBase<Derived>& matrix, const Transpose& trt) |
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417 | { |
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418 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>(trt.m_transpositions, matrix.derived()); |
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419 | } |
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420 | |
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421 | /** \returns the \a matrix with the inverse transpositions applied to the rows. |
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422 | */ |
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423 | template<typename Derived> |
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424 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true> |
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425 | operator*(const MatrixBase<Derived>& matrix) const |
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426 | { |
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427 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>(m_transpositions, matrix.derived()); |
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428 | } |
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429 | |
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430 | protected: |
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431 | const TranspositionType& m_transpositions; |
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432 | }; |
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433 | |
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434 | } // end namespace Eigen |
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435 | |
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436 | #endif // EIGEN_TRANSPOSITIONS_H |
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