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 newSize)
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103 | {
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104 | indices().resize(newSize);
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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>& a_indices) : m_indices(a_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* indicesPtr)
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238 | : m_indices(indicesPtr)
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239 | {}
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240 |
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241 | inline Map(const Index* indicesPtr, Index size)
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242 | : m_indices(indicesPtr,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& a_indices)
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295 | : m_indices(a_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 | const typename Dest::Scalar *dst_data = internal::extract_data(dst);
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380 | if(!(is_same<MatrixTypeNestedCleaned,Dest>::value && dst_data!=0 && dst_data == extract_data(m_matrix)))
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381 | dst = m_matrix;
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382 |
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383 | for(int k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
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384 | if((j=m_transpositions.coeff(k))!=k)
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385 | {
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386 | if(Side==OnTheLeft)
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387 | dst.row(k).swap(dst.row(j));
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388 | else if(Side==OnTheRight)
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389 | dst.col(k).swap(dst.col(j));
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390 | }
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391 | }
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392 |
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393 | protected:
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394 | const TranspositionType& m_transpositions;
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395 | typename MatrixType::Nested m_matrix;
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396 | };
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397 |
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398 | } // end namespace internal
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399 |
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400 | /* Template partial specialization for transposed/inverse transpositions */
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401 |
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402 | template<typename TranspositionsDerived>
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403 | class Transpose<TranspositionsBase<TranspositionsDerived> >
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404 | {
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405 | typedef TranspositionsDerived TranspositionType;
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406 | typedef typename TranspositionType::IndicesType IndicesType;
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407 | public:
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408 |
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409 | Transpose(const TranspositionType& t) : m_transpositions(t) {}
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410 |
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411 | inline int size() const { return m_transpositions.size(); }
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412 |
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413 | /** \returns the \a matrix with the inverse transpositions applied to the columns.
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414 | */
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415 | template<typename Derived> friend
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416 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>
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417 | operator*(const MatrixBase<Derived>& matrix, const Transpose& trt)
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418 | {
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419 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>(trt.m_transpositions, matrix.derived());
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420 | }
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421 |
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422 | /** \returns the \a matrix with the inverse transpositions applied to the rows.
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423 | */
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424 | template<typename Derived>
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425 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>
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426 | operator*(const MatrixBase<Derived>& matrix) const
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427 | {
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428 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>(m_transpositions, matrix.derived());
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429 | }
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430 |
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431 | protected:
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432 | const TranspositionType& m_transpositions;
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433 | };
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434 |
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435 | } // end namespace Eigen
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436 |
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437 | #endif // EIGEN_TRANSPOSITIONS_H
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