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) 2008-2009 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_SOLVETRIANGULAR_H
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11 | #define EIGEN_SOLVETRIANGULAR_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | namespace internal {
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16 |
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17 | // Forward declarations:
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18 | // The following two routines are implemented in the products/TriangularSolver*.h files
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19 | template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
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20 | struct triangular_solve_vector;
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21 |
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22 | template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
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23 | struct triangular_solve_matrix;
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24 |
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25 | // small helper struct extracting some traits on the underlying solver operation
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26 | template<typename Lhs, typename Rhs, int Side>
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27 | class trsolve_traits
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28 | {
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29 | private:
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30 | enum {
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31 | RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
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32 | };
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33 | public:
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34 | enum {
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35 | Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
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36 | ? CompleteUnrolling : NoUnrolling,
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37 | RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
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38 | };
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39 | };
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40 |
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41 | template<typename Lhs, typename Rhs,
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42 | int Side, // can be OnTheLeft/OnTheRight
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43 | int Mode, // can be Upper/Lower | UnitDiag
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44 | int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
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45 | int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
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46 | >
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47 | struct triangular_solver_selector;
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48 |
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49 | template<typename Lhs, typename Rhs, int Side, int Mode>
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50 | struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
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51 | {
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52 | typedef typename Lhs::Scalar LhsScalar;
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53 | typedef typename Rhs::Scalar RhsScalar;
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54 | typedef blas_traits<Lhs> LhsProductTraits;
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55 | typedef typename LhsProductTraits::ExtractType ActualLhsType;
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56 | typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
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57 | static void run(const Lhs& lhs, Rhs& rhs)
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58 | {
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59 | ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
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60 |
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61 | // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
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62 |
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63 | bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
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64 |
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65 | ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
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66 | (useRhsDirectly ? rhs.data() : 0));
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67 |
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68 | if(!useRhsDirectly)
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69 | MappedRhs(actualRhs,rhs.size()) = rhs;
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70 |
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71 | triangular_solve_vector<LhsScalar, RhsScalar, typename Lhs::Index, Side, Mode, LhsProductTraits::NeedToConjugate,
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72 | (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
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73 | ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
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74 |
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75 | if(!useRhsDirectly)
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76 | rhs = MappedRhs(actualRhs, rhs.size());
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77 | }
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78 | };
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79 |
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80 | // the rhs is a matrix
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81 | template<typename Lhs, typename Rhs, int Side, int Mode>
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82 | struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
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83 | {
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84 | typedef typename Rhs::Scalar Scalar;
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85 | typedef typename Rhs::Index Index;
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86 | typedef blas_traits<Lhs> LhsProductTraits;
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87 | typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
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88 |
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89 | static void run(const Lhs& lhs, Rhs& rhs)
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90 | {
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91 | typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
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92 |
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93 | const Index size = lhs.rows();
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94 | const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
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95 |
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96 | typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
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97 | Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
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98 |
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99 | BlockingType blocking(rhs.rows(), rhs.cols(), size);
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100 |
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101 | triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
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102 | (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
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103 | ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
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104 | }
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105 | };
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106 |
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107 | /***************************************************************************
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108 | * meta-unrolling implementation
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109 | ***************************************************************************/
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110 |
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111 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size,
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112 | bool Stop = Index==Size>
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113 | struct triangular_solver_unroller;
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114 |
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115 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
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116 | struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> {
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117 | enum {
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118 | IsLower = ((Mode&Lower)==Lower),
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119 | RowIndex = IsLower ? Index : Size - Index - 1,
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120 | S = IsLower ? 0 : RowIndex+1
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121 | };
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122 | static void run(const Lhs& lhs, Rhs& rhs)
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123 | {
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124 | if (Index>0)
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125 | rhs.coeffRef(RowIndex) -= lhs.row(RowIndex).template segment<Index>(S).transpose()
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126 | .cwiseProduct(rhs.template segment<Index>(S)).sum();
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127 |
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128 | if(!(Mode & UnitDiag))
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129 | rhs.coeffRef(RowIndex) /= lhs.coeff(RowIndex,RowIndex);
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130 |
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131 | triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs);
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132 | }
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133 | };
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134 |
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135 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
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136 | struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> {
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137 | static void run(const Lhs&, Rhs&) {}
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138 | };
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139 |
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140 | template<typename Lhs, typename Rhs, int Mode>
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141 | struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
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142 | static void run(const Lhs& lhs, Rhs& rhs)
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143 | { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
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144 | };
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145 |
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146 | template<typename Lhs, typename Rhs, int Mode>
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147 | struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
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148 | static void run(const Lhs& lhs, Rhs& rhs)
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149 | {
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150 | Transpose<const Lhs> trLhs(lhs);
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151 | Transpose<Rhs> trRhs(rhs);
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152 |
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153 | triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
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154 | ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
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155 | 0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
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156 | }
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157 | };
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158 |
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159 | } // end namespace internal
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160 |
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161 | /***************************************************************************
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162 | * TriangularView methods
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163 | ***************************************************************************/
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164 |
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165 | /** "in-place" version of TriangularView::solve() where the result is written in \a other
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166 | *
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167 | * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
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168 | * This function will const_cast it, so constness isn't honored here.
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169 | *
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170 | * See TriangularView:solve() for the details.
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171 | */
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172 | template<typename MatrixType, unsigned int Mode>
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173 | template<int Side, typename OtherDerived>
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174 | void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
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175 | {
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176 | OtherDerived& other = _other.const_cast_derived();
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177 | eigen_assert( cols() == rows() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
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178 | eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
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179 |
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180 | enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit && OtherDerived::IsVectorAtCompileTime };
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181 | typedef typename internal::conditional<copy,
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182 | typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
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183 | OtherCopy otherCopy(other);
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184 |
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185 | internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
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186 | Side, Mode>::run(nestedExpression(), otherCopy);
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187 |
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188 | if (copy)
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189 | other = otherCopy;
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190 | }
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191 |
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192 | /** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
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193 | *
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194 | * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
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195 | * \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
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196 | * \a Side==OnTheRight.
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197 | *
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198 | * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
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199 | * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
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200 | * is an upper (resp. lower) triangular matrix.
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201 | *
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202 | * Example: \include MatrixBase_marked.cpp
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203 | * Output: \verbinclude MatrixBase_marked.out
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204 | *
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205 | * This function returns an expression of the inverse-multiply and can works in-place if it is assigned
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206 | * to the same matrix or vector \a other.
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207 | *
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208 | * For users coming from BLAS, this function (and more specifically solveInPlace()) offer
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209 | * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
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210 | *
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211 | * \sa TriangularView::solveInPlace()
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212 | */
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213 | template<typename Derived, unsigned int Mode>
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214 | template<int Side, typename Other>
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215 | const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
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216 | TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const
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217 | {
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218 | return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
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219 | }
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220 |
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221 | namespace internal {
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222 |
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223 |
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224 | template<int Side, typename TriangularType, typename Rhs>
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225 | struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
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226 | {
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227 | typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
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228 | };
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229 |
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230 | template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
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231 | : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
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232 | {
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233 | typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
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234 | typedef ReturnByValue<triangular_solve_retval> Base;
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235 | typedef typename Base::Index Index;
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236 |
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237 | triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
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238 | : m_triangularMatrix(tri), m_rhs(rhs)
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239 | {}
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240 |
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241 | inline Index rows() const { return m_rhs.rows(); }
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242 | inline Index cols() const { return m_rhs.cols(); }
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243 |
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244 | template<typename Dest> inline void evalTo(Dest& dst) const
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245 | {
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246 | const typename Dest::Scalar *dst_data = internal::extract_data(dst);
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247 | if(!(is_same<RhsNestedCleaned,Dest>::value && dst_data!=0 && extract_data(dst) == extract_data(m_rhs)))
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248 | dst = m_rhs;
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249 | m_triangularMatrix.template solveInPlace<Side>(dst);
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250 | }
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251 |
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252 | protected:
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253 | const TriangularType& m_triangularMatrix;
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254 | typename Rhs::Nested m_rhs;
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255 | };
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256 |
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257 | } // namespace internal
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258 |
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259 | } // end namespace Eigen
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260 |
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261 | #endif // EIGEN_SOLVETRIANGULAR_H
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