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) 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_SPARSE_SELFADJOINTVIEW_H
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11 | #define EIGEN_SPARSE_SELFADJOINTVIEW_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /** \ingroup SparseCore_Module
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16 | * \class SparseSelfAdjointView
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17 | *
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18 | * \brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.
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19 | *
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20 | * \param MatrixType the type of the dense matrix storing the coefficients
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21 | * \param UpLo can be either \c #Lower or \c #Upper
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22 | *
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23 | * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
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24 | * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
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25 | * and most of the time this is the only way that it is used.
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26 | *
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27 | * \sa SparseMatrixBase::selfadjointView()
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28 | */
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29 | template<typename Lhs, typename Rhs, int UpLo>
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30 | class SparseSelfAdjointTimeDenseProduct;
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31 |
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32 | template<typename Lhs, typename Rhs, int UpLo>
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33 | class DenseTimeSparseSelfAdjointProduct;
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34 |
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35 | namespace internal {
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36 |
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37 | template<typename MatrixType, unsigned int UpLo>
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38 | struct traits<SparseSelfAdjointView<MatrixType,UpLo> > : traits<MatrixType> {
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39 | };
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40 |
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41 | template<int SrcUpLo,int DstUpLo,typename MatrixType,int DestOrder>
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42 | void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
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43 |
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44 | template<int UpLo,typename MatrixType,int DestOrder>
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45 | void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
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46 |
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47 | }
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48 |
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49 | template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView
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50 | : public EigenBase<SparseSelfAdjointView<MatrixType,UpLo> >
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51 | {
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52 | public:
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53 |
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54 | typedef typename MatrixType::Scalar Scalar;
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55 | typedef typename MatrixType::Index Index;
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56 | typedef Matrix<Index,Dynamic,1> VectorI;
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57 | typedef typename MatrixType::Nested MatrixTypeNested;
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58 | typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
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59 |
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60 | inline SparseSelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
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61 | {
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62 | eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
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63 | }
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64 |
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65 | inline Index rows() const { return m_matrix.rows(); }
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66 | inline Index cols() const { return m_matrix.cols(); }
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67 |
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68 | /** \internal \returns a reference to the nested matrix */
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69 | const _MatrixTypeNested& matrix() const { return m_matrix; }
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70 | _MatrixTypeNested& matrix() { return m_matrix.const_cast_derived(); }
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71 |
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72 | /** \returns an expression of the matrix product between a sparse self-adjoint matrix \c *this and a sparse matrix \a rhs.
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73 | *
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74 | * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
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75 | * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
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76 | */
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77 | template<typename OtherDerived>
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78 | SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>
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79 | operator*(const SparseMatrixBase<OtherDerived>& rhs) const
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80 | {
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81 | return SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>(*this, rhs.derived());
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82 | }
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83 |
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84 | /** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
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85 | *
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86 | * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
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87 | * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
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88 | */
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89 | template<typename OtherDerived> friend
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90 | SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject >
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91 | operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
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92 | {
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93 | return SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject>(lhs.derived(), rhs);
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94 | }
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95 |
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96 | /** Efficient sparse self-adjoint matrix times dense vector/matrix product */
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97 | template<typename OtherDerived>
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98 | SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>
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99 | operator*(const MatrixBase<OtherDerived>& rhs) const
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100 | {
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101 | return SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>(m_matrix, rhs.derived());
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102 | }
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103 |
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104 | /** Efficient dense vector/matrix times sparse self-adjoint matrix product */
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105 | template<typename OtherDerived> friend
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106 | DenseTimeSparseSelfAdjointProduct<OtherDerived,MatrixType,UpLo>
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107 | operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
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108 | {
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109 | return DenseTimeSparseSelfAdjointProduct<OtherDerived,_MatrixTypeNested,UpLo>(lhs.derived(), rhs.m_matrix);
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110 | }
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111 |
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112 | /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
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113 | * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
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114 | *
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115 | * \returns a reference to \c *this
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116 | *
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117 | * To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
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118 | * call this function with u.adjoint().
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119 | */
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120 | template<typename DerivedU>
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121 | SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
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122 |
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123 | /** \internal triggered by sparse_matrix = SparseSelfadjointView; */
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124 | template<typename DestScalar,int StorageOrder> void evalTo(SparseMatrix<DestScalar,StorageOrder,Index>& _dest) const
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125 | {
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126 | internal::permute_symm_to_fullsymm<UpLo>(m_matrix, _dest);
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127 | }
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128 |
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129 | template<typename DestScalar> void evalTo(DynamicSparseMatrix<DestScalar,ColMajor,Index>& _dest) const
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130 | {
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131 | // TODO directly evaluate into _dest;
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132 | SparseMatrix<DestScalar,ColMajor,Index> tmp(_dest.rows(),_dest.cols());
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133 | internal::permute_symm_to_fullsymm<UpLo>(m_matrix, tmp);
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134 | _dest = tmp;
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135 | }
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136 |
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137 | /** \returns an expression of P H P^-1 */
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138 | SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const
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139 | {
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140 | return SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo>(m_matrix, perm);
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141 | }
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142 |
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143 | template<typename SrcMatrixType,int SrcUpLo>
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144 | SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcUpLo>& permutedMatrix)
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145 | {
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146 | permutedMatrix.evalTo(*this);
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147 | return *this;
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148 | }
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149 |
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150 |
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151 | SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)
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152 | {
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153 | PermutationMatrix<Dynamic> pnull;
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154 | return *this = src.twistedBy(pnull);
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155 | }
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156 |
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157 | template<typename SrcMatrixType,unsigned int SrcUpLo>
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158 | SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcUpLo>& src)
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159 | {
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160 | PermutationMatrix<Dynamic> pnull;
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161 | return *this = src.twistedBy(pnull);
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162 | }
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163 |
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164 |
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165 | // const SparseLLT<PlainObject, UpLo> llt() const;
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166 | // const SparseLDLT<PlainObject, UpLo> ldlt() const;
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167 |
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168 | protected:
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169 |
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170 | typename MatrixType::Nested m_matrix;
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171 | mutable VectorI m_countPerRow;
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172 | mutable VectorI m_countPerCol;
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173 | };
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174 |
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175 | /***************************************************************************
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176 | * Implementation of SparseMatrixBase methods
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177 | ***************************************************************************/
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178 |
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179 | template<typename Derived>
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180 | template<unsigned int UpLo>
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181 | const SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView() const
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182 | {
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183 | return derived();
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184 | }
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185 |
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186 | template<typename Derived>
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187 | template<unsigned int UpLo>
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188 | SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView()
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189 | {
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190 | return derived();
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191 | }
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192 |
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193 | /***************************************************************************
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194 | * Implementation of SparseSelfAdjointView methods
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195 | ***************************************************************************/
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196 |
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197 | template<typename MatrixType, unsigned int UpLo>
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198 | template<typename DerivedU>
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199 | SparseSelfAdjointView<MatrixType,UpLo>&
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200 | SparseSelfAdjointView<MatrixType,UpLo>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)
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201 | {
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202 | SparseMatrix<Scalar,MatrixType::Flags&RowMajorBit?RowMajor:ColMajor> tmp = u * u.adjoint();
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203 | if(alpha==Scalar(0))
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204 | m_matrix.const_cast_derived() = tmp.template triangularView<UpLo>();
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205 | else
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206 | m_matrix.const_cast_derived() += alpha * tmp.template triangularView<UpLo>();
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207 |
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208 | return *this;
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209 | }
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210 |
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211 | /***************************************************************************
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212 | * Implementation of sparse self-adjoint time dense matrix
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213 | ***************************************************************************/
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214 |
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215 | namespace internal {
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216 | template<typename Lhs, typename Rhs, int UpLo>
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217 | struct traits<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo> >
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218 | : traits<ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
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219 | {
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220 | typedef Dense StorageKind;
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221 | };
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222 | }
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223 |
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224 | template<typename Lhs, typename Rhs, int UpLo>
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225 | class SparseSelfAdjointTimeDenseProduct
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226 | : public ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
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227 | {
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228 | public:
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229 | EIGEN_PRODUCT_PUBLIC_INTERFACE(SparseSelfAdjointTimeDenseProduct)
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230 |
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231 | SparseSelfAdjointTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
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232 | {}
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233 |
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234 | template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
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235 | {
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236 | EIGEN_ONLY_USED_FOR_DEBUG(alpha);
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237 | // TODO use alpha
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238 | eigen_assert(alpha==Scalar(1) && "alpha != 1 is not implemented yet, sorry");
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239 | typedef typename internal::remove_all<Lhs>::type _Lhs;
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240 | typedef typename _Lhs::InnerIterator LhsInnerIterator;
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241 | enum {
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242 | LhsIsRowMajor = (_Lhs::Flags&RowMajorBit)==RowMajorBit,
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243 | ProcessFirstHalf =
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244 | ((UpLo&(Upper|Lower))==(Upper|Lower))
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245 | || ( (UpLo&Upper) && !LhsIsRowMajor)
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246 | || ( (UpLo&Lower) && LhsIsRowMajor),
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247 | ProcessSecondHalf = !ProcessFirstHalf
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248 | };
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249 | for (Index j=0; j<m_lhs.outerSize(); ++j)
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250 | {
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251 | LhsInnerIterator i(m_lhs,j);
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252 | if (ProcessSecondHalf)
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253 | {
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254 | while (i && i.index()<j) ++i;
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255 | if(i && i.index()==j)
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256 | {
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257 | dest.row(j) += i.value() * m_rhs.row(j);
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258 | ++i;
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259 | }
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260 | }
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261 | for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
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262 | {
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263 | Index a = LhsIsRowMajor ? j : i.index();
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264 | Index b = LhsIsRowMajor ? i.index() : j;
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265 | typename Lhs::Scalar v = i.value();
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266 | dest.row(a) += (v) * m_rhs.row(b);
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267 | dest.row(b) += numext::conj(v) * m_rhs.row(a);
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268 | }
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269 | if (ProcessFirstHalf && i && (i.index()==j))
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270 | dest.row(j) += i.value() * m_rhs.row(j);
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271 | }
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272 | }
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273 |
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274 | private:
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275 | SparseSelfAdjointTimeDenseProduct& operator=(const SparseSelfAdjointTimeDenseProduct&);
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276 | };
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277 |
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278 | namespace internal {
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279 | template<typename Lhs, typename Rhs, int UpLo>
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280 | struct traits<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo> >
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281 | : traits<ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
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282 | {};
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283 | }
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284 |
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285 | template<typename Lhs, typename Rhs, int UpLo>
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286 | class DenseTimeSparseSelfAdjointProduct
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287 | : public ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
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288 | {
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289 | public:
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290 | EIGEN_PRODUCT_PUBLIC_INTERFACE(DenseTimeSparseSelfAdjointProduct)
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291 |
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292 | DenseTimeSparseSelfAdjointProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
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293 | {}
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294 |
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295 | template<typename Dest> void scaleAndAddTo(Dest& /*dest*/, const Scalar& /*alpha*/) const
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296 | {
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297 | // TODO
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298 | }
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299 |
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300 | private:
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301 | DenseTimeSparseSelfAdjointProduct& operator=(const DenseTimeSparseSelfAdjointProduct&);
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302 | };
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303 |
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304 | /***************************************************************************
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305 | * Implementation of symmetric copies and permutations
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306 | ***************************************************************************/
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307 | namespace internal {
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308 |
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309 | template<typename MatrixType, int UpLo>
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310 | struct traits<SparseSymmetricPermutationProduct<MatrixType,UpLo> > : traits<MatrixType> {
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311 | };
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312 |
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313 | template<int UpLo,typename MatrixType,int DestOrder>
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314 | void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
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315 | {
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316 | typedef typename MatrixType::Index Index;
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317 | typedef typename MatrixType::Scalar Scalar;
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318 | typedef SparseMatrix<Scalar,DestOrder,Index> Dest;
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319 | typedef Matrix<Index,Dynamic,1> VectorI;
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320 |
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321 | Dest& dest(_dest.derived());
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322 | enum {
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323 | StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)
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324 | };
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325 |
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326 | Index size = mat.rows();
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327 | VectorI count;
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328 | count.resize(size);
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329 | count.setZero();
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330 | dest.resize(size,size);
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331 | for(Index j = 0; j<size; ++j)
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332 | {
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333 | Index jp = perm ? perm[j] : j;
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334 | for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
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335 | {
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336 | Index i = it.index();
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337 | Index r = it.row();
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338 | Index c = it.col();
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339 | Index ip = perm ? perm[i] : i;
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340 | if(UpLo==(Upper|Lower))
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341 | count[StorageOrderMatch ? jp : ip]++;
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342 | else if(r==c)
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343 | count[ip]++;
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344 | else if(( UpLo==Lower && r>c) || ( UpLo==Upper && r<c))
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345 | {
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346 | count[ip]++;
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347 | count[jp]++;
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348 | }
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349 | }
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350 | }
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351 | Index nnz = count.sum();
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352 |
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353 | // reserve space
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354 | dest.resizeNonZeros(nnz);
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355 | dest.outerIndexPtr()[0] = 0;
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356 | for(Index j=0; j<size; ++j)
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357 | dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
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358 | for(Index j=0; j<size; ++j)
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359 | count[j] = dest.outerIndexPtr()[j];
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360 |
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361 | // copy data
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362 | for(Index j = 0; j<size; ++j)
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363 | {
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364 | for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
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365 | {
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366 | Index i = it.index();
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367 | Index r = it.row();
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368 | Index c = it.col();
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369 |
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370 | Index jp = perm ? perm[j] : j;
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371 | Index ip = perm ? perm[i] : i;
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372 |
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373 | if(UpLo==(Upper|Lower))
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374 | {
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375 | Index k = count[StorageOrderMatch ? jp : ip]++;
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376 | dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;
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377 | dest.valuePtr()[k] = it.value();
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378 | }
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379 | else if(r==c)
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380 | {
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381 | Index k = count[ip]++;
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382 | dest.innerIndexPtr()[k] = ip;
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383 | dest.valuePtr()[k] = it.value();
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384 | }
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385 | else if(( (UpLo&Lower)==Lower && r>c) || ( (UpLo&Upper)==Upper && r<c))
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386 | {
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387 | if(!StorageOrderMatch)
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388 | std::swap(ip,jp);
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389 | Index k = count[jp]++;
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390 | dest.innerIndexPtr()[k] = ip;
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391 | dest.valuePtr()[k] = it.value();
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392 | k = count[ip]++;
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393 | dest.innerIndexPtr()[k] = jp;
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394 | dest.valuePtr()[k] = numext::conj(it.value());
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395 | }
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396 | }
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397 | }
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398 | }
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399 |
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400 | template<int _SrcUpLo,int _DstUpLo,typename MatrixType,int DstOrder>
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401 | void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
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402 | {
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403 | typedef typename MatrixType::Index Index;
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404 | typedef typename MatrixType::Scalar Scalar;
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405 | SparseMatrix<Scalar,DstOrder,Index>& dest(_dest.derived());
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406 | typedef Matrix<Index,Dynamic,1> VectorI;
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407 | enum {
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408 | SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,
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409 | StorageOrderMatch = int(SrcOrder) == int(DstOrder),
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410 | DstUpLo = DstOrder==RowMajor ? (_DstUpLo==Upper ? Lower : Upper) : _DstUpLo,
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411 | SrcUpLo = SrcOrder==RowMajor ? (_SrcUpLo==Upper ? Lower : Upper) : _SrcUpLo
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412 | };
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413 |
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414 | Index size = mat.rows();
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415 | VectorI count(size);
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416 | count.setZero();
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417 | dest.resize(size,size);
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418 | for(Index j = 0; j<size; ++j)
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419 | {
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420 | Index jp = perm ? perm[j] : j;
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421 | for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
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422 | {
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423 | Index i = it.index();
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424 | if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
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425 | continue;
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426 |
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427 | Index ip = perm ? perm[i] : i;
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428 | count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
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429 | }
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430 | }
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431 | dest.outerIndexPtr()[0] = 0;
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432 | for(Index j=0; j<size; ++j)
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433 | dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
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434 | dest.resizeNonZeros(dest.outerIndexPtr()[size]);
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435 | for(Index j=0; j<size; ++j)
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436 | count[j] = dest.outerIndexPtr()[j];
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437 |
|
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438 | for(Index j = 0; j<size; ++j)
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439 | {
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440 |
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441 | for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
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442 | {
|
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443 | Index i = it.index();
|
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444 | if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
|
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445 | continue;
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446 |
|
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447 | Index jp = perm ? perm[j] : j;
|
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448 | Index ip = perm? perm[i] : i;
|
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449 |
|
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450 | Index k = count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
|
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451 | dest.innerIndexPtr()[k] = int(DstUpLo)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);
|
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452 |
|
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453 | if(!StorageOrderMatch) std::swap(ip,jp);
|
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454 | if( ((int(DstUpLo)==int(Lower) && ip<jp) || (int(DstUpLo)==int(Upper) && ip>jp)))
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455 | dest.valuePtr()[k] = numext::conj(it.value());
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456 | else
|
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457 | dest.valuePtr()[k] = it.value();
|
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458 | }
|
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459 | }
|
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460 | }
|
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461 |
|
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462 | }
|
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463 |
|
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464 | template<typename MatrixType,int UpLo>
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465 | class SparseSymmetricPermutationProduct
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466 | : public EigenBase<SparseSymmetricPermutationProduct<MatrixType,UpLo> >
|
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467 | {
|
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468 | public:
|
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469 | typedef typename MatrixType::Scalar Scalar;
|
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470 | typedef typename MatrixType::Index Index;
|
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471 | protected:
|
---|
472 | typedef PermutationMatrix<Dynamic,Dynamic,Index> Perm;
|
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473 | public:
|
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474 | typedef Matrix<Index,Dynamic,1> VectorI;
|
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475 | typedef typename MatrixType::Nested MatrixTypeNested;
|
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476 | typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
|
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477 |
|
---|
478 | SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)
|
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479 | : m_matrix(mat), m_perm(perm)
|
---|
480 | {}
|
---|
481 |
|
---|
482 | inline Index rows() const { return m_matrix.rows(); }
|
---|
483 | inline Index cols() const { return m_matrix.cols(); }
|
---|
484 |
|
---|
485 | template<typename DestScalar, int Options, typename DstIndex>
|
---|
486 | void evalTo(SparseMatrix<DestScalar,Options,DstIndex>& _dest) const
|
---|
487 | {
|
---|
488 | // internal::permute_symm_to_fullsymm<UpLo>(m_matrix,_dest,m_perm.indices().data());
|
---|
489 | SparseMatrix<DestScalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
|
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490 | internal::permute_symm_to_fullsymm<UpLo>(m_matrix,tmp,m_perm.indices().data());
|
---|
491 | _dest = tmp;
|
---|
492 | }
|
---|
493 |
|
---|
494 | template<typename DestType,unsigned int DestUpLo> void evalTo(SparseSelfAdjointView<DestType,DestUpLo>& dest) const
|
---|
495 | {
|
---|
496 | internal::permute_symm_to_symm<UpLo,DestUpLo>(m_matrix,dest.matrix(),m_perm.indices().data());
|
---|
497 | }
|
---|
498 |
|
---|
499 | protected:
|
---|
500 | MatrixTypeNested m_matrix;
|
---|
501 | const Perm& m_perm;
|
---|
502 |
|
---|
503 | };
|
---|
504 |
|
---|
505 | } // end namespace Eigen
|
---|
506 |
|
---|
507 | #endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
|
---|