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) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@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_PASTIXSUPPORT_H |
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11 | #define EIGEN_PASTIXSUPPORT_H |
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12 | |
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13 | namespace Eigen { |
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14 | |
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15 | /** \ingroup PaStiXSupport_Module |
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16 | * \brief Interface to the PaStix solver |
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17 | * |
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18 | * This class is used to solve the linear systems A.X = B via the PaStix library. |
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19 | * The matrix can be either real or complex, symmetric or not. |
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20 | * |
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21 | * \sa TutorialSparseDirectSolvers |
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22 | */ |
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23 | template<typename _MatrixType, bool IsStrSym = false> class PastixLU; |
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24 | template<typename _MatrixType, int Options> class PastixLLT; |
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25 | template<typename _MatrixType, int Options> class PastixLDLT; |
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26 | |
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27 | namespace internal |
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28 | { |
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29 | |
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30 | template<class Pastix> struct pastix_traits; |
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31 | |
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32 | template<typename _MatrixType> |
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33 | struct pastix_traits< PastixLU<_MatrixType> > |
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34 | { |
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35 | typedef _MatrixType MatrixType; |
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36 | typedef typename _MatrixType::Scalar Scalar; |
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37 | typedef typename _MatrixType::RealScalar RealScalar; |
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38 | typedef typename _MatrixType::Index Index; |
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39 | }; |
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40 | |
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41 | template<typename _MatrixType, int Options> |
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42 | struct pastix_traits< PastixLLT<_MatrixType,Options> > |
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43 | { |
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44 | typedef _MatrixType MatrixType; |
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45 | typedef typename _MatrixType::Scalar Scalar; |
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46 | typedef typename _MatrixType::RealScalar RealScalar; |
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47 | typedef typename _MatrixType::Index Index; |
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48 | }; |
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49 | |
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50 | template<typename _MatrixType, int Options> |
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51 | struct pastix_traits< PastixLDLT<_MatrixType,Options> > |
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52 | { |
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53 | typedef _MatrixType MatrixType; |
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54 | typedef typename _MatrixType::Scalar Scalar; |
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55 | typedef typename _MatrixType::RealScalar RealScalar; |
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56 | typedef typename _MatrixType::Index Index; |
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57 | }; |
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58 | |
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59 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm) |
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60 | { |
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61 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; } |
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62 | if (nbrhs == 0) {x = NULL; nbrhs=1;} |
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63 | s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); |
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64 | } |
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65 | |
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66 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm) |
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67 | { |
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68 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; } |
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69 | if (nbrhs == 0) {x = NULL; nbrhs=1;} |
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70 | d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); |
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71 | } |
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72 | |
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73 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm) |
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74 | { |
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75 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; } |
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76 | if (nbrhs == 0) {x = NULL; nbrhs=1;} |
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77 | c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<COMPLEX*>(vals), perm, invp, reinterpret_cast<COMPLEX*>(x), nbrhs, iparm, dparm); |
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78 | } |
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79 | |
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80 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm) |
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81 | { |
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82 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; } |
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83 | if (nbrhs == 0) {x = NULL; nbrhs=1;} |
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84 | z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<DCOMPLEX*>(vals), perm, invp, reinterpret_cast<DCOMPLEX*>(x), nbrhs, iparm, dparm); |
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85 | } |
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86 | |
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87 | // Convert the matrix to Fortran-style Numbering |
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88 | template <typename MatrixType> |
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89 | void c_to_fortran_numbering (MatrixType& mat) |
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90 | { |
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91 | if ( !(mat.outerIndexPtr()[0]) ) |
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92 | { |
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93 | int i; |
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94 | for(i = 0; i <= mat.rows(); ++i) |
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95 | ++mat.outerIndexPtr()[i]; |
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96 | for(i = 0; i < mat.nonZeros(); ++i) |
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97 | ++mat.innerIndexPtr()[i]; |
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98 | } |
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99 | } |
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100 | |
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101 | // Convert to C-style Numbering |
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102 | template <typename MatrixType> |
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103 | void fortran_to_c_numbering (MatrixType& mat) |
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104 | { |
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105 | // Check the Numbering |
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106 | if ( mat.outerIndexPtr()[0] == 1 ) |
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107 | { // Convert to C-style numbering |
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108 | int i; |
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109 | for(i = 0; i <= mat.rows(); ++i) |
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110 | --mat.outerIndexPtr()[i]; |
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111 | for(i = 0; i < mat.nonZeros(); ++i) |
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112 | --mat.innerIndexPtr()[i]; |
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113 | } |
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114 | } |
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115 | } |
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116 | |
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117 | // This is the base class to interface with PaStiX functions. |
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118 | // Users should not used this class directly. |
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119 | template <class Derived> |
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120 | class PastixBase : internal::noncopyable |
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121 | { |
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122 | public: |
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123 | typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType; |
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124 | typedef _MatrixType MatrixType; |
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125 | typedef typename MatrixType::Scalar Scalar; |
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126 | typedef typename MatrixType::RealScalar RealScalar; |
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127 | typedef typename MatrixType::Index Index; |
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128 | typedef Matrix<Scalar,Dynamic,1> Vector; |
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129 | typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix; |
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130 | |
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131 | public: |
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132 | |
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133 | PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false), m_pastixdata(0), m_size(0) |
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134 | { |
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135 | init(); |
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136 | } |
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137 | |
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138 | ~PastixBase() |
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139 | { |
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140 | clean(); |
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141 | } |
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142 | |
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143 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. |
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144 | * |
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145 | * \sa compute() |
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146 | */ |
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147 | template<typename Rhs> |
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148 | inline const internal::solve_retval<PastixBase, Rhs> |
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149 | solve(const MatrixBase<Rhs>& b) const |
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150 | { |
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151 | eigen_assert(m_isInitialized && "Pastix solver is not initialized."); |
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152 | eigen_assert(rows()==b.rows() |
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153 | && "PastixBase::solve(): invalid number of rows of the right hand side matrix b"); |
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154 | return internal::solve_retval<PastixBase, Rhs>(*this, b.derived()); |
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155 | } |
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156 | |
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157 | template<typename Rhs,typename Dest> |
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158 | bool _solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const; |
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159 | |
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160 | /** \internal */ |
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161 | template<typename Rhs, typename DestScalar, int DestOptions, typename DestIndex> |
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162 | void _solve_sparse(const Rhs& b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const |
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163 | { |
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164 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); |
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165 | eigen_assert(rows()==b.rows()); |
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166 | |
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167 | // we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix. |
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168 | static const int NbColsAtOnce = 1; |
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169 | int rhsCols = b.cols(); |
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170 | int size = b.rows(); |
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171 | Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmp(size,rhsCols); |
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172 | for(int k=0; k<rhsCols; k+=NbColsAtOnce) |
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173 | { |
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174 | int actualCols = std::min<int>(rhsCols-k, NbColsAtOnce); |
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175 | tmp.leftCols(actualCols) = b.middleCols(k,actualCols); |
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176 | tmp.leftCols(actualCols) = derived().solve(tmp.leftCols(actualCols)); |
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177 | dest.middleCols(k,actualCols) = tmp.leftCols(actualCols).sparseView(); |
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178 | } |
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179 | } |
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180 | |
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181 | Derived& derived() |
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182 | { |
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183 | return *static_cast<Derived*>(this); |
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184 | } |
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185 | const Derived& derived() const |
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186 | { |
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187 | return *static_cast<const Derived*>(this); |
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188 | } |
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189 | |
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190 | /** Returns a reference to the integer vector IPARM of PaStiX parameters |
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191 | * to modify the default parameters. |
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192 | * The statistics related to the different phases of factorization and solve are saved here as well |
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193 | * \sa analyzePattern() factorize() |
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194 | */ |
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195 | Array<Index,IPARM_SIZE,1>& iparm() |
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196 | { |
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197 | return m_iparm; |
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198 | } |
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199 | |
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200 | /** Return a reference to a particular index parameter of the IPARM vector |
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201 | * \sa iparm() |
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202 | */ |
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203 | |
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204 | int& iparm(int idxparam) |
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205 | { |
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206 | return m_iparm(idxparam); |
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207 | } |
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208 | |
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209 | /** Returns a reference to the double vector DPARM of PaStiX parameters |
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210 | * The statistics related to the different phases of factorization and solve are saved here as well |
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211 | * \sa analyzePattern() factorize() |
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212 | */ |
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213 | Array<RealScalar,IPARM_SIZE,1>& dparm() |
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214 | { |
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215 | return m_dparm; |
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216 | } |
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217 | |
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218 | |
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219 | /** Return a reference to a particular index parameter of the DPARM vector |
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220 | * \sa dparm() |
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221 | */ |
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222 | double& dparm(int idxparam) |
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223 | { |
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224 | return m_dparm(idxparam); |
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225 | } |
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226 | |
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227 | inline Index cols() const { return m_size; } |
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228 | inline Index rows() const { return m_size; } |
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229 | |
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230 | /** \brief Reports whether previous computation was successful. |
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231 | * |
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232 | * \returns \c Success if computation was succesful, |
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233 | * \c NumericalIssue if the PaStiX reports a problem |
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234 | * \c InvalidInput if the input matrix is invalid |
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235 | * |
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236 | * \sa iparm() |
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237 | */ |
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238 | ComputationInfo info() const |
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239 | { |
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240 | eigen_assert(m_isInitialized && "Decomposition is not initialized."); |
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241 | return m_info; |
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242 | } |
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243 | |
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244 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. |
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245 | * |
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246 | * \sa compute() |
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247 | */ |
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248 | template<typename Rhs> |
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249 | inline const internal::sparse_solve_retval<PastixBase, Rhs> |
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250 | solve(const SparseMatrixBase<Rhs>& b) const |
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251 | { |
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252 | eigen_assert(m_isInitialized && "Pastix LU, LLT or LDLT is not initialized."); |
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253 | eigen_assert(rows()==b.rows() |
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254 | && "PastixBase::solve(): invalid number of rows of the right hand side matrix b"); |
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255 | return internal::sparse_solve_retval<PastixBase, Rhs>(*this, b.derived()); |
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256 | } |
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257 | |
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258 | protected: |
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259 | |
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260 | // Initialize the Pastix data structure, check the matrix |
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261 | void init(); |
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262 | |
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263 | // Compute the ordering and the symbolic factorization |
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264 | void analyzePattern(ColSpMatrix& mat); |
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265 | |
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266 | // Compute the numerical factorization |
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267 | void factorize(ColSpMatrix& mat); |
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268 | |
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269 | // Free all the data allocated by Pastix |
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270 | void clean() |
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271 | { |
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272 | eigen_assert(m_initisOk && "The Pastix structure should be allocated first"); |
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273 | m_iparm(IPARM_START_TASK) = API_TASK_CLEAN; |
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274 | m_iparm(IPARM_END_TASK) = API_TASK_CLEAN; |
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275 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0, |
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276 | m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data()); |
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277 | } |
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278 | |
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279 | void compute(ColSpMatrix& mat); |
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280 | |
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281 | int m_initisOk; |
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282 | int m_analysisIsOk; |
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283 | int m_factorizationIsOk; |
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284 | bool m_isInitialized; |
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285 | mutable ComputationInfo m_info; |
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286 | mutable pastix_data_t *m_pastixdata; // Data structure for pastix |
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287 | mutable int m_comm; // The MPI communicator identifier |
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288 | mutable Matrix<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters |
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289 | mutable Matrix<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters |
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290 | mutable Matrix<Index,Dynamic,1> m_perm; // Permutation vector |
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291 | mutable Matrix<Index,Dynamic,1> m_invp; // Inverse permutation vector |
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292 | mutable int m_size; // Size of the matrix |
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293 | }; |
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294 | |
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295 | /** Initialize the PaStiX data structure. |
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296 | *A first call to this function fills iparm and dparm with the default PaStiX parameters |
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297 | * \sa iparm() dparm() |
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298 | */ |
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299 | template <class Derived> |
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300 | void PastixBase<Derived>::init() |
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301 | { |
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302 | m_size = 0; |
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303 | m_iparm.setZero(IPARM_SIZE); |
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304 | m_dparm.setZero(DPARM_SIZE); |
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305 | |
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306 | m_iparm(IPARM_MODIFY_PARAMETER) = API_NO; |
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307 | pastix(&m_pastixdata, MPI_COMM_WORLD, |
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308 | 0, 0, 0, 0, |
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309 | 0, 0, 0, 1, m_iparm.data(), m_dparm.data()); |
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310 | |
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311 | m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO; |
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312 | m_iparm[IPARM_VERBOSE] = 2; |
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313 | m_iparm[IPARM_ORDERING] = API_ORDER_SCOTCH; |
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314 | m_iparm[IPARM_INCOMPLETE] = API_NO; |
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315 | m_iparm[IPARM_OOC_LIMIT] = 2000; |
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316 | m_iparm[IPARM_RHS_MAKING] = API_RHS_B; |
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317 | m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO; |
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318 | |
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319 | m_iparm(IPARM_START_TASK) = API_TASK_INIT; |
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320 | m_iparm(IPARM_END_TASK) = API_TASK_INIT; |
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321 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0, |
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322 | 0, 0, 0, 0, m_iparm.data(), m_dparm.data()); |
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323 | |
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324 | // Check the returned error |
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325 | if(m_iparm(IPARM_ERROR_NUMBER)) { |
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326 | m_info = InvalidInput; |
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327 | m_initisOk = false; |
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328 | } |
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329 | else { |
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330 | m_info = Success; |
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331 | m_initisOk = true; |
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332 | } |
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333 | } |
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334 | |
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335 | template <class Derived> |
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336 | void PastixBase<Derived>::compute(ColSpMatrix& mat) |
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337 | { |
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338 | eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared"); |
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339 | |
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340 | analyzePattern(mat); |
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341 | factorize(mat); |
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342 | |
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343 | m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO; |
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344 | m_isInitialized = m_factorizationIsOk; |
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345 | } |
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346 | |
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347 | |
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348 | template <class Derived> |
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349 | void PastixBase<Derived>::analyzePattern(ColSpMatrix& mat) |
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350 | { |
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351 | eigen_assert(m_initisOk && "The initialization of PaSTiX failed"); |
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352 | |
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353 | // clean previous calls |
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354 | if(m_size>0) |
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355 | clean(); |
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356 | |
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357 | m_size = mat.rows(); |
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358 | m_perm.resize(m_size); |
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359 | m_invp.resize(m_size); |
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360 | |
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361 | m_iparm(IPARM_START_TASK) = API_TASK_ORDERING; |
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362 | m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE; |
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363 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(), |
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364 | mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data()); |
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365 | |
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366 | // Check the returned error |
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367 | if(m_iparm(IPARM_ERROR_NUMBER)) |
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368 | { |
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369 | m_info = NumericalIssue; |
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370 | m_analysisIsOk = false; |
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371 | } |
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372 | else |
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373 | { |
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374 | m_info = Success; |
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375 | m_analysisIsOk = true; |
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376 | } |
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377 | } |
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378 | |
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379 | template <class Derived> |
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380 | void PastixBase<Derived>::factorize(ColSpMatrix& mat) |
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381 | { |
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382 | // if(&m_cpyMat != &mat) m_cpyMat = mat; |
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383 | eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase"); |
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384 | m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT; |
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385 | m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT; |
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386 | m_size = mat.rows(); |
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387 | |
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388 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(), |
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389 | mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data()); |
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390 | |
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391 | // Check the returned error |
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392 | if(m_iparm(IPARM_ERROR_NUMBER)) |
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393 | { |
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394 | m_info = NumericalIssue; |
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395 | m_factorizationIsOk = false; |
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396 | m_isInitialized = false; |
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397 | } |
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398 | else |
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399 | { |
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400 | m_info = Success; |
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401 | m_factorizationIsOk = true; |
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402 | m_isInitialized = true; |
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403 | } |
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404 | } |
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405 | |
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406 | /* Solve the system */ |
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407 | template<typename Base> |
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408 | template<typename Rhs,typename Dest> |
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409 | bool PastixBase<Base>::_solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const |
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410 | { |
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411 | eigen_assert(m_isInitialized && "The matrix should be factorized first"); |
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412 | EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0, |
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413 | THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); |
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414 | int rhs = 1; |
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415 | |
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416 | x = b; /* on return, x is overwritten by the computed solution */ |
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417 | |
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418 | for (int i = 0; i < b.cols(); i++){ |
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419 | m_iparm[IPARM_START_TASK] = API_TASK_SOLVE; |
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420 | m_iparm[IPARM_END_TASK] = API_TASK_REFINE; |
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421 | |
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422 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, x.rows(), 0, 0, 0, |
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423 | m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data()); |
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424 | } |
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425 | |
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426 | // Check the returned error |
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427 | m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue; |
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428 | |
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429 | return m_iparm(IPARM_ERROR_NUMBER)==0; |
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430 | } |
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431 | |
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432 | /** \ingroup PaStiXSupport_Module |
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433 | * \class PastixLU |
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434 | * \brief Sparse direct LU solver based on PaStiX library |
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435 | * |
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436 | * This class is used to solve the linear systems A.X = B with a supernodal LU |
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437 | * factorization in the PaStiX library. The matrix A should be squared and nonsingular |
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438 | * PaStiX requires that the matrix A has a symmetric structural pattern. |
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439 | * This interface can symmetrize the input matrix otherwise. |
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440 | * The vectors or matrices X and B can be either dense or sparse. |
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441 | * |
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442 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> |
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443 | * \tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false |
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444 | * NOTE : Note that if the analysis and factorization phase are called separately, |
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445 | * the input matrix will be symmetrized at each call, hence it is advised to |
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446 | * symmetrize the matrix in a end-user program and set \p IsStrSym to true |
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447 | * |
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448 | * \sa \ref TutorialSparseDirectSolvers |
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449 | * |
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450 | */ |
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451 | template<typename _MatrixType, bool IsStrSym> |
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452 | class PastixLU : public PastixBase< PastixLU<_MatrixType> > |
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453 | { |
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454 | public: |
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455 | typedef _MatrixType MatrixType; |
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456 | typedef PastixBase<PastixLU<MatrixType> > Base; |
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457 | typedef typename Base::ColSpMatrix ColSpMatrix; |
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458 | typedef typename MatrixType::Index Index; |
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459 | |
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460 | public: |
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461 | PastixLU() : Base() |
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462 | { |
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463 | init(); |
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464 | } |
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465 | |
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466 | PastixLU(const MatrixType& matrix):Base() |
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467 | { |
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468 | init(); |
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469 | compute(matrix); |
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470 | } |
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471 | /** Compute the LU supernodal factorization of \p matrix. |
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472 | * iparm and dparm can be used to tune the PaStiX parameters. |
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473 | * see the PaStiX user's manual |
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474 | * \sa analyzePattern() factorize() |
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475 | */ |
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476 | void compute (const MatrixType& matrix) |
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477 | { |
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478 | m_structureIsUptodate = false; |
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479 | ColSpMatrix temp; |
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480 | grabMatrix(matrix, temp); |
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481 | Base::compute(temp); |
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482 | } |
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483 | /** Compute the LU symbolic factorization of \p matrix using its sparsity pattern. |
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484 | * Several ordering methods can be used at this step. See the PaStiX user's manual. |
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485 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix |
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486 | * \sa factorize() |
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487 | */ |
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488 | void analyzePattern(const MatrixType& matrix) |
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489 | { |
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490 | m_structureIsUptodate = false; |
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491 | ColSpMatrix temp; |
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492 | grabMatrix(matrix, temp); |
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493 | Base::analyzePattern(temp); |
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494 | } |
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495 | |
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496 | /** Compute the LU supernodal factorization of \p matrix |
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497 | * WARNING The matrix \p matrix should have the same structural pattern |
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498 | * as the same used in the analysis phase. |
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499 | * \sa analyzePattern() |
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500 | */ |
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501 | void factorize(const MatrixType& matrix) |
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502 | { |
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503 | ColSpMatrix temp; |
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504 | grabMatrix(matrix, temp); |
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505 | Base::factorize(temp); |
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506 | } |
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507 | protected: |
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508 | |
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509 | void init() |
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510 | { |
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511 | m_structureIsUptodate = false; |
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512 | m_iparm(IPARM_SYM) = API_SYM_NO; |
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513 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LU; |
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514 | } |
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515 | |
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516 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out) |
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517 | { |
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518 | if(IsStrSym) |
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519 | out = matrix; |
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520 | else |
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521 | { |
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522 | if(!m_structureIsUptodate) |
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523 | { |
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524 | // update the transposed structure |
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525 | m_transposedStructure = matrix.transpose(); |
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526 | |
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527 | // Set the elements of the matrix to zero |
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528 | for (Index j=0; j<m_transposedStructure.outerSize(); ++j) |
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529 | for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it) |
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530 | it.valueRef() = 0.0; |
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531 | |
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532 | m_structureIsUptodate = true; |
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533 | } |
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534 | |
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535 | out = m_transposedStructure + matrix; |
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536 | } |
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537 | internal::c_to_fortran_numbering(out); |
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538 | } |
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539 | |
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540 | using Base::m_iparm; |
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541 | using Base::m_dparm; |
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542 | |
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543 | ColSpMatrix m_transposedStructure; |
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544 | bool m_structureIsUptodate; |
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545 | }; |
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546 | |
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547 | /** \ingroup PaStiXSupport_Module |
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548 | * \class PastixLLT |
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549 | * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library |
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550 | * |
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551 | * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization |
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552 | * available in the PaStiX library. The matrix A should be symmetric and positive definite |
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553 | * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX |
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554 | * The vectors or matrices X and B can be either dense or sparse |
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555 | * |
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556 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> |
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557 | * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX |
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558 | * |
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559 | * \sa \ref TutorialSparseDirectSolvers |
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560 | */ |
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561 | template<typename _MatrixType, int _UpLo> |
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562 | class PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> > |
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563 | { |
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564 | public: |
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565 | typedef _MatrixType MatrixType; |
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566 | typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base; |
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567 | typedef typename Base::ColSpMatrix ColSpMatrix; |
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568 | |
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569 | public: |
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570 | enum { UpLo = _UpLo }; |
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571 | PastixLLT() : Base() |
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572 | { |
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573 | init(); |
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574 | } |
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575 | |
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576 | PastixLLT(const MatrixType& matrix):Base() |
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577 | { |
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578 | init(); |
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579 | compute(matrix); |
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580 | } |
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581 | |
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582 | /** Compute the L factor of the LL^T supernodal factorization of \p matrix |
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583 | * \sa analyzePattern() factorize() |
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584 | */ |
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585 | void compute (const MatrixType& matrix) |
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586 | { |
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587 | ColSpMatrix temp; |
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588 | grabMatrix(matrix, temp); |
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589 | Base::compute(temp); |
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590 | } |
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591 | |
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592 | /** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern |
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593 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix |
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594 | * \sa factorize() |
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595 | */ |
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596 | void analyzePattern(const MatrixType& matrix) |
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597 | { |
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598 | ColSpMatrix temp; |
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599 | grabMatrix(matrix, temp); |
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600 | Base::analyzePattern(temp); |
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601 | } |
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602 | /** Compute the LL^T supernodal numerical factorization of \p matrix |
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603 | * \sa analyzePattern() |
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604 | */ |
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605 | void factorize(const MatrixType& matrix) |
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606 | { |
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607 | ColSpMatrix temp; |
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608 | grabMatrix(matrix, temp); |
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609 | Base::factorize(temp); |
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610 | } |
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611 | protected: |
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612 | using Base::m_iparm; |
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613 | |
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614 | void init() |
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615 | { |
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616 | m_iparm(IPARM_SYM) = API_SYM_YES; |
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617 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT; |
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618 | } |
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619 | |
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620 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out) |
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621 | { |
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622 | // Pastix supports only lower, column-major matrices |
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623 | out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>(); |
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624 | internal::c_to_fortran_numbering(out); |
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625 | } |
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626 | }; |
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627 | |
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628 | /** \ingroup PaStiXSupport_Module |
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629 | * \class PastixLDLT |
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630 | * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library |
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631 | * |
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632 | * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization |
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633 | * available in the PaStiX library. The matrix A should be symmetric and positive definite |
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634 | * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX |
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635 | * The vectors or matrices X and B can be either dense or sparse |
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636 | * |
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637 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> |
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638 | * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX |
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639 | * |
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640 | * \sa \ref TutorialSparseDirectSolvers |
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641 | */ |
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642 | template<typename _MatrixType, int _UpLo> |
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643 | class PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> > |
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644 | { |
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645 | public: |
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646 | typedef _MatrixType MatrixType; |
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647 | typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base; |
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648 | typedef typename Base::ColSpMatrix ColSpMatrix; |
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649 | |
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650 | public: |
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651 | enum { UpLo = _UpLo }; |
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652 | PastixLDLT():Base() |
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653 | { |
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654 | init(); |
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655 | } |
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656 | |
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657 | PastixLDLT(const MatrixType& matrix):Base() |
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658 | { |
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659 | init(); |
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660 | compute(matrix); |
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661 | } |
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662 | |
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663 | /** Compute the L and D factors of the LDL^T factorization of \p matrix |
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664 | * \sa analyzePattern() factorize() |
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665 | */ |
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666 | void compute (const MatrixType& matrix) |
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667 | { |
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668 | ColSpMatrix temp; |
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669 | grabMatrix(matrix, temp); |
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670 | Base::compute(temp); |
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671 | } |
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672 | |
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673 | /** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern |
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674 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix |
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675 | * \sa factorize() |
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676 | */ |
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677 | void analyzePattern(const MatrixType& matrix) |
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678 | { |
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679 | ColSpMatrix temp; |
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680 | grabMatrix(matrix, temp); |
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681 | Base::analyzePattern(temp); |
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682 | } |
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683 | /** Compute the LDL^T supernodal numerical factorization of \p matrix |
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684 | * |
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685 | */ |
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686 | void factorize(const MatrixType& matrix) |
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687 | { |
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688 | ColSpMatrix temp; |
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689 | grabMatrix(matrix, temp); |
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690 | Base::factorize(temp); |
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691 | } |
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692 | |
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693 | protected: |
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694 | using Base::m_iparm; |
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695 | |
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696 | void init() |
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697 | { |
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698 | m_iparm(IPARM_SYM) = API_SYM_YES; |
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699 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT; |
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700 | } |
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701 | |
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702 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out) |
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703 | { |
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704 | // Pastix supports only lower, column-major matrices |
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705 | out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>(); |
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706 | internal::c_to_fortran_numbering(out); |
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707 | } |
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708 | }; |
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709 | |
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710 | namespace internal { |
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711 | |
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712 | template<typename _MatrixType, typename Rhs> |
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713 | struct solve_retval<PastixBase<_MatrixType>, Rhs> |
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714 | : solve_retval_base<PastixBase<_MatrixType>, Rhs> |
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715 | { |
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716 | typedef PastixBase<_MatrixType> Dec; |
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717 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) |
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718 | |
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719 | template<typename Dest> void evalTo(Dest& dst) const |
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720 | { |
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721 | dec()._solve(rhs(),dst); |
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722 | } |
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723 | }; |
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724 | |
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725 | template<typename _MatrixType, typename Rhs> |
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726 | struct sparse_solve_retval<PastixBase<_MatrixType>, Rhs> |
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727 | : sparse_solve_retval_base<PastixBase<_MatrixType>, Rhs> |
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728 | { |
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729 | typedef PastixBase<_MatrixType> Dec; |
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730 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs) |
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731 | |
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732 | template<typename Dest> void evalTo(Dest& dst) const |
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733 | { |
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734 | dec()._solve_sparse(rhs(),dst); |
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735 | } |
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736 | }; |
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737 | |
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738 | } // end namespace internal |
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739 | |
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740 | } // end namespace Eigen |
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741 | |
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742 | #endif |
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