1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_UMFPACKSUPPORT_H
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11 | #define EIGEN_UMFPACKSUPPORT_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /* TODO extract L, extract U, compute det, etc... */
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16 |
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17 | // generic double/complex<double> wrapper functions:
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18 |
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19 | inline void umfpack_free_numeric(void **Numeric, double)
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20 | { umfpack_di_free_numeric(Numeric); *Numeric = 0; }
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21 |
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22 | inline void umfpack_free_numeric(void **Numeric, std::complex<double>)
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23 | { umfpack_zi_free_numeric(Numeric); *Numeric = 0; }
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24 |
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25 | inline void umfpack_free_symbolic(void **Symbolic, double)
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26 | { umfpack_di_free_symbolic(Symbolic); *Symbolic = 0; }
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27 |
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28 | inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>)
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29 | { umfpack_zi_free_symbolic(Symbolic); *Symbolic = 0; }
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30 |
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31 | inline int umfpack_symbolic(int n_row,int n_col,
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32 | const int Ap[], const int Ai[], const double Ax[], void **Symbolic,
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33 | const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
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34 | {
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35 | return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
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36 | }
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37 |
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38 | inline int umfpack_symbolic(int n_row,int n_col,
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39 | const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
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40 | const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
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41 | {
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42 | return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
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43 | }
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44 |
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45 | inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
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46 | void *Symbolic, void **Numeric,
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47 | const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
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48 | {
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49 | return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
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50 | }
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51 |
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52 | inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],
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53 | void *Symbolic, void **Numeric,
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54 | const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
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55 | {
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56 | return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
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57 | }
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58 |
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59 | inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
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60 | double X[], const double B[], void *Numeric,
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61 | const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
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62 | {
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63 | return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
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64 | }
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65 |
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66 | inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],
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67 | std::complex<double> X[], const std::complex<double> B[], void *Numeric,
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68 | const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
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69 | {
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70 | return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
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71 | }
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72 |
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73 | inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
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74 | {
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75 | return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
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76 | }
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77 |
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78 | inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)
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79 | {
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80 | return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
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81 | }
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82 |
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83 | inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],
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84 | int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)
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85 | {
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86 | return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
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87 | }
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88 |
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89 | inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
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90 | int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
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91 | {
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92 | double& lx0_real = numext::real_ref(Lx[0]);
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93 | double& ux0_real = numext::real_ref(Ux[0]);
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94 | double& dx0_real = numext::real_ref(Dx[0]);
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95 | return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
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96 | Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
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97 | }
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98 |
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99 | inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
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100 | {
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101 | return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);
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102 | }
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103 |
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104 | inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
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105 | {
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106 | double& mx_real = numext::real_ref(*Mx);
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107 | return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
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108 | }
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109 |
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110 | namespace internal {
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111 | template<typename T> struct umfpack_helper_is_sparse_plain : false_type {};
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112 | template<typename Scalar, int Options, typename StorageIndex>
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113 | struct umfpack_helper_is_sparse_plain<SparseMatrix<Scalar,Options,StorageIndex> >
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114 | : true_type {};
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115 | template<typename Scalar, int Options, typename StorageIndex>
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116 | struct umfpack_helper_is_sparse_plain<MappedSparseMatrix<Scalar,Options,StorageIndex> >
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117 | : true_type {};
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118 | }
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119 |
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120 | /** \ingroup UmfPackSupport_Module
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121 | * \brief A sparse LU factorization and solver based on UmfPack
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122 | *
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123 | * This class allows to solve for A.X = B sparse linear problems via a LU factorization
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124 | * using the UmfPack library. The sparse matrix A must be squared and full rank.
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125 | * The vectors or matrices X and B can be either dense or sparse.
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126 | *
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127 | * \warning The input matrix A should be in a \b compressed and \b column-major form.
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128 | * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
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129 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
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130 | *
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131 | * \sa \ref TutorialSparseDirectSolvers
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132 | */
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133 | template<typename _MatrixType>
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134 | class UmfPackLU : internal::noncopyable
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135 | {
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136 | public:
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137 | typedef _MatrixType MatrixType;
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138 | typedef typename MatrixType::Scalar Scalar;
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139 | typedef typename MatrixType::RealScalar RealScalar;
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140 | typedef typename MatrixType::Index Index;
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141 | typedef Matrix<Scalar,Dynamic,1> Vector;
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142 | typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
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143 | typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
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144 | typedef SparseMatrix<Scalar> LUMatrixType;
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145 | typedef SparseMatrix<Scalar,ColMajor,int> UmfpackMatrixType;
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146 |
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147 | public:
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148 |
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149 | UmfPackLU() { init(); }
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150 |
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151 | UmfPackLU(const MatrixType& matrix)
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152 | {
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153 | init();
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154 | compute(matrix);
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155 | }
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156 |
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157 | ~UmfPackLU()
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158 | {
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159 | if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
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160 | if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
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161 | }
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162 |
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163 | inline Index rows() const { return m_copyMatrix.rows(); }
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164 | inline Index cols() const { return m_copyMatrix.cols(); }
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165 |
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166 | /** \brief Reports whether previous computation was successful.
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167 | *
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168 | * \returns \c Success if computation was succesful,
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169 | * \c NumericalIssue if the matrix.appears to be negative.
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170 | */
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171 | ComputationInfo info() const
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172 | {
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173 | eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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174 | return m_info;
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175 | }
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176 |
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177 | inline const LUMatrixType& matrixL() const
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178 | {
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179 | if (m_extractedDataAreDirty) extractData();
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180 | return m_l;
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181 | }
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182 |
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183 | inline const LUMatrixType& matrixU() const
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184 | {
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185 | if (m_extractedDataAreDirty) extractData();
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186 | return m_u;
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187 | }
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188 |
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189 | inline const IntColVectorType& permutationP() const
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190 | {
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191 | if (m_extractedDataAreDirty) extractData();
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192 | return m_p;
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193 | }
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194 |
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195 | inline const IntRowVectorType& permutationQ() const
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196 | {
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197 | if (m_extractedDataAreDirty) extractData();
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198 | return m_q;
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199 | }
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200 |
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201 | /** Computes the sparse Cholesky decomposition of \a matrix
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202 | * Note that the matrix should be column-major, and in compressed format for best performance.
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203 | * \sa SparseMatrix::makeCompressed().
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204 | */
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205 | template<typename InputMatrixType>
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206 | void compute(const InputMatrixType& matrix)
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207 | {
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208 | if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
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209 | if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
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210 | grapInput(matrix.derived());
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211 | analyzePattern_impl();
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212 | factorize_impl();
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213 | }
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214 |
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215 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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216 | *
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217 | * \sa compute()
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218 | */
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219 | template<typename Rhs>
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220 | inline const internal::solve_retval<UmfPackLU, Rhs> solve(const MatrixBase<Rhs>& b) const
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221 | {
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222 | eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
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223 | eigen_assert(rows()==b.rows()
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224 | && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
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225 | return internal::solve_retval<UmfPackLU, Rhs>(*this, b.derived());
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226 | }
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227 |
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228 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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229 | *
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230 | * \sa compute()
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231 | */
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232 | template<typename Rhs>
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233 | inline const internal::sparse_solve_retval<UmfPackLU, Rhs> solve(const SparseMatrixBase<Rhs>& b) const
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234 | {
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235 | eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
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236 | eigen_assert(rows()==b.rows()
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237 | && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
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238 | return internal::sparse_solve_retval<UmfPackLU, Rhs>(*this, b.derived());
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239 | }
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240 |
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241 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
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242 | *
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243 | * This function is particularly useful when solving for several problems having the same structure.
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244 | *
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245 | * \sa factorize(), compute()
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246 | */
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247 | template<typename InputMatrixType>
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248 | void analyzePattern(const InputMatrixType& matrix)
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249 | {
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250 | if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
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251 | if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
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252 |
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253 | grapInput(matrix.derived());
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254 |
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255 | analyzePattern_impl();
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256 | }
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257 |
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258 | /** Performs a numeric decomposition of \a matrix
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259 | *
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260 | * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
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261 | *
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262 | * \sa analyzePattern(), compute()
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263 | */
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264 | template<typename InputMatrixType>
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265 | void factorize(const InputMatrixType& matrix)
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266 | {
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267 | eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
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268 | if(m_numeric)
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269 | umfpack_free_numeric(&m_numeric,Scalar());
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270 |
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271 | grapInput(matrix.derived());
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272 |
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273 | factorize_impl();
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274 | }
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275 |
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276 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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277 | /** \internal */
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278 | template<typename BDerived,typename XDerived>
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279 | bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;
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280 | #endif
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281 |
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282 | Scalar determinant() const;
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283 |
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284 | void extractData() const;
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285 |
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286 | protected:
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287 |
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288 | void init()
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289 | {
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290 | m_info = InvalidInput;
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291 | m_isInitialized = false;
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292 | m_numeric = 0;
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293 | m_symbolic = 0;
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294 | m_outerIndexPtr = 0;
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295 | m_innerIndexPtr = 0;
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296 | m_valuePtr = 0;
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297 | m_extractedDataAreDirty = true;
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298 | }
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299 |
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300 | template<typename InputMatrixType>
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301 | void grapInput_impl(const InputMatrixType& mat, internal::true_type)
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302 | {
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303 | m_copyMatrix.resize(mat.rows(), mat.cols());
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304 | if( ((MatrixType::Flags&RowMajorBit)==RowMajorBit) || sizeof(typename MatrixType::Index)!=sizeof(int) || !mat.isCompressed() )
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305 | {
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306 | // non supported input -> copy
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307 | m_copyMatrix = mat;
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308 | m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
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309 | m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
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310 | m_valuePtr = m_copyMatrix.valuePtr();
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311 | }
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312 | else
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313 | {
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314 | m_outerIndexPtr = mat.outerIndexPtr();
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315 | m_innerIndexPtr = mat.innerIndexPtr();
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316 | m_valuePtr = mat.valuePtr();
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317 | }
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318 | }
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319 |
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320 | template<typename InputMatrixType>
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321 | void grapInput_impl(const InputMatrixType& mat, internal::false_type)
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322 | {
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323 | m_copyMatrix = mat;
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324 | m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
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325 | m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
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326 | m_valuePtr = m_copyMatrix.valuePtr();
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327 | }
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328 |
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329 | template<typename InputMatrixType>
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330 | void grapInput(const InputMatrixType& mat)
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331 | {
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332 | grapInput_impl(mat, internal::umfpack_helper_is_sparse_plain<InputMatrixType>());
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333 | }
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334 |
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335 | void analyzePattern_impl()
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336 | {
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337 | int errorCode = 0;
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338 | errorCode = umfpack_symbolic(m_copyMatrix.rows(), m_copyMatrix.cols(), m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
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339 | &m_symbolic, 0, 0);
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340 |
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341 | m_isInitialized = true;
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342 | m_info = errorCode ? InvalidInput : Success;
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343 | m_analysisIsOk = true;
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344 | m_factorizationIsOk = false;
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345 | m_extractedDataAreDirty = true;
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346 | }
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347 |
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348 | void factorize_impl()
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349 | {
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350 | int errorCode;
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351 | errorCode = umfpack_numeric(m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
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352 | m_symbolic, &m_numeric, 0, 0);
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353 |
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354 | m_info = errorCode ? NumericalIssue : Success;
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355 | m_factorizationIsOk = true;
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356 | m_extractedDataAreDirty = true;
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357 | }
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358 |
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359 | // cached data to reduce reallocation, etc.
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360 | mutable LUMatrixType m_l;
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361 | mutable LUMatrixType m_u;
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362 | mutable IntColVectorType m_p;
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363 | mutable IntRowVectorType m_q;
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364 |
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365 | UmfpackMatrixType m_copyMatrix;
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366 | const Scalar* m_valuePtr;
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367 | const int* m_outerIndexPtr;
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368 | const int* m_innerIndexPtr;
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369 | void* m_numeric;
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370 | void* m_symbolic;
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371 |
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372 | mutable ComputationInfo m_info;
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373 | bool m_isInitialized;
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374 | int m_factorizationIsOk;
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375 | int m_analysisIsOk;
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376 | mutable bool m_extractedDataAreDirty;
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377 |
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378 | private:
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379 | UmfPackLU(UmfPackLU& ) { }
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380 | };
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381 |
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382 |
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383 | template<typename MatrixType>
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384 | void UmfPackLU<MatrixType>::extractData() const
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385 | {
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386 | if (m_extractedDataAreDirty)
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387 | {
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388 | // get size of the data
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389 | int lnz, unz, rows, cols, nz_udiag;
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390 | umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
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391 |
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392 | // allocate data
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393 | m_l.resize(rows,(std::min)(rows,cols));
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394 | m_l.resizeNonZeros(lnz);
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395 |
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396 | m_u.resize((std::min)(rows,cols),cols);
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397 | m_u.resizeNonZeros(unz);
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398 |
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399 | m_p.resize(rows);
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400 | m_q.resize(cols);
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401 |
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402 | // extract
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403 | umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
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404 | m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
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405 | m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
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406 |
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407 | m_extractedDataAreDirty = false;
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408 | }
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409 | }
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410 |
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411 | template<typename MatrixType>
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412 | typename UmfPackLU<MatrixType>::Scalar UmfPackLU<MatrixType>::determinant() const
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413 | {
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414 | Scalar det;
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415 | umfpack_get_determinant(&det, 0, m_numeric, 0);
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416 | return det;
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417 | }
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418 |
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419 | template<typename MatrixType>
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420 | template<typename BDerived,typename XDerived>
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421 | bool UmfPackLU<MatrixType>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const
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422 | {
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423 | const int rhsCols = b.cols();
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424 | eigen_assert((BDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major rhs yet");
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425 | eigen_assert((XDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major result yet");
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426 | eigen_assert(b.derived().data() != x.derived().data() && " Umfpack does not support inplace solve");
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427 |
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428 | int errorCode;
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429 | for (int j=0; j<rhsCols; ++j)
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430 | {
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431 | errorCode = umfpack_solve(UMFPACK_A,
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432 | m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
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433 | &x.col(j).coeffRef(0), &b.const_cast_derived().col(j).coeffRef(0), m_numeric, 0, 0);
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434 | if (errorCode!=0)
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435 | return false;
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436 | }
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437 |
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438 | return true;
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439 | }
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440 |
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441 |
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442 | namespace internal {
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443 |
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444 | template<typename _MatrixType, typename Rhs>
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445 | struct solve_retval<UmfPackLU<_MatrixType>, Rhs>
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446 | : solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
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447 | {
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448 | typedef UmfPackLU<_MatrixType> Dec;
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449 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
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450 |
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451 | template<typename Dest> void evalTo(Dest& dst) const
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452 | {
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453 | dec()._solve(rhs(),dst);
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454 | }
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455 | };
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456 |
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457 | template<typename _MatrixType, typename Rhs>
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458 | struct sparse_solve_retval<UmfPackLU<_MatrixType>, Rhs>
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459 | : sparse_solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
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460 | {
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461 | typedef UmfPackLU<_MatrixType> Dec;
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462 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
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463 |
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464 | template<typename Dest> void evalTo(Dest& dst) const
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465 | {
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466 | this->defaultEvalTo(dst);
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467 | }
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468 | };
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469 |
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470 | } // end namespace internal
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471 |
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472 | } // end namespace Eigen
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473 |
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474 | #endif // EIGEN_UMFPACKSUPPORT_H
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