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_SUPERLUSUPPORT_H
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11 | #define EIGEN_SUPERLUSUPPORT_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | #define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
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16 | extern "C" { \
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17 | typedef struct { FLOATTYPE for_lu; FLOATTYPE total_needed; int expansions; } PREFIX##mem_usage_t; \
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18 | extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
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19 | char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
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20 | void *, int, SuperMatrix *, SuperMatrix *, \
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21 | FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
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22 | PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \
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23 | } \
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24 | inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
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25 | int *perm_c, int *perm_r, int *etree, char *equed, \
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26 | FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
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27 | SuperMatrix *U, void *work, int lwork, \
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28 | SuperMatrix *B, SuperMatrix *X, \
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29 | FLOATTYPE *recip_pivot_growth, \
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30 | FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
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31 | SuperLUStat_t *stats, int *info, KEYTYPE) { \
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32 | PREFIX##mem_usage_t mem_usage; \
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33 | PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
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34 | U, work, lwork, B, X, recip_pivot_growth, rcond, \
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35 | ferr, berr, &mem_usage, stats, info); \
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36 | return mem_usage.for_lu; /* bytes used by the factor storage */ \
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37 | }
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38 |
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39 | DECL_GSSVX(s,float,float)
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40 | DECL_GSSVX(c,float,std::complex<float>)
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41 | DECL_GSSVX(d,double,double)
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42 | DECL_GSSVX(z,double,std::complex<double>)
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43 |
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44 | #ifdef MILU_ALPHA
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45 | #define EIGEN_SUPERLU_HAS_ILU
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46 | #endif
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47 |
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48 | #ifdef EIGEN_SUPERLU_HAS_ILU
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49 |
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50 | // similarly for the incomplete factorization using gsisx
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51 | #define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE) \
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52 | extern "C" { \
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53 | extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
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54 | char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
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55 | void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *, \
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56 | PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \
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57 | } \
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58 | inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A, \
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59 | int *perm_c, int *perm_r, int *etree, char *equed, \
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60 | FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
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61 | SuperMatrix *U, void *work, int lwork, \
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62 | SuperMatrix *B, SuperMatrix *X, \
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63 | FLOATTYPE *recip_pivot_growth, \
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64 | FLOATTYPE *rcond, \
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65 | SuperLUStat_t *stats, int *info, KEYTYPE) { \
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66 | PREFIX##mem_usage_t mem_usage; \
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67 | PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
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68 | U, work, lwork, B, X, recip_pivot_growth, rcond, \
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69 | &mem_usage, stats, info); \
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70 | return mem_usage.for_lu; /* bytes used by the factor storage */ \
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71 | }
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72 |
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73 | DECL_GSISX(s,float,float)
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74 | DECL_GSISX(c,float,std::complex<float>)
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75 | DECL_GSISX(d,double,double)
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76 | DECL_GSISX(z,double,std::complex<double>)
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77 |
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78 | #endif
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79 |
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80 | template<typename MatrixType>
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81 | struct SluMatrixMapHelper;
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82 |
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83 | /** \internal
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84 | *
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85 | * A wrapper class for SuperLU matrices. It supports only compressed sparse matrices
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86 | * and dense matrices. Supernodal and other fancy format are not supported by this wrapper.
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87 | *
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88 | * This wrapper class mainly aims to avoids the need of dynamic allocation of the storage structure.
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89 | */
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90 | struct SluMatrix : SuperMatrix
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91 | {
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92 | SluMatrix()
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93 | {
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94 | Store = &storage;
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95 | }
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96 |
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97 | SluMatrix(const SluMatrix& other)
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98 | : SuperMatrix(other)
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99 | {
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100 | Store = &storage;
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101 | storage = other.storage;
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102 | }
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103 |
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104 | SluMatrix& operator=(const SluMatrix& other)
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105 | {
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106 | SuperMatrix::operator=(static_cast<const SuperMatrix&>(other));
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107 | Store = &storage;
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108 | storage = other.storage;
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109 | return *this;
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110 | }
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111 |
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112 | struct
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113 | {
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114 | union {int nnz;int lda;};
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115 | void *values;
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116 | int *innerInd;
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117 | int *outerInd;
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118 | } storage;
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119 |
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120 | void setStorageType(Stype_t t)
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121 | {
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122 | Stype = t;
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123 | if (t==SLU_NC || t==SLU_NR || t==SLU_DN)
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124 | Store = &storage;
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125 | else
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126 | {
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127 | eigen_assert(false && "storage type not supported");
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128 | Store = 0;
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129 | }
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130 | }
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131 |
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132 | template<typename Scalar>
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133 | void setScalarType()
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134 | {
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135 | if (internal::is_same<Scalar,float>::value)
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136 | Dtype = SLU_S;
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137 | else if (internal::is_same<Scalar,double>::value)
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138 | Dtype = SLU_D;
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139 | else if (internal::is_same<Scalar,std::complex<float> >::value)
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140 | Dtype = SLU_C;
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141 | else if (internal::is_same<Scalar,std::complex<double> >::value)
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142 | Dtype = SLU_Z;
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143 | else
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144 | {
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145 | eigen_assert(false && "Scalar type not supported by SuperLU");
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146 | }
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147 | }
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148 |
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149 | template<typename MatrixType>
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150 | static SluMatrix Map(MatrixBase<MatrixType>& _mat)
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151 | {
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152 | MatrixType& mat(_mat.derived());
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153 | eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && "row-major dense matrices are not supported by SuperLU");
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154 | SluMatrix res;
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155 | res.setStorageType(SLU_DN);
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156 | res.setScalarType<typename MatrixType::Scalar>();
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157 | res.Mtype = SLU_GE;
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158 |
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159 | res.nrow = mat.rows();
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160 | res.ncol = mat.cols();
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161 |
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162 | res.storage.lda = MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride();
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163 | res.storage.values = (void*)(mat.data());
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164 | return res;
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165 | }
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166 |
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167 | template<typename MatrixType>
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168 | static SluMatrix Map(SparseMatrixBase<MatrixType>& mat)
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169 | {
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170 | SluMatrix res;
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171 | if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
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172 | {
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173 | res.setStorageType(SLU_NR);
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174 | res.nrow = mat.cols();
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175 | res.ncol = mat.rows();
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176 | }
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177 | else
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178 | {
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179 | res.setStorageType(SLU_NC);
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180 | res.nrow = mat.rows();
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181 | res.ncol = mat.cols();
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182 | }
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183 |
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184 | res.Mtype = SLU_GE;
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185 |
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186 | res.storage.nnz = mat.nonZeros();
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187 | res.storage.values = mat.derived().valuePtr();
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188 | res.storage.innerInd = mat.derived().innerIndexPtr();
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189 | res.storage.outerInd = mat.derived().outerIndexPtr();
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190 |
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191 | res.setScalarType<typename MatrixType::Scalar>();
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192 |
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193 | // FIXME the following is not very accurate
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194 | if (MatrixType::Flags & Upper)
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195 | res.Mtype = SLU_TRU;
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196 | if (MatrixType::Flags & Lower)
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197 | res.Mtype = SLU_TRL;
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198 |
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199 | eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
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200 |
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201 | return res;
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202 | }
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203 | };
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204 |
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205 | template<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols>
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206 | struct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> >
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207 | {
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208 | typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType;
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209 | static void run(MatrixType& mat, SluMatrix& res)
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210 | {
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211 | eigen_assert( ((Options&RowMajor)!=RowMajor) && "row-major dense matrices is not supported by SuperLU");
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212 | res.setStorageType(SLU_DN);
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213 | res.setScalarType<Scalar>();
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214 | res.Mtype = SLU_GE;
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215 |
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216 | res.nrow = mat.rows();
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217 | res.ncol = mat.cols();
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218 |
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219 | res.storage.lda = mat.outerStride();
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220 | res.storage.values = mat.data();
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221 | }
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222 | };
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223 |
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224 | template<typename Derived>
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225 | struct SluMatrixMapHelper<SparseMatrixBase<Derived> >
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226 | {
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227 | typedef Derived MatrixType;
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228 | static void run(MatrixType& mat, SluMatrix& res)
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229 | {
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230 | if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
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231 | {
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232 | res.setStorageType(SLU_NR);
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233 | res.nrow = mat.cols();
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234 | res.ncol = mat.rows();
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235 | }
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236 | else
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237 | {
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238 | res.setStorageType(SLU_NC);
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239 | res.nrow = mat.rows();
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240 | res.ncol = mat.cols();
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241 | }
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242 |
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243 | res.Mtype = SLU_GE;
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244 |
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245 | res.storage.nnz = mat.nonZeros();
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246 | res.storage.values = mat.valuePtr();
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247 | res.storage.innerInd = mat.innerIndexPtr();
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248 | res.storage.outerInd = mat.outerIndexPtr();
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249 |
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250 | res.setScalarType<typename MatrixType::Scalar>();
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251 |
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252 | // FIXME the following is not very accurate
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253 | if (MatrixType::Flags & Upper)
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254 | res.Mtype = SLU_TRU;
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255 | if (MatrixType::Flags & Lower)
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256 | res.Mtype = SLU_TRL;
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257 |
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258 | eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
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259 | }
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260 | };
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261 |
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262 | namespace internal {
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263 |
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264 | template<typename MatrixType>
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265 | SluMatrix asSluMatrix(MatrixType& mat)
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266 | {
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267 | return SluMatrix::Map(mat);
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268 | }
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269 |
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270 | /** View a Super LU matrix as an Eigen expression */
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271 | template<typename Scalar, int Flags, typename Index>
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272 | MappedSparseMatrix<Scalar,Flags,Index> map_superlu(SluMatrix& sluMat)
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273 | {
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274 | eigen_assert((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR
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275 | || (Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC);
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276 |
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277 | Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow;
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278 |
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279 | return MappedSparseMatrix<Scalar,Flags,Index>(
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280 | sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize],
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281 | sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) );
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282 | }
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283 |
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284 | } // end namespace internal
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285 |
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286 | /** \ingroup SuperLUSupport_Module
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287 | * \class SuperLUBase
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288 | * \brief The base class for the direct and incomplete LU factorization of SuperLU
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289 | */
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290 | template<typename _MatrixType, typename Derived>
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291 | class SuperLUBase : internal::noncopyable
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292 | {
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293 | public:
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294 | typedef _MatrixType MatrixType;
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295 | typedef typename MatrixType::Scalar Scalar;
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296 | typedef typename MatrixType::RealScalar RealScalar;
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297 | typedef typename MatrixType::Index Index;
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298 | typedef Matrix<Scalar,Dynamic,1> Vector;
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299 | typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
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300 | typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
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301 | typedef SparseMatrix<Scalar> LUMatrixType;
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302 |
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303 | public:
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304 |
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305 | SuperLUBase() {}
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306 |
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307 | ~SuperLUBase()
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308 | {
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309 | clearFactors();
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310 | }
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311 |
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312 | Derived& derived() { return *static_cast<Derived*>(this); }
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313 | const Derived& derived() const { return *static_cast<const Derived*>(this); }
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314 |
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315 | inline Index rows() const { return m_matrix.rows(); }
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316 | inline Index cols() const { return m_matrix.cols(); }
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317 |
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318 | /** \returns a reference to the Super LU option object to configure the Super LU algorithms. */
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319 | inline superlu_options_t& options() { return m_sluOptions; }
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320 |
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321 | /** \brief Reports whether previous computation was successful.
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322 | *
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323 | * \returns \c Success if computation was succesful,
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324 | * \c NumericalIssue if the matrix.appears to be negative.
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325 | */
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326 | ComputationInfo info() const
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327 | {
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328 | eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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329 | return m_info;
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330 | }
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331 |
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332 | /** Computes the sparse Cholesky decomposition of \a matrix */
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333 | void compute(const MatrixType& matrix)
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334 | {
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335 | derived().analyzePattern(matrix);
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336 | derived().factorize(matrix);
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337 | }
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338 |
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339 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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340 | *
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341 | * \sa compute()
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342 | */
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343 | template<typename Rhs>
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344 | inline const internal::solve_retval<SuperLUBase, Rhs> solve(const MatrixBase<Rhs>& b) const
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345 | {
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346 | eigen_assert(m_isInitialized && "SuperLU is not initialized.");
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347 | eigen_assert(rows()==b.rows()
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348 | && "SuperLU::solve(): invalid number of rows of the right hand side matrix b");
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349 | return internal::solve_retval<SuperLUBase, Rhs>(*this, b.derived());
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350 | }
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351 |
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352 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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353 | *
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354 | * \sa compute()
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355 | */
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356 | template<typename Rhs>
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357 | inline const internal::sparse_solve_retval<SuperLUBase, Rhs> solve(const SparseMatrixBase<Rhs>& b) const
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358 | {
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359 | eigen_assert(m_isInitialized && "SuperLU is not initialized.");
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360 | eigen_assert(rows()==b.rows()
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361 | && "SuperLU::solve(): invalid number of rows of the right hand side matrix b");
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362 | return internal::sparse_solve_retval<SuperLUBase, Rhs>(*this, b.derived());
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363 | }
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364 |
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365 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
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366 | *
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367 | * This function is particularly useful when solving for several problems having the same structure.
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368 | *
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369 | * \sa factorize()
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370 | */
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371 | void analyzePattern(const MatrixType& /*matrix*/)
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372 | {
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373 | m_isInitialized = true;
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374 | m_info = Success;
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375 | m_analysisIsOk = true;
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376 | m_factorizationIsOk = false;
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377 | }
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378 |
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379 | template<typename Stream>
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380 | void dumpMemory(Stream& /*s*/)
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381 | {}
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382 |
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383 | protected:
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384 |
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385 | void initFactorization(const MatrixType& a)
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386 | {
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387 | set_default_options(&this->m_sluOptions);
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388 |
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389 | const int size = a.rows();
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390 | m_matrix = a;
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391 |
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392 | m_sluA = internal::asSluMatrix(m_matrix);
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393 | clearFactors();
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394 |
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395 | m_p.resize(size);
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396 | m_q.resize(size);
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397 | m_sluRscale.resize(size);
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398 | m_sluCscale.resize(size);
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399 | m_sluEtree.resize(size);
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400 |
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401 | // set empty B and X
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402 | m_sluB.setStorageType(SLU_DN);
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403 | m_sluB.setScalarType<Scalar>();
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404 | m_sluB.Mtype = SLU_GE;
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405 | m_sluB.storage.values = 0;
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406 | m_sluB.nrow = 0;
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407 | m_sluB.ncol = 0;
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408 | m_sluB.storage.lda = size;
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409 | m_sluX = m_sluB;
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410 |
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411 | m_extractedDataAreDirty = true;
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412 | }
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413 |
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414 | void init()
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415 | {
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416 | m_info = InvalidInput;
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417 | m_isInitialized = false;
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418 | m_sluL.Store = 0;
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419 | m_sluU.Store = 0;
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420 | }
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421 |
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422 | void extractData() const;
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423 |
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424 | void clearFactors()
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425 | {
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426 | if(m_sluL.Store)
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427 | Destroy_SuperNode_Matrix(&m_sluL);
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428 | if(m_sluU.Store)
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429 | Destroy_CompCol_Matrix(&m_sluU);
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430 |
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431 | m_sluL.Store = 0;
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432 | m_sluU.Store = 0;
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433 |
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434 | memset(&m_sluL,0,sizeof m_sluL);
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435 | memset(&m_sluU,0,sizeof m_sluU);
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436 | }
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437 |
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438 | // cached data to reduce reallocation, etc.
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439 | mutable LUMatrixType m_l;
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440 | mutable LUMatrixType m_u;
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441 | mutable IntColVectorType m_p;
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442 | mutable IntRowVectorType m_q;
|
---|
443 |
|
---|
444 | mutable LUMatrixType m_matrix; // copy of the factorized matrix
|
---|
445 | mutable SluMatrix m_sluA;
|
---|
446 | mutable SuperMatrix m_sluL, m_sluU;
|
---|
447 | mutable SluMatrix m_sluB, m_sluX;
|
---|
448 | mutable SuperLUStat_t m_sluStat;
|
---|
449 | mutable superlu_options_t m_sluOptions;
|
---|
450 | mutable std::vector<int> m_sluEtree;
|
---|
451 | mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale;
|
---|
452 | mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr;
|
---|
453 | mutable char m_sluEqued;
|
---|
454 |
|
---|
455 | mutable ComputationInfo m_info;
|
---|
456 | bool m_isInitialized;
|
---|
457 | int m_factorizationIsOk;
|
---|
458 | int m_analysisIsOk;
|
---|
459 | mutable bool m_extractedDataAreDirty;
|
---|
460 |
|
---|
461 | private:
|
---|
462 | SuperLUBase(SuperLUBase& ) { }
|
---|
463 | };
|
---|
464 |
|
---|
465 |
|
---|
466 | /** \ingroup SuperLUSupport_Module
|
---|
467 | * \class SuperLU
|
---|
468 | * \brief A sparse direct LU factorization and solver based on the SuperLU library
|
---|
469 | *
|
---|
470 | * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
|
---|
471 | * using the SuperLU library. The sparse matrix A must be squared and invertible. The vectors or matrices
|
---|
472 | * X and B can be either dense or sparse.
|
---|
473 | *
|
---|
474 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
475 | *
|
---|
476 | * \sa \ref TutorialSparseDirectSolvers
|
---|
477 | */
|
---|
478 | template<typename _MatrixType>
|
---|
479 | class SuperLU : public SuperLUBase<_MatrixType,SuperLU<_MatrixType> >
|
---|
480 | {
|
---|
481 | public:
|
---|
482 | typedef SuperLUBase<_MatrixType,SuperLU> Base;
|
---|
483 | typedef _MatrixType MatrixType;
|
---|
484 | typedef typename Base::Scalar Scalar;
|
---|
485 | typedef typename Base::RealScalar RealScalar;
|
---|
486 | typedef typename Base::Index Index;
|
---|
487 | typedef typename Base::IntRowVectorType IntRowVectorType;
|
---|
488 | typedef typename Base::IntColVectorType IntColVectorType;
|
---|
489 | typedef typename Base::LUMatrixType LUMatrixType;
|
---|
490 | typedef TriangularView<LUMatrixType, Lower|UnitDiag> LMatrixType;
|
---|
491 | typedef TriangularView<LUMatrixType, Upper> UMatrixType;
|
---|
492 |
|
---|
493 | public:
|
---|
494 |
|
---|
495 | SuperLU() : Base() { init(); }
|
---|
496 |
|
---|
497 | SuperLU(const MatrixType& matrix) : Base()
|
---|
498 | {
|
---|
499 | init();
|
---|
500 | Base::compute(matrix);
|
---|
501 | }
|
---|
502 |
|
---|
503 | ~SuperLU()
|
---|
504 | {
|
---|
505 | }
|
---|
506 |
|
---|
507 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
|
---|
508 | *
|
---|
509 | * This function is particularly useful when solving for several problems having the same structure.
|
---|
510 | *
|
---|
511 | * \sa factorize()
|
---|
512 | */
|
---|
513 | void analyzePattern(const MatrixType& matrix)
|
---|
514 | {
|
---|
515 | m_info = InvalidInput;
|
---|
516 | m_isInitialized = false;
|
---|
517 | Base::analyzePattern(matrix);
|
---|
518 | }
|
---|
519 |
|
---|
520 | /** Performs a numeric decomposition of \a matrix
|
---|
521 | *
|
---|
522 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
|
---|
523 | *
|
---|
524 | * \sa analyzePattern()
|
---|
525 | */
|
---|
526 | void factorize(const MatrixType& matrix);
|
---|
527 |
|
---|
528 | #ifndef EIGEN_PARSED_BY_DOXYGEN
|
---|
529 | /** \internal */
|
---|
530 | template<typename Rhs,typename Dest>
|
---|
531 | void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
|
---|
532 | #endif // EIGEN_PARSED_BY_DOXYGEN
|
---|
533 |
|
---|
534 | inline const LMatrixType& matrixL() const
|
---|
535 | {
|
---|
536 | if (m_extractedDataAreDirty) this->extractData();
|
---|
537 | return m_l;
|
---|
538 | }
|
---|
539 |
|
---|
540 | inline const UMatrixType& matrixU() const
|
---|
541 | {
|
---|
542 | if (m_extractedDataAreDirty) this->extractData();
|
---|
543 | return m_u;
|
---|
544 | }
|
---|
545 |
|
---|
546 | inline const IntColVectorType& permutationP() const
|
---|
547 | {
|
---|
548 | if (m_extractedDataAreDirty) this->extractData();
|
---|
549 | return m_p;
|
---|
550 | }
|
---|
551 |
|
---|
552 | inline const IntRowVectorType& permutationQ() const
|
---|
553 | {
|
---|
554 | if (m_extractedDataAreDirty) this->extractData();
|
---|
555 | return m_q;
|
---|
556 | }
|
---|
557 |
|
---|
558 | Scalar determinant() const;
|
---|
559 |
|
---|
560 | protected:
|
---|
561 |
|
---|
562 | using Base::m_matrix;
|
---|
563 | using Base::m_sluOptions;
|
---|
564 | using Base::m_sluA;
|
---|
565 | using Base::m_sluB;
|
---|
566 | using Base::m_sluX;
|
---|
567 | using Base::m_p;
|
---|
568 | using Base::m_q;
|
---|
569 | using Base::m_sluEtree;
|
---|
570 | using Base::m_sluEqued;
|
---|
571 | using Base::m_sluRscale;
|
---|
572 | using Base::m_sluCscale;
|
---|
573 | using Base::m_sluL;
|
---|
574 | using Base::m_sluU;
|
---|
575 | using Base::m_sluStat;
|
---|
576 | using Base::m_sluFerr;
|
---|
577 | using Base::m_sluBerr;
|
---|
578 | using Base::m_l;
|
---|
579 | using Base::m_u;
|
---|
580 |
|
---|
581 | using Base::m_analysisIsOk;
|
---|
582 | using Base::m_factorizationIsOk;
|
---|
583 | using Base::m_extractedDataAreDirty;
|
---|
584 | using Base::m_isInitialized;
|
---|
585 | using Base::m_info;
|
---|
586 |
|
---|
587 | void init()
|
---|
588 | {
|
---|
589 | Base::init();
|
---|
590 |
|
---|
591 | set_default_options(&this->m_sluOptions);
|
---|
592 | m_sluOptions.PrintStat = NO;
|
---|
593 | m_sluOptions.ConditionNumber = NO;
|
---|
594 | m_sluOptions.Trans = NOTRANS;
|
---|
595 | m_sluOptions.ColPerm = COLAMD;
|
---|
596 | }
|
---|
597 |
|
---|
598 |
|
---|
599 | private:
|
---|
600 | SuperLU(SuperLU& ) { }
|
---|
601 | };
|
---|
602 |
|
---|
603 | template<typename MatrixType>
|
---|
604 | void SuperLU<MatrixType>::factorize(const MatrixType& a)
|
---|
605 | {
|
---|
606 | eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
|
---|
607 | if(!m_analysisIsOk)
|
---|
608 | {
|
---|
609 | m_info = InvalidInput;
|
---|
610 | return;
|
---|
611 | }
|
---|
612 |
|
---|
613 | this->initFactorization(a);
|
---|
614 |
|
---|
615 | m_sluOptions.ColPerm = COLAMD;
|
---|
616 | int info = 0;
|
---|
617 | RealScalar recip_pivot_growth, rcond;
|
---|
618 | RealScalar ferr, berr;
|
---|
619 |
|
---|
620 | StatInit(&m_sluStat);
|
---|
621 | SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
|
---|
622 | &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
|
---|
623 | &m_sluL, &m_sluU,
|
---|
624 | NULL, 0,
|
---|
625 | &m_sluB, &m_sluX,
|
---|
626 | &recip_pivot_growth, &rcond,
|
---|
627 | &ferr, &berr,
|
---|
628 | &m_sluStat, &info, Scalar());
|
---|
629 | StatFree(&m_sluStat);
|
---|
630 |
|
---|
631 | m_extractedDataAreDirty = true;
|
---|
632 |
|
---|
633 | // FIXME how to better check for errors ???
|
---|
634 | m_info = info == 0 ? Success : NumericalIssue;
|
---|
635 | m_factorizationIsOk = true;
|
---|
636 | }
|
---|
637 |
|
---|
638 | template<typename MatrixType>
|
---|
639 | template<typename Rhs,typename Dest>
|
---|
640 | void SuperLU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
|
---|
641 | {
|
---|
642 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
|
---|
643 |
|
---|
644 | const int size = m_matrix.rows();
|
---|
645 | const int rhsCols = b.cols();
|
---|
646 | eigen_assert(size==b.rows());
|
---|
647 |
|
---|
648 | m_sluOptions.Trans = NOTRANS;
|
---|
649 | m_sluOptions.Fact = FACTORED;
|
---|
650 | m_sluOptions.IterRefine = NOREFINE;
|
---|
651 |
|
---|
652 |
|
---|
653 | m_sluFerr.resize(rhsCols);
|
---|
654 | m_sluBerr.resize(rhsCols);
|
---|
655 | m_sluB = SluMatrix::Map(b.const_cast_derived());
|
---|
656 | m_sluX = SluMatrix::Map(x.derived());
|
---|
657 |
|
---|
658 | typename Rhs::PlainObject b_cpy;
|
---|
659 | if(m_sluEqued!='N')
|
---|
660 | {
|
---|
661 | b_cpy = b;
|
---|
662 | m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
|
---|
663 | }
|
---|
664 |
|
---|
665 | StatInit(&m_sluStat);
|
---|
666 | int info = 0;
|
---|
667 | RealScalar recip_pivot_growth, rcond;
|
---|
668 | SuperLU_gssvx(&m_sluOptions, &m_sluA,
|
---|
669 | m_q.data(), m_p.data(),
|
---|
670 | &m_sluEtree[0], &m_sluEqued,
|
---|
671 | &m_sluRscale[0], &m_sluCscale[0],
|
---|
672 | &m_sluL, &m_sluU,
|
---|
673 | NULL, 0,
|
---|
674 | &m_sluB, &m_sluX,
|
---|
675 | &recip_pivot_growth, &rcond,
|
---|
676 | &m_sluFerr[0], &m_sluBerr[0],
|
---|
677 | &m_sluStat, &info, Scalar());
|
---|
678 | StatFree(&m_sluStat);
|
---|
679 | m_info = info==0 ? Success : NumericalIssue;
|
---|
680 | }
|
---|
681 |
|
---|
682 | // the code of this extractData() function has been adapted from the SuperLU's Matlab support code,
|
---|
683 | //
|
---|
684 | // Copyright (c) 1994 by Xerox Corporation. All rights reserved.
|
---|
685 | //
|
---|
686 | // THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
|
---|
687 | // EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
|
---|
688 | //
|
---|
689 | template<typename MatrixType, typename Derived>
|
---|
690 | void SuperLUBase<MatrixType,Derived>::extractData() const
|
---|
691 | {
|
---|
692 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()");
|
---|
693 | if (m_extractedDataAreDirty)
|
---|
694 | {
|
---|
695 | int upper;
|
---|
696 | int fsupc, istart, nsupr;
|
---|
697 | int lastl = 0, lastu = 0;
|
---|
698 | SCformat *Lstore = static_cast<SCformat*>(m_sluL.Store);
|
---|
699 | NCformat *Ustore = static_cast<NCformat*>(m_sluU.Store);
|
---|
700 | Scalar *SNptr;
|
---|
701 |
|
---|
702 | const int size = m_matrix.rows();
|
---|
703 | m_l.resize(size,size);
|
---|
704 | m_l.resizeNonZeros(Lstore->nnz);
|
---|
705 | m_u.resize(size,size);
|
---|
706 | m_u.resizeNonZeros(Ustore->nnz);
|
---|
707 |
|
---|
708 | int* Lcol = m_l.outerIndexPtr();
|
---|
709 | int* Lrow = m_l.innerIndexPtr();
|
---|
710 | Scalar* Lval = m_l.valuePtr();
|
---|
711 |
|
---|
712 | int* Ucol = m_u.outerIndexPtr();
|
---|
713 | int* Urow = m_u.innerIndexPtr();
|
---|
714 | Scalar* Uval = m_u.valuePtr();
|
---|
715 |
|
---|
716 | Ucol[0] = 0;
|
---|
717 | Ucol[0] = 0;
|
---|
718 |
|
---|
719 | /* for each supernode */
|
---|
720 | for (int k = 0; k <= Lstore->nsuper; ++k)
|
---|
721 | {
|
---|
722 | fsupc = L_FST_SUPC(k);
|
---|
723 | istart = L_SUB_START(fsupc);
|
---|
724 | nsupr = L_SUB_START(fsupc+1) - istart;
|
---|
725 | upper = 1;
|
---|
726 |
|
---|
727 | /* for each column in the supernode */
|
---|
728 | for (int j = fsupc; j < L_FST_SUPC(k+1); ++j)
|
---|
729 | {
|
---|
730 | SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)];
|
---|
731 |
|
---|
732 | /* Extract U */
|
---|
733 | for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i)
|
---|
734 | {
|
---|
735 | Uval[lastu] = ((Scalar*)Ustore->nzval)[i];
|
---|
736 | /* Matlab doesn't like explicit zero. */
|
---|
737 | if (Uval[lastu] != 0.0)
|
---|
738 | Urow[lastu++] = U_SUB(i);
|
---|
739 | }
|
---|
740 | for (int i = 0; i < upper; ++i)
|
---|
741 | {
|
---|
742 | /* upper triangle in the supernode */
|
---|
743 | Uval[lastu] = SNptr[i];
|
---|
744 | /* Matlab doesn't like explicit zero. */
|
---|
745 | if (Uval[lastu] != 0.0)
|
---|
746 | Urow[lastu++] = L_SUB(istart+i);
|
---|
747 | }
|
---|
748 | Ucol[j+1] = lastu;
|
---|
749 |
|
---|
750 | /* Extract L */
|
---|
751 | Lval[lastl] = 1.0; /* unit diagonal */
|
---|
752 | Lrow[lastl++] = L_SUB(istart + upper - 1);
|
---|
753 | for (int i = upper; i < nsupr; ++i)
|
---|
754 | {
|
---|
755 | Lval[lastl] = SNptr[i];
|
---|
756 | /* Matlab doesn't like explicit zero. */
|
---|
757 | if (Lval[lastl] != 0.0)
|
---|
758 | Lrow[lastl++] = L_SUB(istart+i);
|
---|
759 | }
|
---|
760 | Lcol[j+1] = lastl;
|
---|
761 |
|
---|
762 | ++upper;
|
---|
763 | } /* for j ... */
|
---|
764 |
|
---|
765 | } /* for k ... */
|
---|
766 |
|
---|
767 | // squeeze the matrices :
|
---|
768 | m_l.resizeNonZeros(lastl);
|
---|
769 | m_u.resizeNonZeros(lastu);
|
---|
770 |
|
---|
771 | m_extractedDataAreDirty = false;
|
---|
772 | }
|
---|
773 | }
|
---|
774 |
|
---|
775 | template<typename MatrixType>
|
---|
776 | typename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const
|
---|
777 | {
|
---|
778 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()");
|
---|
779 |
|
---|
780 | if (m_extractedDataAreDirty)
|
---|
781 | this->extractData();
|
---|
782 |
|
---|
783 | Scalar det = Scalar(1);
|
---|
784 | for (int j=0; j<m_u.cols(); ++j)
|
---|
785 | {
|
---|
786 | if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0)
|
---|
787 | {
|
---|
788 | int lastId = m_u.outerIndexPtr()[j+1]-1;
|
---|
789 | eigen_assert(m_u.innerIndexPtr()[lastId]<=j);
|
---|
790 | if (m_u.innerIndexPtr()[lastId]==j)
|
---|
791 | det *= m_u.valuePtr()[lastId];
|
---|
792 | }
|
---|
793 | }
|
---|
794 | if(m_sluEqued!='N')
|
---|
795 | return det/m_sluRscale.prod()/m_sluCscale.prod();
|
---|
796 | else
|
---|
797 | return det;
|
---|
798 | }
|
---|
799 |
|
---|
800 | #ifdef EIGEN_PARSED_BY_DOXYGEN
|
---|
801 | #define EIGEN_SUPERLU_HAS_ILU
|
---|
802 | #endif
|
---|
803 |
|
---|
804 | #ifdef EIGEN_SUPERLU_HAS_ILU
|
---|
805 |
|
---|
806 | /** \ingroup SuperLUSupport_Module
|
---|
807 | * \class SuperILU
|
---|
808 | * \brief A sparse direct \b incomplete LU factorization and solver based on the SuperLU library
|
---|
809 | *
|
---|
810 | * This class allows to solve for an approximate solution of A.X = B sparse linear problems via an incomplete LU factorization
|
---|
811 | * using the SuperLU library. This class is aimed to be used as a preconditioner of the iterative linear solvers.
|
---|
812 | *
|
---|
813 | * \warning This class requires SuperLU 4 or later.
|
---|
814 | *
|
---|
815 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
816 | *
|
---|
817 | * \sa \ref TutorialSparseDirectSolvers, class ConjugateGradient, class BiCGSTAB
|
---|
818 | */
|
---|
819 |
|
---|
820 | template<typename _MatrixType>
|
---|
821 | class SuperILU : public SuperLUBase<_MatrixType,SuperILU<_MatrixType> >
|
---|
822 | {
|
---|
823 | public:
|
---|
824 | typedef SuperLUBase<_MatrixType,SuperILU> Base;
|
---|
825 | typedef _MatrixType MatrixType;
|
---|
826 | typedef typename Base::Scalar Scalar;
|
---|
827 | typedef typename Base::RealScalar RealScalar;
|
---|
828 | typedef typename Base::Index Index;
|
---|
829 |
|
---|
830 | public:
|
---|
831 |
|
---|
832 | SuperILU() : Base() { init(); }
|
---|
833 |
|
---|
834 | SuperILU(const MatrixType& matrix) : Base()
|
---|
835 | {
|
---|
836 | init();
|
---|
837 | Base::compute(matrix);
|
---|
838 | }
|
---|
839 |
|
---|
840 | ~SuperILU()
|
---|
841 | {
|
---|
842 | }
|
---|
843 |
|
---|
844 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
|
---|
845 | *
|
---|
846 | * This function is particularly useful when solving for several problems having the same structure.
|
---|
847 | *
|
---|
848 | * \sa factorize()
|
---|
849 | */
|
---|
850 | void analyzePattern(const MatrixType& matrix)
|
---|
851 | {
|
---|
852 | Base::analyzePattern(matrix);
|
---|
853 | }
|
---|
854 |
|
---|
855 | /** Performs a numeric decomposition of \a matrix
|
---|
856 | *
|
---|
857 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
|
---|
858 | *
|
---|
859 | * \sa analyzePattern()
|
---|
860 | */
|
---|
861 | void factorize(const MatrixType& matrix);
|
---|
862 |
|
---|
863 | #ifndef EIGEN_PARSED_BY_DOXYGEN
|
---|
864 | /** \internal */
|
---|
865 | template<typename Rhs,typename Dest>
|
---|
866 | void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
|
---|
867 | #endif // EIGEN_PARSED_BY_DOXYGEN
|
---|
868 |
|
---|
869 | protected:
|
---|
870 |
|
---|
871 | using Base::m_matrix;
|
---|
872 | using Base::m_sluOptions;
|
---|
873 | using Base::m_sluA;
|
---|
874 | using Base::m_sluB;
|
---|
875 | using Base::m_sluX;
|
---|
876 | using Base::m_p;
|
---|
877 | using Base::m_q;
|
---|
878 | using Base::m_sluEtree;
|
---|
879 | using Base::m_sluEqued;
|
---|
880 | using Base::m_sluRscale;
|
---|
881 | using Base::m_sluCscale;
|
---|
882 | using Base::m_sluL;
|
---|
883 | using Base::m_sluU;
|
---|
884 | using Base::m_sluStat;
|
---|
885 | using Base::m_sluFerr;
|
---|
886 | using Base::m_sluBerr;
|
---|
887 | using Base::m_l;
|
---|
888 | using Base::m_u;
|
---|
889 |
|
---|
890 | using Base::m_analysisIsOk;
|
---|
891 | using Base::m_factorizationIsOk;
|
---|
892 | using Base::m_extractedDataAreDirty;
|
---|
893 | using Base::m_isInitialized;
|
---|
894 | using Base::m_info;
|
---|
895 |
|
---|
896 | void init()
|
---|
897 | {
|
---|
898 | Base::init();
|
---|
899 |
|
---|
900 | ilu_set_default_options(&m_sluOptions);
|
---|
901 | m_sluOptions.PrintStat = NO;
|
---|
902 | m_sluOptions.ConditionNumber = NO;
|
---|
903 | m_sluOptions.Trans = NOTRANS;
|
---|
904 | m_sluOptions.ColPerm = MMD_AT_PLUS_A;
|
---|
905 |
|
---|
906 | // no attempt to preserve column sum
|
---|
907 | m_sluOptions.ILU_MILU = SILU;
|
---|
908 | // only basic ILU(k) support -- no direct control over memory consumption
|
---|
909 | // better to use ILU_DropRule = DROP_BASIC | DROP_AREA
|
---|
910 | // and set ILU_FillFactor to max memory growth
|
---|
911 | m_sluOptions.ILU_DropRule = DROP_BASIC;
|
---|
912 | m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10;
|
---|
913 | }
|
---|
914 |
|
---|
915 | private:
|
---|
916 | SuperILU(SuperILU& ) { }
|
---|
917 | };
|
---|
918 |
|
---|
919 | template<typename MatrixType>
|
---|
920 | void SuperILU<MatrixType>::factorize(const MatrixType& a)
|
---|
921 | {
|
---|
922 | eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
|
---|
923 | if(!m_analysisIsOk)
|
---|
924 | {
|
---|
925 | m_info = InvalidInput;
|
---|
926 | return;
|
---|
927 | }
|
---|
928 |
|
---|
929 | this->initFactorization(a);
|
---|
930 |
|
---|
931 | int info = 0;
|
---|
932 | RealScalar recip_pivot_growth, rcond;
|
---|
933 |
|
---|
934 | StatInit(&m_sluStat);
|
---|
935 | SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
|
---|
936 | &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
|
---|
937 | &m_sluL, &m_sluU,
|
---|
938 | NULL, 0,
|
---|
939 | &m_sluB, &m_sluX,
|
---|
940 | &recip_pivot_growth, &rcond,
|
---|
941 | &m_sluStat, &info, Scalar());
|
---|
942 | StatFree(&m_sluStat);
|
---|
943 |
|
---|
944 | // FIXME how to better check for errors ???
|
---|
945 | m_info = info == 0 ? Success : NumericalIssue;
|
---|
946 | m_factorizationIsOk = true;
|
---|
947 | }
|
---|
948 |
|
---|
949 | template<typename MatrixType>
|
---|
950 | template<typename Rhs,typename Dest>
|
---|
951 | void SuperILU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
|
---|
952 | {
|
---|
953 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
|
---|
954 |
|
---|
955 | const int size = m_matrix.rows();
|
---|
956 | const int rhsCols = b.cols();
|
---|
957 | eigen_assert(size==b.rows());
|
---|
958 |
|
---|
959 | m_sluOptions.Trans = NOTRANS;
|
---|
960 | m_sluOptions.Fact = FACTORED;
|
---|
961 | m_sluOptions.IterRefine = NOREFINE;
|
---|
962 |
|
---|
963 | m_sluFerr.resize(rhsCols);
|
---|
964 | m_sluBerr.resize(rhsCols);
|
---|
965 | m_sluB = SluMatrix::Map(b.const_cast_derived());
|
---|
966 | m_sluX = SluMatrix::Map(x.derived());
|
---|
967 |
|
---|
968 | typename Rhs::PlainObject b_cpy;
|
---|
969 | if(m_sluEqued!='N')
|
---|
970 | {
|
---|
971 | b_cpy = b;
|
---|
972 | m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
|
---|
973 | }
|
---|
974 |
|
---|
975 | int info = 0;
|
---|
976 | RealScalar recip_pivot_growth, rcond;
|
---|
977 |
|
---|
978 | StatInit(&m_sluStat);
|
---|
979 | SuperLU_gsisx(&m_sluOptions, &m_sluA,
|
---|
980 | m_q.data(), m_p.data(),
|
---|
981 | &m_sluEtree[0], &m_sluEqued,
|
---|
982 | &m_sluRscale[0], &m_sluCscale[0],
|
---|
983 | &m_sluL, &m_sluU,
|
---|
984 | NULL, 0,
|
---|
985 | &m_sluB, &m_sluX,
|
---|
986 | &recip_pivot_growth, &rcond,
|
---|
987 | &m_sluStat, &info, Scalar());
|
---|
988 | StatFree(&m_sluStat);
|
---|
989 |
|
---|
990 | m_info = info==0 ? Success : NumericalIssue;
|
---|
991 | }
|
---|
992 | #endif
|
---|
993 |
|
---|
994 | namespace internal {
|
---|
995 |
|
---|
996 | template<typename _MatrixType, typename Derived, typename Rhs>
|
---|
997 | struct solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs>
|
---|
998 | : solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs>
|
---|
999 | {
|
---|
1000 | typedef SuperLUBase<_MatrixType,Derived> Dec;
|
---|
1001 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
|
---|
1002 |
|
---|
1003 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
1004 | {
|
---|
1005 | dec().derived()._solve(rhs(),dst);
|
---|
1006 | }
|
---|
1007 | };
|
---|
1008 |
|
---|
1009 | template<typename _MatrixType, typename Derived, typename Rhs>
|
---|
1010 | struct sparse_solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs>
|
---|
1011 | : sparse_solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs>
|
---|
1012 | {
|
---|
1013 | typedef SuperLUBase<_MatrixType,Derived> Dec;
|
---|
1014 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
|
---|
1015 |
|
---|
1016 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
1017 | {
|
---|
1018 | this->defaultEvalTo(dst);
|
---|
1019 | }
|
---|
1020 | };
|
---|
1021 |
|
---|
1022 | } // end namespace internal
|
---|
1023 |
|
---|
1024 | } // end namespace Eigen
|
---|
1025 |
|
---|
1026 | #endif // EIGEN_SUPERLUSUPPORT_H
|
---|