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1 /* |
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2 |
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3 Copyright (C) 2004 David Bateman |
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4 Copyright (C) 1998-2004 Andy Adler |
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5 |
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6 Octave is free software; you can redistribute it and/or modify it |
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7 under the terms of the GNU General Public License as published by the |
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8 Free Software Foundation; either version 2, or (at your option) any |
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9 later version. |
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10 |
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11 Octave is distributed in the hope that it will be useful, but WITHOUT |
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 for more details. |
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15 |
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16 You should have received a copy of the GNU General Public License |
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17 along with this program; see the file COPYING. If not, write to the |
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18 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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19 Boston, MA 02110-1301, USA. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include <cfloat> |
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28 |
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29 #include <iostream> |
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30 #include <vector> |
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31 |
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32 #include "quit.h" |
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33 #include "lo-ieee.h" |
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34 #include "lo-mappers.h" |
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35 #include "f77-fcn.h" |
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36 #include "dRowVector.h" |
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37 |
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38 #include "CSparse.h" |
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39 #include "boolSparse.h" |
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40 #include "dSparse.h" |
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41 #include "oct-spparms.h" |
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42 #include "SparsedbleLU.h" |
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43 #include "MatrixType.h" |
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44 #include "oct-sparse.h" |
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45 #include "sparse-util.h" |
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46 #include "SparsedbleCHOL.h" |
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5610
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47 #include "SparseQR.h" |
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48 |
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5587
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49 #include "oct-sort.h" |
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50 |
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51 // Define whether to use a basic QR solver or one that uses a Dulmange |
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52 // Mendelsohn factorization to seperate the problem into under-determined, |
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53 // well-determined and over-determined parts and solves them seperately |
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54 #ifndef USE_QRSOLVE |
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55 #include "sparse-dmsolve.cc" |
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56 #endif |
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57 |
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58 // Fortran functions we call. |
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59 extern "C" |
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60 { |
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61 F77_RET_T |
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62 F77_FUNC (dgbtrf, DGBTRF) (const octave_idx_type&, const octave_idx_type&, |
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63 const octave_idx_type&, const octave_idx_type&, |
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64 double*, const octave_idx_type&, |
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65 octave_idx_type*, octave_idx_type&); |
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66 |
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67 F77_RET_T |
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68 F77_FUNC (dgbtrs, DGBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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69 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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70 const double*, const octave_idx_type&, |
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71 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& |
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72 F77_CHAR_ARG_LEN_DECL); |
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73 |
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74 F77_RET_T |
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75 F77_FUNC (dgbcon, DGBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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76 const octave_idx_type&, const octave_idx_type&, double*, |
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77 const octave_idx_type&, const octave_idx_type*, const double&, |
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78 double&, double*, octave_idx_type*, octave_idx_type& |
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79 F77_CHAR_ARG_LEN_DECL); |
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80 |
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81 F77_RET_T |
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82 F77_FUNC (dpbtrf, DPBTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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83 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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84 F77_CHAR_ARG_LEN_DECL); |
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85 |
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86 F77_RET_T |
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87 F77_FUNC (dpbtrs, DPBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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88 const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
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89 double*, const octave_idx_type&, octave_idx_type& |
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90 F77_CHAR_ARG_LEN_DECL); |
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91 |
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92 F77_RET_T |
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93 F77_FUNC (dpbcon, DPBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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94 const octave_idx_type&, double*, const octave_idx_type&, |
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95 const double&, double&, double*, octave_idx_type*, octave_idx_type& |
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96 F77_CHAR_ARG_LEN_DECL); |
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97 F77_RET_T |
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98 F77_FUNC (dptsv, DPTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*, |
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99 double*, const octave_idx_type&, octave_idx_type&); |
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100 |
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101 F77_RET_T |
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102 F77_FUNC (dgtsv, DGTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*, |
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103 double*, double*, const octave_idx_type&, octave_idx_type&); |
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104 |
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105 F77_RET_T |
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106 F77_FUNC (dgttrf, DGTTRF) (const octave_idx_type&, double*, double*, double*, double*, |
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107 octave_idx_type*, octave_idx_type&); |
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108 |
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109 F77_RET_T |
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110 F77_FUNC (dgttrs, DGTTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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111 const octave_idx_type&, const double*, const double*, |
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112 const double*, const double*, const octave_idx_type*, |
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113 double *, const octave_idx_type&, octave_idx_type& |
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114 F77_CHAR_ARG_LEN_DECL); |
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115 |
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116 F77_RET_T |
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117 F77_FUNC (zptsv, ZPTSV) (const octave_idx_type&, const octave_idx_type&, double*, Complex*, |
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118 Complex*, const octave_idx_type&, octave_idx_type&); |
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119 |
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120 F77_RET_T |
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121 F77_FUNC (zgtsv, ZGTSV) (const octave_idx_type&, const octave_idx_type&, Complex*, Complex*, |
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122 Complex*, Complex*, const octave_idx_type&, octave_idx_type&); |
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123 |
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124 } |
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125 |
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126 SparseMatrix::SparseMatrix (const SparseBoolMatrix &a) |
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127 : MSparse<double> (a.rows (), a.cols (), a.nnz ()) |
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128 { |
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129 octave_idx_type nc = cols (); |
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130 octave_idx_type nz = a.nnz (); |
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131 |
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132 for (octave_idx_type i = 0; i < nc + 1; i++) |
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133 cidx (i) = a.cidx (i); |
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134 |
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135 for (octave_idx_type i = 0; i < nz; i++) |
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136 { |
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137 data (i) = a.data (i); |
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138 ridx (i) = a.ridx (i); |
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139 } |
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140 } |
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141 |
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142 bool |
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143 SparseMatrix::operator == (const SparseMatrix& a) const |
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144 { |
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145 octave_idx_type nr = rows (); |
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146 octave_idx_type nc = cols (); |
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147 octave_idx_type nz = nnz (); |
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148 octave_idx_type nr_a = a.rows (); |
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149 octave_idx_type nc_a = a.cols (); |
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150 octave_idx_type nz_a = a.nnz (); |
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151 |
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152 if (nr != nr_a || nc != nc_a || nz != nz_a) |
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153 return false; |
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154 |
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155 for (octave_idx_type i = 0; i < nc + 1; i++) |
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156 if (cidx(i) != a.cidx(i)) |
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157 return false; |
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158 |
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159 for (octave_idx_type i = 0; i < nz; i++) |
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160 if (data(i) != a.data(i) || ridx(i) != a.ridx(i)) |
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161 return false; |
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162 |
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163 return true; |
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164 } |
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165 |
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166 bool |
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167 SparseMatrix::operator != (const SparseMatrix& a) const |
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168 { |
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169 return !(*this == a); |
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170 } |
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171 |
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172 bool |
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173 SparseMatrix::is_symmetric (void) const |
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174 { |
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175 octave_idx_type nr = rows (); |
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176 octave_idx_type nc = cols (); |
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177 |
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178 if (nr == nc && nr > 0) |
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179 { |
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180 for (octave_idx_type j = 0; j < nc; j++) |
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181 { |
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182 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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183 { |
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184 octave_idx_type ri = ridx(i); |
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185 |
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186 if (ri != j) |
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187 { |
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188 bool found = false; |
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189 |
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190 for (octave_idx_type k = cidx(ri); k < cidx(ri+1); k++) |
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191 { |
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192 if (ridx(k) == j) |
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193 { |
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194 if (data(i) == data(k)) |
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195 found = true; |
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196 break; |
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197 } |
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198 } |
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199 |
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200 if (! found) |
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201 return false; |
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202 } |
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203 } |
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204 } |
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205 |
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206 return true; |
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207 } |
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208 |
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209 return false; |
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210 } |
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211 |
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212 SparseMatrix& |
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213 SparseMatrix::insert (const SparseMatrix& a, octave_idx_type r, octave_idx_type c) |
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214 { |
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215 MSparse<double>::insert (a, r, c); |
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216 return *this; |
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217 } |
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218 |
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219 SparseMatrix& |
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220 SparseMatrix::insert (const SparseMatrix& a, const Array<octave_idx_type>& indx) |
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221 { |
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222 MSparse<double>::insert (a, indx); |
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223 return *this; |
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224 } |
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225 |
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226 SparseMatrix |
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227 SparseMatrix::max (int dim) const |
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228 { |
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229 Array2<octave_idx_type> dummy_idx; |
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230 return max (dummy_idx, dim); |
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231 } |
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232 |
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233 SparseMatrix |
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234 SparseMatrix::max (Array2<octave_idx_type>& idx_arg, int dim) const |
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235 { |
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236 SparseMatrix result; |
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237 dim_vector dv = dims (); |
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238 |
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239 if (dv.numel () == 0 || dim > dv.length () || dim < 0) |
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240 return result; |
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241 |
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242 octave_idx_type nr = dv(0); |
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243 octave_idx_type nc = dv(1); |
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244 |
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245 if (dim == 0) |
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246 { |
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247 idx_arg.resize (1, nc); |
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248 octave_idx_type nel = 0; |
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249 for (octave_idx_type j = 0; j < nc; j++) |
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250 { |
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251 double tmp_max = octave_NaN; |
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252 octave_idx_type idx_j = 0; |
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253 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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254 { |
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255 if (ridx(i) != idx_j) |
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256 break; |
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257 else |
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258 idx_j++; |
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259 } |
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260 |
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261 if (idx_j != nr) |
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262 tmp_max = 0.; |
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263 |
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264 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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265 { |
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266 double tmp = data (i); |
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267 |
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268 if (xisnan (tmp)) |
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269 continue; |
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270 else if (xisnan (tmp_max) || tmp > tmp_max) |
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271 { |
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272 idx_j = ridx (i); |
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273 tmp_max = tmp; |
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274 } |
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275 |
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276 } |
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277 |
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278 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_j; |
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279 if (tmp_max != 0.) |
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280 nel++; |
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281 } |
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282 |
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283 result = SparseMatrix (1, nc, nel); |
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284 |
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285 octave_idx_type ii = 0; |
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286 result.xcidx (0) = 0; |
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287 for (octave_idx_type j = 0; j < nc; j++) |
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288 { |
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289 double tmp = elem (idx_arg(j), j); |
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290 if (tmp != 0.) |
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291 { |
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292 result.xdata (ii) = tmp; |
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293 result.xridx (ii++) = 0; |
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294 } |
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295 result.xcidx (j+1) = ii; |
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296 |
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297 } |
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298 } |
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299 else |
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300 { |
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301 idx_arg.resize (nr, 1, 0); |
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302 |
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303 for (octave_idx_type i = cidx(0); i < cidx(1); i++) |
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304 idx_arg.elem(ridx(i)) = -1; |
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305 |
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306 for (octave_idx_type j = 0; j < nc; j++) |
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307 for (octave_idx_type i = 0; i < nr; i++) |
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308 { |
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309 if (idx_arg.elem(i) != -1) |
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310 continue; |
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311 bool found = false; |
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312 for (octave_idx_type k = cidx(j); k < cidx(j+1); k++) |
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313 if (ridx(k) == i) |
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314 { |
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315 found = true; |
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316 break; |
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317 } |
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318 |
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319 if (!found) |
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320 idx_arg.elem(i) = j; |
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321 |
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322 } |
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323 |
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324 for (octave_idx_type j = 0; j < nc; j++) |
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325 { |
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326 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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327 { |
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328 octave_idx_type ir = ridx (i); |
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329 octave_idx_type ix = idx_arg.elem (ir); |
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330 double tmp = data (i); |
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331 |
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332 if (xisnan (tmp)) |
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333 continue; |
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334 else if (ix == -1 || tmp > elem (ir, ix)) |
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335 idx_arg.elem (ir) = j; |
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336 } |
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337 } |
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338 |
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339 octave_idx_type nel = 0; |
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340 for (octave_idx_type j = 0; j < nr; j++) |
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341 if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.) |
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342 nel++; |
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343 |
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344 result = SparseMatrix (nr, 1, nel); |
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345 |
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346 octave_idx_type ii = 0; |
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347 result.xcidx (0) = 0; |
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348 result.xcidx (1) = nel; |
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349 for (octave_idx_type j = 0; j < nr; j++) |
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350 { |
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351 if (idx_arg(j) == -1) |
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352 { |
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353 idx_arg(j) = 0; |
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354 result.xdata (ii) = octave_NaN; |
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355 result.xridx (ii++) = j; |
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356 } |
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357 else |
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358 { |
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359 double tmp = elem (j, idx_arg(j)); |
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360 if (tmp != 0.) |
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361 { |
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362 result.xdata (ii) = tmp; |
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363 result.xridx (ii++) = j; |
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364 } |
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365 } |
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366 } |
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367 } |
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368 |
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369 return result; |
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370 } |
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371 |
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372 SparseMatrix |
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373 SparseMatrix::min (int dim) const |
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374 { |
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375 Array2<octave_idx_type> dummy_idx; |
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376 return min (dummy_idx, dim); |
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377 } |
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378 |
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379 SparseMatrix |
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380 SparseMatrix::min (Array2<octave_idx_type>& idx_arg, int dim) const |
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381 { |
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382 SparseMatrix result; |
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383 dim_vector dv = dims (); |
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384 |
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385 if (dv.numel () == 0 || dim > dv.length () || dim < 0) |
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386 return result; |
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387 |
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388 octave_idx_type nr = dv(0); |
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389 octave_idx_type nc = dv(1); |
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390 |
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391 if (dim == 0) |
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392 { |
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393 idx_arg.resize (1, nc); |
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394 octave_idx_type nel = 0; |
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395 for (octave_idx_type j = 0; j < nc; j++) |
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396 { |
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397 double tmp_min = octave_NaN; |
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398 octave_idx_type idx_j = 0; |
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399 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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400 { |
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401 if (ridx(i) != idx_j) |
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402 break; |
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403 else |
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404 idx_j++; |
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405 } |
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406 |
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407 if (idx_j != nr) |
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408 tmp_min = 0.; |
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409 |
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410 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
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411 { |
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412 double tmp = data (i); |
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413 |
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5389
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414 if (xisnan (tmp)) |
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5164
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415 continue; |
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416 else if (xisnan (tmp_min) || tmp < tmp_min) |
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5164
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417 { |
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418 idx_j = ridx (i); |
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419 tmp_min = tmp; |
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420 } |
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421 |
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422 } |
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423 |
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5389
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424 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_j; |
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5164
|
425 if (tmp_min != 0.) |
|
|
426 nel++; |
|
|
427 } |
|
|
428 |
|
|
429 result = SparseMatrix (1, nc, nel); |
|
|
430 |
|
5275
|
431 octave_idx_type ii = 0; |
|
5164
|
432 result.xcidx (0) = 0; |
|
5275
|
433 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
434 { |
|
|
435 double tmp = elem (idx_arg(j), j); |
|
|
436 if (tmp != 0.) |
|
|
437 { |
|
|
438 result.xdata (ii) = tmp; |
|
|
439 result.xridx (ii++) = 0; |
|
|
440 } |
|
|
441 result.xcidx (j+1) = ii; |
|
|
442 |
|
|
443 } |
|
|
444 } |
|
|
445 else |
|
|
446 { |
|
|
447 idx_arg.resize (nr, 1, 0); |
|
|
448 |
|
5275
|
449 for (octave_idx_type i = cidx(0); i < cidx(1); i++) |
|
5164
|
450 idx_arg.elem(ridx(i)) = -1; |
|
|
451 |
|
5275
|
452 for (octave_idx_type j = 0; j < nc; j++) |
|
|
453 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
454 { |
|
|
455 if (idx_arg.elem(i) != -1) |
|
|
456 continue; |
|
|
457 bool found = false; |
|
5275
|
458 for (octave_idx_type k = cidx(j); k < cidx(j+1); k++) |
|
5164
|
459 if (ridx(k) == i) |
|
|
460 { |
|
|
461 found = true; |
|
|
462 break; |
|
|
463 } |
|
|
464 |
|
|
465 if (!found) |
|
|
466 idx_arg.elem(i) = j; |
|
|
467 |
|
|
468 } |
|
|
469 |
|
5275
|
470 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
471 { |
|
5275
|
472 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
473 { |
|
5275
|
474 octave_idx_type ir = ridx (i); |
|
|
475 octave_idx_type ix = idx_arg.elem (ir); |
|
5164
|
476 double tmp = data (i); |
|
|
477 |
|
5389
|
478 if (xisnan (tmp)) |
|
5164
|
479 continue; |
|
|
480 else if (ix == -1 || tmp < elem (ir, ix)) |
|
|
481 idx_arg.elem (ir) = j; |
|
|
482 } |
|
|
483 } |
|
|
484 |
|
5275
|
485 octave_idx_type nel = 0; |
|
|
486 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
487 if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.) |
|
|
488 nel++; |
|
|
489 |
|
|
490 result = SparseMatrix (nr, 1, nel); |
|
|
491 |
|
5275
|
492 octave_idx_type ii = 0; |
|
5164
|
493 result.xcidx (0) = 0; |
|
|
494 result.xcidx (1) = nel; |
|
5275
|
495 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
496 { |
|
|
497 if (idx_arg(j) == -1) |
|
|
498 { |
|
|
499 idx_arg(j) = 0; |
|
|
500 result.xdata (ii) = octave_NaN; |
|
|
501 result.xridx (ii++) = j; |
|
|
502 } |
|
|
503 else |
|
|
504 { |
|
|
505 double tmp = elem (j, idx_arg(j)); |
|
|
506 if (tmp != 0.) |
|
|
507 { |
|
|
508 result.xdata (ii) = tmp; |
|
|
509 result.xridx (ii++) = j; |
|
|
510 } |
|
|
511 } |
|
|
512 } |
|
|
513 } |
|
|
514 |
|
|
515 return result; |
|
|
516 } |
|
|
517 |
|
|
518 SparseMatrix |
|
5275
|
519 SparseMatrix::concat (const SparseMatrix& rb, const Array<octave_idx_type>& ra_idx) |
|
5164
|
520 { |
|
|
521 // Don't use numel to avoid all possiblity of an overflow |
|
|
522 if (rb.rows () > 0 && rb.cols () > 0) |
|
|
523 insert (rb, ra_idx(0), ra_idx(1)); |
|
|
524 return *this; |
|
|
525 } |
|
|
526 |
|
|
527 SparseComplexMatrix |
|
5275
|
528 SparseMatrix::concat (const SparseComplexMatrix& rb, const Array<octave_idx_type>& ra_idx) |
|
5164
|
529 { |
|
|
530 SparseComplexMatrix retval (*this); |
|
|
531 if (rb.rows () > 0 && rb.cols () > 0) |
|
|
532 retval.insert (rb, ra_idx(0), ra_idx(1)); |
|
|
533 return retval; |
|
|
534 } |
|
|
535 |
|
|
536 SparseMatrix |
|
|
537 real (const SparseComplexMatrix& a) |
|
|
538 { |
|
5275
|
539 octave_idx_type nr = a.rows (); |
|
|
540 octave_idx_type nc = a.cols (); |
|
5681
|
541 octave_idx_type nz = a.nnz (); |
|
5164
|
542 SparseMatrix r (nr, nc, nz); |
|
|
543 |
|
5275
|
544 for (octave_idx_type i = 0; i < nc +1; i++) |
|
5164
|
545 r.cidx(i) = a.cidx(i); |
|
|
546 |
|
5275
|
547 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
548 { |
|
5261
|
549 r.data(i) = std::real (a.data(i)); |
|
5164
|
550 r.ridx(i) = a.ridx(i); |
|
|
551 } |
|
|
552 |
|
|
553 return r; |
|
|
554 } |
|
|
555 |
|
|
556 SparseMatrix |
|
|
557 imag (const SparseComplexMatrix& a) |
|
|
558 { |
|
5275
|
559 octave_idx_type nr = a.rows (); |
|
|
560 octave_idx_type nc = a.cols (); |
|
5681
|
561 octave_idx_type nz = a.nnz (); |
|
5164
|
562 SparseMatrix r (nr, nc, nz); |
|
|
563 |
|
5275
|
564 for (octave_idx_type i = 0; i < nc +1; i++) |
|
5164
|
565 r.cidx(i) = a.cidx(i); |
|
|
566 |
|
5275
|
567 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
568 { |
|
5261
|
569 r.data(i) = std::imag (a.data(i)); |
|
5164
|
570 r.ridx(i) = a.ridx(i); |
|
|
571 } |
|
|
572 |
|
|
573 return r; |
|
|
574 } |
|
|
575 |
|
|
576 SparseMatrix |
|
|
577 atan2 (const double& x, const SparseMatrix& y) |
|
|
578 { |
|
5275
|
579 octave_idx_type nr = y.rows (); |
|
|
580 octave_idx_type nc = y.cols (); |
|
5164
|
581 |
|
|
582 if (x == 0.) |
|
|
583 return SparseMatrix (nr, nc); |
|
|
584 else |
|
|
585 { |
|
|
586 // Its going to be basically full, so this is probably the |
|
|
587 // best way to handle it. |
|
|
588 Matrix tmp (nr, nc, atan2 (x, 0.)); |
|
|
589 |
|
5275
|
590 for (octave_idx_type j = 0; j < nc; j++) |
|
|
591 for (octave_idx_type i = y.cidx (j); i < y.cidx (j+1); i++) |
|
5164
|
592 tmp.elem (y.ridx(i), j) = atan2 (x, y.data(i)); |
|
|
593 |
|
|
594 return SparseMatrix (tmp); |
|
|
595 } |
|
|
596 } |
|
|
597 |
|
|
598 SparseMatrix |
|
|
599 atan2 (const SparseMatrix& x, const double& y) |
|
|
600 { |
|
5275
|
601 octave_idx_type nr = x.rows (); |
|
|
602 octave_idx_type nc = x.cols (); |
|
5681
|
603 octave_idx_type nz = x.nnz (); |
|
5164
|
604 |
|
|
605 SparseMatrix retval (nr, nc, nz); |
|
|
606 |
|
5275
|
607 octave_idx_type ii = 0; |
|
5164
|
608 retval.xcidx(0) = 0; |
|
5275
|
609 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
610 { |
|
5275
|
611 for (octave_idx_type j = x.cidx(i); j < x.cidx(i+1); j++) |
|
5164
|
612 { |
|
|
613 double tmp = atan2 (x.data(j), y); |
|
|
614 if (tmp != 0.) |
|
|
615 { |
|
|
616 retval.xdata (ii) = tmp; |
|
|
617 retval.xridx (ii++) = x.ridx (j); |
|
|
618 } |
|
|
619 } |
|
|
620 retval.xcidx (i+1) = ii; |
|
|
621 } |
|
|
622 |
|
|
623 if (ii != nz) |
|
|
624 { |
|
|
625 SparseMatrix retval2 (nr, nc, ii); |
|
5275
|
626 for (octave_idx_type i = 0; i < nc+1; i++) |
|
5164
|
627 retval2.xcidx (i) = retval.cidx (i); |
|
5275
|
628 for (octave_idx_type i = 0; i < ii; i++) |
|
5164
|
629 { |
|
|
630 retval2.xdata (i) = retval.data (i); |
|
|
631 retval2.xridx (i) = retval.ridx (i); |
|
|
632 } |
|
|
633 return retval2; |
|
|
634 } |
|
|
635 else |
|
|
636 return retval; |
|
|
637 } |
|
|
638 |
|
|
639 SparseMatrix |
|
|
640 atan2 (const SparseMatrix& x, const SparseMatrix& y) |
|
|
641 { |
|
|
642 SparseMatrix r; |
|
|
643 |
|
|
644 if ((x.rows() == y.rows()) && (x.cols() == y.cols())) |
|
|
645 { |
|
5275
|
646 octave_idx_type x_nr = x.rows (); |
|
|
647 octave_idx_type x_nc = x.cols (); |
|
|
648 |
|
|
649 octave_idx_type y_nr = y.rows (); |
|
|
650 octave_idx_type y_nc = y.cols (); |
|
5164
|
651 |
|
|
652 if (x_nr != y_nr || x_nc != y_nc) |
|
|
653 gripe_nonconformant ("atan2", x_nr, x_nc, y_nr, y_nc); |
|
|
654 else |
|
|
655 { |
|
5681
|
656 r = SparseMatrix (x_nr, x_nc, (x.nnz () + y.nnz ())); |
|
5164
|
657 |
|
5275
|
658 octave_idx_type jx = 0; |
|
5164
|
659 r.cidx (0) = 0; |
|
5275
|
660 for (octave_idx_type i = 0 ; i < x_nc ; i++) |
|
5164
|
661 { |
|
5275
|
662 octave_idx_type ja = x.cidx(i); |
|
|
663 octave_idx_type ja_max = x.cidx(i+1); |
|
5164
|
664 bool ja_lt_max= ja < ja_max; |
|
|
665 |
|
5275
|
666 octave_idx_type jb = y.cidx(i); |
|
|
667 octave_idx_type jb_max = y.cidx(i+1); |
|
5164
|
668 bool jb_lt_max = jb < jb_max; |
|
|
669 |
|
|
670 while (ja_lt_max || jb_lt_max ) |
|
|
671 { |
|
|
672 OCTAVE_QUIT; |
|
|
673 if ((! jb_lt_max) || |
|
|
674 (ja_lt_max && (x.ridx(ja) < y.ridx(jb)))) |
|
|
675 { |
|
|
676 r.ridx(jx) = x.ridx(ja); |
|
|
677 r.data(jx) = atan2 (x.data(ja), 0.); |
|
|
678 jx++; |
|
|
679 ja++; |
|
|
680 ja_lt_max= ja < ja_max; |
|
|
681 } |
|
|
682 else if (( !ja_lt_max ) || |
|
|
683 (jb_lt_max && (y.ridx(jb) < x.ridx(ja)) ) ) |
|
|
684 { |
|
|
685 jb++; |
|
|
686 jb_lt_max= jb < jb_max; |
|
|
687 } |
|
|
688 else |
|
|
689 { |
|
|
690 double tmp = atan2 (x.data(ja), y.data(jb)); |
|
|
691 if (tmp != 0.) |
|
|
692 { |
|
|
693 r.data(jx) = tmp; |
|
|
694 r.ridx(jx) = x.ridx(ja); |
|
|
695 jx++; |
|
|
696 } |
|
|
697 ja++; |
|
|
698 ja_lt_max= ja < ja_max; |
|
|
699 jb++; |
|
|
700 jb_lt_max= jb < jb_max; |
|
|
701 } |
|
|
702 } |
|
|
703 r.cidx(i+1) = jx; |
|
|
704 } |
|
|
705 |
|
|
706 r.maybe_compress (); |
|
|
707 } |
|
|
708 } |
|
|
709 else |
|
|
710 (*current_liboctave_error_handler) ("matrix size mismatch"); |
|
|
711 |
|
|
712 return r; |
|
|
713 } |
|
|
714 |
|
|
715 SparseMatrix |
|
|
716 SparseMatrix::inverse (void) const |
|
|
717 { |
|
5275
|
718 octave_idx_type info; |
|
5164
|
719 double rcond; |
|
5785
|
720 MatrixType mattype (*this); |
|
5506
|
721 return inverse (mattype, info, rcond, 0, 0); |
|
|
722 } |
|
|
723 |
|
|
724 SparseMatrix |
|
5785
|
725 SparseMatrix::inverse (MatrixType& mattype) const |
|
5506
|
726 { |
|
|
727 octave_idx_type info; |
|
|
728 double rcond; |
|
|
729 return inverse (mattype, info, rcond, 0, 0); |
|
5164
|
730 } |
|
|
731 |
|
|
732 SparseMatrix |
|
5785
|
733 SparseMatrix::inverse (MatrixType& mattype, octave_idx_type& info) const |
|
5164
|
734 { |
|
|
735 double rcond; |
|
5506
|
736 return inverse (mattype, info, rcond, 0, 0); |
|
|
737 } |
|
|
738 |
|
|
739 SparseMatrix |
|
5785
|
740 SparseMatrix::dinverse (MatrixType &mattyp, octave_idx_type& info, |
|
5610
|
741 double& rcond, const bool, |
|
5506
|
742 const bool calccond) const |
|
|
743 { |
|
|
744 SparseMatrix retval; |
|
|
745 |
|
|
746 octave_idx_type nr = rows (); |
|
|
747 octave_idx_type nc = cols (); |
|
|
748 info = 0; |
|
|
749 |
|
|
750 if (nr == 0 || nc == 0 || nr != nc) |
|
|
751 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
752 else |
|
|
753 { |
|
|
754 // Print spparms("spumoni") info if requested |
|
|
755 int typ = mattyp.type (); |
|
|
756 mattyp.info (); |
|
|
757 |
|
5785
|
758 if (typ == MatrixType::Diagonal || |
|
|
759 typ == MatrixType::Permuted_Diagonal) |
|
5506
|
760 { |
|
5785
|
761 if (typ == MatrixType::Permuted_Diagonal) |
|
5506
|
762 retval = transpose(); |
|
|
763 else |
|
|
764 retval = *this; |
|
|
765 |
|
|
766 // Force make_unique to be called |
|
|
767 double *v = retval.data(); |
|
|
768 |
|
|
769 if (calccond) |
|
|
770 { |
|
|
771 double dmax = 0., dmin = octave_Inf; |
|
|
772 for (octave_idx_type i = 0; i < nr; i++) |
|
|
773 { |
|
|
774 double tmp = fabs(v[i]); |
|
|
775 if (tmp > dmax) |
|
|
776 dmax = tmp; |
|
|
777 if (tmp < dmin) |
|
|
778 dmin = tmp; |
|
|
779 } |
|
|
780 rcond = dmin / dmax; |
|
|
781 } |
|
|
782 |
|
|
783 for (octave_idx_type i = 0; i < nr; i++) |
|
|
784 v[i] = 1.0 / v[i]; |
|
|
785 } |
|
|
786 else |
|
|
787 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
788 } |
|
|
789 |
|
|
790 return retval; |
|
|
791 } |
|
|
792 |
|
|
793 SparseMatrix |
|
5785
|
794 SparseMatrix::tinverse (MatrixType &mattyp, octave_idx_type& info, |
|
5610
|
795 double& rcond, const bool, |
|
5506
|
796 const bool calccond) const |
|
|
797 { |
|
|
798 SparseMatrix retval; |
|
|
799 |
|
|
800 octave_idx_type nr = rows (); |
|
|
801 octave_idx_type nc = cols (); |
|
|
802 info = 0; |
|
|
803 |
|
|
804 if (nr == 0 || nc == 0 || nr != nc) |
|
|
805 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
806 else |
|
|
807 { |
|
|
808 // Print spparms("spumoni") info if requested |
|
|
809 int typ = mattyp.type (); |
|
|
810 mattyp.info (); |
|
|
811 |
|
5785
|
812 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper || |
|
|
813 typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
5506
|
814 { |
|
|
815 double anorm = 0.; |
|
|
816 double ainvnorm = 0.; |
|
|
817 |
|
|
818 if (calccond) |
|
|
819 { |
|
|
820 // Calculate the 1-norm of matrix for rcond calculation |
|
|
821 for (octave_idx_type j = 0; j < nr; j++) |
|
|
822 { |
|
|
823 double atmp = 0.; |
|
|
824 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
825 atmp += fabs(data(i)); |
|
|
826 if (atmp > anorm) |
|
|
827 anorm = atmp; |
|
|
828 } |
|
|
829 } |
|
|
830 |
|
5785
|
831 if (typ == MatrixType::Upper || typ == MatrixType::Lower) |
|
5506
|
832 { |
|
5681
|
833 octave_idx_type nz = nnz (); |
|
5506
|
834 octave_idx_type cx = 0; |
|
|
835 octave_idx_type nz2 = nz; |
|
|
836 retval = SparseMatrix (nr, nc, nz2); |
|
|
837 |
|
|
838 for (octave_idx_type i = 0; i < nr; i++) |
|
|
839 { |
|
|
840 OCTAVE_QUIT; |
|
|
841 // place the 1 in the identity position |
|
|
842 octave_idx_type cx_colstart = cx; |
|
|
843 |
|
|
844 if (cx == nz2) |
|
|
845 { |
|
|
846 nz2 *= 2; |
|
|
847 retval.change_capacity (nz2); |
|
|
848 } |
|
|
849 |
|
|
850 retval.xcidx(i) = cx; |
|
|
851 retval.xridx(cx) = i; |
|
|
852 retval.xdata(cx) = 1.0; |
|
|
853 cx++; |
|
|
854 |
|
|
855 // iterate accross columns of input matrix |
|
|
856 for (octave_idx_type j = i+1; j < nr; j++) |
|
|
857 { |
|
|
858 double v = 0.; |
|
|
859 // iterate to calculate sum |
|
|
860 octave_idx_type colXp = retval.xcidx(i); |
|
|
861 octave_idx_type colUp = cidx(j); |
|
|
862 octave_idx_type rpX, rpU; |
|
5876
|
863 |
|
|
864 if (cidx(j) == cidx(j+1)) |
|
|
865 { |
|
|
866 (*current_liboctave_error_handler) |
|
|
867 ("division by zero"); |
|
|
868 goto inverse_singular; |
|
|
869 } |
|
|
870 |
|
5506
|
871 do |
|
|
872 { |
|
|
873 OCTAVE_QUIT; |
|
|
874 rpX = retval.xridx(colXp); |
|
|
875 rpU = ridx(colUp); |
|
|
876 |
|
|
877 if (rpX < rpU) |
|
|
878 colXp++; |
|
|
879 else if (rpX > rpU) |
|
|
880 colUp++; |
|
|
881 else |
|
|
882 { |
|
|
883 v -= retval.xdata(colXp) * data(colUp); |
|
|
884 colXp++; |
|
|
885 colUp++; |
|
|
886 } |
|
|
887 } while ((rpX<j) && (rpU<j) && |
|
|
888 (colXp<cx) && (colUp<nz)); |
|
|
889 |
|
|
890 // get A(m,m) |
|
5876
|
891 if (typ == MatrixType::Upper) |
|
|
892 colUp = cidx(j+1) - 1; |
|
|
893 else |
|
5877
|
894 colUp = cidx(j); |
|
5506
|
895 double pivot = data(colUp); |
|
5877
|
896 if (pivot == 0. || ridx(colUp) != j) |
|
5876
|
897 { |
|
|
898 (*current_liboctave_error_handler) |
|
|
899 ("division by zero"); |
|
|
900 goto inverse_singular; |
|
|
901 } |
|
5506
|
902 |
|
|
903 if (v != 0.) |
|
|
904 { |
|
|
905 if (cx == nz2) |
|
|
906 { |
|
|
907 nz2 *= 2; |
|
|
908 retval.change_capacity (nz2); |
|
|
909 } |
|
|
910 |
|
|
911 retval.xridx(cx) = j; |
|
|
912 retval.xdata(cx) = v / pivot; |
|
|
913 cx++; |
|
|
914 } |
|
|
915 } |
|
|
916 |
|
|
917 // get A(m,m) |
|
5876
|
918 octave_idx_type colUp; |
|
|
919 if (typ == MatrixType::Upper) |
|
|
920 colUp = cidx(i+1) - 1; |
|
|
921 else |
|
5877
|
922 colUp = cidx(i); |
|
5506
|
923 double pivot = data(colUp); |
|
5877
|
924 if (pivot == 0. || ridx(colUp) != i) |
|
5876
|
925 { |
|
|
926 (*current_liboctave_error_handler) ("division by zero"); |
|
|
927 goto inverse_singular; |
|
|
928 } |
|
5506
|
929 |
|
|
930 if (pivot != 1.0) |
|
|
931 for (octave_idx_type j = cx_colstart; j < cx; j++) |
|
|
932 retval.xdata(j) /= pivot; |
|
|
933 } |
|
|
934 retval.xcidx(nr) = cx; |
|
|
935 retval.maybe_compress (); |
|
|
936 } |
|
|
937 else |
|
|
938 { |
|
5681
|
939 octave_idx_type nz = nnz (); |
|
5506
|
940 octave_idx_type cx = 0; |
|
|
941 octave_idx_type nz2 = nz; |
|
|
942 retval = SparseMatrix (nr, nc, nz2); |
|
|
943 |
|
|
944 OCTAVE_LOCAL_BUFFER (double, work, nr); |
|
|
945 OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nr); |
|
|
946 |
|
|
947 octave_idx_type *perm = mattyp.triangular_perm(); |
|
5785
|
948 if (typ == MatrixType::Permuted_Upper) |
|
5506
|
949 { |
|
|
950 for (octave_idx_type i = 0; i < nr; i++) |
|
|
951 rperm[perm[i]] = i; |
|
|
952 } |
|
|
953 else |
|
|
954 { |
|
|
955 for (octave_idx_type i = 0; i < nr; i++) |
|
|
956 rperm[i] = perm[i]; |
|
|
957 for (octave_idx_type i = 0; i < nr; i++) |
|
|
958 perm[rperm[i]] = i; |
|
|
959 } |
|
|
960 |
|
|
961 for (octave_idx_type i = 0; i < nr; i++) |
|
|
962 { |
|
|
963 OCTAVE_QUIT; |
|
|
964 octave_idx_type iidx = rperm[i]; |
|
|
965 |
|
|
966 for (octave_idx_type j = 0; j < nr; j++) |
|
|
967 work[j] = 0.; |
|
|
968 |
|
|
969 // place the 1 in the identity position |
|
|
970 work[iidx] = 1.0; |
|
|
971 |
|
|
972 // iterate accross columns of input matrix |
|
|
973 for (octave_idx_type j = iidx+1; j < nr; j++) |
|
|
974 { |
|
|
975 double v = 0.; |
|
|
976 octave_idx_type jidx = perm[j]; |
|
|
977 // iterate to calculate sum |
|
|
978 for (octave_idx_type k = cidx(jidx); |
|
|
979 k < cidx(jidx+1); k++) |
|
|
980 { |
|
|
981 OCTAVE_QUIT; |
|
|
982 v -= work[ridx(k)] * data(k); |
|
|
983 } |
|
|
984 |
|
|
985 // get A(m,m) |
|
5876
|
986 double pivot; |
|
|
987 if (typ == MatrixType::Permuted_Upper) |
|
|
988 pivot = data(cidx(jidx+1) - 1); |
|
|
989 else |
|
5877
|
990 pivot = data(cidx(jidx)); |
|
5506
|
991 if (pivot == 0.) |
|
5876
|
992 { |
|
|
993 (*current_liboctave_error_handler) |
|
|
994 ("division by zero"); |
|
|
995 goto inverse_singular; |
|
|
996 } |
|
5506
|
997 |
|
|
998 work[j] = v / pivot; |
|
|
999 } |
|
|
1000 |
|
|
1001 // get A(m,m) |
|
5876
|
1002 octave_idx_type colUp; |
|
|
1003 if (typ == MatrixType::Permuted_Upper) |
|
|
1004 colUp = cidx(perm[iidx]+1) - 1; |
|
|
1005 else |
|
5877
|
1006 colUp = cidx(perm[iidx]); |
|
5876
|
1007 |
|
5506
|
1008 double pivot = data(colUp); |
|
5876
|
1009 if (pivot == 0.) |
|
|
1010 { |
|
|
1011 (*current_liboctave_error_handler) |
|
|
1012 ("division by zero"); |
|
|
1013 goto inverse_singular; |
|
|
1014 } |
|
5506
|
1015 |
|
|
1016 octave_idx_type new_cx = cx; |
|
|
1017 for (octave_idx_type j = iidx; j < nr; j++) |
|
|
1018 if (work[j] != 0.0) |
|
|
1019 { |
|
|
1020 new_cx++; |
|
|
1021 if (pivot != 1.0) |
|
|
1022 work[j] /= pivot; |
|
|
1023 } |
|
|
1024 |
|
|
1025 if (cx < new_cx) |
|
|
1026 { |
|
|
1027 nz2 = (2*nz2 < new_cx ? new_cx : 2*nz2); |
|
|
1028 retval.change_capacity (nz2); |
|
|
1029 } |
|
|
1030 |
|
|
1031 retval.xcidx(i) = cx; |
|
|
1032 for (octave_idx_type j = iidx; j < nr; j++) |
|
|
1033 if (work[j] != 0.) |
|
|
1034 { |
|
|
1035 retval.xridx(cx) = j; |
|
|
1036 retval.xdata(cx++) = work[j]; |
|
|
1037 } |
|
|
1038 } |
|
|
1039 |
|
|
1040 retval.xcidx(nr) = cx; |
|
|
1041 retval.maybe_compress (); |
|
|
1042 } |
|
|
1043 |
|
|
1044 if (calccond) |
|
|
1045 { |
|
|
1046 // Calculate the 1-norm of inverse matrix for rcond calculation |
|
|
1047 for (octave_idx_type j = 0; j < nr; j++) |
|
|
1048 { |
|
|
1049 double atmp = 0.; |
|
|
1050 for (octave_idx_type i = retval.cidx(j); |
|
|
1051 i < retval.cidx(j+1); i++) |
|
|
1052 atmp += fabs(retval.data(i)); |
|
|
1053 if (atmp > ainvnorm) |
|
|
1054 ainvnorm = atmp; |
|
|
1055 } |
|
|
1056 |
|
|
1057 rcond = 1. / ainvnorm / anorm; |
|
|
1058 } |
|
|
1059 } |
|
|
1060 else |
|
|
1061 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1062 } |
|
|
1063 |
|
|
1064 return retval; |
|
5876
|
1065 |
|
|
1066 inverse_singular: |
|
|
1067 return SparseMatrix(); |
|
5164
|
1068 } |
|
|
1069 |
|
|
1070 SparseMatrix |
|
5785
|
1071 SparseMatrix::inverse (MatrixType &mattype, octave_idx_type& info, |
|
5610
|
1072 double& rcond, int, int calc_cond) const |
|
5506
|
1073 { |
|
|
1074 int typ = mattype.type (false); |
|
|
1075 SparseMatrix ret; |
|
|
1076 |
|
5785
|
1077 if (typ == MatrixType::Unknown) |
|
5506
|
1078 typ = mattype.type (*this); |
|
|
1079 |
|
5785
|
1080 if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) |
|
5506
|
1081 ret = dinverse (mattype, info, rcond, true, calc_cond); |
|
5785
|
1082 else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
5506
|
1083 ret = tinverse (mattype, info, rcond, true, calc_cond).transpose(); |
|
5785
|
1084 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
6185
|
1085 { |
|
|
1086 MatrixType newtype = mattype.transpose(); |
|
|
1087 ret = transpose().tinverse (newtype, info, rcond, true, calc_cond); |
|
|
1088 } |
|
5785
|
1089 else if (typ != MatrixType::Rectangular) |
|
5506
|
1090 { |
|
|
1091 if (mattype.is_hermitian()) |
|
|
1092 { |
|
5785
|
1093 MatrixType tmp_typ (MatrixType::Upper); |
|
5506
|
1094 SparseCHOL fact (*this, info, false); |
|
|
1095 rcond = fact.rcond(); |
|
|
1096 if (info == 0) |
|
|
1097 { |
|
|
1098 double rcond2; |
|
|
1099 SparseMatrix Q = fact.Q(); |
|
|
1100 SparseMatrix InvL = fact.L().transpose().tinverse(tmp_typ, |
|
|
1101 info, rcond2, true, false); |
|
|
1102 ret = Q * InvL.transpose() * InvL * Q.transpose(); |
|
|
1103 } |
|
|
1104 else |
|
|
1105 { |
|
|
1106 // Matrix is either singular or not positive definite |
|
|
1107 mattype.mark_as_unsymmetric (); |
|
5785
|
1108 typ = MatrixType::Full; |
|
5506
|
1109 } |
|
|
1110 } |
|
|
1111 |
|
|
1112 if (!mattype.is_hermitian()) |
|
|
1113 { |
|
|
1114 octave_idx_type n = rows(); |
|
|
1115 ColumnVector Qinit(n); |
|
|
1116 for (octave_idx_type i = 0; i < n; i++) |
|
|
1117 Qinit(i) = i; |
|
|
1118 |
|
5785
|
1119 MatrixType tmp_typ (MatrixType::Upper); |
|
5506
|
1120 SparseLU fact (*this, Qinit, -1.0, false); |
|
|
1121 rcond = fact.rcond(); |
|
|
1122 double rcond2; |
|
|
1123 SparseMatrix InvL = fact.L().transpose().tinverse(tmp_typ, |
|
|
1124 info, rcond2, true, false); |
|
|
1125 SparseMatrix InvU = fact.U().tinverse(tmp_typ, info, rcond2, |
|
|
1126 true, false).transpose(); |
|
|
1127 ret = fact.Pc().transpose() * InvU * InvL * fact.Pr(); |
|
|
1128 } |
|
|
1129 } |
|
|
1130 else |
|
|
1131 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
1132 |
|
|
1133 return ret; |
|
5164
|
1134 } |
|
|
1135 |
|
|
1136 DET |
|
|
1137 SparseMatrix::determinant (void) const |
|
|
1138 { |
|
5275
|
1139 octave_idx_type info; |
|
5164
|
1140 double rcond; |
|
|
1141 return determinant (info, rcond, 0); |
|
|
1142 } |
|
|
1143 |
|
|
1144 DET |
|
5275
|
1145 SparseMatrix::determinant (octave_idx_type& info) const |
|
5164
|
1146 { |
|
|
1147 double rcond; |
|
|
1148 return determinant (info, rcond, 0); |
|
|
1149 } |
|
|
1150 |
|
|
1151 DET |
|
5275
|
1152 SparseMatrix::determinant (octave_idx_type& err, double& rcond, int) const |
|
5164
|
1153 { |
|
|
1154 DET retval; |
|
|
1155 |
|
5203
|
1156 #ifdef HAVE_UMFPACK |
|
5275
|
1157 octave_idx_type nr = rows (); |
|
|
1158 octave_idx_type nc = cols (); |
|
5164
|
1159 |
|
|
1160 if (nr == 0 || nc == 0 || nr != nc) |
|
|
1161 { |
|
|
1162 double d[2]; |
|
|
1163 d[0] = 1.0; |
|
|
1164 d[1] = 0.0; |
|
|
1165 retval = DET (d); |
|
|
1166 } |
|
|
1167 else |
|
|
1168 { |
|
|
1169 err = 0; |
|
|
1170 |
|
|
1171 // Setup the control parameters |
|
|
1172 Matrix Control (UMFPACK_CONTROL, 1); |
|
|
1173 double *control = Control.fortran_vec (); |
|
5322
|
1174 UMFPACK_DNAME (defaults) (control); |
|
5164
|
1175 |
|
5893
|
1176 double tmp = octave_sparse_params::get_key ("spumoni"); |
|
5164
|
1177 if (!xisnan (tmp)) |
|
|
1178 Control (UMFPACK_PRL) = tmp; |
|
|
1179 |
|
5893
|
1180 tmp = octave_sparse_params::get_key ("piv_tol"); |
|
5164
|
1181 if (!xisnan (tmp)) |
|
|
1182 { |
|
|
1183 Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp; |
|
|
1184 Control (UMFPACK_PIVOT_TOLERANCE) = tmp; |
|
|
1185 } |
|
|
1186 |
|
|
1187 // Set whether we are allowed to modify Q or not |
|
5893
|
1188 tmp = octave_sparse_params::get_key ("autoamd"); |
|
5164
|
1189 if (!xisnan (tmp)) |
|
|
1190 Control (UMFPACK_FIXQ) = tmp; |
|
|
1191 |
|
|
1192 // Turn-off UMFPACK scaling for LU |
|
|
1193 Control (UMFPACK_SCALE) = UMFPACK_SCALE_NONE; |
|
|
1194 |
|
5322
|
1195 UMFPACK_DNAME (report_control) (control); |
|
5164
|
1196 |
|
5275
|
1197 const octave_idx_type *Ap = cidx (); |
|
|
1198 const octave_idx_type *Ai = ridx (); |
|
5164
|
1199 const double *Ax = data (); |
|
|
1200 |
|
5322
|
1201 UMFPACK_DNAME (report_matrix) (nr, nc, Ap, Ai, Ax, 1, control); |
|
5164
|
1202 |
|
|
1203 void *Symbolic; |
|
|
1204 Matrix Info (1, UMFPACK_INFO); |
|
|
1205 double *info = Info.fortran_vec (); |
|
5322
|
1206 int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, |
|
|
1207 Ax, NULL, &Symbolic, control, info); |
|
5164
|
1208 |
|
|
1209 if (status < 0) |
|
|
1210 { |
|
|
1211 (*current_liboctave_error_handler) |
|
|
1212 ("SparseMatrix::determinant symbolic factorization failed"); |
|
|
1213 |
|
5322
|
1214 UMFPACK_DNAME (report_status) (control, status); |
|
|
1215 UMFPACK_DNAME (report_info) (control, info); |
|
|
1216 |
|
|
1217 UMFPACK_DNAME (free_symbolic) (&Symbolic) ; |
|
5164
|
1218 } |
|
|
1219 else |
|
|
1220 { |
|
5322
|
1221 UMFPACK_DNAME (report_symbolic) (Symbolic, control); |
|
5164
|
1222 |
|
|
1223 void *Numeric; |
|
5322
|
1224 status = UMFPACK_DNAME (numeric) (Ap, Ai, Ax, Symbolic, |
|
|
1225 &Numeric, control, info) ; |
|
|
1226 UMFPACK_DNAME (free_symbolic) (&Symbolic) ; |
|
5164
|
1227 |
|
|
1228 rcond = Info (UMFPACK_RCOND); |
|
|
1229 |
|
|
1230 if (status < 0) |
|
|
1231 { |
|
|
1232 (*current_liboctave_error_handler) |
|
|
1233 ("SparseMatrix::determinant numeric factorization failed"); |
|
|
1234 |
|
5322
|
1235 UMFPACK_DNAME (report_status) (control, status); |
|
|
1236 UMFPACK_DNAME (report_info) (control, info); |
|
|
1237 |
|
|
1238 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
1239 } |
|
|
1240 else |
|
|
1241 { |
|
5322
|
1242 UMFPACK_DNAME (report_numeric) (Numeric, control); |
|
5164
|
1243 |
|
|
1244 double d[2]; |
|
|
1245 |
|
5322
|
1246 status = UMFPACK_DNAME (get_determinant) (&d[0], |
|
|
1247 &d[1], Numeric, info); |
|
5164
|
1248 |
|
|
1249 if (status < 0) |
|
|
1250 { |
|
|
1251 (*current_liboctave_error_handler) |
|
|
1252 ("SparseMatrix::determinant error calculating determinant"); |
|
|
1253 |
|
5322
|
1254 UMFPACK_DNAME (report_status) (control, status); |
|
|
1255 UMFPACK_DNAME (report_info) (control, info); |
|
5164
|
1256 } |
|
|
1257 else |
|
|
1258 retval = DET (d); |
|
5346
|
1259 |
|
|
1260 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
1261 } |
|
|
1262 } |
|
|
1263 } |
|
5203
|
1264 #else |
|
|
1265 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
1266 #endif |
|
5164
|
1267 |
|
|
1268 return retval; |
|
|
1269 } |
|
|
1270 |
|
|
1271 Matrix |
|
5785
|
1272 SparseMatrix::dsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& err, |
|
5681
|
1273 double& rcond, solve_singularity_handler, |
|
|
1274 bool calc_cond) const |
|
5164
|
1275 { |
|
|
1276 Matrix retval; |
|
|
1277 |
|
5275
|
1278 octave_idx_type nr = rows (); |
|
|
1279 octave_idx_type nc = cols (); |
|
5630
|
1280 octave_idx_type nm = (nc < nr ? nc : nr); |
|
5164
|
1281 err = 0; |
|
|
1282 |
|
5630
|
1283 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1284 (*current_liboctave_error_handler) |
|
|
1285 ("matrix dimension mismatch solution of linear equations"); |
|
|
1286 else |
|
|
1287 { |
|
|
1288 // Print spparms("spumoni") info if requested |
|
|
1289 int typ = mattype.type (); |
|
|
1290 mattype.info (); |
|
|
1291 |
|
5785
|
1292 if (typ == MatrixType::Diagonal || |
|
|
1293 typ == MatrixType::Permuted_Diagonal) |
|
5164
|
1294 { |
|
5630
|
1295 retval.resize (nc, b.cols(), 0.); |
|
5785
|
1296 if (typ == MatrixType::Diagonal) |
|
5275
|
1297 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5630
|
1298 for (octave_idx_type i = 0; i < nm; i++) |
|
5164
|
1299 retval(i,j) = b(i,j) / data (i); |
|
|
1300 else |
|
5275
|
1301 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5630
|
1302 for (octave_idx_type k = 0; k < nc; k++) |
|
|
1303 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
1304 retval(k,j) = b(ridx(i),j) / data (i); |
|
|
1305 |
|
5681
|
1306 if (calc_cond) |
|
|
1307 { |
|
|
1308 double dmax = 0., dmin = octave_Inf; |
|
|
1309 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1310 { |
|
|
1311 double tmp = fabs(data(i)); |
|
|
1312 if (tmp > dmax) |
|
|
1313 dmax = tmp; |
|
|
1314 if (tmp < dmin) |
|
|
1315 dmin = tmp; |
|
|
1316 } |
|
|
1317 rcond = dmin / dmax; |
|
|
1318 } |
|
|
1319 else |
|
|
1320 rcond = 1.; |
|
5164
|
1321 } |
|
|
1322 else |
|
|
1323 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1324 } |
|
|
1325 |
|
|
1326 return retval; |
|
|
1327 } |
|
|
1328 |
|
|
1329 SparseMatrix |
|
5785
|
1330 SparseMatrix::dsolve (MatrixType &mattype, const SparseMatrix& b, |
|
5681
|
1331 octave_idx_type& err, double& rcond, |
|
|
1332 solve_singularity_handler, bool calc_cond) const |
|
5164
|
1333 { |
|
|
1334 SparseMatrix retval; |
|
|
1335 |
|
5275
|
1336 octave_idx_type nr = rows (); |
|
|
1337 octave_idx_type nc = cols (); |
|
5630
|
1338 octave_idx_type nm = (nc < nr ? nc : nr); |
|
5164
|
1339 err = 0; |
|
|
1340 |
|
5630
|
1341 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1342 (*current_liboctave_error_handler) |
|
|
1343 ("matrix dimension mismatch solution of linear equations"); |
|
|
1344 else |
|
|
1345 { |
|
|
1346 // Print spparms("spumoni") info if requested |
|
|
1347 int typ = mattype.type (); |
|
|
1348 mattype.info (); |
|
|
1349 |
|
5785
|
1350 if (typ == MatrixType::Diagonal || |
|
|
1351 typ == MatrixType::Permuted_Diagonal) |
|
5164
|
1352 { |
|
5275
|
1353 octave_idx_type b_nc = b.cols (); |
|
5681
|
1354 octave_idx_type b_nz = b.nnz (); |
|
5630
|
1355 retval = SparseMatrix (nc, b_nc, b_nz); |
|
5164
|
1356 |
|
|
1357 retval.xcidx(0) = 0; |
|
5275
|
1358 octave_idx_type ii = 0; |
|
5785
|
1359 if (typ == MatrixType::Diagonal) |
|
5681
|
1360 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1361 { |
|
5275
|
1362 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
1363 { |
|
5681
|
1364 if (b.ridx(i) >= nm) |
|
|
1365 break; |
|
5164
|
1366 retval.xridx (ii) = b.ridx(i); |
|
|
1367 retval.xdata (ii++) = b.data(i) / data (b.ridx (i)); |
|
|
1368 } |
|
|
1369 retval.xcidx(j+1) = ii; |
|
|
1370 } |
|
|
1371 else |
|
5681
|
1372 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1373 { |
|
5630
|
1374 for (octave_idx_type l = 0; l < nc; l++) |
|
|
1375 for (octave_idx_type i = cidx(l); i < cidx(l+1); i++) |
|
|
1376 { |
|
|
1377 bool found = false; |
|
|
1378 octave_idx_type k; |
|
|
1379 for (k = b.cidx(j); k < b.cidx(j+1); k++) |
|
|
1380 if (ridx(i) == b.ridx(k)) |
|
|
1381 { |
|
|
1382 found = true; |
|
|
1383 break; |
|
|
1384 } |
|
|
1385 if (found) |
|
5164
|
1386 { |
|
5630
|
1387 retval.xridx (ii) = l; |
|
|
1388 retval.xdata (ii++) = b.data(k) / data (i); |
|
5164
|
1389 } |
|
5630
|
1390 } |
|
5164
|
1391 retval.xcidx(j+1) = ii; |
|
|
1392 } |
|
5630
|
1393 |
|
5681
|
1394 if (calc_cond) |
|
|
1395 { |
|
|
1396 double dmax = 0., dmin = octave_Inf; |
|
|
1397 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1398 { |
|
|
1399 double tmp = fabs(data(i)); |
|
|
1400 if (tmp > dmax) |
|
|
1401 dmax = tmp; |
|
|
1402 if (tmp < dmin) |
|
|
1403 dmin = tmp; |
|
|
1404 } |
|
|
1405 rcond = dmin / dmax; |
|
|
1406 } |
|
|
1407 else |
|
|
1408 rcond = 1.; |
|
5164
|
1409 } |
|
|
1410 else |
|
|
1411 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1412 } |
|
|
1413 |
|
|
1414 return retval; |
|
|
1415 } |
|
|
1416 |
|
|
1417 ComplexMatrix |
|
5785
|
1418 SparseMatrix::dsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5681
|
1419 octave_idx_type& err, double& rcond, |
|
|
1420 solve_singularity_handler, bool calc_cond) const |
|
5164
|
1421 { |
|
|
1422 ComplexMatrix retval; |
|
|
1423 |
|
5275
|
1424 octave_idx_type nr = rows (); |
|
|
1425 octave_idx_type nc = cols (); |
|
5630
|
1426 octave_idx_type nm = (nc < nr ? nc : nr); |
|
5164
|
1427 err = 0; |
|
|
1428 |
|
5630
|
1429 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1430 (*current_liboctave_error_handler) |
|
|
1431 ("matrix dimension mismatch solution of linear equations"); |
|
|
1432 else |
|
|
1433 { |
|
|
1434 // Print spparms("spumoni") info if requested |
|
|
1435 int typ = mattype.type (); |
|
|
1436 mattype.info (); |
|
|
1437 |
|
5785
|
1438 if (typ == MatrixType::Diagonal || |
|
|
1439 typ == MatrixType::Permuted_Diagonal) |
|
5164
|
1440 { |
|
5630
|
1441 retval.resize (nc, b.cols(), 0); |
|
5785
|
1442 if (typ == MatrixType::Diagonal) |
|
5275
|
1443 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5630
|
1444 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1445 retval(i,j) = b(i,j) / data (i); |
|
5164
|
1446 else |
|
5275
|
1447 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5630
|
1448 for (octave_idx_type k = 0; k < nc; k++) |
|
|
1449 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
1450 retval(k,j) = b(ridx(i),j) / data (i); |
|
5164
|
1451 |
|
5681
|
1452 if (calc_cond) |
|
|
1453 { |
|
|
1454 double dmax = 0., dmin = octave_Inf; |
|
|
1455 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1456 { |
|
|
1457 double tmp = fabs(data(i)); |
|
|
1458 if (tmp > dmax) |
|
|
1459 dmax = tmp; |
|
|
1460 if (tmp < dmin) |
|
|
1461 dmin = tmp; |
|
|
1462 } |
|
|
1463 rcond = dmin / dmax; |
|
|
1464 } |
|
|
1465 else |
|
|
1466 rcond = 1.; |
|
5164
|
1467 } |
|
|
1468 else |
|
|
1469 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1470 } |
|
|
1471 |
|
|
1472 return retval; |
|
|
1473 } |
|
|
1474 |
|
|
1475 SparseComplexMatrix |
|
5785
|
1476 SparseMatrix::dsolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5275
|
1477 octave_idx_type& err, double& rcond, |
|
5681
|
1478 solve_singularity_handler, bool calc_cond) const |
|
5164
|
1479 { |
|
|
1480 SparseComplexMatrix retval; |
|
|
1481 |
|
5275
|
1482 octave_idx_type nr = rows (); |
|
|
1483 octave_idx_type nc = cols (); |
|
5630
|
1484 octave_idx_type nm = (nc < nr ? nc : nr); |
|
5164
|
1485 err = 0; |
|
|
1486 |
|
5630
|
1487 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1488 (*current_liboctave_error_handler) |
|
|
1489 ("matrix dimension mismatch solution of linear equations"); |
|
|
1490 else |
|
|
1491 { |
|
|
1492 // Print spparms("spumoni") info if requested |
|
|
1493 int typ = mattype.type (); |
|
|
1494 mattype.info (); |
|
|
1495 |
|
5785
|
1496 if (typ == MatrixType::Diagonal || |
|
|
1497 typ == MatrixType::Permuted_Diagonal) |
|
5164
|
1498 { |
|
5275
|
1499 octave_idx_type b_nc = b.cols (); |
|
5681
|
1500 octave_idx_type b_nz = b.nnz (); |
|
5630
|
1501 retval = SparseComplexMatrix (nc, b_nc, b_nz); |
|
5164
|
1502 |
|
|
1503 retval.xcidx(0) = 0; |
|
5275
|
1504 octave_idx_type ii = 0; |
|
5785
|
1505 if (typ == MatrixType::Diagonal) |
|
5275
|
1506 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5164
|
1507 { |
|
5275
|
1508 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
1509 { |
|
5681
|
1510 if (b.ridx(i) >= nm) |
|
|
1511 break; |
|
5164
|
1512 retval.xridx (ii) = b.ridx(i); |
|
|
1513 retval.xdata (ii++) = b.data(i) / data (b.ridx (i)); |
|
|
1514 } |
|
|
1515 retval.xcidx(j+1) = ii; |
|
|
1516 } |
|
|
1517 else |
|
5275
|
1518 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
5164
|
1519 { |
|
5630
|
1520 for (octave_idx_type l = 0; l < nc; l++) |
|
|
1521 for (octave_idx_type i = cidx(l); i < cidx(l+1); i++) |
|
|
1522 { |
|
|
1523 bool found = false; |
|
|
1524 octave_idx_type k; |
|
|
1525 for (k = b.cidx(j); k < b.cidx(j+1); k++) |
|
|
1526 if (ridx(i) == b.ridx(k)) |
|
|
1527 { |
|
|
1528 found = true; |
|
|
1529 break; |
|
|
1530 } |
|
|
1531 if (found) |
|
5164
|
1532 { |
|
5630
|
1533 retval.xridx (ii) = l; |
|
|
1534 retval.xdata (ii++) = b.data(k) / data (i); |
|
5164
|
1535 } |
|
5630
|
1536 } |
|
5164
|
1537 retval.xcidx(j+1) = ii; |
|
|
1538 } |
|
|
1539 |
|
5681
|
1540 if (calc_cond) |
|
|
1541 { |
|
|
1542 double dmax = 0., dmin = octave_Inf; |
|
|
1543 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1544 { |
|
|
1545 double tmp = fabs(data(i)); |
|
|
1546 if (tmp > dmax) |
|
|
1547 dmax = tmp; |
|
|
1548 if (tmp < dmin) |
|
|
1549 dmin = tmp; |
|
|
1550 } |
|
|
1551 rcond = dmin / dmax; |
|
|
1552 } |
|
|
1553 else |
|
|
1554 rcond = 1.; |
|
5164
|
1555 } |
|
|
1556 else |
|
|
1557 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1558 } |
|
|
1559 |
|
|
1560 return retval; |
|
|
1561 } |
|
|
1562 |
|
|
1563 Matrix |
|
5785
|
1564 SparseMatrix::utsolve (MatrixType &mattype, const Matrix& b, |
|
5630
|
1565 octave_idx_type& err, double& rcond, |
|
5681
|
1566 solve_singularity_handler sing_handler, |
|
|
1567 bool calc_cond) const |
|
5164
|
1568 { |
|
|
1569 Matrix retval; |
|
|
1570 |
|
5275
|
1571 octave_idx_type nr = rows (); |
|
|
1572 octave_idx_type nc = cols (); |
|
5630
|
1573 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
1574 err = 0; |
|
|
1575 |
|
5630
|
1576 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1577 (*current_liboctave_error_handler) |
|
|
1578 ("matrix dimension mismatch solution of linear equations"); |
|
|
1579 else |
|
|
1580 { |
|
|
1581 // Print spparms("spumoni") info if requested |
|
|
1582 int typ = mattype.type (); |
|
|
1583 mattype.info (); |
|
|
1584 |
|
5785
|
1585 if (typ == MatrixType::Permuted_Upper || |
|
|
1586 typ == MatrixType::Upper) |
|
5164
|
1587 { |
|
|
1588 double anorm = 0.; |
|
|
1589 double ainvnorm = 0.; |
|
5630
|
1590 octave_idx_type b_nc = b.cols (); |
|
5681
|
1591 rcond = 1.; |
|
|
1592 |
|
|
1593 if (calc_cond) |
|
|
1594 { |
|
|
1595 // Calculate the 1-norm of matrix for rcond calculation |
|
|
1596 for (octave_idx_type j = 0; j < nc; j++) |
|
|
1597 { |
|
|
1598 double atmp = 0.; |
|
|
1599 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
1600 atmp += fabs(data(i)); |
|
|
1601 if (atmp > anorm) |
|
|
1602 anorm = atmp; |
|
|
1603 } |
|
5164
|
1604 } |
|
|
1605 |
|
5785
|
1606 if (typ == MatrixType::Permuted_Upper) |
|
5164
|
1607 { |
|
5630
|
1608 retval.resize (nc, b_nc); |
|
5322
|
1609 octave_idx_type *perm = mattype.triangular_perm (); |
|
5630
|
1610 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
1611 |
|
|
1612 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1613 { |
|
5275
|
1614 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
1615 work[i] = b(i,j); |
|
5630
|
1616 for (octave_idx_type i = nr; i < nc; i++) |
|
|
1617 work[i] = 0.; |
|
|
1618 |
|
|
1619 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
1620 { |
|
5322
|
1621 octave_idx_type kidx = perm[k]; |
|
|
1622 |
|
|
1623 if (work[k] != 0.) |
|
5164
|
1624 { |
|
5681
|
1625 if (ridx(cidx(kidx+1)-1) != k || |
|
|
1626 data(cidx(kidx+1)-1) == 0.) |
|
5164
|
1627 { |
|
|
1628 err = -2; |
|
|
1629 goto triangular_error; |
|
|
1630 } |
|
|
1631 |
|
5322
|
1632 double tmp = work[k] / data(cidx(kidx+1)-1); |
|
|
1633 work[k] = tmp; |
|
|
1634 for (octave_idx_type i = cidx(kidx); |
|
|
1635 i < cidx(kidx+1)-1; i++) |
|
5164
|
1636 { |
|
5322
|
1637 octave_idx_type iidx = ridx(i); |
|
|
1638 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
1639 } |
|
|
1640 } |
|
|
1641 } |
|
|
1642 |
|
5630
|
1643 for (octave_idx_type i = 0; i < nc; i++) |
|
|
1644 retval.xelem (perm[i], j) = work[i]; |
|
5164
|
1645 } |
|
|
1646 |
|
5681
|
1647 if (calc_cond) |
|
|
1648 { |
|
|
1649 // Calculation of 1-norm of inv(*this) |
|
|
1650 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1651 work[i] = 0.; |
|
|
1652 |
|
|
1653 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
1654 { |
|
5681
|
1655 work[j] = 1.; |
|
|
1656 |
|
|
1657 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
1658 { |
|
5681
|
1659 octave_idx_type iidx = perm[k]; |
|
|
1660 |
|
|
1661 if (work[k] != 0.) |
|
5164
|
1662 { |
|
5681
|
1663 double tmp = work[k] / data(cidx(iidx+1)-1); |
|
|
1664 work[k] = tmp; |
|
|
1665 for (octave_idx_type i = cidx(iidx); |
|
|
1666 i < cidx(iidx+1)-1; i++) |
|
|
1667 { |
|
|
1668 octave_idx_type idx2 = ridx(i); |
|
|
1669 work[idx2] = work[idx2] - tmp * data(i); |
|
|
1670 } |
|
5164
|
1671 } |
|
|
1672 } |
|
5681
|
1673 double atmp = 0; |
|
|
1674 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
1675 { |
|
|
1676 atmp += fabs(work[i]); |
|
|
1677 work[i] = 0.; |
|
|
1678 } |
|
|
1679 if (atmp > ainvnorm) |
|
|
1680 ainvnorm = atmp; |
|
5164
|
1681 } |
|
5681
|
1682 rcond = 1. / ainvnorm / anorm; |
|
5164
|
1683 } |
|
|
1684 } |
|
|
1685 else |
|
|
1686 { |
|
5630
|
1687 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
1688 retval.resize (nc, b_nc); |
|
|
1689 |
|
|
1690 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1691 { |
|
5630
|
1692 for (octave_idx_type i = 0; i < nr; i++) |
|
|
1693 work[i] = b(i,j); |
|
|
1694 for (octave_idx_type i = nr; i < nc; i++) |
|
|
1695 work[i] = 0.; |
|
|
1696 |
|
|
1697 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
1698 { |
|
5630
|
1699 if (work[k] != 0.) |
|
5164
|
1700 { |
|
5681
|
1701 if (ridx(cidx(k+1)-1) != k || |
|
|
1702 data(cidx(k+1)-1) == 0.) |
|
5164
|
1703 { |
|
|
1704 err = -2; |
|
|
1705 goto triangular_error; |
|
|
1706 } |
|
|
1707 |
|
5630
|
1708 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
1709 work[k] = tmp; |
|
5275
|
1710 for (octave_idx_type i = cidx(k); i < cidx(k+1)-1; i++) |
|
5164
|
1711 { |
|
5275
|
1712 octave_idx_type iidx = ridx(i); |
|
5630
|
1713 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
1714 } |
|
|
1715 } |
|
|
1716 } |
|
5630
|
1717 |
|
|
1718 for (octave_idx_type i = 0; i < nc; i++) |
|
|
1719 retval.xelem (i, j) = work[i]; |
|
5164
|
1720 } |
|
|
1721 |
|
5681
|
1722 if (calc_cond) |
|
|
1723 { |
|
|
1724 // Calculation of 1-norm of inv(*this) |
|
|
1725 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1726 work[i] = 0.; |
|
|
1727 |
|
|
1728 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
1729 { |
|
5681
|
1730 work[j] = 1.; |
|
|
1731 |
|
|
1732 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
1733 { |
|
5681
|
1734 if (work[k] != 0.) |
|
5164
|
1735 { |
|
5681
|
1736 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
1737 work[k] = tmp; |
|
|
1738 for (octave_idx_type i = cidx(k); i < cidx(k+1)-1; i++) |
|
|
1739 { |
|
|
1740 octave_idx_type iidx = ridx(i); |
|
|
1741 work[iidx] = work[iidx] - tmp * data(i); |
|
|
1742 } |
|
5164
|
1743 } |
|
|
1744 } |
|
5681
|
1745 double atmp = 0; |
|
|
1746 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
1747 { |
|
|
1748 atmp += fabs(work[i]); |
|
|
1749 work[i] = 0.; |
|
|
1750 } |
|
|
1751 if (atmp > ainvnorm) |
|
|
1752 ainvnorm = atmp; |
|
5164
|
1753 } |
|
5681
|
1754 rcond = 1. / ainvnorm / anorm; |
|
|
1755 } |
|
|
1756 } |
|
5164
|
1757 |
|
|
1758 triangular_error: |
|
|
1759 if (err != 0) |
|
|
1760 { |
|
|
1761 if (sing_handler) |
|
5681
|
1762 { |
|
|
1763 sing_handler (rcond); |
|
|
1764 mattype.mark_as_rectangular (); |
|
|
1765 } |
|
5164
|
1766 else |
|
|
1767 (*current_liboctave_error_handler) |
|
|
1768 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
1769 rcond); |
|
|
1770 } |
|
|
1771 |
|
|
1772 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1773 |
|
|
1774 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1775 { |
|
|
1776 err = -2; |
|
|
1777 |
|
|
1778 if (sing_handler) |
|
5681
|
1779 { |
|
|
1780 sing_handler (rcond); |
|
|
1781 mattype.mark_as_rectangular (); |
|
|
1782 } |
|
5164
|
1783 else |
|
|
1784 (*current_liboctave_error_handler) |
|
|
1785 ("matrix singular to machine precision, rcond = %g", |
|
|
1786 rcond); |
|
|
1787 } |
|
|
1788 } |
|
|
1789 else |
|
|
1790 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1791 } |
|
|
1792 |
|
|
1793 return retval; |
|
|
1794 } |
|
|
1795 |
|
|
1796 SparseMatrix |
|
5785
|
1797 SparseMatrix::utsolve (MatrixType &mattype, const SparseMatrix& b, |
|
5630
|
1798 octave_idx_type& err, double& rcond, |
|
5681
|
1799 solve_singularity_handler sing_handler, |
|
|
1800 bool calc_cond) const |
|
5164
|
1801 { |
|
|
1802 SparseMatrix retval; |
|
|
1803 |
|
5275
|
1804 octave_idx_type nr = rows (); |
|
|
1805 octave_idx_type nc = cols (); |
|
5630
|
1806 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
1807 err = 0; |
|
|
1808 |
|
5630
|
1809 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
1810 (*current_liboctave_error_handler) |
|
|
1811 ("matrix dimension mismatch solution of linear equations"); |
|
|
1812 else |
|
|
1813 { |
|
|
1814 // Print spparms("spumoni") info if requested |
|
|
1815 int typ = mattype.type (); |
|
|
1816 mattype.info (); |
|
|
1817 |
|
5785
|
1818 if (typ == MatrixType::Permuted_Upper || |
|
|
1819 typ == MatrixType::Upper) |
|
5164
|
1820 { |
|
|
1821 double anorm = 0.; |
|
|
1822 double ainvnorm = 0.; |
|
5681
|
1823 rcond = 1.; |
|
|
1824 |
|
|
1825 if (calc_cond) |
|
|
1826 { |
|
|
1827 // Calculate the 1-norm of matrix for rcond calculation |
|
|
1828 for (octave_idx_type j = 0; j < nc; j++) |
|
|
1829 { |
|
|
1830 double atmp = 0.; |
|
|
1831 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
1832 atmp += fabs(data(i)); |
|
|
1833 if (atmp > anorm) |
|
|
1834 anorm = atmp; |
|
|
1835 } |
|
5164
|
1836 } |
|
|
1837 |
|
5275
|
1838 octave_idx_type b_nc = b.cols (); |
|
5681
|
1839 octave_idx_type b_nz = b.nnz (); |
|
5630
|
1840 retval = SparseMatrix (nc, b_nc, b_nz); |
|
5164
|
1841 retval.xcidx(0) = 0; |
|
5275
|
1842 octave_idx_type ii = 0; |
|
|
1843 octave_idx_type x_nz = b_nz; |
|
5164
|
1844 |
|
5785
|
1845 if (typ == MatrixType::Permuted_Upper) |
|
5164
|
1846 { |
|
5322
|
1847 octave_idx_type *perm = mattype.triangular_perm (); |
|
5630
|
1848 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
1849 |
|
|
1850 OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc); |
|
|
1851 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
1852 rperm[perm[i]] = i; |
|
5164
|
1853 |
|
5275
|
1854 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1855 { |
|
5630
|
1856 for (octave_idx_type i = 0; i < nm; i++) |
|
5164
|
1857 work[i] = 0.; |
|
5275
|
1858 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
1859 work[b.ridx(i)] = b.data(i); |
|
|
1860 |
|
5630
|
1861 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
1862 { |
|
5322
|
1863 octave_idx_type kidx = perm[k]; |
|
|
1864 |
|
|
1865 if (work[k] != 0.) |
|
5164
|
1866 { |
|
5681
|
1867 if (ridx(cidx(kidx+1)-1) != k || |
|
|
1868 data(cidx(kidx+1)-1) == 0.) |
|
5164
|
1869 { |
|
|
1870 err = -2; |
|
|
1871 goto triangular_error; |
|
|
1872 } |
|
|
1873 |
|
5322
|
1874 double tmp = work[k] / data(cidx(kidx+1)-1); |
|
|
1875 work[k] = tmp; |
|
|
1876 for (octave_idx_type i = cidx(kidx); |
|
|
1877 i < cidx(kidx+1)-1; i++) |
|
5164
|
1878 { |
|
5322
|
1879 octave_idx_type iidx = ridx(i); |
|
|
1880 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
1881 } |
|
|
1882 } |
|
|
1883 } |
|
|
1884 |
|
|
1885 // Count non-zeros in work vector and adjust space in |
|
|
1886 // retval if needed |
|
5275
|
1887 octave_idx_type new_nnz = 0; |
|
5630
|
1888 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
1889 if (work[i] != 0.) |
|
|
1890 new_nnz++; |
|
|
1891 |
|
|
1892 if (ii + new_nnz > x_nz) |
|
|
1893 { |
|
|
1894 // Resize the sparse matrix |
|
5275
|
1895 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
1896 retval.change_capacity (sz); |
|
|
1897 x_nz = sz; |
|
|
1898 } |
|
|
1899 |
|
5630
|
1900 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
1901 if (work[rperm[i]] != 0.) |
|
5164
|
1902 { |
|
|
1903 retval.xridx(ii) = i; |
|
5322
|
1904 retval.xdata(ii++) = work[rperm[i]]; |
|
5164
|
1905 } |
|
|
1906 retval.xcidx(j+1) = ii; |
|
|
1907 } |
|
|
1908 |
|
|
1909 retval.maybe_compress (); |
|
|
1910 |
|
5681
|
1911 if (calc_cond) |
|
|
1912 { |
|
|
1913 // Calculation of 1-norm of inv(*this) |
|
|
1914 for (octave_idx_type i = 0; i < nm; i++) |
|
|
1915 work[i] = 0.; |
|
|
1916 |
|
|
1917 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
1918 { |
|
5681
|
1919 work[j] = 1.; |
|
|
1920 |
|
|
1921 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
1922 { |
|
5681
|
1923 octave_idx_type iidx = perm[k]; |
|
|
1924 |
|
|
1925 if (work[k] != 0.) |
|
5164
|
1926 { |
|
5681
|
1927 double tmp = work[k] / data(cidx(iidx+1)-1); |
|
|
1928 work[k] = tmp; |
|
|
1929 for (octave_idx_type i = cidx(iidx); |
|
|
1930 i < cidx(iidx+1)-1; i++) |
|
|
1931 { |
|
|
1932 octave_idx_type idx2 = ridx(i); |
|
|
1933 work[idx2] = work[idx2] - tmp * data(i); |
|
|
1934 } |
|
5164
|
1935 } |
|
|
1936 } |
|
5681
|
1937 double atmp = 0; |
|
|
1938 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
1939 { |
|
|
1940 atmp += fabs(work[i]); |
|
|
1941 work[i] = 0.; |
|
|
1942 } |
|
|
1943 if (atmp > ainvnorm) |
|
|
1944 ainvnorm = atmp; |
|
5164
|
1945 } |
|
5681
|
1946 rcond = 1. / ainvnorm / anorm; |
|
5164
|
1947 } |
|
|
1948 } |
|
|
1949 else |
|
|
1950 { |
|
5630
|
1951 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
5164
|
1952 |
|
5275
|
1953 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
1954 { |
|
5630
|
1955 for (octave_idx_type i = 0; i < nm; i++) |
|
5164
|
1956 work[i] = 0.; |
|
5275
|
1957 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
1958 work[b.ridx(i)] = b.data(i); |
|
|
1959 |
|
5630
|
1960 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
1961 { |
|
|
1962 if (work[k] != 0.) |
|
|
1963 { |
|
5681
|
1964 if (ridx(cidx(k+1)-1) != k || |
|
|
1965 data(cidx(k+1)-1) == 0.) |
|
5164
|
1966 { |
|
|
1967 err = -2; |
|
|
1968 goto triangular_error; |
|
|
1969 } |
|
|
1970 |
|
|
1971 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
1972 work[k] = tmp; |
|
5275
|
1973 for (octave_idx_type i = cidx(k); i < cidx(k+1)-1; i++) |
|
5164
|
1974 { |
|
5275
|
1975 octave_idx_type iidx = ridx(i); |
|
5164
|
1976 work[iidx] = work[iidx] - tmp * data(i); |
|
|
1977 } |
|
|
1978 } |
|
|
1979 } |
|
|
1980 |
|
|
1981 // Count non-zeros in work vector and adjust space in |
|
|
1982 // retval if needed |
|
5275
|
1983 octave_idx_type new_nnz = 0; |
|
5630
|
1984 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
1985 if (work[i] != 0.) |
|
|
1986 new_nnz++; |
|
|
1987 |
|
|
1988 if (ii + new_nnz > x_nz) |
|
|
1989 { |
|
|
1990 // Resize the sparse matrix |
|
5275
|
1991 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
1992 retval.change_capacity (sz); |
|
|
1993 x_nz = sz; |
|
|
1994 } |
|
|
1995 |
|
5630
|
1996 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
1997 if (work[i] != 0.) |
|
|
1998 { |
|
|
1999 retval.xridx(ii) = i; |
|
|
2000 retval.xdata(ii++) = work[i]; |
|
|
2001 } |
|
|
2002 retval.xcidx(j+1) = ii; |
|
|
2003 } |
|
|
2004 |
|
|
2005 retval.maybe_compress (); |
|
|
2006 |
|
5681
|
2007 if (calc_cond) |
|
|
2008 { |
|
|
2009 // Calculation of 1-norm of inv(*this) |
|
|
2010 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2011 work[i] = 0.; |
|
|
2012 |
|
|
2013 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2014 { |
|
5681
|
2015 work[j] = 1.; |
|
|
2016 |
|
|
2017 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
2018 { |
|
5681
|
2019 if (work[k] != 0.) |
|
5164
|
2020 { |
|
5681
|
2021 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
2022 work[k] = tmp; |
|
|
2023 for (octave_idx_type i = cidx(k); |
|
|
2024 i < cidx(k+1)-1; i++) |
|
|
2025 { |
|
|
2026 octave_idx_type iidx = ridx(i); |
|
|
2027 work[iidx] = work[iidx] - tmp * data(i); |
|
|
2028 } |
|
5164
|
2029 } |
|
|
2030 } |
|
5681
|
2031 double atmp = 0; |
|
|
2032 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
2033 { |
|
|
2034 atmp += fabs(work[i]); |
|
|
2035 work[i] = 0.; |
|
|
2036 } |
|
|
2037 if (atmp > ainvnorm) |
|
|
2038 ainvnorm = atmp; |
|
5164
|
2039 } |
|
5681
|
2040 rcond = 1. / ainvnorm / anorm; |
|
|
2041 } |
|
|
2042 } |
|
5164
|
2043 |
|
|
2044 triangular_error: |
|
|
2045 if (err != 0) |
|
|
2046 { |
|
|
2047 if (sing_handler) |
|
5681
|
2048 { |
|
|
2049 sing_handler (rcond); |
|
|
2050 mattype.mark_as_rectangular (); |
|
|
2051 } |
|
5164
|
2052 else |
|
|
2053 (*current_liboctave_error_handler) |
|
|
2054 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
2055 rcond); |
|
|
2056 } |
|
|
2057 |
|
|
2058 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2059 |
|
|
2060 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2061 { |
|
|
2062 err = -2; |
|
|
2063 |
|
|
2064 if (sing_handler) |
|
5681
|
2065 { |
|
|
2066 sing_handler (rcond); |
|
|
2067 mattype.mark_as_rectangular (); |
|
|
2068 } |
|
5164
|
2069 else |
|
|
2070 (*current_liboctave_error_handler) |
|
|
2071 ("matrix singular to machine precision, rcond = %g", |
|
|
2072 rcond); |
|
|
2073 } |
|
|
2074 } |
|
|
2075 else |
|
|
2076 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
2077 } |
|
|
2078 return retval; |
|
|
2079 } |
|
|
2080 |
|
|
2081 ComplexMatrix |
|
5785
|
2082 SparseMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5630
|
2083 octave_idx_type& err, double& rcond, |
|
5681
|
2084 solve_singularity_handler sing_handler, |
|
|
2085 bool calc_cond) const |
|
5164
|
2086 { |
|
|
2087 ComplexMatrix retval; |
|
|
2088 |
|
5275
|
2089 octave_idx_type nr = rows (); |
|
|
2090 octave_idx_type nc = cols (); |
|
5630
|
2091 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
2092 err = 0; |
|
|
2093 |
|
5630
|
2094 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
2095 (*current_liboctave_error_handler) |
|
|
2096 ("matrix dimension mismatch solution of linear equations"); |
|
|
2097 else |
|
|
2098 { |
|
|
2099 // Print spparms("spumoni") info if requested |
|
|
2100 int typ = mattype.type (); |
|
|
2101 mattype.info (); |
|
|
2102 |
|
5785
|
2103 if (typ == MatrixType::Permuted_Upper || |
|
|
2104 typ == MatrixType::Upper) |
|
5164
|
2105 { |
|
|
2106 double anorm = 0.; |
|
|
2107 double ainvnorm = 0.; |
|
5275
|
2108 octave_idx_type b_nc = b.cols (); |
|
5681
|
2109 rcond = 1.; |
|
|
2110 |
|
|
2111 if (calc_cond) |
|
|
2112 { |
|
|
2113 // Calculate the 1-norm of matrix for rcond calculation |
|
|
2114 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2115 { |
|
|
2116 double atmp = 0.; |
|
|
2117 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
2118 atmp += fabs(data(i)); |
|
|
2119 if (atmp > anorm) |
|
|
2120 anorm = atmp; |
|
|
2121 } |
|
5164
|
2122 } |
|
|
2123 |
|
5785
|
2124 if (typ == MatrixType::Permuted_Upper) |
|
5164
|
2125 { |
|
5630
|
2126 retval.resize (nc, b_nc); |
|
5322
|
2127 octave_idx_type *perm = mattype.triangular_perm (); |
|
5630
|
2128 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
5164
|
2129 |
|
5275
|
2130 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2131 { |
|
5275
|
2132 for (octave_idx_type i = 0; i < nr; i++) |
|
5322
|
2133 cwork[i] = b(i,j); |
|
5630
|
2134 for (octave_idx_type i = nr; i < nc; i++) |
|
|
2135 cwork[i] = 0.; |
|
|
2136 |
|
|
2137 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
2138 { |
|
5322
|
2139 octave_idx_type kidx = perm[k]; |
|
|
2140 |
|
|
2141 if (cwork[k] != 0.) |
|
5164
|
2142 { |
|
5681
|
2143 if (ridx(cidx(kidx+1)-1) != k || |
|
|
2144 data(cidx(kidx+1)-1) == 0.) |
|
5164
|
2145 { |
|
|
2146 err = -2; |
|
|
2147 goto triangular_error; |
|
|
2148 } |
|
|
2149 |
|
5322
|
2150 Complex tmp = cwork[k] / data(cidx(kidx+1)-1); |
|
|
2151 cwork[k] = tmp; |
|
|
2152 for (octave_idx_type i = cidx(kidx); |
|
|
2153 i < cidx(kidx+1)-1; i++) |
|
5164
|
2154 { |
|
5322
|
2155 octave_idx_type iidx = ridx(i); |
|
|
2156 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
2157 } |
|
|
2158 } |
|
|
2159 } |
|
|
2160 |
|
5630
|
2161 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2162 retval.xelem (perm[i], j) = cwork[i]; |
|
5164
|
2163 } |
|
|
2164 |
|
5681
|
2165 if (calc_cond) |
|
|
2166 { |
|
|
2167 // Calculation of 1-norm of inv(*this) |
|
|
2168 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
2169 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2170 work[i] = 0.; |
|
|
2171 |
|
|
2172 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2173 { |
|
5681
|
2174 work[j] = 1.; |
|
|
2175 |
|
|
2176 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
2177 { |
|
5681
|
2178 octave_idx_type iidx = perm[k]; |
|
|
2179 |
|
|
2180 if (work[k] != 0.) |
|
5164
|
2181 { |
|
5681
|
2182 double tmp = work[k] / data(cidx(iidx+1)-1); |
|
|
2183 work[k] = tmp; |
|
|
2184 for (octave_idx_type i = cidx(iidx); |
|
|
2185 i < cidx(iidx+1)-1; i++) |
|
|
2186 { |
|
|
2187 octave_idx_type idx2 = ridx(i); |
|
|
2188 work[idx2] = work[idx2] - tmp * data(i); |
|
|
2189 } |
|
5164
|
2190 } |
|
|
2191 } |
|
5681
|
2192 double atmp = 0; |
|
|
2193 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
2194 { |
|
|
2195 atmp += fabs(work[i]); |
|
|
2196 work[i] = 0.; |
|
|
2197 } |
|
|
2198 if (atmp > ainvnorm) |
|
|
2199 ainvnorm = atmp; |
|
5164
|
2200 } |
|
5681
|
2201 rcond = 1. / ainvnorm / anorm; |
|
5164
|
2202 } |
|
|
2203 } |
|
|
2204 else |
|
|
2205 { |
|
5630
|
2206 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
|
2207 retval.resize (nc, b_nc); |
|
5164
|
2208 |
|
5275
|
2209 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2210 { |
|
5630
|
2211 for (octave_idx_type i = 0; i < nr; i++) |
|
|
2212 cwork[i] = b(i,j); |
|
|
2213 for (octave_idx_type i = nr; i < nc; i++) |
|
|
2214 cwork[i] = 0.; |
|
|
2215 |
|
|
2216 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
2217 { |
|
5630
|
2218 if (cwork[k] != 0.) |
|
5164
|
2219 { |
|
5681
|
2220 if (ridx(cidx(k+1)-1) != k || |
|
|
2221 data(cidx(k+1)-1) == 0.) |
|
5164
|
2222 { |
|
|
2223 err = -2; |
|
|
2224 goto triangular_error; |
|
|
2225 } |
|
|
2226 |
|
5630
|
2227 Complex tmp = cwork[k] / data(cidx(k+1)-1); |
|
|
2228 cwork[k] = tmp; |
|
5275
|
2229 for (octave_idx_type i = cidx(k); i < cidx(k+1)-1; i++) |
|
5164
|
2230 { |
|
5275
|
2231 octave_idx_type iidx = ridx(i); |
|
5630
|
2232 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
2233 } |
|
|
2234 } |
|
|
2235 } |
|
5630
|
2236 |
|
|
2237 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2238 retval.xelem (i, j) = cwork[i]; |
|
5164
|
2239 } |
|
|
2240 |
|
5681
|
2241 if (calc_cond) |
|
|
2242 { |
|
|
2243 // Calculation of 1-norm of inv(*this) |
|
|
2244 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
2245 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2246 work[i] = 0.; |
|
|
2247 |
|
|
2248 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2249 { |
|
5681
|
2250 work[j] = 1.; |
|
|
2251 |
|
|
2252 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
2253 { |
|
5681
|
2254 if (work[k] != 0.) |
|
5164
|
2255 { |
|
5681
|
2256 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
2257 work[k] = tmp; |
|
|
2258 for (octave_idx_type i = cidx(k); |
|
|
2259 i < cidx(k+1)-1; i++) |
|
|
2260 { |
|
|
2261 octave_idx_type iidx = ridx(i); |
|
|
2262 work[iidx] = work[iidx] - tmp * data(i); |
|
|
2263 } |
|
5164
|
2264 } |
|
|
2265 } |
|
5681
|
2266 double atmp = 0; |
|
|
2267 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
2268 { |
|
|
2269 atmp += fabs(work[i]); |
|
|
2270 work[i] = 0.; |
|
|
2271 } |
|
|
2272 if (atmp > ainvnorm) |
|
|
2273 ainvnorm = atmp; |
|
5164
|
2274 } |
|
5681
|
2275 rcond = 1. / ainvnorm / anorm; |
|
|
2276 } |
|
|
2277 } |
|
5164
|
2278 |
|
|
2279 triangular_error: |
|
|
2280 if (err != 0) |
|
|
2281 { |
|
|
2282 if (sing_handler) |
|
5681
|
2283 { |
|
|
2284 sing_handler (rcond); |
|
|
2285 mattype.mark_as_rectangular (); |
|
|
2286 } |
|
5164
|
2287 else |
|
|
2288 (*current_liboctave_error_handler) |
|
|
2289 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
2290 rcond); |
|
|
2291 } |
|
|
2292 |
|
|
2293 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2294 |
|
|
2295 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2296 { |
|
|
2297 err = -2; |
|
|
2298 |
|
|
2299 if (sing_handler) |
|
5681
|
2300 { |
|
|
2301 sing_handler (rcond); |
|
|
2302 mattype.mark_as_rectangular (); |
|
|
2303 } |
|
5164
|
2304 else |
|
|
2305 (*current_liboctave_error_handler) |
|
|
2306 ("matrix singular to machine precision, rcond = %g", |
|
|
2307 rcond); |
|
|
2308 } |
|
|
2309 } |
|
|
2310 else |
|
|
2311 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
2312 } |
|
|
2313 |
|
|
2314 return retval; |
|
|
2315 } |
|
|
2316 |
|
|
2317 SparseComplexMatrix |
|
5785
|
2318 SparseMatrix::utsolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5630
|
2319 octave_idx_type& err, double& rcond, |
|
5681
|
2320 solve_singularity_handler sing_handler, |
|
|
2321 bool calc_cond) const |
|
5164
|
2322 { |
|
|
2323 SparseComplexMatrix retval; |
|
|
2324 |
|
5275
|
2325 octave_idx_type nr = rows (); |
|
|
2326 octave_idx_type nc = cols (); |
|
5630
|
2327 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
2328 err = 0; |
|
|
2329 |
|
5630
|
2330 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
2331 (*current_liboctave_error_handler) |
|
|
2332 ("matrix dimension mismatch solution of linear equations"); |
|
|
2333 else |
|
|
2334 { |
|
|
2335 // Print spparms("spumoni") info if requested |
|
|
2336 int typ = mattype.type (); |
|
|
2337 mattype.info (); |
|
|
2338 |
|
5785
|
2339 if (typ == MatrixType::Permuted_Upper || |
|
|
2340 typ == MatrixType::Upper) |
|
5164
|
2341 { |
|
|
2342 double anorm = 0.; |
|
|
2343 double ainvnorm = 0.; |
|
5681
|
2344 rcond = 1.; |
|
|
2345 |
|
|
2346 if (calc_cond) |
|
|
2347 { |
|
|
2348 // Calculate the 1-norm of matrix for rcond calculation |
|
|
2349 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2350 { |
|
|
2351 double atmp = 0.; |
|
|
2352 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
2353 atmp += fabs(data(i)); |
|
|
2354 if (atmp > anorm) |
|
|
2355 anorm = atmp; |
|
|
2356 } |
|
5164
|
2357 } |
|
|
2358 |
|
5275
|
2359 octave_idx_type b_nc = b.cols (); |
|
5681
|
2360 octave_idx_type b_nz = b.nnz (); |
|
5630
|
2361 retval = SparseComplexMatrix (nc, b_nc, b_nz); |
|
5164
|
2362 retval.xcidx(0) = 0; |
|
5275
|
2363 octave_idx_type ii = 0; |
|
|
2364 octave_idx_type x_nz = b_nz; |
|
5164
|
2365 |
|
5785
|
2366 if (typ == MatrixType::Permuted_Upper) |
|
5164
|
2367 { |
|
5322
|
2368 octave_idx_type *perm = mattype.triangular_perm (); |
|
5630
|
2369 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
|
2370 |
|
|
2371 OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc); |
|
|
2372 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
2373 rperm[perm[i]] = i; |
|
5164
|
2374 |
|
5275
|
2375 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2376 { |
|
5630
|
2377 for (octave_idx_type i = 0; i < nm; i++) |
|
5322
|
2378 cwork[i] = 0.; |
|
5275
|
2379 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5322
|
2380 cwork[b.ridx(i)] = b.data(i); |
|
5164
|
2381 |
|
5630
|
2382 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
2383 { |
|
5322
|
2384 octave_idx_type kidx = perm[k]; |
|
|
2385 |
|
|
2386 if (cwork[k] != 0.) |
|
5164
|
2387 { |
|
5681
|
2388 if (ridx(cidx(kidx+1)-1) != k || |
|
|
2389 data(cidx(kidx+1)-1) == 0.) |
|
5164
|
2390 { |
|
|
2391 err = -2; |
|
|
2392 goto triangular_error; |
|
|
2393 } |
|
|
2394 |
|
5322
|
2395 Complex tmp = cwork[k] / data(cidx(kidx+1)-1); |
|
|
2396 cwork[k] = tmp; |
|
|
2397 for (octave_idx_type i = cidx(kidx); |
|
|
2398 i < cidx(kidx+1)-1; i++) |
|
5164
|
2399 { |
|
5322
|
2400 octave_idx_type iidx = ridx(i); |
|
|
2401 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
2402 } |
|
|
2403 } |
|
|
2404 } |
|
|
2405 |
|
|
2406 // Count non-zeros in work vector and adjust space in |
|
|
2407 // retval if needed |
|
5275
|
2408 octave_idx_type new_nnz = 0; |
|
5630
|
2409 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
2410 if (cwork[i] != 0.) |
|
5164
|
2411 new_nnz++; |
|
|
2412 |
|
|
2413 if (ii + new_nnz > x_nz) |
|
|
2414 { |
|
|
2415 // Resize the sparse matrix |
|
5275
|
2416 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
2417 retval.change_capacity (sz); |
|
|
2418 x_nz = sz; |
|
|
2419 } |
|
|
2420 |
|
5630
|
2421 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
2422 if (cwork[rperm[i]] != 0.) |
|
5164
|
2423 { |
|
|
2424 retval.xridx(ii) = i; |
|
5322
|
2425 retval.xdata(ii++) = cwork[rperm[i]]; |
|
5164
|
2426 } |
|
|
2427 retval.xcidx(j+1) = ii; |
|
|
2428 } |
|
|
2429 |
|
|
2430 retval.maybe_compress (); |
|
|
2431 |
|
5681
|
2432 if (calc_cond) |
|
|
2433 { |
|
|
2434 // Calculation of 1-norm of inv(*this) |
|
|
2435 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
2436 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2437 work[i] = 0.; |
|
|
2438 |
|
|
2439 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2440 { |
|
5681
|
2441 work[j] = 1.; |
|
|
2442 |
|
|
2443 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
2444 { |
|
5681
|
2445 octave_idx_type iidx = perm[k]; |
|
|
2446 |
|
|
2447 if (work[k] != 0.) |
|
5164
|
2448 { |
|
5681
|
2449 double tmp = work[k] / data(cidx(iidx+1)-1); |
|
|
2450 work[k] = tmp; |
|
|
2451 for (octave_idx_type i = cidx(iidx); |
|
|
2452 i < cidx(iidx+1)-1; i++) |
|
|
2453 { |
|
|
2454 octave_idx_type idx2 = ridx(i); |
|
|
2455 work[idx2] = work[idx2] - tmp * data(i); |
|
|
2456 } |
|
5164
|
2457 } |
|
|
2458 } |
|
5681
|
2459 double atmp = 0; |
|
|
2460 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
2461 { |
|
|
2462 atmp += fabs(work[i]); |
|
|
2463 work[i] = 0.; |
|
|
2464 } |
|
|
2465 if (atmp > ainvnorm) |
|
|
2466 ainvnorm = atmp; |
|
5164
|
2467 } |
|
5681
|
2468 rcond = 1. / ainvnorm / anorm; |
|
5164
|
2469 } |
|
|
2470 } |
|
|
2471 else |
|
|
2472 { |
|
5630
|
2473 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
5164
|
2474 |
|
5275
|
2475 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2476 { |
|
5630
|
2477 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2478 cwork[i] = 0.; |
|
5275
|
2479 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5630
|
2480 cwork[b.ridx(i)] = b.data(i); |
|
|
2481 |
|
|
2482 for (octave_idx_type k = nc-1; k >= 0; k--) |
|
5164
|
2483 { |
|
5630
|
2484 if (cwork[k] != 0.) |
|
5164
|
2485 { |
|
5681
|
2486 if (ridx(cidx(k+1)-1) != k || |
|
|
2487 data(cidx(k+1)-1) == 0.) |
|
5164
|
2488 { |
|
|
2489 err = -2; |
|
|
2490 goto triangular_error; |
|
|
2491 } |
|
|
2492 |
|
5630
|
2493 Complex tmp = cwork[k] / data(cidx(k+1)-1); |
|
|
2494 cwork[k] = tmp; |
|
5275
|
2495 for (octave_idx_type i = cidx(k); i < cidx(k+1)-1; i++) |
|
5164
|
2496 { |
|
5275
|
2497 octave_idx_type iidx = ridx(i); |
|
5630
|
2498 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
2499 } |
|
|
2500 } |
|
|
2501 } |
|
|
2502 |
|
|
2503 // Count non-zeros in work vector and adjust space in |
|
|
2504 // retval if needed |
|
5275
|
2505 octave_idx_type new_nnz = 0; |
|
5630
|
2506 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2507 if (cwork[i] != 0.) |
|
5164
|
2508 new_nnz++; |
|
|
2509 |
|
|
2510 if (ii + new_nnz > x_nz) |
|
|
2511 { |
|
|
2512 // Resize the sparse matrix |
|
5275
|
2513 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
2514 retval.change_capacity (sz); |
|
|
2515 x_nz = sz; |
|
|
2516 } |
|
|
2517 |
|
5630
|
2518 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2519 if (cwork[i] != 0.) |
|
5164
|
2520 { |
|
|
2521 retval.xridx(ii) = i; |
|
5630
|
2522 retval.xdata(ii++) = cwork[i]; |
|
5164
|
2523 } |
|
|
2524 retval.xcidx(j+1) = ii; |
|
|
2525 } |
|
|
2526 |
|
|
2527 retval.maybe_compress (); |
|
|
2528 |
|
5681
|
2529 if (calc_cond) |
|
|
2530 { |
|
|
2531 // Calculation of 1-norm of inv(*this) |
|
|
2532 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
2533 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2534 work[i] = 0.; |
|
|
2535 |
|
|
2536 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2537 { |
|
5681
|
2538 work[j] = 1.; |
|
|
2539 |
|
|
2540 for (octave_idx_type k = j; k >= 0; k--) |
|
5164
|
2541 { |
|
5681
|
2542 if (work[k] != 0.) |
|
5164
|
2543 { |
|
5681
|
2544 double tmp = work[k] / data(cidx(k+1)-1); |
|
|
2545 work[k] = tmp; |
|
|
2546 for (octave_idx_type i = cidx(k); |
|
|
2547 i < cidx(k+1)-1; i++) |
|
|
2548 { |
|
|
2549 octave_idx_type iidx = ridx(i); |
|
|
2550 work[iidx] = work[iidx] - tmp * data(i); |
|
|
2551 } |
|
5164
|
2552 } |
|
|
2553 } |
|
5681
|
2554 double atmp = 0; |
|
|
2555 for (octave_idx_type i = 0; i < j+1; i++) |
|
|
2556 { |
|
|
2557 atmp += fabs(work[i]); |
|
|
2558 work[i] = 0.; |
|
|
2559 } |
|
|
2560 if (atmp > ainvnorm) |
|
|
2561 ainvnorm = atmp; |
|
5164
|
2562 } |
|
5681
|
2563 rcond = 1. / ainvnorm / anorm; |
|
|
2564 } |
|
|
2565 } |
|
5164
|
2566 |
|
|
2567 triangular_error: |
|
|
2568 if (err != 0) |
|
|
2569 { |
|
|
2570 if (sing_handler) |
|
5681
|
2571 { |
|
|
2572 sing_handler (rcond); |
|
|
2573 mattype.mark_as_rectangular (); |
|
|
2574 } |
|
5164
|
2575 else |
|
|
2576 (*current_liboctave_error_handler) |
|
|
2577 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
2578 rcond); |
|
|
2579 } |
|
|
2580 |
|
|
2581 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2582 |
|
|
2583 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2584 { |
|
|
2585 err = -2; |
|
|
2586 |
|
|
2587 if (sing_handler) |
|
5681
|
2588 { |
|
|
2589 sing_handler (rcond); |
|
|
2590 mattype.mark_as_rectangular (); |
|
|
2591 } |
|
5164
|
2592 else |
|
|
2593 (*current_liboctave_error_handler) |
|
|
2594 ("matrix singular to machine precision, rcond = %g", |
|
|
2595 rcond); |
|
|
2596 } |
|
|
2597 } |
|
|
2598 else |
|
|
2599 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
2600 } |
|
|
2601 |
|
|
2602 return retval; |
|
|
2603 } |
|
|
2604 |
|
|
2605 Matrix |
|
5785
|
2606 SparseMatrix::ltsolve (MatrixType &mattype, const Matrix& b, |
|
5630
|
2607 octave_idx_type& err, double& rcond, |
|
5681
|
2608 solve_singularity_handler sing_handler, |
|
|
2609 bool calc_cond) const |
|
5164
|
2610 { |
|
|
2611 Matrix retval; |
|
|
2612 |
|
5275
|
2613 octave_idx_type nr = rows (); |
|
|
2614 octave_idx_type nc = cols (); |
|
5630
|
2615 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
2616 err = 0; |
|
|
2617 |
|
5630
|
2618 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
2619 (*current_liboctave_error_handler) |
|
|
2620 ("matrix dimension mismatch solution of linear equations"); |
|
|
2621 else |
|
|
2622 { |
|
|
2623 // Print spparms("spumoni") info if requested |
|
|
2624 int typ = mattype.type (); |
|
|
2625 mattype.info (); |
|
|
2626 |
|
5785
|
2627 if (typ == MatrixType::Permuted_Lower || |
|
|
2628 typ == MatrixType::Lower) |
|
5164
|
2629 { |
|
|
2630 double anorm = 0.; |
|
|
2631 double ainvnorm = 0.; |
|
5630
|
2632 octave_idx_type b_nc = b.cols (); |
|
5681
|
2633 rcond = 1.; |
|
|
2634 |
|
|
2635 if (calc_cond) |
|
|
2636 { |
|
|
2637 // Calculate the 1-norm of matrix for rcond calculation |
|
|
2638 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2639 { |
|
|
2640 double atmp = 0.; |
|
|
2641 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
2642 atmp += fabs(data(i)); |
|
|
2643 if (atmp > anorm) |
|
|
2644 anorm = atmp; |
|
|
2645 } |
|
5164
|
2646 } |
|
|
2647 |
|
5785
|
2648 if (typ == MatrixType::Permuted_Lower) |
|
5164
|
2649 { |
|
5630
|
2650 retval.resize (nc, b_nc); |
|
|
2651 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
5322
|
2652 octave_idx_type *perm = mattype.triangular_perm (); |
|
5164
|
2653 |
|
5630
|
2654 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2655 { |
|
5630
|
2656 if (nc > nr) |
|
|
2657 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2658 work[i] = 0.; |
|
5275
|
2659 for (octave_idx_type i = 0; i < nr; i++) |
|
5322
|
2660 work[perm[i]] = b(i,j); |
|
5164
|
2661 |
|
5630
|
2662 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
2663 { |
|
5322
|
2664 if (work[k] != 0.) |
|
5164
|
2665 { |
|
5322
|
2666 octave_idx_type minr = nr; |
|
|
2667 octave_idx_type mini = 0; |
|
|
2668 |
|
|
2669 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
2670 if (perm[ridx(i)] < minr) |
|
|
2671 { |
|
|
2672 minr = perm[ridx(i)]; |
|
|
2673 mini = i; |
|
|
2674 } |
|
|
2675 |
|
5681
|
2676 if (minr != k || data(mini) == 0) |
|
5164
|
2677 { |
|
|
2678 err = -2; |
|
|
2679 goto triangular_error; |
|
|
2680 } |
|
|
2681 |
|
5322
|
2682 double tmp = work[k] / data(mini); |
|
|
2683 work[k] = tmp; |
|
|
2684 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
5164
|
2685 { |
|
5322
|
2686 if (i == mini) |
|
|
2687 continue; |
|
|
2688 |
|
|
2689 octave_idx_type iidx = perm[ridx(i)]; |
|
|
2690 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
2691 } |
|
|
2692 } |
|
|
2693 } |
|
|
2694 |
|
5630
|
2695 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
2696 retval (i, j) = work[i]; |
|
5164
|
2697 } |
|
|
2698 |
|
5681
|
2699 if (calc_cond) |
|
|
2700 { |
|
|
2701 // Calculation of 1-norm of inv(*this) |
|
|
2702 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2703 work[i] = 0.; |
|
|
2704 |
|
|
2705 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2706 { |
|
5681
|
2707 work[j] = 1.; |
|
|
2708 |
|
|
2709 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
2710 { |
|
5681
|
2711 if (work[k] != 0.) |
|
5164
|
2712 { |
|
5681
|
2713 octave_idx_type minr = nr; |
|
|
2714 octave_idx_type mini = 0; |
|
|
2715 |
|
|
2716 for (octave_idx_type i = cidx(k); |
|
|
2717 i < cidx(k+1); i++) |
|
|
2718 if (perm[ridx(i)] < minr) |
|
|
2719 { |
|
|
2720 minr = perm[ridx(i)]; |
|
|
2721 mini = i; |
|
|
2722 } |
|
|
2723 |
|
|
2724 double tmp = work[k] / data(mini); |
|
|
2725 work[k] = tmp; |
|
|
2726 for (octave_idx_type i = cidx(k); |
|
|
2727 i < cidx(k+1); i++) |
|
|
2728 { |
|
|
2729 if (i == mini) |
|
|
2730 continue; |
|
|
2731 |
|
|
2732 octave_idx_type iidx = perm[ridx(i)]; |
|
|
2733 work[iidx] = work[iidx] - tmp * data(i); |
|
|
2734 } |
|
5164
|
2735 } |
|
|
2736 } |
|
5681
|
2737 |
|
|
2738 double atmp = 0; |
|
|
2739 for (octave_idx_type i = j; i < nc; i++) |
|
|
2740 { |
|
|
2741 atmp += fabs(work[i]); |
|
|
2742 work[i] = 0.; |
|
|
2743 } |
|
|
2744 if (atmp > ainvnorm) |
|
|
2745 ainvnorm = atmp; |
|
5164
|
2746 } |
|
5681
|
2747 rcond = 1. / ainvnorm / anorm; |
|
5164
|
2748 } |
|
|
2749 } |
|
|
2750 else |
|
|
2751 { |
|
5630
|
2752 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
2753 retval.resize (nc, b_nc, 0.); |
|
|
2754 |
|
|
2755 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2756 { |
|
5630
|
2757 for (octave_idx_type i = 0; i < nr; i++) |
|
|
2758 work[i] = b(i,j); |
|
|
2759 for (octave_idx_type i = nr; i < nc; i++) |
|
|
2760 work[i] = 0.; |
|
|
2761 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
2762 { |
|
5630
|
2763 if (work[k] != 0.) |
|
5164
|
2764 { |
|
5681
|
2765 if (ridx(cidx(k)) != k || |
|
|
2766 data(cidx(k)) == 0.) |
|
5164
|
2767 { |
|
|
2768 err = -2; |
|
|
2769 goto triangular_error; |
|
|
2770 } |
|
|
2771 |
|
5630
|
2772 double tmp = work[k] / data(cidx(k)); |
|
|
2773 work[k] = tmp; |
|
|
2774 for (octave_idx_type i = cidx(k)+1; |
|
|
2775 i < cidx(k+1); i++) |
|
5164
|
2776 { |
|
5275
|
2777 octave_idx_type iidx = ridx(i); |
|
5630
|
2778 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
2779 } |
|
|
2780 } |
|
|
2781 } |
|
5630
|
2782 |
|
|
2783 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2784 retval.xelem (i, j) = work[i]; |
|
5164
|
2785 } |
|
|
2786 |
|
5681
|
2787 if (calc_cond) |
|
|
2788 { |
|
|
2789 // Calculation of 1-norm of inv(*this) |
|
|
2790 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2791 work[i] = 0.; |
|
|
2792 |
|
|
2793 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2794 { |
|
5681
|
2795 work[j] = 1.; |
|
|
2796 |
|
|
2797 for (octave_idx_type k = j; k < nc; k++) |
|
5164
|
2798 { |
|
5681
|
2799 |
|
|
2800 if (work[k] != 0.) |
|
5164
|
2801 { |
|
5681
|
2802 double tmp = work[k] / data(cidx(k)); |
|
|
2803 work[k] = tmp; |
|
|
2804 for (octave_idx_type i = cidx(k)+1; |
|
|
2805 i < cidx(k+1); i++) |
|
|
2806 { |
|
|
2807 octave_idx_type iidx = ridx(i); |
|
|
2808 work[iidx] = work[iidx] - tmp * data(i); |
|
|
2809 } |
|
5164
|
2810 } |
|
|
2811 } |
|
5681
|
2812 double atmp = 0; |
|
|
2813 for (octave_idx_type i = j; i < nc; i++) |
|
|
2814 { |
|
|
2815 atmp += fabs(work[i]); |
|
|
2816 work[i] = 0.; |
|
|
2817 } |
|
|
2818 if (atmp > ainvnorm) |
|
|
2819 ainvnorm = atmp; |
|
5164
|
2820 } |
|
5681
|
2821 rcond = 1. / ainvnorm / anorm; |
|
|
2822 } |
|
|
2823 } |
|
5164
|
2824 |
|
|
2825 triangular_error: |
|
|
2826 if (err != 0) |
|
|
2827 { |
|
|
2828 if (sing_handler) |
|
5681
|
2829 { |
|
|
2830 sing_handler (rcond); |
|
|
2831 mattype.mark_as_rectangular (); |
|
|
2832 } |
|
5164
|
2833 else |
|
|
2834 (*current_liboctave_error_handler) |
|
|
2835 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
2836 rcond); |
|
|
2837 } |
|
|
2838 |
|
|
2839 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2840 |
|
|
2841 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2842 { |
|
|
2843 err = -2; |
|
|
2844 |
|
|
2845 if (sing_handler) |
|
5681
|
2846 { |
|
|
2847 sing_handler (rcond); |
|
|
2848 mattype.mark_as_rectangular (); |
|
|
2849 } |
|
5164
|
2850 else |
|
|
2851 (*current_liboctave_error_handler) |
|
|
2852 ("matrix singular to machine precision, rcond = %g", |
|
|
2853 rcond); |
|
|
2854 } |
|
|
2855 } |
|
|
2856 else |
|
|
2857 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
2858 } |
|
|
2859 |
|
|
2860 return retval; |
|
|
2861 } |
|
|
2862 |
|
|
2863 SparseMatrix |
|
5785
|
2864 SparseMatrix::ltsolve (MatrixType &mattype, const SparseMatrix& b, |
|
5630
|
2865 octave_idx_type& err, double& rcond, |
|
5681
|
2866 solve_singularity_handler sing_handler, |
|
|
2867 bool calc_cond) const |
|
5164
|
2868 { |
|
|
2869 SparseMatrix retval; |
|
|
2870 |
|
5275
|
2871 octave_idx_type nr = rows (); |
|
|
2872 octave_idx_type nc = cols (); |
|
5630
|
2873 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
2874 err = 0; |
|
|
2875 |
|
5630
|
2876 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
2877 (*current_liboctave_error_handler) |
|
|
2878 ("matrix dimension mismatch solution of linear equations"); |
|
|
2879 else |
|
|
2880 { |
|
|
2881 // Print spparms("spumoni") info if requested |
|
|
2882 int typ = mattype.type (); |
|
|
2883 mattype.info (); |
|
|
2884 |
|
5785
|
2885 if (typ == MatrixType::Permuted_Lower || |
|
|
2886 typ == MatrixType::Lower) |
|
5164
|
2887 { |
|
|
2888 double anorm = 0.; |
|
|
2889 double ainvnorm = 0.; |
|
5681
|
2890 rcond = 1.; |
|
|
2891 |
|
|
2892 if (calc_cond) |
|
|
2893 { |
|
|
2894 // Calculate the 1-norm of matrix for rcond calculation |
|
|
2895 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2896 { |
|
|
2897 double atmp = 0.; |
|
|
2898 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
2899 atmp += fabs(data(i)); |
|
|
2900 if (atmp > anorm) |
|
|
2901 anorm = atmp; |
|
|
2902 } |
|
|
2903 } |
|
|
2904 |
|
5275
|
2905 octave_idx_type b_nc = b.cols (); |
|
5681
|
2906 octave_idx_type b_nz = b.nnz (); |
|
|
2907 retval = SparseMatrix (nc, b_nc, b_nz); |
|
5164
|
2908 retval.xcidx(0) = 0; |
|
5275
|
2909 octave_idx_type ii = 0; |
|
|
2910 octave_idx_type x_nz = b_nz; |
|
5164
|
2911 |
|
5785
|
2912 if (typ == MatrixType::Permuted_Lower) |
|
5164
|
2913 { |
|
5681
|
2914 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
5322
|
2915 octave_idx_type *perm = mattype.triangular_perm (); |
|
5164
|
2916 |
|
5275
|
2917 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
2918 { |
|
5630
|
2919 for (octave_idx_type i = 0; i < nm; i++) |
|
5164
|
2920 work[i] = 0.; |
|
5275
|
2921 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5322
|
2922 work[perm[b.ridx(i)]] = b.data(i); |
|
5164
|
2923 |
|
5630
|
2924 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
2925 { |
|
5322
|
2926 if (work[k] != 0.) |
|
5164
|
2927 { |
|
5322
|
2928 octave_idx_type minr = nr; |
|
|
2929 octave_idx_type mini = 0; |
|
|
2930 |
|
|
2931 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
2932 if (perm[ridx(i)] < minr) |
|
|
2933 { |
|
|
2934 minr = perm[ridx(i)]; |
|
|
2935 mini = i; |
|
|
2936 } |
|
|
2937 |
|
5681
|
2938 if (minr != k || data(mini) == 0) |
|
5164
|
2939 { |
|
|
2940 err = -2; |
|
|
2941 goto triangular_error; |
|
|
2942 } |
|
|
2943 |
|
5322
|
2944 double tmp = work[k] / data(mini); |
|
|
2945 work[k] = tmp; |
|
|
2946 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
5164
|
2947 { |
|
5322
|
2948 if (i == mini) |
|
|
2949 continue; |
|
|
2950 |
|
|
2951 octave_idx_type iidx = perm[ridx(i)]; |
|
|
2952 work[iidx] = work[iidx] - tmp * data(i); |
|
5164
|
2953 } |
|
|
2954 } |
|
|
2955 } |
|
|
2956 |
|
|
2957 // Count non-zeros in work vector and adjust space in |
|
|
2958 // retval if needed |
|
5275
|
2959 octave_idx_type new_nnz = 0; |
|
5630
|
2960 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
2961 if (work[i] != 0.) |
|
|
2962 new_nnz++; |
|
|
2963 |
|
|
2964 if (ii + new_nnz > x_nz) |
|
|
2965 { |
|
|
2966 // Resize the sparse matrix |
|
5275
|
2967 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
2968 retval.change_capacity (sz); |
|
|
2969 x_nz = sz; |
|
|
2970 } |
|
|
2971 |
|
5630
|
2972 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
2973 if (work[i] != 0.) |
|
5164
|
2974 { |
|
|
2975 retval.xridx(ii) = i; |
|
5322
|
2976 retval.xdata(ii++) = work[i]; |
|
5164
|
2977 } |
|
|
2978 retval.xcidx(j+1) = ii; |
|
|
2979 } |
|
|
2980 |
|
|
2981 retval.maybe_compress (); |
|
|
2982 |
|
5681
|
2983 if (calc_cond) |
|
|
2984 { |
|
|
2985 // Calculation of 1-norm of inv(*this) |
|
|
2986 for (octave_idx_type i = 0; i < nm; i++) |
|
|
2987 work[i] = 0.; |
|
|
2988 |
|
|
2989 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
2990 { |
|
5681
|
2991 work[j] = 1.; |
|
|
2992 |
|
|
2993 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
2994 { |
|
5681
|
2995 if (work[k] != 0.) |
|
5164
|
2996 { |
|
5681
|
2997 octave_idx_type minr = nr; |
|
|
2998 octave_idx_type mini = 0; |
|
|
2999 |
|
|
3000 for (octave_idx_type i = cidx(k); |
|
|
3001 i < cidx(k+1); i++) |
|
|
3002 if (perm[ridx(i)] < minr) |
|
|
3003 { |
|
|
3004 minr = perm[ridx(i)]; |
|
|
3005 mini = i; |
|
|
3006 } |
|
|
3007 |
|
|
3008 double tmp = work[k] / data(mini); |
|
|
3009 work[k] = tmp; |
|
|
3010 for (octave_idx_type i = cidx(k); |
|
|
3011 i < cidx(k+1); i++) |
|
|
3012 { |
|
|
3013 if (i == mini) |
|
|
3014 continue; |
|
|
3015 |
|
|
3016 octave_idx_type iidx = perm[ridx(i)]; |
|
|
3017 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3018 } |
|
5164
|
3019 } |
|
|
3020 } |
|
5681
|
3021 |
|
|
3022 double atmp = 0; |
|
|
3023 for (octave_idx_type i = j; i < nr; i++) |
|
|
3024 { |
|
|
3025 atmp += fabs(work[i]); |
|
|
3026 work[i] = 0.; |
|
|
3027 } |
|
|
3028 if (atmp > ainvnorm) |
|
|
3029 ainvnorm = atmp; |
|
5164
|
3030 } |
|
5681
|
3031 rcond = 1. / ainvnorm / anorm; |
|
5164
|
3032 } |
|
|
3033 } |
|
|
3034 else |
|
|
3035 { |
|
5681
|
3036 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
5164
|
3037 |
|
5275
|
3038 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3039 { |
|
5630
|
3040 for (octave_idx_type i = 0; i < nm; i++) |
|
5164
|
3041 work[i] = 0.; |
|
5275
|
3042 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
3043 work[b.ridx(i)] = b.data(i); |
|
|
3044 |
|
5630
|
3045 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3046 { |
|
|
3047 if (work[k] != 0.) |
|
|
3048 { |
|
5681
|
3049 if (ridx(cidx(k)) != k || |
|
|
3050 data(cidx(k)) == 0.) |
|
5164
|
3051 { |
|
|
3052 err = -2; |
|
|
3053 goto triangular_error; |
|
|
3054 } |
|
|
3055 |
|
|
3056 double tmp = work[k] / data(cidx(k)); |
|
|
3057 work[k] = tmp; |
|
5275
|
3058 for (octave_idx_type i = cidx(k)+1; i < cidx(k+1); i++) |
|
5164
|
3059 { |
|
5275
|
3060 octave_idx_type iidx = ridx(i); |
|
5164
|
3061 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3062 } |
|
|
3063 } |
|
|
3064 } |
|
|
3065 |
|
|
3066 // Count non-zeros in work vector and adjust space in |
|
|
3067 // retval if needed |
|
5275
|
3068 octave_idx_type new_nnz = 0; |
|
5630
|
3069 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
3070 if (work[i] != 0.) |
|
|
3071 new_nnz++; |
|
|
3072 |
|
|
3073 if (ii + new_nnz > x_nz) |
|
|
3074 { |
|
|
3075 // Resize the sparse matrix |
|
5275
|
3076 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
3077 retval.change_capacity (sz); |
|
|
3078 x_nz = sz; |
|
|
3079 } |
|
|
3080 |
|
5630
|
3081 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
3082 if (work[i] != 0.) |
|
|
3083 { |
|
|
3084 retval.xridx(ii) = i; |
|
|
3085 retval.xdata(ii++) = work[i]; |
|
|
3086 } |
|
|
3087 retval.xcidx(j+1) = ii; |
|
|
3088 } |
|
|
3089 |
|
|
3090 retval.maybe_compress (); |
|
|
3091 |
|
5681
|
3092 if (calc_cond) |
|
|
3093 { |
|
|
3094 // Calculation of 1-norm of inv(*this) |
|
|
3095 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3096 work[i] = 0.; |
|
|
3097 |
|
|
3098 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
3099 { |
|
5681
|
3100 work[j] = 1.; |
|
|
3101 |
|
|
3102 for (octave_idx_type k = j; k < nc; k++) |
|
5164
|
3103 { |
|
5681
|
3104 |
|
|
3105 if (work[k] != 0.) |
|
5164
|
3106 { |
|
5681
|
3107 double tmp = work[k] / data(cidx(k)); |
|
|
3108 work[k] = tmp; |
|
|
3109 for (octave_idx_type i = cidx(k)+1; |
|
|
3110 i < cidx(k+1); i++) |
|
|
3111 { |
|
|
3112 octave_idx_type iidx = ridx(i); |
|
|
3113 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3114 } |
|
5164
|
3115 } |
|
|
3116 } |
|
5681
|
3117 double atmp = 0; |
|
|
3118 for (octave_idx_type i = j; i < nc; i++) |
|
|
3119 { |
|
|
3120 atmp += fabs(work[i]); |
|
|
3121 work[i] = 0.; |
|
|
3122 } |
|
|
3123 if (atmp > ainvnorm) |
|
|
3124 ainvnorm = atmp; |
|
5164
|
3125 } |
|
5681
|
3126 rcond = 1. / ainvnorm / anorm; |
|
|
3127 } |
|
|
3128 } |
|
5164
|
3129 |
|
|
3130 triangular_error: |
|
|
3131 if (err != 0) |
|
|
3132 { |
|
|
3133 if (sing_handler) |
|
5681
|
3134 { |
|
|
3135 sing_handler (rcond); |
|
|
3136 mattype.mark_as_rectangular (); |
|
|
3137 } |
|
5164
|
3138 else |
|
|
3139 (*current_liboctave_error_handler) |
|
|
3140 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
3141 rcond); |
|
|
3142 } |
|
|
3143 |
|
|
3144 volatile double rcond_plus_one = rcond + 1.0; |
|
|
3145 |
|
|
3146 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
3147 { |
|
|
3148 err = -2; |
|
|
3149 |
|
|
3150 if (sing_handler) |
|
5681
|
3151 { |
|
|
3152 sing_handler (rcond); |
|
|
3153 mattype.mark_as_rectangular (); |
|
|
3154 } |
|
5164
|
3155 else |
|
|
3156 (*current_liboctave_error_handler) |
|
|
3157 ("matrix singular to machine precision, rcond = %g", |
|
|
3158 rcond); |
|
|
3159 } |
|
|
3160 } |
|
|
3161 else |
|
|
3162 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
3163 } |
|
|
3164 |
|
|
3165 return retval; |
|
|
3166 } |
|
|
3167 |
|
|
3168 ComplexMatrix |
|
5785
|
3169 SparseMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5630
|
3170 octave_idx_type& err, double& rcond, |
|
5681
|
3171 solve_singularity_handler sing_handler, |
|
|
3172 bool calc_cond) const |
|
5164
|
3173 { |
|
|
3174 ComplexMatrix retval; |
|
|
3175 |
|
5275
|
3176 octave_idx_type nr = rows (); |
|
|
3177 octave_idx_type nc = cols (); |
|
5630
|
3178 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
3179 err = 0; |
|
|
3180 |
|
5630
|
3181 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
3182 (*current_liboctave_error_handler) |
|
|
3183 ("matrix dimension mismatch solution of linear equations"); |
|
|
3184 else |
|
|
3185 { |
|
|
3186 // Print spparms("spumoni") info if requested |
|
|
3187 int typ = mattype.type (); |
|
|
3188 mattype.info (); |
|
|
3189 |
|
5785
|
3190 if (typ == MatrixType::Permuted_Lower || |
|
|
3191 typ == MatrixType::Lower) |
|
5164
|
3192 { |
|
|
3193 double anorm = 0.; |
|
|
3194 double ainvnorm = 0.; |
|
5275
|
3195 octave_idx_type b_nc = b.cols (); |
|
5681
|
3196 rcond = 1.; |
|
|
3197 |
|
|
3198 if (calc_cond) |
|
|
3199 { |
|
|
3200 // Calculate the 1-norm of matrix for rcond calculation |
|
|
3201 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3202 { |
|
|
3203 double atmp = 0.; |
|
|
3204 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
3205 atmp += fabs(data(i)); |
|
|
3206 if (atmp > anorm) |
|
|
3207 anorm = atmp; |
|
|
3208 } |
|
5164
|
3209 } |
|
|
3210 |
|
5785
|
3211 if (typ == MatrixType::Permuted_Lower) |
|
5164
|
3212 { |
|
5630
|
3213 retval.resize (nc, b_nc); |
|
5681
|
3214 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
5322
|
3215 octave_idx_type *perm = mattype.triangular_perm (); |
|
5164
|
3216 |
|
5275
|
3217 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3218 { |
|
5630
|
3219 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3220 cwork[i] = 0.; |
|
5275
|
3221 for (octave_idx_type i = 0; i < nr; i++) |
|
5322
|
3222 cwork[perm[i]] = b(i,j); |
|
5164
|
3223 |
|
5630
|
3224 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3225 { |
|
5322
|
3226 if (cwork[k] != 0.) |
|
5164
|
3227 { |
|
5322
|
3228 octave_idx_type minr = nr; |
|
|
3229 octave_idx_type mini = 0; |
|
|
3230 |
|
|
3231 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
3232 if (perm[ridx(i)] < minr) |
|
|
3233 { |
|
|
3234 minr = perm[ridx(i)]; |
|
|
3235 mini = i; |
|
|
3236 } |
|
|
3237 |
|
5681
|
3238 if (minr != k || data(mini) == 0) |
|
5164
|
3239 { |
|
|
3240 err = -2; |
|
|
3241 goto triangular_error; |
|
|
3242 } |
|
|
3243 |
|
5322
|
3244 Complex tmp = cwork[k] / data(mini); |
|
|
3245 cwork[k] = tmp; |
|
|
3246 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
5164
|
3247 { |
|
5322
|
3248 if (i == mini) |
|
|
3249 continue; |
|
|
3250 |
|
|
3251 octave_idx_type iidx = perm[ridx(i)]; |
|
|
3252 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
3253 } |
|
|
3254 } |
|
|
3255 } |
|
|
3256 |
|
5630
|
3257 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
3258 retval (i, j) = cwork[i]; |
|
5164
|
3259 } |
|
|
3260 |
|
5681
|
3261 if (calc_cond) |
|
|
3262 { |
|
|
3263 // Calculation of 1-norm of inv(*this) |
|
|
3264 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
3265 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3266 work[i] = 0.; |
|
|
3267 |
|
|
3268 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
3269 { |
|
5681
|
3270 work[j] = 1.; |
|
|
3271 |
|
|
3272 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3273 { |
|
5681
|
3274 if (work[k] != 0.) |
|
5164
|
3275 { |
|
5681
|
3276 octave_idx_type minr = nr; |
|
|
3277 octave_idx_type mini = 0; |
|
|
3278 |
|
|
3279 for (octave_idx_type i = cidx(k); |
|
|
3280 i < cidx(k+1); i++) |
|
|
3281 if (perm[ridx(i)] < minr) |
|
|
3282 { |
|
|
3283 minr = perm[ridx(i)]; |
|
|
3284 mini = i; |
|
|
3285 } |
|
|
3286 |
|
|
3287 double tmp = work[k] / data(mini); |
|
|
3288 work[k] = tmp; |
|
|
3289 for (octave_idx_type i = cidx(k); |
|
|
3290 i < cidx(k+1); i++) |
|
|
3291 { |
|
|
3292 if (i == mini) |
|
|
3293 continue; |
|
|
3294 |
|
|
3295 octave_idx_type iidx = perm[ridx(i)]; |
|
|
3296 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3297 } |
|
5164
|
3298 } |
|
|
3299 } |
|
5681
|
3300 |
|
|
3301 double atmp = 0; |
|
|
3302 for (octave_idx_type i = j; i < nc; i++) |
|
|
3303 { |
|
|
3304 atmp += fabs(work[i]); |
|
|
3305 work[i] = 0.; |
|
|
3306 } |
|
|
3307 if (atmp > ainvnorm) |
|
|
3308 ainvnorm = atmp; |
|
5164
|
3309 } |
|
5681
|
3310 rcond = 1. / ainvnorm / anorm; |
|
5164
|
3311 } |
|
|
3312 } |
|
|
3313 else |
|
|
3314 { |
|
5630
|
3315 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
|
3316 retval.resize (nc, b_nc, 0.); |
|
5164
|
3317 |
|
5275
|
3318 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3319 { |
|
5630
|
3320 for (octave_idx_type i = 0; i < nr; i++) |
|
|
3321 cwork[i] = b(i,j); |
|
|
3322 for (octave_idx_type i = nr; i < nc; i++) |
|
|
3323 cwork[i] = 0.; |
|
|
3324 |
|
|
3325 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3326 { |
|
5630
|
3327 if (cwork[k] != 0.) |
|
5164
|
3328 { |
|
5681
|
3329 if (ridx(cidx(k)) != k || |
|
|
3330 data(cidx(k)) == 0.) |
|
5164
|
3331 { |
|
|
3332 err = -2; |
|
|
3333 goto triangular_error; |
|
|
3334 } |
|
|
3335 |
|
5630
|
3336 Complex tmp = cwork[k] / data(cidx(k)); |
|
|
3337 cwork[k] = tmp; |
|
5275
|
3338 for (octave_idx_type i = cidx(k)+1; i < cidx(k+1); i++) |
|
5164
|
3339 { |
|
5275
|
3340 octave_idx_type iidx = ridx(i); |
|
5630
|
3341 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
3342 } |
|
|
3343 } |
|
|
3344 } |
|
5630
|
3345 |
|
|
3346 for (octave_idx_type i = 0; i < nc; i++) |
|
|
3347 retval.xelem (i, j) = cwork[i]; |
|
5164
|
3348 } |
|
|
3349 |
|
5681
|
3350 if (calc_cond) |
|
|
3351 { |
|
|
3352 // Calculation of 1-norm of inv(*this) |
|
|
3353 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
3354 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3355 work[i] = 0.; |
|
|
3356 |
|
|
3357 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
3358 { |
|
5681
|
3359 work[j] = 1.; |
|
|
3360 |
|
|
3361 for (octave_idx_type k = j; k < nc; k++) |
|
5164
|
3362 { |
|
5681
|
3363 |
|
|
3364 if (work[k] != 0.) |
|
5164
|
3365 { |
|
5681
|
3366 double tmp = work[k] / data(cidx(k)); |
|
|
3367 work[k] = tmp; |
|
|
3368 for (octave_idx_type i = cidx(k)+1; |
|
|
3369 i < cidx(k+1); i++) |
|
|
3370 { |
|
|
3371 octave_idx_type iidx = ridx(i); |
|
|
3372 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3373 } |
|
5164
|
3374 } |
|
|
3375 } |
|
5681
|
3376 double atmp = 0; |
|
|
3377 for (octave_idx_type i = j; i < nc; i++) |
|
|
3378 { |
|
|
3379 atmp += fabs(work[i]); |
|
|
3380 work[i] = 0.; |
|
|
3381 } |
|
|
3382 if (atmp > ainvnorm) |
|
|
3383 ainvnorm = atmp; |
|
5164
|
3384 } |
|
5681
|
3385 rcond = 1. / ainvnorm / anorm; |
|
|
3386 } |
|
|
3387 } |
|
5164
|
3388 |
|
|
3389 triangular_error: |
|
|
3390 if (err != 0) |
|
|
3391 { |
|
|
3392 if (sing_handler) |
|
5681
|
3393 { |
|
|
3394 sing_handler (rcond); |
|
|
3395 mattype.mark_as_rectangular (); |
|
|
3396 } |
|
5164
|
3397 else |
|
|
3398 (*current_liboctave_error_handler) |
|
|
3399 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
3400 rcond); |
|
|
3401 } |
|
|
3402 |
|
|
3403 volatile double rcond_plus_one = rcond + 1.0; |
|
|
3404 |
|
|
3405 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
3406 { |
|
|
3407 err = -2; |
|
|
3408 |
|
|
3409 if (sing_handler) |
|
5681
|
3410 { |
|
|
3411 sing_handler (rcond); |
|
|
3412 mattype.mark_as_rectangular (); |
|
|
3413 } |
|
5164
|
3414 else |
|
|
3415 (*current_liboctave_error_handler) |
|
|
3416 ("matrix singular to machine precision, rcond = %g", |
|
|
3417 rcond); |
|
|
3418 } |
|
|
3419 } |
|
|
3420 else |
|
|
3421 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
3422 } |
|
|
3423 |
|
|
3424 return retval; |
|
|
3425 } |
|
|
3426 |
|
|
3427 SparseComplexMatrix |
|
5785
|
3428 SparseMatrix::ltsolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5630
|
3429 octave_idx_type& err, double& rcond, |
|
5681
|
3430 solve_singularity_handler sing_handler, |
|
|
3431 bool calc_cond) const |
|
5164
|
3432 { |
|
|
3433 SparseComplexMatrix retval; |
|
|
3434 |
|
5275
|
3435 octave_idx_type nr = rows (); |
|
|
3436 octave_idx_type nc = cols (); |
|
5630
|
3437 octave_idx_type nm = (nc > nr ? nc : nr); |
|
5164
|
3438 err = 0; |
|
|
3439 |
|
5630
|
3440 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
5164
|
3441 (*current_liboctave_error_handler) |
|
|
3442 ("matrix dimension mismatch solution of linear equations"); |
|
|
3443 else |
|
|
3444 { |
|
|
3445 // Print spparms("spumoni") info if requested |
|
|
3446 int typ = mattype.type (); |
|
|
3447 mattype.info (); |
|
|
3448 |
|
5785
|
3449 if (typ == MatrixType::Permuted_Lower || |
|
|
3450 typ == MatrixType::Lower) |
|
5164
|
3451 { |
|
|
3452 double anorm = 0.; |
|
|
3453 double ainvnorm = 0.; |
|
5681
|
3454 rcond = 1.; |
|
|
3455 |
|
|
3456 if (calc_cond) |
|
|
3457 { |
|
|
3458 // Calculate the 1-norm of matrix for rcond calculation |
|
|
3459 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3460 { |
|
|
3461 double atmp = 0.; |
|
|
3462 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
3463 atmp += fabs(data(i)); |
|
|
3464 if (atmp > anorm) |
|
|
3465 anorm = atmp; |
|
|
3466 } |
|
5164
|
3467 } |
|
|
3468 |
|
5275
|
3469 octave_idx_type b_nc = b.cols (); |
|
5681
|
3470 octave_idx_type b_nz = b.nnz (); |
|
5630
|
3471 retval = SparseComplexMatrix (nc, b_nc, b_nz); |
|
5164
|
3472 retval.xcidx(0) = 0; |
|
5275
|
3473 octave_idx_type ii = 0; |
|
|
3474 octave_idx_type x_nz = b_nz; |
|
5164
|
3475 |
|
5785
|
3476 if (typ == MatrixType::Permuted_Lower) |
|
5164
|
3477 { |
|
5630
|
3478 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
5322
|
3479 octave_idx_type *perm = mattype.triangular_perm (); |
|
5164
|
3480 |
|
5275
|
3481 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3482 { |
|
5630
|
3483 for (octave_idx_type i = 0; i < nm; i++) |
|
5322
|
3484 cwork[i] = 0.; |
|
5275
|
3485 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5322
|
3486 cwork[perm[b.ridx(i)]] = b.data(i); |
|
5164
|
3487 |
|
5630
|
3488 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3489 { |
|
5322
|
3490 if (cwork[k] != 0.) |
|
5164
|
3491 { |
|
5322
|
3492 octave_idx_type minr = nr; |
|
|
3493 octave_idx_type mini = 0; |
|
|
3494 |
|
|
3495 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
|
3496 if (perm[ridx(i)] < minr) |
|
|
3497 { |
|
|
3498 minr = perm[ridx(i)]; |
|
|
3499 mini = i; |
|
|
3500 } |
|
|
3501 |
|
5681
|
3502 if (minr != k || data(mini) == 0) |
|
5164
|
3503 { |
|
|
3504 err = -2; |
|
|
3505 goto triangular_error; |
|
|
3506 } |
|
|
3507 |
|
5322
|
3508 Complex tmp = cwork[k] / data(mini); |
|
|
3509 cwork[k] = tmp; |
|
|
3510 for (octave_idx_type i = cidx(k); i < cidx(k+1); i++) |
|
5164
|
3511 { |
|
5322
|
3512 if (i == mini) |
|
|
3513 continue; |
|
|
3514 |
|
|
3515 octave_idx_type iidx = perm[ridx(i)]; |
|
|
3516 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
3517 } |
|
|
3518 } |
|
|
3519 } |
|
|
3520 |
|
|
3521 // Count non-zeros in work vector and adjust space in |
|
|
3522 // retval if needed |
|
5275
|
3523 octave_idx_type new_nnz = 0; |
|
5630
|
3524 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
3525 if (cwork[i] != 0.) |
|
5164
|
3526 new_nnz++; |
|
|
3527 |
|
|
3528 if (ii + new_nnz > x_nz) |
|
|
3529 { |
|
|
3530 // Resize the sparse matrix |
|
5275
|
3531 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
3532 retval.change_capacity (sz); |
|
|
3533 x_nz = sz; |
|
|
3534 } |
|
|
3535 |
|
5630
|
3536 for (octave_idx_type i = 0; i < nc; i++) |
|
5322
|
3537 if (cwork[i] != 0.) |
|
5164
|
3538 { |
|
|
3539 retval.xridx(ii) = i; |
|
5322
|
3540 retval.xdata(ii++) = cwork[i]; |
|
5164
|
3541 } |
|
|
3542 retval.xcidx(j+1) = ii; |
|
|
3543 } |
|
|
3544 |
|
|
3545 retval.maybe_compress (); |
|
|
3546 |
|
5681
|
3547 if (calc_cond) |
|
|
3548 { |
|
|
3549 // Calculation of 1-norm of inv(*this) |
|
|
3550 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
3551 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3552 work[i] = 0.; |
|
|
3553 |
|
|
3554 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
3555 { |
|
5681
|
3556 work[j] = 1.; |
|
|
3557 |
|
|
3558 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3559 { |
|
5681
|
3560 if (work[k] != 0.) |
|
5164
|
3561 { |
|
5681
|
3562 octave_idx_type minr = nr; |
|
|
3563 octave_idx_type mini = 0; |
|
|
3564 |
|
|
3565 for (octave_idx_type i = cidx(k); |
|
|
3566 i < cidx(k+1); i++) |
|
|
3567 if (perm[ridx(i)] < minr) |
|
|
3568 { |
|
|
3569 minr = perm[ridx(i)]; |
|
|
3570 mini = i; |
|
|
3571 } |
|
|
3572 |
|
|
3573 double tmp = work[k] / data(mini); |
|
|
3574 work[k] = tmp; |
|
|
3575 for (octave_idx_type i = cidx(k); |
|
|
3576 i < cidx(k+1); i++) |
|
|
3577 { |
|
|
3578 if (i == mini) |
|
|
3579 continue; |
|
|
3580 |
|
|
3581 octave_idx_type iidx = perm[ridx(i)]; |
|
|
3582 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3583 } |
|
5164
|
3584 } |
|
|
3585 } |
|
5681
|
3586 |
|
|
3587 double atmp = 0; |
|
|
3588 for (octave_idx_type i = j; i < nc; i++) |
|
|
3589 { |
|
|
3590 atmp += fabs(work[i]); |
|
|
3591 work[i] = 0.; |
|
|
3592 } |
|
|
3593 if (atmp > ainvnorm) |
|
|
3594 ainvnorm = atmp; |
|
5164
|
3595 } |
|
5681
|
3596 rcond = 1. / ainvnorm / anorm; |
|
5164
|
3597 } |
|
|
3598 } |
|
|
3599 else |
|
|
3600 { |
|
5630
|
3601 OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); |
|
5164
|
3602 |
|
5275
|
3603 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3604 { |
|
5630
|
3605 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3606 cwork[i] = 0.; |
|
5275
|
3607 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5630
|
3608 cwork[b.ridx(i)] = b.data(i); |
|
|
3609 |
|
|
3610 for (octave_idx_type k = 0; k < nc; k++) |
|
5164
|
3611 { |
|
5630
|
3612 if (cwork[k] != 0.) |
|
5164
|
3613 { |
|
5681
|
3614 if (ridx(cidx(k)) != k || |
|
|
3615 data(cidx(k)) == 0.) |
|
5164
|
3616 { |
|
|
3617 err = -2; |
|
|
3618 goto triangular_error; |
|
|
3619 } |
|
|
3620 |
|
5630
|
3621 Complex tmp = cwork[k] / data(cidx(k)); |
|
|
3622 cwork[k] = tmp; |
|
5275
|
3623 for (octave_idx_type i = cidx(k)+1; i < cidx(k+1); i++) |
|
5164
|
3624 { |
|
5275
|
3625 octave_idx_type iidx = ridx(i); |
|
5630
|
3626 cwork[iidx] = cwork[iidx] - tmp * data(i); |
|
5164
|
3627 } |
|
|
3628 } |
|
|
3629 } |
|
|
3630 |
|
|
3631 // Count non-zeros in work vector and adjust space in |
|
|
3632 // retval if needed |
|
5275
|
3633 octave_idx_type new_nnz = 0; |
|
5630
|
3634 for (octave_idx_type i = 0; i < nc; i++) |
|
|
3635 if (cwork[i] != 0.) |
|
5164
|
3636 new_nnz++; |
|
|
3637 |
|
|
3638 if (ii + new_nnz > x_nz) |
|
|
3639 { |
|
|
3640 // Resize the sparse matrix |
|
5275
|
3641 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
3642 retval.change_capacity (sz); |
|
|
3643 x_nz = sz; |
|
|
3644 } |
|
|
3645 |
|
5630
|
3646 for (octave_idx_type i = 0; i < nc; i++) |
|
|
3647 if (cwork[i] != 0.) |
|
5164
|
3648 { |
|
|
3649 retval.xridx(ii) = i; |
|
5630
|
3650 retval.xdata(ii++) = cwork[i]; |
|
5164
|
3651 } |
|
|
3652 retval.xcidx(j+1) = ii; |
|
|
3653 } |
|
|
3654 |
|
|
3655 retval.maybe_compress (); |
|
|
3656 |
|
5681
|
3657 if (calc_cond) |
|
|
3658 { |
|
|
3659 // Calculation of 1-norm of inv(*this) |
|
|
3660 OCTAVE_LOCAL_BUFFER (double, work, nm); |
|
|
3661 for (octave_idx_type i = 0; i < nm; i++) |
|
|
3662 work[i] = 0.; |
|
|
3663 |
|
|
3664 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
3665 { |
|
5681
|
3666 work[j] = 1.; |
|
|
3667 |
|
|
3668 for (octave_idx_type k = j; k < nc; k++) |
|
5164
|
3669 { |
|
5681
|
3670 |
|
|
3671 if (work[k] != 0.) |
|
5164
|
3672 { |
|
5681
|
3673 double tmp = work[k] / data(cidx(k)); |
|
|
3674 work[k] = tmp; |
|
|
3675 for (octave_idx_type i = cidx(k)+1; |
|
|
3676 i < cidx(k+1); i++) |
|
|
3677 { |
|
|
3678 octave_idx_type iidx = ridx(i); |
|
|
3679 work[iidx] = work[iidx] - tmp * data(i); |
|
|
3680 } |
|
5164
|
3681 } |
|
|
3682 } |
|
5681
|
3683 double atmp = 0; |
|
|
3684 for (octave_idx_type i = j; i < nc; i++) |
|
|
3685 { |
|
|
3686 atmp += fabs(work[i]); |
|
|
3687 work[i] = 0.; |
|
|
3688 } |
|
|
3689 if (atmp > ainvnorm) |
|
|
3690 ainvnorm = atmp; |
|
5164
|
3691 } |
|
5681
|
3692 rcond = 1. / ainvnorm / anorm; |
|
|
3693 } |
|
|
3694 } |
|
5164
|
3695 |
|
|
3696 triangular_error: |
|
|
3697 if (err != 0) |
|
|
3698 { |
|
|
3699 if (sing_handler) |
|
5681
|
3700 { |
|
|
3701 sing_handler (rcond); |
|
|
3702 mattype.mark_as_rectangular (); |
|
|
3703 } |
|
5164
|
3704 else |
|
|
3705 (*current_liboctave_error_handler) |
|
|
3706 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
3707 rcond); |
|
|
3708 } |
|
|
3709 |
|
|
3710 volatile double rcond_plus_one = rcond + 1.0; |
|
|
3711 |
|
|
3712 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
3713 { |
|
|
3714 err = -2; |
|
|
3715 |
|
|
3716 if (sing_handler) |
|
5681
|
3717 { |
|
|
3718 sing_handler (rcond); |
|
|
3719 mattype.mark_as_rectangular (); |
|
|
3720 } |
|
5164
|
3721 else |
|
|
3722 (*current_liboctave_error_handler) |
|
|
3723 ("matrix singular to machine precision, rcond = %g", |
|
|
3724 rcond); |
|
|
3725 } |
|
|
3726 } |
|
|
3727 else |
|
|
3728 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
3729 } |
|
|
3730 |
|
|
3731 return retval; |
|
|
3732 } |
|
|
3733 |
|
|
3734 Matrix |
|
5785
|
3735 SparseMatrix::trisolve (MatrixType &mattype, const Matrix& b, |
|
5681
|
3736 octave_idx_type& err, double& rcond, |
|
|
3737 solve_singularity_handler sing_handler, |
|
|
3738 bool calc_cond) const |
|
5164
|
3739 { |
|
|
3740 Matrix retval; |
|
|
3741 |
|
5275
|
3742 octave_idx_type nr = rows (); |
|
|
3743 octave_idx_type nc = cols (); |
|
5164
|
3744 err = 0; |
|
|
3745 |
|
|
3746 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
3747 (*current_liboctave_error_handler) |
|
|
3748 ("matrix dimension mismatch solution of linear equations"); |
|
5681
|
3749 else if (calc_cond) |
|
|
3750 (*current_liboctave_error_handler) |
|
|
3751 ("calculation of condition number not implemented"); |
|
5164
|
3752 else |
|
|
3753 { |
|
|
3754 // Print spparms("spumoni") info if requested |
|
|
3755 volatile int typ = mattype.type (); |
|
|
3756 mattype.info (); |
|
|
3757 |
|
5785
|
3758 if (typ == MatrixType::Tridiagonal_Hermitian) |
|
5164
|
3759 { |
|
|
3760 OCTAVE_LOCAL_BUFFER (double, D, nr); |
|
|
3761 OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); |
|
|
3762 |
|
|
3763 if (mattype.is_dense ()) |
|
|
3764 { |
|
5275
|
3765 octave_idx_type ii = 0; |
|
|
3766 |
|
|
3767 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
3768 { |
|
|
3769 D[j] = data(ii++); |
|
|
3770 DL[j] = data(ii); |
|
|
3771 ii += 2; |
|
|
3772 } |
|
|
3773 D[nc-1] = data(ii); |
|
|
3774 } |
|
|
3775 else |
|
|
3776 { |
|
|
3777 D[0] = 0.; |
|
5275
|
3778 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
3779 { |
|
|
3780 D[i+1] = 0.; |
|
|
3781 DL[i] = 0.; |
|
|
3782 } |
|
|
3783 |
|
5275
|
3784 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3785 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
3786 { |
|
|
3787 if (ridx(i) == j) |
|
|
3788 D[j] = data(i); |
|
|
3789 else if (ridx(i) == j + 1) |
|
|
3790 DL[j] = data(i); |
|
|
3791 } |
|
|
3792 } |
|
|
3793 |
|
5275
|
3794 octave_idx_type b_nc = b.cols(); |
|
5164
|
3795 retval = b; |
|
|
3796 double *result = retval.fortran_vec (); |
|
|
3797 |
|
|
3798 F77_XFCN (dptsv, DPTSV, (nr, b_nc, D, DL, result, |
|
|
3799 b.rows(), err)); |
|
|
3800 |
|
|
3801 if (f77_exception_encountered) |
|
|
3802 (*current_liboctave_error_handler) |
|
|
3803 ("unrecoverable error in dptsv"); |
|
|
3804 else if (err != 0) |
|
|
3805 { |
|
|
3806 err = 0; |
|
|
3807 mattype.mark_as_unsymmetric (); |
|
5785
|
3808 typ = MatrixType::Tridiagonal; |
|
5164
|
3809 } |
|
|
3810 else |
|
|
3811 rcond = 1.; |
|
|
3812 } |
|
|
3813 |
|
5785
|
3814 if (typ == MatrixType::Tridiagonal) |
|
5164
|
3815 { |
|
|
3816 OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); |
|
|
3817 OCTAVE_LOCAL_BUFFER (double, D, nr); |
|
|
3818 OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); |
|
|
3819 |
|
|
3820 if (mattype.is_dense ()) |
|
|
3821 { |
|
5275
|
3822 octave_idx_type ii = 0; |
|
|
3823 |
|
|
3824 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
3825 { |
|
|
3826 D[j] = data(ii++); |
|
|
3827 DL[j] = data(ii++); |
|
|
3828 DU[j] = data(ii++); |
|
|
3829 } |
|
|
3830 D[nc-1] = data(ii); |
|
|
3831 } |
|
|
3832 else |
|
|
3833 { |
|
|
3834 D[0] = 0.; |
|
5275
|
3835 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
3836 { |
|
|
3837 D[i+1] = 0.; |
|
|
3838 DL[i] = 0.; |
|
|
3839 DU[i] = 0.; |
|
|
3840 } |
|
|
3841 |
|
5275
|
3842 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3843 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
3844 { |
|
|
3845 if (ridx(i) == j) |
|
|
3846 D[j] = data(i); |
|
|
3847 else if (ridx(i) == j + 1) |
|
|
3848 DL[j] = data(i); |
|
|
3849 else if (ridx(i) == j - 1) |
|
5322
|
3850 DU[j-1] = data(i); |
|
5164
|
3851 } |
|
|
3852 } |
|
|
3853 |
|
5275
|
3854 octave_idx_type b_nc = b.cols(); |
|
5164
|
3855 retval = b; |
|
|
3856 double *result = retval.fortran_vec (); |
|
|
3857 |
|
|
3858 F77_XFCN (dgtsv, DGTSV, (nr, b_nc, DL, D, DU, result, |
|
|
3859 b.rows(), err)); |
|
|
3860 |
|
|
3861 if (f77_exception_encountered) |
|
|
3862 (*current_liboctave_error_handler) |
|
|
3863 ("unrecoverable error in dgtsv"); |
|
|
3864 else if (err != 0) |
|
|
3865 { |
|
|
3866 rcond = 0.; |
|
|
3867 err = -2; |
|
|
3868 |
|
|
3869 if (sing_handler) |
|
5681
|
3870 { |
|
|
3871 sing_handler (rcond); |
|
|
3872 mattype.mark_as_rectangular (); |
|
|
3873 } |
|
5164
|
3874 else |
|
|
3875 (*current_liboctave_error_handler) |
|
|
3876 ("matrix singular to machine precision"); |
|
|
3877 |
|
|
3878 } |
|
|
3879 else |
|
|
3880 rcond = 1.; |
|
|
3881 } |
|
5785
|
3882 else if (typ != MatrixType::Tridiagonal_Hermitian) |
|
5164
|
3883 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
3884 } |
|
|
3885 |
|
|
3886 return retval; |
|
|
3887 } |
|
|
3888 |
|
|
3889 SparseMatrix |
|
5785
|
3890 SparseMatrix::trisolve (MatrixType &mattype, const SparseMatrix& b, |
|
5681
|
3891 octave_idx_type& err, double& rcond, |
|
|
3892 solve_singularity_handler sing_handler, |
|
|
3893 bool calc_cond) const |
|
5164
|
3894 { |
|
|
3895 SparseMatrix retval; |
|
|
3896 |
|
5275
|
3897 octave_idx_type nr = rows (); |
|
|
3898 octave_idx_type nc = cols (); |
|
5164
|
3899 err = 0; |
|
|
3900 |
|
|
3901 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
3902 (*current_liboctave_error_handler) |
|
|
3903 ("matrix dimension mismatch solution of linear equations"); |
|
5681
|
3904 else if (calc_cond) |
|
|
3905 (*current_liboctave_error_handler) |
|
|
3906 ("calculation of condition number not implemented"); |
|
5164
|
3907 else |
|
|
3908 { |
|
|
3909 // Print spparms("spumoni") info if requested |
|
|
3910 int typ = mattype.type (); |
|
|
3911 mattype.info (); |
|
|
3912 |
|
|
3913 // Note can't treat symmetric case as there is no dpttrf function |
|
5785
|
3914 if (typ == MatrixType::Tridiagonal || |
|
|
3915 typ == MatrixType::Tridiagonal_Hermitian) |
|
5164
|
3916 { |
|
|
3917 OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2); |
|
|
3918 OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); |
|
|
3919 OCTAVE_LOCAL_BUFFER (double, D, nr); |
|
|
3920 OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); |
|
5275
|
3921 Array<octave_idx_type> ipvt (nr); |
|
|
3922 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
3923 |
|
|
3924 if (mattype.is_dense ()) |
|
|
3925 { |
|
5275
|
3926 octave_idx_type ii = 0; |
|
|
3927 |
|
|
3928 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
3929 { |
|
|
3930 D[j] = data(ii++); |
|
|
3931 DL[j] = data(ii++); |
|
|
3932 DU[j] = data(ii++); |
|
|
3933 } |
|
|
3934 D[nc-1] = data(ii); |
|
|
3935 } |
|
|
3936 else |
|
|
3937 { |
|
|
3938 D[0] = 0.; |
|
5275
|
3939 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
3940 { |
|
|
3941 D[i+1] = 0.; |
|
|
3942 DL[i] = 0.; |
|
|
3943 DU[i] = 0.; |
|
|
3944 } |
|
|
3945 |
|
5275
|
3946 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3947 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
3948 { |
|
|
3949 if (ridx(i) == j) |
|
|
3950 D[j] = data(i); |
|
|
3951 else if (ridx(i) == j + 1) |
|
|
3952 DL[j] = data(i); |
|
|
3953 else if (ridx(i) == j - 1) |
|
5322
|
3954 DU[j-1] = data(i); |
|
5164
|
3955 } |
|
|
3956 } |
|
|
3957 |
|
|
3958 F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); |
|
|
3959 |
|
|
3960 if (f77_exception_encountered) |
|
|
3961 (*current_liboctave_error_handler) |
|
|
3962 ("unrecoverable error in dgttrf"); |
|
|
3963 else |
|
|
3964 { |
|
|
3965 if (err != 0) |
|
|
3966 { |
|
5681
|
3967 rcond = 0.0; |
|
5164
|
3968 err = -2; |
|
|
3969 |
|
|
3970 if (sing_handler) |
|
5681
|
3971 { |
|
|
3972 sing_handler (rcond); |
|
|
3973 mattype.mark_as_rectangular (); |
|
|
3974 } |
|
5164
|
3975 else |
|
|
3976 (*current_liboctave_error_handler) |
|
|
3977 ("matrix singular to machine precision"); |
|
|
3978 |
|
|
3979 } |
|
|
3980 else |
|
|
3981 { |
|
5681
|
3982 rcond = 1.0; |
|
5164
|
3983 char job = 'N'; |
|
5681
|
3984 volatile octave_idx_type x_nz = b.nnz (); |
|
5275
|
3985 octave_idx_type b_nc = b.cols (); |
|
5164
|
3986 retval = SparseMatrix (nr, b_nc, x_nz); |
|
|
3987 retval.xcidx(0) = 0; |
|
5275
|
3988 volatile octave_idx_type ii = 0; |
|
5164
|
3989 |
|
|
3990 OCTAVE_LOCAL_BUFFER (double, work, nr); |
|
|
3991 |
|
5275
|
3992 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
3993 { |
|
5275
|
3994 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
3995 work[i] = 0.; |
|
5275
|
3996 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
|
5164
|
3997 work[b.ridx(i)] = b.data(i); |
|
|
3998 |
|
|
3999 F77_XFCN (dgttrs, DGTTRS, |
|
|
4000 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4001 nr, 1, DL, D, DU, DU2, pipvt, |
|
|
4002 work, b.rows (), err |
|
|
4003 F77_CHAR_ARG_LEN (1))); |
|
|
4004 |
|
|
4005 if (f77_exception_encountered) |
|
|
4006 { |
|
|
4007 (*current_liboctave_error_handler) |
|
|
4008 ("unrecoverable error in dgttrs"); |
|
|
4009 break; |
|
|
4010 } |
|
|
4011 |
|
|
4012 // Count non-zeros in work vector and adjust |
|
|
4013 // space in retval if needed |
|
5275
|
4014 octave_idx_type new_nnz = 0; |
|
|
4015 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
4016 if (work[i] != 0.) |
|
|
4017 new_nnz++; |
|
|
4018 |
|
|
4019 if (ii + new_nnz > x_nz) |
|
|
4020 { |
|
|
4021 // Resize the sparse matrix |
|
5275
|
4022 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
4023 retval.change_capacity (sz); |
|
|
4024 x_nz = sz; |
|
|
4025 } |
|
|
4026 |
|
5275
|
4027 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
4028 if (work[i] != 0.) |
|
|
4029 { |
|
|
4030 retval.xridx(ii) = i; |
|
|
4031 retval.xdata(ii++) = work[i]; |
|
|
4032 } |
|
|
4033 retval.xcidx(j+1) = ii; |
|
|
4034 } |
|
|
4035 |
|
|
4036 retval.maybe_compress (); |
|
|
4037 } |
|
|
4038 } |
|
|
4039 } |
|
5785
|
4040 else if (typ != MatrixType::Tridiagonal_Hermitian) |
|
5164
|
4041 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
4042 } |
|
|
4043 |
|
|
4044 return retval; |
|
|
4045 } |
|
|
4046 |
|
|
4047 ComplexMatrix |
|
5785
|
4048 SparseMatrix::trisolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5681
|
4049 octave_idx_type& err, double& rcond, |
|
|
4050 solve_singularity_handler sing_handler, |
|
|
4051 bool calc_cond) const |
|
5164
|
4052 { |
|
|
4053 ComplexMatrix retval; |
|
|
4054 |
|
5275
|
4055 octave_idx_type nr = rows (); |
|
|
4056 octave_idx_type nc = cols (); |
|
5164
|
4057 err = 0; |
|
|
4058 |
|
|
4059 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
4060 (*current_liboctave_error_handler) |
|
|
4061 ("matrix dimension mismatch solution of linear equations"); |
|
5681
|
4062 else if (calc_cond) |
|
|
4063 (*current_liboctave_error_handler) |
|
|
4064 ("calculation of condition number not implemented"); |
|
5164
|
4065 else |
|
|
4066 { |
|
|
4067 // Print spparms("spumoni") info if requested |
|
|
4068 volatile int typ = mattype.type (); |
|
|
4069 mattype.info (); |
|
|
4070 |
|
5785
|
4071 if (typ == MatrixType::Tridiagonal_Hermitian) |
|
5164
|
4072 { |
|
5322
|
4073 OCTAVE_LOCAL_BUFFER (double, D, nr); |
|
5164
|
4074 OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1); |
|
|
4075 |
|
|
4076 if (mattype.is_dense ()) |
|
|
4077 { |
|
5275
|
4078 octave_idx_type ii = 0; |
|
|
4079 |
|
|
4080 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
4081 { |
|
|
4082 D[j] = data(ii++); |
|
|
4083 DL[j] = data(ii); |
|
|
4084 ii += 2; |
|
|
4085 } |
|
|
4086 D[nc-1] = data(ii); |
|
|
4087 } |
|
|
4088 else |
|
|
4089 { |
|
|
4090 D[0] = 0.; |
|
5275
|
4091 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
4092 { |
|
|
4093 D[i+1] = 0.; |
|
|
4094 DL[i] = 0.; |
|
|
4095 } |
|
|
4096 |
|
5275
|
4097 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4098 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4099 { |
|
|
4100 if (ridx(i) == j) |
|
|
4101 D[j] = data(i); |
|
|
4102 else if (ridx(i) == j + 1) |
|
|
4103 DL[j] = data(i); |
|
|
4104 } |
|
|
4105 } |
|
|
4106 |
|
5275
|
4107 octave_idx_type b_nr = b.rows (); |
|
|
4108 octave_idx_type b_nc = b.cols(); |
|
5164
|
4109 rcond = 1.; |
|
|
4110 |
|
|
4111 retval = b; |
|
|
4112 Complex *result = retval.fortran_vec (); |
|
|
4113 |
|
|
4114 F77_XFCN (zptsv, ZPTSV, (nr, b_nc, D, DL, result, |
|
|
4115 b_nr, err)); |
|
|
4116 |
|
|
4117 if (f77_exception_encountered) |
|
|
4118 { |
|
|
4119 (*current_liboctave_error_handler) |
|
|
4120 ("unrecoverable error in zptsv"); |
|
|
4121 err = -1; |
|
|
4122 } |
|
|
4123 else if (err != 0) |
|
|
4124 { |
|
|
4125 err = 0; |
|
|
4126 mattype.mark_as_unsymmetric (); |
|
5785
|
4127 typ = MatrixType::Tridiagonal; |
|
5164
|
4128 } |
|
|
4129 } |
|
|
4130 |
|
5785
|
4131 if (typ == MatrixType::Tridiagonal) |
|
5164
|
4132 { |
|
|
4133 OCTAVE_LOCAL_BUFFER (Complex, DU, nr - 1); |
|
|
4134 OCTAVE_LOCAL_BUFFER (Complex, D, nr); |
|
|
4135 OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1); |
|
|
4136 |
|
|
4137 if (mattype.is_dense ()) |
|
|
4138 { |
|
5275
|
4139 octave_idx_type ii = 0; |
|
|
4140 |
|
|
4141 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
4142 { |
|
|
4143 D[j] = data(ii++); |
|
|
4144 DL[j] = data(ii++); |
|
|
4145 DU[j] = data(ii++); |
|
|
4146 } |
|
|
4147 D[nc-1] = data(ii); |
|
|
4148 } |
|
|
4149 else |
|
|
4150 { |
|
|
4151 D[0] = 0.; |
|
5275
|
4152 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
4153 { |
|
|
4154 D[i+1] = 0.; |
|
|
4155 DL[i] = 0.; |
|
|
4156 DU[i] = 0.; |
|
|
4157 } |
|
|
4158 |
|
5275
|
4159 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4160 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4161 { |
|
|
4162 if (ridx(i) == j) |
|
|
4163 D[j] = data(i); |
|
|
4164 else if (ridx(i) == j + 1) |
|
|
4165 DL[j] = data(i); |
|
|
4166 else if (ridx(i) == j - 1) |
|
5322
|
4167 DU[j-1] = data(i); |
|
5164
|
4168 } |
|
|
4169 } |
|
|
4170 |
|
5275
|
4171 octave_idx_type b_nr = b.rows(); |
|
|
4172 octave_idx_type b_nc = b.cols(); |
|
5164
|
4173 rcond = 1.; |
|
|
4174 |
|
|
4175 retval = b; |
|
|
4176 Complex *result = retval.fortran_vec (); |
|
|
4177 |
|
|
4178 F77_XFCN (zgtsv, ZGTSV, (nr, b_nc, DL, D, DU, result, |
|
|
4179 b_nr, err)); |
|
|
4180 |
|
|
4181 if (f77_exception_encountered) |
|
|
4182 { |
|
|
4183 (*current_liboctave_error_handler) |
|
|
4184 ("unrecoverable error in zgtsv"); |
|
|
4185 err = -1; |
|
|
4186 } |
|
|
4187 else if (err != 0) |
|
|
4188 { |
|
|
4189 rcond = 0.; |
|
|
4190 err = -2; |
|
|
4191 |
|
|
4192 if (sing_handler) |
|
5681
|
4193 { |
|
|
4194 sing_handler (rcond); |
|
|
4195 mattype.mark_as_rectangular (); |
|
|
4196 } |
|
5164
|
4197 else |
|
|
4198 (*current_liboctave_error_handler) |
|
|
4199 ("matrix singular to machine precision"); |
|
|
4200 } |
|
|
4201 } |
|
5785
|
4202 else if (typ != MatrixType::Tridiagonal_Hermitian) |
|
5164
|
4203 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
4204 } |
|
|
4205 |
|
|
4206 return retval; |
|
|
4207 } |
|
|
4208 |
|
|
4209 SparseComplexMatrix |
|
5785
|
4210 SparseMatrix::trisolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5681
|
4211 octave_idx_type& err, double& rcond, |
|
|
4212 solve_singularity_handler sing_handler, |
|
|
4213 bool calc_cond) const |
|
5164
|
4214 { |
|
|
4215 SparseComplexMatrix retval; |
|
|
4216 |
|
5275
|
4217 octave_idx_type nr = rows (); |
|
|
4218 octave_idx_type nc = cols (); |
|
5164
|
4219 err = 0; |
|
|
4220 |
|
|
4221 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
4222 (*current_liboctave_error_handler) |
|
|
4223 ("matrix dimension mismatch solution of linear equations"); |
|
5681
|
4224 else if (calc_cond) |
|
|
4225 (*current_liboctave_error_handler) |
|
|
4226 ("calculation of condition number not implemented"); |
|
5164
|
4227 else |
|
|
4228 { |
|
|
4229 // Print spparms("spumoni") info if requested |
|
|
4230 int typ = mattype.type (); |
|
|
4231 mattype.info (); |
|
|
4232 |
|
|
4233 // Note can't treat symmetric case as there is no dpttrf function |
|
5785
|
4234 if (typ == MatrixType::Tridiagonal || |
|
|
4235 typ == MatrixType::Tridiagonal_Hermitian) |
|
5164
|
4236 { |
|
|
4237 OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2); |
|
|
4238 OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); |
|
|
4239 OCTAVE_LOCAL_BUFFER (double, D, nr); |
|
|
4240 OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); |
|
5275
|
4241 Array<octave_idx_type> ipvt (nr); |
|
|
4242 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
4243 |
|
|
4244 if (mattype.is_dense ()) |
|
|
4245 { |
|
5275
|
4246 octave_idx_type ii = 0; |
|
|
4247 |
|
|
4248 for (octave_idx_type j = 0; j < nc-1; j++) |
|
5164
|
4249 { |
|
|
4250 D[j] = data(ii++); |
|
|
4251 DL[j] = data(ii++); |
|
|
4252 DU[j] = data(ii++); |
|
|
4253 } |
|
|
4254 D[nc-1] = data(ii); |
|
|
4255 } |
|
|
4256 else |
|
|
4257 { |
|
|
4258 D[0] = 0.; |
|
5275
|
4259 for (octave_idx_type i = 0; i < nr - 1; i++) |
|
5164
|
4260 { |
|
|
4261 D[i+1] = 0.; |
|
|
4262 DL[i] = 0.; |
|
|
4263 DU[i] = 0.; |
|
|
4264 } |
|
|
4265 |
|
5275
|
4266 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4267 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4268 { |
|
|
4269 if (ridx(i) == j) |
|
|
4270 D[j] = data(i); |
|
|
4271 else if (ridx(i) == j + 1) |
|
|
4272 DL[j] = data(i); |
|
|
4273 else if (ridx(i) == j - 1) |
|
5322
|
4274 DU[j-1] = data(i); |
|
5164
|
4275 } |
|
|
4276 } |
|
|
4277 |
|
|
4278 F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); |
|
|
4279 |
|
|
4280 if (f77_exception_encountered) |
|
|
4281 (*current_liboctave_error_handler) |
|
|
4282 ("unrecoverable error in dgttrf"); |
|
|
4283 else |
|
|
4284 { |
|
|
4285 if (err != 0) |
|
|
4286 { |
|
5681
|
4287 rcond = 0.0; |
|
5164
|
4288 err = -2; |
|
|
4289 |
|
|
4290 if (sing_handler) |
|
5681
|
4291 { |
|
|
4292 sing_handler (rcond); |
|
|
4293 mattype.mark_as_rectangular (); |
|
|
4294 } |
|
5164
|
4295 else |
|
|
4296 (*current_liboctave_error_handler) |
|
|
4297 ("matrix singular to machine precision"); |
|
|
4298 } |
|
|
4299 else |
|
|
4300 { |
|
|
4301 rcond = 1.; |
|
|
4302 char job = 'N'; |
|
5275
|
4303 octave_idx_type b_nr = b.rows (); |
|
|
4304 octave_idx_type b_nc = b.cols (); |
|
5164
|
4305 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
4306 OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); |
|
|
4307 |
|
|
4308 // Take a first guess that the number of non-zero terms |
|
|
4309 // will be as many as in b |
|
5681
|
4310 volatile octave_idx_type x_nz = b.nnz (); |
|
5275
|
4311 volatile octave_idx_type ii = 0; |
|
5164
|
4312 retval = SparseComplexMatrix (b_nr, b_nc, x_nz); |
|
|
4313 |
|
|
4314 retval.xcidx(0) = 0; |
|
5275
|
4315 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
4316 { |
|
|
4317 |
|
5275
|
4318 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
4319 { |
|
|
4320 Complex c = b (i,j); |
|
5261
|
4321 Bx[i] = std::real (c); |
|
|
4322 Bz[i] = std::imag (c); |
|
5164
|
4323 } |
|
|
4324 |
|
|
4325 F77_XFCN (dgttrs, DGTTRS, |
|
|
4326 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4327 nr, 1, DL, D, DU, DU2, pipvt, |
|
|
4328 Bx, b_nr, err |
|
|
4329 F77_CHAR_ARG_LEN (1))); |
|
|
4330 |
|
|
4331 if (f77_exception_encountered) |
|
|
4332 { |
|
|
4333 (*current_liboctave_error_handler) |
|
|
4334 ("unrecoverable error in dgttrs"); |
|
|
4335 break; |
|
|
4336 } |
|
|
4337 |
|
|
4338 if (err != 0) |
|
|
4339 { |
|
|
4340 (*current_liboctave_error_handler) |
|
|
4341 ("SparseMatrix::solve solve failed"); |
|
|
4342 |
|
|
4343 err = -1; |
|
|
4344 break; |
|
|
4345 } |
|
|
4346 |
|
|
4347 F77_XFCN (dgttrs, DGTTRS, |
|
|
4348 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4349 nr, 1, DL, D, DU, DU2, pipvt, |
|
|
4350 Bz, b_nr, err |
|
|
4351 F77_CHAR_ARG_LEN (1))); |
|
|
4352 |
|
|
4353 if (f77_exception_encountered) |
|
|
4354 { |
|
|
4355 (*current_liboctave_error_handler) |
|
|
4356 ("unrecoverable error in dgttrs"); |
|
|
4357 break; |
|
|
4358 } |
|
|
4359 |
|
|
4360 if (err != 0) |
|
|
4361 { |
|
|
4362 (*current_liboctave_error_handler) |
|
|
4363 ("SparseMatrix::solve solve failed"); |
|
|
4364 |
|
|
4365 err = -1; |
|
|
4366 break; |
|
|
4367 } |
|
|
4368 |
|
|
4369 // Count non-zeros in work vector and adjust |
|
|
4370 // space in retval if needed |
|
5275
|
4371 octave_idx_type new_nnz = 0; |
|
|
4372 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
4373 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
4374 new_nnz++; |
|
|
4375 |
|
|
4376 if (ii + new_nnz > x_nz) |
|
|
4377 { |
|
|
4378 // Resize the sparse matrix |
|
5275
|
4379 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
5164
|
4380 retval.change_capacity (sz); |
|
|
4381 x_nz = sz; |
|
|
4382 } |
|
|
4383 |
|
5275
|
4384 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
4385 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
4386 { |
|
|
4387 retval.xridx(ii) = i; |
|
|
4388 retval.xdata(ii++) = |
|
|
4389 Complex (Bx[i], Bz[i]); |
|
|
4390 } |
|
|
4391 |
|
|
4392 retval.xcidx(j+1) = ii; |
|
|
4393 } |
|
|
4394 |
|
|
4395 retval.maybe_compress (); |
|
|
4396 } |
|
|
4397 } |
|
|
4398 } |
|
5785
|
4399 else if (typ != MatrixType::Tridiagonal_Hermitian) |
|
5164
|
4400 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
4401 } |
|
|
4402 |
|
|
4403 return retval; |
|
|
4404 } |
|
|
4405 |
|
|
4406 Matrix |
|
5785
|
4407 SparseMatrix::bsolve (MatrixType &mattype, const Matrix& b, |
|
5681
|
4408 octave_idx_type& err, double& rcond, |
|
|
4409 solve_singularity_handler sing_handler, |
|
|
4410 bool calc_cond) const |
|
5164
|
4411 { |
|
|
4412 Matrix retval; |
|
|
4413 |
|
5275
|
4414 octave_idx_type nr = rows (); |
|
|
4415 octave_idx_type nc = cols (); |
|
5164
|
4416 err = 0; |
|
|
4417 |
|
|
4418 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
4419 (*current_liboctave_error_handler) |
|
|
4420 ("matrix dimension mismatch solution of linear equations"); |
|
|
4421 else |
|
|
4422 { |
|
|
4423 // Print spparms("spumoni") info if requested |
|
|
4424 volatile int typ = mattype.type (); |
|
|
4425 mattype.info (); |
|
|
4426 |
|
5785
|
4427 if (typ == MatrixType::Banded_Hermitian) |
|
5164
|
4428 { |
|
5275
|
4429 octave_idx_type n_lower = mattype.nlower (); |
|
|
4430 octave_idx_type ldm = n_lower + 1; |
|
5164
|
4431 Matrix m_band (ldm, nc); |
|
|
4432 double *tmp_data = m_band.fortran_vec (); |
|
|
4433 |
|
|
4434 if (! mattype.is_dense ()) |
|
|
4435 { |
|
5275
|
4436 octave_idx_type ii = 0; |
|
|
4437 |
|
|
4438 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
4439 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
4440 tmp_data[ii++] = 0.; |
|
|
4441 } |
|
|
4442 |
|
5275
|
4443 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4444 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4445 { |
|
5275
|
4446 octave_idx_type ri = ridx (i); |
|
5164
|
4447 if (ri >= j) |
|
|
4448 m_band(ri - j, j) = data(i); |
|
|
4449 } |
|
|
4450 |
|
|
4451 // Calculate the norm of the matrix, for later use. |
|
5681
|
4452 double anorm; |
|
|
4453 if (calc_cond) |
|
|
4454 anorm = m_band.abs().sum().row(0).max(); |
|
5164
|
4455 |
|
|
4456 char job = 'L'; |
|
|
4457 F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4458 nr, n_lower, tmp_data, ldm, err |
|
|
4459 F77_CHAR_ARG_LEN (1))); |
|
|
4460 |
|
|
4461 if (f77_exception_encountered) |
|
|
4462 (*current_liboctave_error_handler) |
|
|
4463 ("unrecoverable error in dpbtrf"); |
|
|
4464 else |
|
|
4465 { |
|
|
4466 if (err != 0) |
|
|
4467 { |
|
|
4468 // Matrix is not positive definite!! Fall through to |
|
|
4469 // unsymmetric banded solver. |
|
|
4470 mattype.mark_as_unsymmetric (); |
|
5785
|
4471 typ = MatrixType::Banded; |
|
5681
|
4472 rcond = 0.0; |
|
5164
|
4473 err = 0; |
|
|
4474 } |
|
|
4475 else |
|
|
4476 { |
|
5681
|
4477 if (calc_cond) |
|
|
4478 { |
|
|
4479 Array<double> z (3 * nr); |
|
|
4480 double *pz = z.fortran_vec (); |
|
|
4481 Array<octave_idx_type> iz (nr); |
|
5717
|
4482 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
4483 |
|
|
4484 F77_XFCN (dpbcon, DGBCON, |
|
|
4485 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4486 nr, n_lower, tmp_data, ldm, |
|
|
4487 anorm, rcond, pz, piz, err |
|
|
4488 F77_CHAR_ARG_LEN (1))); |
|
|
4489 |
|
|
4490 if (f77_exception_encountered) |
|
|
4491 (*current_liboctave_error_handler) |
|
|
4492 ("unrecoverable error in dpbcon"); |
|
|
4493 |
|
|
4494 if (err != 0) |
|
|
4495 err = -2; |
|
|
4496 |
|
|
4497 volatile double rcond_plus_one = rcond + 1.0; |
|
|
4498 |
|
|
4499 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
4500 { |
|
|
4501 err = -2; |
|
|
4502 |
|
|
4503 if (sing_handler) |
|
|
4504 { |
|
|
4505 sing_handler (rcond); |
|
|
4506 mattype.mark_as_rectangular (); |
|
|
4507 } |
|
|
4508 else |
|
|
4509 (*current_liboctave_error_handler) |
|
|
4510 ("matrix singular to machine precision, rcond = %g", |
|
|
4511 rcond); |
|
|
4512 } |
|
|
4513 } |
|
|
4514 else |
|
|
4515 rcond = 1.; |
|
|
4516 |
|
|
4517 if (err == 0) |
|
|
4518 { |
|
|
4519 retval = b; |
|
|
4520 double *result = retval.fortran_vec (); |
|
|
4521 |
|
|
4522 octave_idx_type b_nc = b.cols (); |
|
|
4523 |
|
|
4524 F77_XFCN (dpbtrs, DPBTRS, |
|
|
4525 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4526 nr, n_lower, b_nc, tmp_data, |
|
|
4527 ldm, result, b.rows(), err |
|
|
4528 F77_CHAR_ARG_LEN (1))); |
|
5164
|
4529 |
|
5681
|
4530 if (f77_exception_encountered) |
|
|
4531 (*current_liboctave_error_handler) |
|
|
4532 ("unrecoverable error in dpbtrs"); |
|
|
4533 |
|
|
4534 if (err != 0) |
|
|
4535 { |
|
|
4536 (*current_liboctave_error_handler) |
|
|
4537 ("SparseMatrix::solve solve failed"); |
|
|
4538 err = -1; |
|
|
4539 } |
|
5164
|
4540 } |
|
|
4541 } |
|
|
4542 } |
|
|
4543 } |
|
|
4544 |
|
5785
|
4545 if (typ == MatrixType::Banded) |
|
5164
|
4546 { |
|
|
4547 // Create the storage for the banded form of the sparse matrix |
|
6242
|
4548 octave_idx_type n_upper = mattype.nupper (); |
|
|
4549 octave_idx_type n_lower = mattype.nlower (); |
|
|
4550 octave_idx_type ldm = n_upper + 2 * n_lower + 1; |
|
5164
|
4551 |
|
|
4552 Matrix m_band (ldm, nc); |
|
|
4553 double *tmp_data = m_band.fortran_vec (); |
|
|
4554 |
|
|
4555 if (! mattype.is_dense ()) |
|
|
4556 { |
|
5275
|
4557 octave_idx_type ii = 0; |
|
|
4558 |
|
|
4559 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
4560 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
4561 tmp_data[ii++] = 0.; |
|
|
4562 } |
|
|
4563 |
|
5275
|
4564 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4565 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4566 m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); |
|
|
4567 |
|
5681
|
4568 // Calculate the norm of the matrix, for later use. |
|
|
4569 double anorm; |
|
|
4570 if (calc_cond) |
|
|
4571 { |
|
|
4572 for (octave_idx_type j = 0; j < nr; j++) |
|
|
4573 { |
|
|
4574 double atmp = 0.; |
|
|
4575 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
4576 atmp += fabs(data(i)); |
|
|
4577 if (atmp > anorm) |
|
|
4578 anorm = atmp; |
|
|
4579 } |
|
|
4580 } |
|
|
4581 |
|
5275
|
4582 Array<octave_idx_type> ipvt (nr); |
|
|
4583 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
4584 |
|
|
4585 F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, |
|
|
4586 ldm, pipvt, err)); |
|
|
4587 |
|
|
4588 if (f77_exception_encountered) |
|
|
4589 (*current_liboctave_error_handler) |
|
|
4590 ("unrecoverable error in dgbtrf"); |
|
|
4591 else |
|
|
4592 { |
|
|
4593 // Throw-away extra info LAPACK gives so as to not |
|
|
4594 // change output. |
|
|
4595 if (err != 0) |
|
|
4596 { |
|
|
4597 err = -2; |
|
5681
|
4598 rcond = 0.0; |
|
5164
|
4599 |
|
|
4600 if (sing_handler) |
|
5681
|
4601 { |
|
|
4602 sing_handler (rcond); |
|
|
4603 mattype.mark_as_rectangular (); |
|
|
4604 } |
|
5164
|
4605 else |
|
|
4606 (*current_liboctave_error_handler) |
|
|
4607 ("matrix singular to machine precision"); |
|
|
4608 |
|
|
4609 } |
|
|
4610 else |
|
|
4611 { |
|
5681
|
4612 if (calc_cond) |
|
|
4613 { |
|
|
4614 char job = '1'; |
|
|
4615 Array<double> z (3 * nr); |
|
|
4616 double *pz = z.fortran_vec (); |
|
|
4617 Array<octave_idx_type> iz (nr); |
|
5717
|
4618 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
4619 |
|
|
4620 F77_XFCN (dgbcon, DGBCON, |
|
|
4621 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4622 nc, n_lower, n_upper, tmp_data, ldm, pipvt, |
|
|
4623 anorm, rcond, pz, piz, err |
|
|
4624 F77_CHAR_ARG_LEN (1))); |
|
|
4625 |
|
|
4626 if (f77_exception_encountered) |
|
|
4627 (*current_liboctave_error_handler) |
|
|
4628 ("unrecoverable error in dgbcon"); |
|
|
4629 |
|
|
4630 if (err != 0) |
|
|
4631 err = -2; |
|
|
4632 |
|
|
4633 volatile double rcond_plus_one = rcond + 1.0; |
|
|
4634 |
|
|
4635 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
4636 { |
|
|
4637 err = -2; |
|
|
4638 |
|
|
4639 if (sing_handler) |
|
|
4640 { |
|
|
4641 sing_handler (rcond); |
|
|
4642 mattype.mark_as_rectangular (); |
|
|
4643 } |
|
|
4644 else |
|
|
4645 (*current_liboctave_error_handler) |
|
|
4646 ("matrix singular to machine precision, rcond = %g", |
|
|
4647 rcond); |
|
|
4648 } |
|
|
4649 } |
|
|
4650 else |
|
|
4651 rcond = 1.; |
|
|
4652 |
|
|
4653 if (err == 0) |
|
|
4654 { |
|
|
4655 retval = b; |
|
|
4656 double *result = retval.fortran_vec (); |
|
|
4657 |
|
|
4658 octave_idx_type b_nc = b.cols (); |
|
|
4659 |
|
|
4660 char job = 'N'; |
|
|
4661 F77_XFCN (dgbtrs, DGBTRS, |
|
|
4662 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4663 nr, n_lower, n_upper, b_nc, tmp_data, |
|
|
4664 ldm, pipvt, result, b.rows(), err |
|
|
4665 F77_CHAR_ARG_LEN (1))); |
|
5164
|
4666 |
|
5681
|
4667 if (f77_exception_encountered) |
|
|
4668 (*current_liboctave_error_handler) |
|
|
4669 ("unrecoverable error in dgbtrs"); |
|
|
4670 } |
|
5164
|
4671 } |
|
|
4672 } |
|
|
4673 } |
|
5785
|
4674 else if (typ != MatrixType::Banded_Hermitian) |
|
5164
|
4675 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
4676 } |
|
|
4677 |
|
|
4678 return retval; |
|
|
4679 } |
|
|
4680 |
|
|
4681 SparseMatrix |
|
5785
|
4682 SparseMatrix::bsolve (MatrixType &mattype, const SparseMatrix& b, |
|
5681
|
4683 octave_idx_type& err, double& rcond, |
|
|
4684 solve_singularity_handler sing_handler, |
|
|
4685 bool calc_cond) const |
|
5164
|
4686 { |
|
|
4687 SparseMatrix retval; |
|
|
4688 |
|
5275
|
4689 octave_idx_type nr = rows (); |
|
|
4690 octave_idx_type nc = cols (); |
|
5164
|
4691 err = 0; |
|
|
4692 |
|
|
4693 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
4694 (*current_liboctave_error_handler) |
|
|
4695 ("matrix dimension mismatch solution of linear equations"); |
|
|
4696 else |
|
|
4697 { |
|
|
4698 // Print spparms("spumoni") info if requested |
|
|
4699 volatile int typ = mattype.type (); |
|
|
4700 mattype.info (); |
|
|
4701 |
|
5785
|
4702 if (typ == MatrixType::Banded_Hermitian) |
|
5164
|
4703 { |
|
6242
|
4704 octave_idx_type n_lower = mattype.nlower (); |
|
|
4705 octave_idx_type ldm = n_lower + 1; |
|
5164
|
4706 |
|
|
4707 Matrix m_band (ldm, nc); |
|
|
4708 double *tmp_data = m_band.fortran_vec (); |
|
|
4709 |
|
|
4710 if (! mattype.is_dense ()) |
|
|
4711 { |
|
5275
|
4712 octave_idx_type ii = 0; |
|
|
4713 |
|
|
4714 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
4715 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
4716 tmp_data[ii++] = 0.; |
|
|
4717 } |
|
|
4718 |
|
5275
|
4719 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4720 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4721 { |
|
5275
|
4722 octave_idx_type ri = ridx (i); |
|
5164
|
4723 if (ri >= j) |
|
|
4724 m_band(ri - j, j) = data(i); |
|
|
4725 } |
|
|
4726 |
|
5681
|
4727 // Calculate the norm of the matrix, for later use. |
|
|
4728 double anorm; |
|
|
4729 if (calc_cond) |
|
|
4730 anorm = m_band.abs().sum().row(0).max(); |
|
|
4731 |
|
5164
|
4732 char job = 'L'; |
|
|
4733 F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4734 nr, n_lower, tmp_data, ldm, err |
|
|
4735 F77_CHAR_ARG_LEN (1))); |
|
|
4736 |
|
|
4737 if (f77_exception_encountered) |
|
|
4738 (*current_liboctave_error_handler) |
|
|
4739 ("unrecoverable error in dpbtrf"); |
|
|
4740 else |
|
|
4741 { |
|
|
4742 if (err != 0) |
|
|
4743 { |
|
|
4744 mattype.mark_as_unsymmetric (); |
|
5785
|
4745 typ = MatrixType::Banded; |
|
5681
|
4746 rcond = 0.0; |
|
5164
|
4747 err = 0; |
|
|
4748 } |
|
|
4749 else |
|
|
4750 { |
|
5681
|
4751 if (calc_cond) |
|
|
4752 { |
|
|
4753 Array<double> z (3 * nr); |
|
|
4754 double *pz = z.fortran_vec (); |
|
|
4755 Array<octave_idx_type> iz (nr); |
|
5717
|
4756 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
4757 |
|
|
4758 F77_XFCN (dpbcon, DGBCON, |
|
|
4759 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4760 nr, n_lower, tmp_data, ldm, |
|
|
4761 anorm, rcond, pz, piz, err |
|
|
4762 F77_CHAR_ARG_LEN (1))); |
|
|
4763 |
|
|
4764 if (f77_exception_encountered) |
|
|
4765 (*current_liboctave_error_handler) |
|
|
4766 ("unrecoverable error in dpbcon"); |
|
|
4767 |
|
|
4768 if (err != 0) |
|
|
4769 err = -2; |
|
|
4770 |
|
|
4771 volatile double rcond_plus_one = rcond + 1.0; |
|
|
4772 |
|
|
4773 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
4774 { |
|
|
4775 err = -2; |
|
|
4776 |
|
|
4777 if (sing_handler) |
|
|
4778 { |
|
|
4779 sing_handler (rcond); |
|
|
4780 mattype.mark_as_rectangular (); |
|
|
4781 } |
|
|
4782 else |
|
|
4783 (*current_liboctave_error_handler) |
|
|
4784 ("matrix singular to machine precision, rcond = %g", |
|
|
4785 rcond); |
|
|
4786 } |
|
|
4787 } |
|
|
4788 else |
|
|
4789 rcond = 1.; |
|
|
4790 |
|
|
4791 if (err == 0) |
|
5164
|
4792 { |
|
5681
|
4793 octave_idx_type b_nr = b.rows (); |
|
|
4794 octave_idx_type b_nc = b.cols (); |
|
|
4795 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
4796 |
|
|
4797 // Take a first guess that the number of non-zero terms |
|
|
4798 // will be as many as in b |
|
|
4799 volatile octave_idx_type x_nz = b.nnz (); |
|
|
4800 volatile octave_idx_type ii = 0; |
|
|
4801 retval = SparseMatrix (b_nr, b_nc, x_nz); |
|
|
4802 |
|
|
4803 retval.xcidx(0) = 0; |
|
|
4804 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
|
4805 { |
|
|
4806 for (octave_idx_type i = 0; i < b_nr; i++) |
|
|
4807 Bx[i] = b.elem (i, j); |
|
|
4808 |
|
|
4809 F77_XFCN (dpbtrs, DPBTRS, |
|
|
4810 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4811 nr, n_lower, 1, tmp_data, |
|
|
4812 ldm, Bx, b_nr, err |
|
|
4813 F77_CHAR_ARG_LEN (1))); |
|
5164
|
4814 |
|
5681
|
4815 if (f77_exception_encountered) |
|
|
4816 { |
|
|
4817 (*current_liboctave_error_handler) |
|
|
4818 ("unrecoverable error in dpbtrs"); |
|
|
4819 err = -1; |
|
|
4820 break; |
|
|
4821 } |
|
|
4822 |
|
|
4823 if (err != 0) |
|
|
4824 { |
|
|
4825 (*current_liboctave_error_handler) |
|
|
4826 ("SparseMatrix::solve solve failed"); |
|
|
4827 err = -1; |
|
|
4828 break; |
|
|
4829 } |
|
|
4830 |
|
|
4831 for (octave_idx_type i = 0; i < b_nr; i++) |
|
|
4832 { |
|
|
4833 double tmp = Bx[i]; |
|
|
4834 if (tmp != 0.0) |
|
|
4835 { |
|
|
4836 if (ii == x_nz) |
|
|
4837 { |
|
|
4838 // Resize the sparse matrix |
|
|
4839 octave_idx_type sz = x_nz * |
|
|
4840 (b_nc - j) / b_nc; |
|
|
4841 sz = (sz > 10 ? sz : 10) + x_nz; |
|
|
4842 retval.change_capacity (sz); |
|
|
4843 x_nz = sz; |
|
|
4844 } |
|
|
4845 retval.xdata(ii) = tmp; |
|
|
4846 retval.xridx(ii++) = i; |
|
|
4847 } |
|
|
4848 } |
|
|
4849 retval.xcidx(j+1) = ii; |
|
5164
|
4850 } |
|
|
4851 |
|
5681
|
4852 retval.maybe_compress (); |
|
5164
|
4853 } |
|
|
4854 } |
|
|
4855 } |
|
|
4856 } |
|
|
4857 |
|
5785
|
4858 if (typ == MatrixType::Banded) |
|
5164
|
4859 { |
|
|
4860 // Create the storage for the banded form of the sparse matrix |
|
5275
|
4861 octave_idx_type n_upper = mattype.nupper (); |
|
|
4862 octave_idx_type n_lower = mattype.nlower (); |
|
|
4863 octave_idx_type ldm = n_upper + 2 * n_lower + 1; |
|
5164
|
4864 |
|
|
4865 Matrix m_band (ldm, nc); |
|
|
4866 double *tmp_data = m_band.fortran_vec (); |
|
|
4867 |
|
|
4868 if (! mattype.is_dense ()) |
|
|
4869 { |
|
5275
|
4870 octave_idx_type ii = 0; |
|
|
4871 |
|
|
4872 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
4873 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
4874 tmp_data[ii++] = 0.; |
|
|
4875 } |
|
|
4876 |
|
5275
|
4877 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4878 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
4879 m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); |
|
|
4880 |
|
5681
|
4881 // Calculate the norm of the matrix, for later use. |
|
|
4882 double anorm; |
|
|
4883 if (calc_cond) |
|
|
4884 { |
|
|
4885 for (octave_idx_type j = 0; j < nr; j++) |
|
|
4886 { |
|
|
4887 double atmp = 0.; |
|
|
4888 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
4889 atmp += fabs(data(i)); |
|
|
4890 if (atmp > anorm) |
|
|
4891 anorm = atmp; |
|
|
4892 } |
|
|
4893 } |
|
|
4894 |
|
5275
|
4895 Array<octave_idx_type> ipvt (nr); |
|
|
4896 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
4897 |
|
|
4898 F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, |
|
|
4899 ldm, pipvt, err)); |
|
|
4900 |
|
|
4901 if (f77_exception_encountered) |
|
|
4902 (*current_liboctave_error_handler) |
|
|
4903 ("unrecoverable error in dgbtrf"); |
|
|
4904 else |
|
|
4905 { |
|
|
4906 if (err != 0) |
|
|
4907 { |
|
|
4908 err = -2; |
|
5681
|
4909 rcond = 0.0; |
|
5164
|
4910 |
|
|
4911 if (sing_handler) |
|
5681
|
4912 { |
|
|
4913 sing_handler (rcond); |
|
|
4914 mattype.mark_as_rectangular (); |
|
|
4915 } |
|
5164
|
4916 else |
|
|
4917 (*current_liboctave_error_handler) |
|
|
4918 ("matrix singular to machine precision"); |
|
|
4919 |
|
|
4920 } |
|
|
4921 else |
|
|
4922 { |
|
5681
|
4923 if (calc_cond) |
|
5164
|
4924 { |
|
5681
|
4925 char job = '1'; |
|
|
4926 Array<double> z (3 * nr); |
|
|
4927 double *pz = z.fortran_vec (); |
|
|
4928 Array<octave_idx_type> iz (nr); |
|
5717
|
4929 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
4930 |
|
|
4931 F77_XFCN (dgbcon, DGBCON, |
|
|
4932 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4933 nc, n_lower, n_upper, tmp_data, ldm, pipvt, |
|
|
4934 anorm, rcond, pz, piz, err |
|
|
4935 F77_CHAR_ARG_LEN (1))); |
|
|
4936 |
|
5164
|
4937 if (f77_exception_encountered) |
|
5681
|
4938 (*current_liboctave_error_handler) |
|
|
4939 ("unrecoverable error in dgbcon"); |
|
|
4940 |
|
|
4941 if (err != 0) |
|
|
4942 err = -2; |
|
|
4943 |
|
|
4944 volatile double rcond_plus_one = rcond + 1.0; |
|
|
4945 |
|
|
4946 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
4947 { |
|
|
4948 err = -2; |
|
|
4949 |
|
|
4950 if (sing_handler) |
|
|
4951 { |
|
|
4952 sing_handler (rcond); |
|
|
4953 mattype.mark_as_rectangular (); |
|
|
4954 } |
|
|
4955 else |
|
|
4956 (*current_liboctave_error_handler) |
|
|
4957 ("matrix singular to machine precision, rcond = %g", |
|
|
4958 rcond); |
|
|
4959 } |
|
|
4960 } |
|
|
4961 else |
|
|
4962 rcond = 1.; |
|
|
4963 |
|
|
4964 if (err == 0) |
|
|
4965 { |
|
|
4966 char job = 'N'; |
|
|
4967 volatile octave_idx_type x_nz = b.nnz (); |
|
|
4968 octave_idx_type b_nc = b.cols (); |
|
|
4969 retval = SparseMatrix (nr, b_nc, x_nz); |
|
|
4970 retval.xcidx(0) = 0; |
|
|
4971 volatile octave_idx_type ii = 0; |
|
|
4972 |
|
|
4973 OCTAVE_LOCAL_BUFFER (double, work, nr); |
|
|
4974 |
|
|
4975 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
4976 { |
|
5681
|
4977 for (octave_idx_type i = 0; i < nr; i++) |
|
|
4978 work[i] = 0.; |
|
|
4979 for (octave_idx_type i = b.cidx(j); |
|
|
4980 i < b.cidx(j+1); i++) |
|
|
4981 work[b.ridx(i)] = b.data(i); |
|
|
4982 |
|
|
4983 F77_XFCN (dgbtrs, DGBTRS, |
|
|
4984 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
4985 nr, n_lower, n_upper, 1, tmp_data, |
|
|
4986 ldm, pipvt, work, b.rows (), err |
|
|
4987 F77_CHAR_ARG_LEN (1))); |
|
|
4988 |
|
|
4989 if (f77_exception_encountered) |
|
|
4990 { |
|
|
4991 (*current_liboctave_error_handler) |
|
|
4992 ("unrecoverable error in dgbtrs"); |
|
|
4993 break; |
|
|
4994 } |
|
|
4995 |
|
|
4996 // Count non-zeros in work vector and adjust |
|
|
4997 // space in retval if needed |
|
|
4998 octave_idx_type new_nnz = 0; |
|
|
4999 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5000 if (work[i] != 0.) |
|
|
5001 new_nnz++; |
|
|
5002 |
|
|
5003 if (ii + new_nnz > x_nz) |
|
|
5004 { |
|
|
5005 // Resize the sparse matrix |
|
|
5006 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
|
5007 retval.change_capacity (sz); |
|
|
5008 x_nz = sz; |
|
|
5009 } |
|
|
5010 |
|
|
5011 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5012 if (work[i] != 0.) |
|
|
5013 { |
|
|
5014 retval.xridx(ii) = i; |
|
|
5015 retval.xdata(ii++) = work[i]; |
|
|
5016 } |
|
|
5017 retval.xcidx(j+1) = ii; |
|
5164
|
5018 } |
|
|
5019 |
|
5681
|
5020 retval.maybe_compress (); |
|
5164
|
5021 } |
|
|
5022 } |
|
|
5023 } |
|
|
5024 } |
|
5785
|
5025 else if (typ != MatrixType::Banded_Hermitian) |
|
5164
|
5026 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
5027 } |
|
|
5028 |
|
|
5029 return retval; |
|
|
5030 } |
|
|
5031 |
|
|
5032 ComplexMatrix |
|
5785
|
5033 SparseMatrix::bsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5681
|
5034 octave_idx_type& err, double& rcond, |
|
|
5035 solve_singularity_handler sing_handler, |
|
|
5036 bool calc_cond) const |
|
5164
|
5037 { |
|
|
5038 ComplexMatrix retval; |
|
|
5039 |
|
5275
|
5040 octave_idx_type nr = rows (); |
|
|
5041 octave_idx_type nc = cols (); |
|
5164
|
5042 err = 0; |
|
|
5043 |
|
|
5044 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
5045 (*current_liboctave_error_handler) |
|
|
5046 ("matrix dimension mismatch solution of linear equations"); |
|
|
5047 else |
|
|
5048 { |
|
|
5049 // Print spparms("spumoni") info if requested |
|
|
5050 volatile int typ = mattype.type (); |
|
|
5051 mattype.info (); |
|
|
5052 |
|
5785
|
5053 if (typ == MatrixType::Banded_Hermitian) |
|
5164
|
5054 { |
|
5275
|
5055 octave_idx_type n_lower = mattype.nlower (); |
|
|
5056 octave_idx_type ldm = n_lower + 1; |
|
5164
|
5057 |
|
|
5058 Matrix m_band (ldm, nc); |
|
|
5059 double *tmp_data = m_band.fortran_vec (); |
|
|
5060 |
|
|
5061 if (! mattype.is_dense ()) |
|
|
5062 { |
|
5275
|
5063 octave_idx_type ii = 0; |
|
|
5064 |
|
|
5065 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
5066 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
5067 tmp_data[ii++] = 0.; |
|
|
5068 } |
|
|
5069 |
|
5275
|
5070 for (octave_idx_type j = 0; j < nc; j++) |
|
|
5071 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
5072 { |
|
5275
|
5073 octave_idx_type ri = ridx (i); |
|
5164
|
5074 if (ri >= j) |
|
|
5075 m_band(ri - j, j) = data(i); |
|
|
5076 } |
|
|
5077 |
|
5681
|
5078 // Calculate the norm of the matrix, for later use. |
|
|
5079 double anorm; |
|
|
5080 if (calc_cond) |
|
|
5081 anorm = m_band.abs().sum().row(0).max(); |
|
|
5082 |
|
5164
|
5083 char job = 'L'; |
|
|
5084 F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5085 nr, n_lower, tmp_data, ldm, err |
|
|
5086 F77_CHAR_ARG_LEN (1))); |
|
|
5087 |
|
|
5088 if (f77_exception_encountered) |
|
|
5089 (*current_liboctave_error_handler) |
|
|
5090 ("unrecoverable error in dpbtrf"); |
|
|
5091 else |
|
|
5092 { |
|
|
5093 if (err != 0) |
|
|
5094 { |
|
|
5095 // Matrix is not positive definite!! Fall through to |
|
|
5096 // unsymmetric banded solver. |
|
|
5097 mattype.mark_as_unsymmetric (); |
|
5785
|
5098 typ = MatrixType::Banded; |
|
5681
|
5099 rcond = 0.0; |
|
5164
|
5100 err = 0; |
|
|
5101 } |
|
|
5102 else |
|
|
5103 { |
|
5681
|
5104 if (calc_cond) |
|
|
5105 { |
|
|
5106 Array<double> z (3 * nr); |
|
|
5107 double *pz = z.fortran_vec (); |
|
|
5108 Array<octave_idx_type> iz (nr); |
|
5717
|
5109 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
5110 |
|
|
5111 F77_XFCN (dpbcon, DGBCON, |
|
|
5112 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5113 nr, n_lower, tmp_data, ldm, |
|
|
5114 anorm, rcond, pz, piz, err |
|
|
5115 F77_CHAR_ARG_LEN (1))); |
|
|
5116 |
|
|
5117 if (f77_exception_encountered) |
|
|
5118 (*current_liboctave_error_handler) |
|
|
5119 ("unrecoverable error in dpbcon"); |
|
|
5120 |
|
|
5121 if (err != 0) |
|
|
5122 err = -2; |
|
|
5123 |
|
|
5124 volatile double rcond_plus_one = rcond + 1.0; |
|
|
5125 |
|
|
5126 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
5127 { |
|
|
5128 err = -2; |
|
|
5129 |
|
|
5130 if (sing_handler) |
|
|
5131 { |
|
|
5132 sing_handler (rcond); |
|
|
5133 mattype.mark_as_rectangular (); |
|
|
5134 } |
|
|
5135 else |
|
|
5136 (*current_liboctave_error_handler) |
|
|
5137 ("matrix singular to machine precision, rcond = %g", |
|
|
5138 rcond); |
|
|
5139 } |
|
|
5140 } |
|
|
5141 else |
|
|
5142 rcond = 1.; |
|
|
5143 |
|
|
5144 if (err == 0) |
|
|
5145 { |
|
|
5146 octave_idx_type b_nr = b.rows (); |
|
|
5147 octave_idx_type b_nc = b.cols (); |
|
|
5148 |
|
|
5149 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
5150 OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); |
|
|
5151 |
|
|
5152 retval.resize (b_nr, b_nc); |
|
5164
|
5153 |
|
5681
|
5154 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
5155 { |
|
5681
|
5156 for (octave_idx_type i = 0; i < b_nr; i++) |
|
|
5157 { |
|
|
5158 Complex c = b (i,j); |
|
|
5159 Bx[i] = std::real (c); |
|
|
5160 Bz[i] = std::imag (c); |
|
|
5161 } |
|
5164
|
5162 |
|
5681
|
5163 F77_XFCN (dpbtrs, DPBTRS, |
|
|
5164 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5165 nr, n_lower, 1, tmp_data, |
|
|
5166 ldm, Bx, b_nr, err |
|
|
5167 F77_CHAR_ARG_LEN (1))); |
|
5164
|
5168 |
|
5681
|
5169 if (f77_exception_encountered) |
|
|
5170 { |
|
|
5171 (*current_liboctave_error_handler) |
|
|
5172 ("unrecoverable error in dpbtrs"); |
|
|
5173 err = -1; |
|
|
5174 break; |
|
|
5175 } |
|
|
5176 |
|
|
5177 if (err != 0) |
|
|
5178 { |
|
|
5179 (*current_liboctave_error_handler) |
|
|
5180 ("SparseMatrix::solve solve failed"); |
|
|
5181 err = -1; |
|
|
5182 break; |
|
|
5183 } |
|
|
5184 |
|
|
5185 F77_XFCN (dpbtrs, DPBTRS, |
|
|
5186 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5187 nr, n_lower, 1, tmp_data, |
|
|
5188 ldm, Bz, b.rows(), err |
|
|
5189 F77_CHAR_ARG_LEN (1))); |
|
|
5190 |
|
|
5191 if (f77_exception_encountered) |
|
|
5192 { |
|
|
5193 (*current_liboctave_error_handler) |
|
|
5194 ("unrecoverable error in dpbtrs"); |
|
|
5195 err = -1; |
|
|
5196 break; |
|
|
5197 } |
|
|
5198 |
|
|
5199 if (err != 0) |
|
|
5200 { |
|
|
5201 (*current_liboctave_error_handler) |
|
|
5202 ("SparseMatrix::solve solve failed"); |
|
|
5203 err = -1; |
|
|
5204 break; |
|
|
5205 } |
|
|
5206 |
|
|
5207 for (octave_idx_type i = 0; i < b_nr; i++) |
|
|
5208 retval (i, j) = Complex (Bx[i], Bz[i]); |
|
5164
|
5209 } |
|
|
5210 } |
|
|
5211 } |
|
|
5212 } |
|
|
5213 } |
|
|
5214 |
|
5785
|
5215 if (typ == MatrixType::Banded) |
|
5164
|
5216 { |
|
|
5217 // Create the storage for the banded form of the sparse matrix |
|
6242
|
5218 octave_idx_type n_upper = mattype.nupper (); |
|
|
5219 octave_idx_type n_lower = mattype.nlower (); |
|
|
5220 octave_idx_type ldm = n_upper + 2 * n_lower + 1; |
|
5164
|
5221 |
|
|
5222 Matrix m_band (ldm, nc); |
|
|
5223 double *tmp_data = m_band.fortran_vec (); |
|
|
5224 |
|
|
5225 if (! mattype.is_dense ()) |
|
|
5226 { |
|
5275
|
5227 octave_idx_type ii = 0; |
|
|
5228 |
|
|
5229 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
5230 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
5231 tmp_data[ii++] = 0.; |
|
|
5232 } |
|
|
5233 |
|
5275
|
5234 for (octave_idx_type j = 0; j < nc; j++) |
|
|
5235 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
5236 m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); |
|
|
5237 |
|
5681
|
5238 // Calculate the norm of the matrix, for later use. |
|
|
5239 double anorm; |
|
|
5240 if (calc_cond) |
|
|
5241 { |
|
|
5242 for (octave_idx_type j = 0; j < nr; j++) |
|
|
5243 { |
|
|
5244 double atmp = 0.; |
|
|
5245 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
5246 atmp += fabs(data(i)); |
|
|
5247 if (atmp > anorm) |
|
|
5248 anorm = atmp; |
|
|
5249 } |
|
|
5250 } |
|
|
5251 |
|
5275
|
5252 Array<octave_idx_type> ipvt (nr); |
|
|
5253 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
5254 |
|
|
5255 F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, |
|
|
5256 ldm, pipvt, err)); |
|
|
5257 |
|
|
5258 if (f77_exception_encountered) |
|
|
5259 (*current_liboctave_error_handler) |
|
|
5260 ("unrecoverable error in dgbtrf"); |
|
|
5261 else |
|
|
5262 { |
|
|
5263 if (err != 0) |
|
|
5264 { |
|
|
5265 err = -2; |
|
5681
|
5266 rcond = 0.0; |
|
5164
|
5267 |
|
|
5268 if (sing_handler) |
|
5681
|
5269 { |
|
5164
|
5270 sing_handler (rcond); |
|
5681
|
5271 mattype.mark_as_rectangular (); |
|
|
5272 } |
|
5164
|
5273 else |
|
|
5274 (*current_liboctave_error_handler) |
|
|
5275 ("matrix singular to machine precision"); |
|
|
5276 |
|
|
5277 } |
|
|
5278 else |
|
|
5279 { |
|
5681
|
5280 if (calc_cond) |
|
5164
|
5281 { |
|
5681
|
5282 char job = '1'; |
|
|
5283 Array<double> z (3 * nr); |
|
|
5284 double *pz = z.fortran_vec (); |
|
|
5285 Array<octave_idx_type> iz (nr); |
|
5717
|
5286 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
5287 |
|
|
5288 F77_XFCN (dpbcon, DGBCON, |
|
|
5289 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5290 nr, n_lower, tmp_data, ldm, |
|
|
5291 anorm, rcond, pz, piz, err |
|
|
5292 F77_CHAR_ARG_LEN (1))); |
|
|
5293 |
|
|
5294 if (f77_exception_encountered) |
|
|
5295 (*current_liboctave_error_handler) |
|
|
5296 ("unrecoverable error in dpbcon"); |
|
|
5297 |
|
|
5298 if (err != 0) |
|
|
5299 err = -2; |
|
|
5300 |
|
|
5301 volatile double rcond_plus_one = rcond + 1.0; |
|
|
5302 |
|
|
5303 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
5304 { |
|
|
5305 err = -2; |
|
|
5306 |
|
|
5307 if (sing_handler) |
|
|
5308 { |
|
|
5309 sing_handler (rcond); |
|
|
5310 mattype.mark_as_rectangular (); |
|
|
5311 } |
|
|
5312 else |
|
|
5313 (*current_liboctave_error_handler) |
|
|
5314 ("matrix singular to machine precision, rcond = %g", |
|
|
5315 rcond); |
|
|
5316 } |
|
|
5317 } |
|
|
5318 else |
|
|
5319 rcond = 1.; |
|
|
5320 |
|
|
5321 if (err == 0) |
|
|
5322 { |
|
|
5323 char job = 'N'; |
|
|
5324 octave_idx_type b_nc = b.cols (); |
|
|
5325 retval.resize (nr,b_nc); |
|
|
5326 |
|
|
5327 OCTAVE_LOCAL_BUFFER (double, Bz, nr); |
|
|
5328 OCTAVE_LOCAL_BUFFER (double, Bx, nr); |
|
|
5329 |
|
|
5330 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
5331 { |
|
5681
|
5332 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5333 { |
|
|
5334 Complex c = b (i, j); |
|
|
5335 Bx[i] = std::real (c); |
|
|
5336 Bz[i] = std::imag (c); |
|
|
5337 } |
|
|
5338 |
|
|
5339 F77_XFCN (dgbtrs, DGBTRS, |
|
|
5340 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5341 nr, n_lower, n_upper, 1, tmp_data, |
|
|
5342 ldm, pipvt, Bx, b.rows (), err |
|
|
5343 F77_CHAR_ARG_LEN (1))); |
|
5164
|
5344 |
|
5681
|
5345 if (f77_exception_encountered) |
|
|
5346 { |
|
|
5347 (*current_liboctave_error_handler) |
|
|
5348 ("unrecoverable error in dgbtrs"); |
|
|
5349 break; |
|
|
5350 } |
|
|
5351 |
|
|
5352 F77_XFCN (dgbtrs, DGBTRS, |
|
|
5353 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5354 nr, n_lower, n_upper, 1, tmp_data, |
|
|
5355 ldm, pipvt, Bz, b.rows (), err |
|
|
5356 F77_CHAR_ARG_LEN (1))); |
|
|
5357 |
|
|
5358 if (f77_exception_encountered) |
|
|
5359 { |
|
|
5360 (*current_liboctave_error_handler) |
|
|
5361 ("unrecoverable error in dgbtrs"); |
|
|
5362 break; |
|
|
5363 } |
|
|
5364 |
|
|
5365 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5366 retval (i, j) = Complex (Bx[i], Bz[i]); |
|
5164
|
5367 } |
|
|
5368 } |
|
|
5369 } |
|
|
5370 } |
|
|
5371 } |
|
5785
|
5372 else if (typ != MatrixType::Banded_Hermitian) |
|
5164
|
5373 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
5374 } |
|
|
5375 |
|
|
5376 return retval; |
|
|
5377 } |
|
|
5378 |
|
|
5379 SparseComplexMatrix |
|
5785
|
5380 SparseMatrix::bsolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5681
|
5381 octave_idx_type& err, double& rcond, |
|
|
5382 solve_singularity_handler sing_handler, |
|
|
5383 bool calc_cond) const |
|
5164
|
5384 { |
|
|
5385 SparseComplexMatrix retval; |
|
|
5386 |
|
5275
|
5387 octave_idx_type nr = rows (); |
|
|
5388 octave_idx_type nc = cols (); |
|
5164
|
5389 err = 0; |
|
|
5390 |
|
|
5391 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
5392 (*current_liboctave_error_handler) |
|
|
5393 ("matrix dimension mismatch solution of linear equations"); |
|
|
5394 else |
|
|
5395 { |
|
|
5396 // Print spparms("spumoni") info if requested |
|
|
5397 volatile int typ = mattype.type (); |
|
|
5398 mattype.info (); |
|
|
5399 |
|
5785
|
5400 if (typ == MatrixType::Banded_Hermitian) |
|
5164
|
5401 { |
|
6242
|
5402 octave_idx_type n_lower = mattype.nlower (); |
|
|
5403 octave_idx_type ldm = n_lower + 1; |
|
5164
|
5404 |
|
|
5405 Matrix m_band (ldm, nc); |
|
|
5406 double *tmp_data = m_band.fortran_vec (); |
|
|
5407 |
|
|
5408 if (! mattype.is_dense ()) |
|
|
5409 { |
|
5275
|
5410 octave_idx_type ii = 0; |
|
|
5411 |
|
|
5412 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
5413 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
5414 tmp_data[ii++] = 0.; |
|
|
5415 } |
|
|
5416 |
|
5275
|
5417 for (octave_idx_type j = 0; j < nc; j++) |
|
|
5418 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
5419 { |
|
5275
|
5420 octave_idx_type ri = ridx (i); |
|
5164
|
5421 if (ri >= j) |
|
|
5422 m_band(ri - j, j) = data(i); |
|
|
5423 } |
|
|
5424 |
|
5681
|
5425 // Calculate the norm of the matrix, for later use. |
|
|
5426 double anorm; |
|
|
5427 if (calc_cond) |
|
|
5428 anorm = m_band.abs().sum().row(0).max(); |
|
|
5429 |
|
5164
|
5430 char job = 'L'; |
|
|
5431 F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5432 nr, n_lower, tmp_data, ldm, err |
|
|
5433 F77_CHAR_ARG_LEN (1))); |
|
|
5434 |
|
|
5435 if (f77_exception_encountered) |
|
|
5436 (*current_liboctave_error_handler) |
|
|
5437 ("unrecoverable error in dpbtrf"); |
|
|
5438 else |
|
|
5439 { |
|
|
5440 if (err != 0) |
|
|
5441 { |
|
|
5442 // Matrix is not positive definite!! Fall through to |
|
|
5443 // unsymmetric banded solver. |
|
|
5444 mattype.mark_as_unsymmetric (); |
|
5785
|
5445 typ = MatrixType::Banded; |
|
5164
|
5446 |
|
5681
|
5447 rcond = 0.0; |
|
5164
|
5448 err = 0; |
|
|
5449 } |
|
|
5450 else |
|
|
5451 { |
|
5681
|
5452 if (calc_cond) |
|
5164
|
5453 { |
|
5681
|
5454 Array<double> z (3 * nr); |
|
|
5455 double *pz = z.fortran_vec (); |
|
|
5456 Array<octave_idx_type> iz (nr); |
|
5717
|
5457 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
5458 |
|
|
5459 F77_XFCN (dpbcon, DGBCON, |
|
|
5460 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5461 nr, n_lower, tmp_data, ldm, |
|
|
5462 anorm, rcond, pz, piz, err |
|
|
5463 F77_CHAR_ARG_LEN (1))); |
|
|
5464 |
|
|
5465 if (f77_exception_encountered) |
|
|
5466 (*current_liboctave_error_handler) |
|
|
5467 ("unrecoverable error in dpbcon"); |
|
|
5468 |
|
|
5469 if (err != 0) |
|
|
5470 err = -2; |
|
|
5471 |
|
|
5472 volatile double rcond_plus_one = rcond + 1.0; |
|
|
5473 |
|
|
5474 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
5475 { |
|
|
5476 err = -2; |
|
|
5477 |
|
|
5478 if (sing_handler) |
|
|
5479 { |
|
|
5480 sing_handler (rcond); |
|
|
5481 mattype.mark_as_rectangular (); |
|
|
5482 } |
|
|
5483 else |
|
|
5484 (*current_liboctave_error_handler) |
|
|
5485 ("matrix singular to machine precision, rcond = %g", |
|
|
5486 rcond); |
|
|
5487 } |
|
|
5488 } |
|
|
5489 else |
|
|
5490 rcond = 1.; |
|
|
5491 |
|
|
5492 if (err == 0) |
|
|
5493 { |
|
|
5494 octave_idx_type b_nr = b.rows (); |
|
|
5495 octave_idx_type b_nc = b.cols (); |
|
|
5496 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
5497 OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); |
|
|
5498 |
|
|
5499 // Take a first guess that the number of non-zero terms |
|
|
5500 // will be as many as in b |
|
|
5501 volatile octave_idx_type x_nz = b.nnz (); |
|
|
5502 volatile octave_idx_type ii = 0; |
|
|
5503 retval = SparseComplexMatrix (b_nr, b_nc, x_nz); |
|
|
5504 |
|
|
5505 retval.xcidx(0) = 0; |
|
|
5506 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
5507 { |
|
5681
|
5508 |
|
|
5509 for (octave_idx_type i = 0; i < b_nr; i++) |
|
|
5510 { |
|
|
5511 Complex c = b (i,j); |
|
|
5512 Bx[i] = std::real (c); |
|
|
5513 Bz[i] = std::imag (c); |
|
|
5514 } |
|
|
5515 |
|
|
5516 F77_XFCN (dpbtrs, DPBTRS, |
|
|
5517 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5518 nr, n_lower, 1, tmp_data, |
|
|
5519 ldm, Bx, b_nr, err |
|
|
5520 F77_CHAR_ARG_LEN (1))); |
|
|
5521 |
|
|
5522 if (f77_exception_encountered) |
|
|
5523 { |
|
|
5524 (*current_liboctave_error_handler) |
|
|
5525 ("unrecoverable error in dpbtrs"); |
|
|
5526 err = -1; |
|
|
5527 break; |
|
|
5528 } |
|
|
5529 |
|
|
5530 if (err != 0) |
|
|
5531 { |
|
|
5532 (*current_liboctave_error_handler) |
|
|
5533 ("SparseMatrix::solve solve failed"); |
|
|
5534 err = -1; |
|
|
5535 break; |
|
|
5536 } |
|
|
5537 |
|
|
5538 F77_XFCN (dpbtrs, DPBTRS, |
|
|
5539 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5540 nr, n_lower, 1, tmp_data, |
|
|
5541 ldm, Bz, b_nr, err |
|
|
5542 F77_CHAR_ARG_LEN (1))); |
|
5164
|
5543 |
|
5681
|
5544 if (f77_exception_encountered) |
|
|
5545 { |
|
|
5546 (*current_liboctave_error_handler) |
|
|
5547 ("unrecoverable error in dpbtrs"); |
|
|
5548 err = -1; |
|
|
5549 break; |
|
|
5550 } |
|
|
5551 |
|
|
5552 if (err != 0) |
|
|
5553 { |
|
|
5554 (*current_liboctave_error_handler) |
|
|
5555 ("SparseMatrix::solve solve failed"); |
|
|
5556 |
|
|
5557 err = -1; |
|
|
5558 break; |
|
|
5559 } |
|
|
5560 |
|
|
5561 // Count non-zeros in work vector and adjust |
|
|
5562 // space in retval if needed |
|
|
5563 octave_idx_type new_nnz = 0; |
|
|
5564 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5565 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
5566 new_nnz++; |
|
|
5567 |
|
|
5568 if (ii + new_nnz > x_nz) |
|
|
5569 { |
|
|
5570 // Resize the sparse matrix |
|
|
5571 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
|
5572 retval.change_capacity (sz); |
|
|
5573 x_nz = sz; |
|
|
5574 } |
|
|
5575 |
|
|
5576 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5577 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
5578 { |
|
|
5579 retval.xridx(ii) = i; |
|
|
5580 retval.xdata(ii++) = |
|
|
5581 Complex (Bx[i], Bz[i]); |
|
|
5582 } |
|
|
5583 |
|
|
5584 retval.xcidx(j+1) = ii; |
|
5164
|
5585 } |
|
|
5586 |
|
5681
|
5587 retval.maybe_compress (); |
|
5164
|
5588 } |
|
|
5589 } |
|
|
5590 } |
|
|
5591 } |
|
|
5592 |
|
5785
|
5593 if (typ == MatrixType::Banded) |
|
5164
|
5594 { |
|
|
5595 // Create the storage for the banded form of the sparse matrix |
|
6242
|
5596 octave_idx_type n_upper = mattype.nupper (); |
|
|
5597 octave_idx_type n_lower = mattype.nlower (); |
|
|
5598 octave_idx_type ldm = n_upper + 2 * n_lower + 1; |
|
5164
|
5599 |
|
|
5600 Matrix m_band (ldm, nc); |
|
|
5601 double *tmp_data = m_band.fortran_vec (); |
|
|
5602 |
|
|
5603 if (! mattype.is_dense ()) |
|
|
5604 { |
|
5275
|
5605 octave_idx_type ii = 0; |
|
|
5606 |
|
|
5607 for (octave_idx_type j = 0; j < ldm; j++) |
|
|
5608 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
5609 tmp_data[ii++] = 0.; |
|
|
5610 } |
|
|
5611 |
|
5275
|
5612 for (octave_idx_type j = 0; j < nc; j++) |
|
|
5613 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
5614 m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); |
|
|
5615 |
|
5681
|
5616 // Calculate the norm of the matrix, for later use. |
|
|
5617 double anorm; |
|
|
5618 if (calc_cond) |
|
|
5619 { |
|
|
5620 for (octave_idx_type j = 0; j < nr; j++) |
|
|
5621 { |
|
|
5622 double atmp = 0.; |
|
|
5623 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
|
5624 atmp += fabs(data(i)); |
|
|
5625 if (atmp > anorm) |
|
|
5626 anorm = atmp; |
|
|
5627 } |
|
|
5628 } |
|
|
5629 |
|
5275
|
5630 Array<octave_idx_type> ipvt (nr); |
|
|
5631 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
5164
|
5632 |
|
|
5633 F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, |
|
|
5634 ldm, pipvt, err)); |
|
|
5635 |
|
|
5636 if (f77_exception_encountered) |
|
|
5637 (*current_liboctave_error_handler) |
|
|
5638 ("unrecoverable error in dgbtrf"); |
|
|
5639 else |
|
|
5640 { |
|
|
5641 if (err != 0) |
|
|
5642 { |
|
|
5643 err = -2; |
|
5681
|
5644 rcond = 0.0; |
|
5164
|
5645 |
|
|
5646 if (sing_handler) |
|
5681
|
5647 { |
|
|
5648 sing_handler (rcond); |
|
|
5649 mattype.mark_as_rectangular (); |
|
|
5650 } |
|
5164
|
5651 else |
|
|
5652 (*current_liboctave_error_handler) |
|
|
5653 ("matrix singular to machine precision"); |
|
|
5654 |
|
|
5655 } |
|
|
5656 else |
|
|
5657 { |
|
5681
|
5658 if (calc_cond) |
|
5164
|
5659 { |
|
5681
|
5660 char job = '1'; |
|
|
5661 Array<double> z (3 * nr); |
|
|
5662 double *pz = z.fortran_vec (); |
|
|
5663 Array<octave_idx_type> iz (nr); |
|
5717
|
5664 octave_idx_type *piz = iz.fortran_vec (); |
|
5681
|
5665 |
|
|
5666 F77_XFCN (dgbcon, DGBCON, |
|
|
5667 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5668 nc, n_lower, n_upper, tmp_data, ldm, pipvt, |
|
|
5669 anorm, rcond, pz, piz, err |
|
|
5670 F77_CHAR_ARG_LEN (1))); |
|
|
5671 |
|
|
5672 if (f77_exception_encountered) |
|
|
5673 (*current_liboctave_error_handler) |
|
|
5674 ("unrecoverable error in dgbcon"); |
|
|
5675 |
|
|
5676 if (err != 0) |
|
|
5677 err = -2; |
|
|
5678 |
|
|
5679 volatile double rcond_plus_one = rcond + 1.0; |
|
|
5680 |
|
|
5681 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
5682 { |
|
|
5683 err = -2; |
|
|
5684 |
|
|
5685 if (sing_handler) |
|
|
5686 { |
|
|
5687 sing_handler (rcond); |
|
|
5688 mattype.mark_as_rectangular (); |
|
|
5689 } |
|
|
5690 else |
|
|
5691 (*current_liboctave_error_handler) |
|
|
5692 ("matrix singular to machine precision, rcond = %g", |
|
|
5693 rcond); |
|
|
5694 } |
|
|
5695 } |
|
|
5696 else |
|
|
5697 rcond = 1.; |
|
|
5698 |
|
|
5699 if (err == 0) |
|
|
5700 { |
|
|
5701 char job = 'N'; |
|
|
5702 volatile octave_idx_type x_nz = b.nnz (); |
|
|
5703 octave_idx_type b_nc = b.cols (); |
|
|
5704 retval = SparseComplexMatrix (nr, b_nc, x_nz); |
|
|
5705 retval.xcidx(0) = 0; |
|
|
5706 volatile octave_idx_type ii = 0; |
|
|
5707 |
|
|
5708 OCTAVE_LOCAL_BUFFER (double, Bx, nr); |
|
|
5709 OCTAVE_LOCAL_BUFFER (double, Bz, nr); |
|
|
5710 |
|
|
5711 for (volatile octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
5712 { |
|
5681
|
5713 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5714 { |
|
|
5715 Bx[i] = 0.; |
|
|
5716 Bz[i] = 0.; |
|
|
5717 } |
|
|
5718 for (octave_idx_type i = b.cidx(j); |
|
|
5719 i < b.cidx(j+1); i++) |
|
|
5720 { |
|
|
5721 Complex c = b.data(i); |
|
|
5722 Bx[b.ridx(i)] = std::real (c); |
|
|
5723 Bz[b.ridx(i)] = std::imag (c); |
|
|
5724 } |
|
|
5725 |
|
|
5726 F77_XFCN (dgbtrs, DGBTRS, |
|
|
5727 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5728 nr, n_lower, n_upper, 1, tmp_data, |
|
|
5729 ldm, pipvt, Bx, b.rows (), err |
|
|
5730 F77_CHAR_ARG_LEN (1))); |
|
5164
|
5731 |
|
5681
|
5732 if (f77_exception_encountered) |
|
|
5733 { |
|
|
5734 (*current_liboctave_error_handler) |
|
|
5735 ("unrecoverable error in dgbtrs"); |
|
|
5736 break; |
|
|
5737 } |
|
|
5738 |
|
|
5739 F77_XFCN (dgbtrs, DGBTRS, |
|
|
5740 (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
5741 nr, n_lower, n_upper, 1, tmp_data, |
|
|
5742 ldm, pipvt, Bz, b.rows (), err |
|
|
5743 F77_CHAR_ARG_LEN (1))); |
|
|
5744 |
|
|
5745 if (f77_exception_encountered) |
|
|
5746 { |
|
|
5747 (*current_liboctave_error_handler) |
|
|
5748 ("unrecoverable error in dgbtrs"); |
|
|
5749 break; |
|
|
5750 } |
|
|
5751 |
|
|
5752 // Count non-zeros in work vector and adjust |
|
|
5753 // space in retval if needed |
|
|
5754 octave_idx_type new_nnz = 0; |
|
|
5755 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5756 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
5757 new_nnz++; |
|
|
5758 |
|
|
5759 if (ii + new_nnz > x_nz) |
|
|
5760 { |
|
|
5761 // Resize the sparse matrix |
|
|
5762 octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; |
|
|
5763 retval.change_capacity (sz); |
|
|
5764 x_nz = sz; |
|
|
5765 } |
|
|
5766 |
|
|
5767 for (octave_idx_type i = 0; i < nr; i++) |
|
|
5768 if (Bx[i] != 0. || Bz[i] != 0.) |
|
|
5769 { |
|
|
5770 retval.xridx(ii) = i; |
|
|
5771 retval.xdata(ii++) = |
|
|
5772 Complex (Bx[i], Bz[i]); |
|
|
5773 } |
|
|
5774 retval.xcidx(j+1) = ii; |
|
5164
|
5775 } |
|
|
5776 |
|
5681
|
5777 retval.maybe_compress (); |
|
5164
|
5778 } |
|
|
5779 } |
|
|
5780 } |
|
|
5781 } |
|
5785
|
5782 else if (typ != MatrixType::Banded_Hermitian) |
|
5164
|
5783 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
5784 } |
|
|
5785 |
|
|
5786 return retval; |
|
|
5787 } |
|
|
5788 |
|
|
5789 void * |
|
5681
|
5790 SparseMatrix::factorize (octave_idx_type& err, double &rcond, Matrix &Control, |
|
|
5791 Matrix &Info, solve_singularity_handler sing_handler, |
|
|
5792 bool calc_cond) const |
|
5164
|
5793 { |
|
|
5794 // The return values |
|
5404
|
5795 void *Numeric = 0; |
|
5164
|
5796 err = 0; |
|
|
5797 |
|
5203
|
5798 #ifdef HAVE_UMFPACK |
|
5164
|
5799 // Setup the control parameters |
|
|
5800 Control = Matrix (UMFPACK_CONTROL, 1); |
|
|
5801 double *control = Control.fortran_vec (); |
|
5322
|
5802 UMFPACK_DNAME (defaults) (control); |
|
5164
|
5803 |
|
5893
|
5804 double tmp = octave_sparse_params::get_key ("spumoni"); |
|
5164
|
5805 if (!xisnan (tmp)) |
|
|
5806 Control (UMFPACK_PRL) = tmp; |
|
5893
|
5807 tmp = octave_sparse_params::get_key ("piv_tol"); |
|
5164
|
5808 if (!xisnan (tmp)) |
|
|
5809 { |
|
|
5810 Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp; |
|
|
5811 Control (UMFPACK_PIVOT_TOLERANCE) = tmp; |
|
|
5812 } |
|
|
5813 |
|
|
5814 // Set whether we are allowed to modify Q or not |
|
5893
|
5815 tmp = octave_sparse_params::get_key ("autoamd"); |
|
5164
|
5816 if (!xisnan (tmp)) |
|
|
5817 Control (UMFPACK_FIXQ) = tmp; |
|
|
5818 |
|
5322
|
5819 UMFPACK_DNAME (report_control) (control); |
|
5164
|
5820 |
|
5275
|
5821 const octave_idx_type *Ap = cidx (); |
|
|
5822 const octave_idx_type *Ai = ridx (); |
|
5164
|
5823 const double *Ax = data (); |
|
5275
|
5824 octave_idx_type nr = rows (); |
|
|
5825 octave_idx_type nc = cols (); |
|
5164
|
5826 |
|
5322
|
5827 UMFPACK_DNAME (report_matrix) (nr, nc, Ap, Ai, Ax, 1, control); |
|
5164
|
5828 |
|
|
5829 void *Symbolic; |
|
|
5830 Info = Matrix (1, UMFPACK_INFO); |
|
|
5831 double *info = Info.fortran_vec (); |
|
5322
|
5832 int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, Ax, NULL, |
|
5164
|
5833 &Symbolic, control, info); |
|
|
5834 |
|
|
5835 if (status < 0) |
|
|
5836 { |
|
|
5837 (*current_liboctave_error_handler) |
|
|
5838 ("SparseMatrix::solve symbolic factorization failed"); |
|
|
5839 err = -1; |
|
|
5840 |
|
5322
|
5841 UMFPACK_DNAME (report_status) (control, status); |
|
|
5842 UMFPACK_DNAME (report_info) (control, info); |
|
|
5843 |
|
|
5844 UMFPACK_DNAME (free_symbolic) (&Symbolic) ; |
|
5164
|
5845 } |
|
|
5846 else |
|
|
5847 { |
|
5322
|
5848 UMFPACK_DNAME (report_symbolic) (Symbolic, control); |
|
|
5849 |
|
|
5850 status = UMFPACK_DNAME (numeric) (Ap, Ai, Ax, Symbolic, |
|
|
5851 &Numeric, control, info) ; |
|
|
5852 UMFPACK_DNAME (free_symbolic) (&Symbolic) ; |
|
5164
|
5853 |
|
5681
|
5854 if (calc_cond) |
|
|
5855 rcond = Info (UMFPACK_RCOND); |
|
|
5856 else |
|
|
5857 rcond = 1.; |
|
5164
|
5858 volatile double rcond_plus_one = rcond + 1.0; |
|
|
5859 |
|
|
5860 if (status == UMFPACK_WARNING_singular_matrix || |
|
|
5861 rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
5862 { |
|
5322
|
5863 UMFPACK_DNAME (report_numeric) (Numeric, control); |
|
5164
|
5864 |
|
|
5865 err = -2; |
|
|
5866 |
|
|
5867 if (sing_handler) |
|
|
5868 sing_handler (rcond); |
|
|
5869 else |
|
|
5870 (*current_liboctave_error_handler) |
|
|
5871 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
5872 rcond); |
|
|
5873 |
|
|
5874 } |
|
5610
|
5875 else if (status < 0) |
|
5164
|
5876 { |
|
|
5877 (*current_liboctave_error_handler) |
|
|
5878 ("SparseMatrix::solve numeric factorization failed"); |
|
|
5879 |
|
5322
|
5880 UMFPACK_DNAME (report_status) (control, status); |
|
|
5881 UMFPACK_DNAME (report_info) (control, info); |
|
5164
|
5882 |
|
|
5883 err = -1; |
|
|
5884 } |
|
|
5885 else |
|
|
5886 { |
|
5322
|
5887 UMFPACK_DNAME (report_numeric) (Numeric, control); |
|
5164
|
5888 } |
|
|
5889 } |
|
|
5890 |
|
|
5891 if (err != 0) |
|
5322
|
5892 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
5893 |
|
5203
|
5894 #else |
|
|
5895 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
5896 #endif |
|
|
5897 |
|
5164
|
5898 return Numeric; |
|
|
5899 } |
|
|
5900 |
|
|
5901 Matrix |
|
5785
|
5902 SparseMatrix::fsolve (MatrixType &mattype, const Matrix& b, |
|
5681
|
5903 octave_idx_type& err, double& rcond, |
|
|
5904 solve_singularity_handler sing_handler, |
|
|
5905 bool calc_cond) const |
|
5164
|
5906 { |
|
|
5907 Matrix retval; |
|
|
5908 |
|
5275
|
5909 octave_idx_type nr = rows (); |
|
|
5910 octave_idx_type nc = cols (); |
|
5164
|
5911 err = 0; |
|
|
5912 |
|
|
5913 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
5914 (*current_liboctave_error_handler) |
|
|
5915 ("matrix dimension mismatch solution of linear equations"); |
|
|
5916 else |
|
|
5917 { |
|
|
5918 // Print spparms("spumoni") info if requested |
|
5506
|
5919 volatile int typ = mattype.type (); |
|
5164
|
5920 mattype.info (); |
|
|
5921 |
|
5785
|
5922 if (typ == MatrixType::Hermitian) |
|
5164
|
5923 { |
|
5506
|
5924 #ifdef HAVE_CHOLMOD |
|
|
5925 cholmod_common Common; |
|
|
5926 cholmod_common *cm = &Common; |
|
|
5927 |
|
|
5928 // Setup initial parameters |
|
|
5929 CHOLMOD_NAME(start) (cm); |
|
5526
|
5930 cm->prefer_zomplex = false; |
|
5506
|
5931 |
|
5893
|
5932 double spu = octave_sparse_params::get_key ("spumoni"); |
|
5506
|
5933 if (spu == 0.) |
|
|
5934 { |
|
|
5935 cm->print = -1; |
|
|
5936 cm->print_function = NULL; |
|
|
5937 } |
|
|
5938 else |
|
|
5939 { |
|
5760
|
5940 cm->print = static_cast<int> (spu) + 2; |
|
5506
|
5941 cm->print_function =&SparseCholPrint; |
|
|
5942 } |
|
|
5943 |
|
|
5944 cm->error_handler = &SparseCholError; |
|
|
5945 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
|
|
5946 cm->hypotenuse = CHOLMOD_NAME(hypot); |
|
|
5947 |
|
|
5948 #ifdef HAVE_METIS |
|
5710
|
5949 // METIS 4.0.1 uses malloc and free, and will terminate if |
|
|
5950 // it runs out of memory. Use CHOLMOD's memory guard for |
|
|
5951 // METIS, which allocates a huge block of memory (and then |
|
|
5952 // immediately frees it) before calling METIS |
|
5506
|
5953 cm->metis_memory = 2.0; |
|
|
5954 |
|
|
5955 #if defined(METIS_VERSION) |
|
|
5956 #if (METIS_VERSION >= METIS_VER(4,0,2)) |
|
5710
|
5957 // METIS 4.0.2 uses function pointers for malloc and free. |
|
5506
|
5958 METIS_malloc = cm->malloc_memory; |
|
|
5959 METIS_free = cm->free_memory; |
|
5710
|
5960 // Turn off METIS memory guard. |
|
5506
|
5961 cm->metis_memory = 0.0; |
|
|
5962 #endif |
|
|
5963 #endif |
|
|
5964 #endif |
|
|
5965 |
|
5526
|
5966 cm->final_ll = true; |
|
5506
|
5967 |
|
|
5968 cholmod_sparse Astore; |
|
|
5969 cholmod_sparse *A = &Astore; |
|
|
5970 double dummy; |
|
|
5971 A->nrow = nr; |
|
|
5972 A->ncol = nc; |
|
|
5973 |
|
|
5974 A->p = cidx(); |
|
|
5975 A->i = ridx(); |
|
5604
|
5976 A->nzmax = nnz(); |
|
5526
|
5977 A->packed = true; |
|
|
5978 A->sorted = true; |
|
5506
|
5979 A->nz = NULL; |
|
|
5980 #ifdef IDX_TYPE_LONG |
|
|
5981 A->itype = CHOLMOD_LONG; |
|
|
5982 #else |
|
|
5983 A->itype = CHOLMOD_INT; |
|
|
5984 #endif |
|
|
5985 A->dtype = CHOLMOD_DOUBLE; |
|
|
5986 A->stype = 1; |
|
|
5987 A->xtype = CHOLMOD_REAL; |
|
|
5988 |
|
|
5989 if (nr < 1) |
|
|
5990 A->x = &dummy; |
|
|
5991 else |
|
|
5992 A->x = data(); |
|
|
5993 |
|
|
5994 cholmod_dense Bstore; |
|
|
5995 cholmod_dense *B = &Bstore; |
|
|
5996 B->nrow = b.rows(); |
|
|
5997 B->ncol = b.cols(); |
|
|
5998 B->d = B->nrow; |
|
|
5999 B->nzmax = B->nrow * B->ncol; |
|
|
6000 B->dtype = CHOLMOD_DOUBLE; |
|
|
6001 B->xtype = CHOLMOD_REAL; |
|
|
6002 if (nc < 1 || b.cols() < 1) |
|
|
6003 B->x = &dummy; |
|
|
6004 else |
|
|
6005 // We won't alter it, honest :-) |
|
|
6006 B->x = const_cast<double *>(b.fortran_vec()); |
|
|
6007 |
|
|
6008 cholmod_factor *L; |
|
|
6009 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6010 L = CHOLMOD_NAME(analyze) (A, cm); |
|
|
6011 CHOLMOD_NAME(factorize) (A, L, cm); |
|
5681
|
6012 if (calc_cond) |
|
|
6013 rcond = CHOLMOD_NAME(rcond)(L, cm); |
|
|
6014 else |
|
|
6015 rcond = 1.0; |
|
|
6016 |
|
5506
|
6017 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6018 |
|
|
6019 if (rcond == 0.0) |
|
|
6020 { |
|
|
6021 // Either its indefinite or singular. Try UMFPACK |
|
|
6022 mattype.mark_as_unsymmetric (); |
|
5785
|
6023 typ = MatrixType::Full; |
|
5506
|
6024 } |
|
|
6025 else |
|
|
6026 { |
|
|
6027 volatile double rcond_plus_one = rcond + 1.0; |
|
|
6028 |
|
|
6029 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
6030 { |
|
|
6031 err = -2; |
|
|
6032 |
|
|
6033 if (sing_handler) |
|
5681
|
6034 { |
|
|
6035 sing_handler (rcond); |
|
|
6036 mattype.mark_as_rectangular (); |
|
|
6037 } |
|
5506
|
6038 else |
|
|
6039 (*current_liboctave_error_handler) |
|
|
6040 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
6041 rcond); |
|
|
6042 |
|
|
6043 return retval; |
|
|
6044 } |
|
|
6045 |
|
|
6046 cholmod_dense *X; |
|
|
6047 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6048 X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); |
|
|
6049 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6050 |
|
|
6051 retval.resize (b.rows (), b.cols()); |
|
|
6052 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
|
6053 { |
|
|
6054 octave_idx_type jr = j * b.rows(); |
|
|
6055 for (octave_idx_type i = 0; i < b.rows(); i++) |
|
|
6056 retval.xelem(i,j) = static_cast<double *>(X->x)[jr + i]; |
|
|
6057 } |
|
|
6058 |
|
|
6059 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6060 CHOLMOD_NAME(free_dense) (&X, cm); |
|
|
6061 CHOLMOD_NAME(free_factor) (&L, cm); |
|
|
6062 CHOLMOD_NAME(finish) (cm); |
|
6482
|
6063 static char tmp[] = " "; |
|
|
6064 CHOLMOD_NAME(print_common) (tmp, cm); |
|
5506
|
6065 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6066 } |
|
|
6067 #else |
|
5164
|
6068 (*current_liboctave_warning_handler) |
|
5506
|
6069 ("CHOLMOD not installed"); |
|
5164
|
6070 |
|
|
6071 mattype.mark_as_unsymmetric (); |
|
5785
|
6072 typ = MatrixType::Full; |
|
5506
|
6073 #endif |
|
5164
|
6074 } |
|
|
6075 |
|
5785
|
6076 if (typ == MatrixType::Full) |
|
5164
|
6077 { |
|
5203
|
6078 #ifdef HAVE_UMFPACK |
|
5164
|
6079 Matrix Control, Info; |
|
|
6080 void *Numeric = |
|
5681
|
6081 factorize (err, rcond, Control, Info, sing_handler, calc_cond); |
|
5164
|
6082 |
|
|
6083 if (err == 0) |
|
|
6084 { |
|
|
6085 const double *Bx = b.fortran_vec (); |
|
|
6086 retval.resize (b.rows (), b.cols()); |
|
|
6087 double *result = retval.fortran_vec (); |
|
5275
|
6088 octave_idx_type b_nr = b.rows (); |
|
|
6089 octave_idx_type b_nc = b.cols (); |
|
5164
|
6090 int status = 0; |
|
|
6091 double *control = Control.fortran_vec (); |
|
|
6092 double *info = Info.fortran_vec (); |
|
5275
|
6093 const octave_idx_type *Ap = cidx (); |
|
|
6094 const octave_idx_type *Ai = ridx (); |
|
5164
|
6095 const double *Ax = data (); |
|
|
6096 |
|
5275
|
6097 for (octave_idx_type j = 0, iidx = 0; j < b_nc; j++, iidx += b_nr) |
|
5164
|
6098 { |
|
5322
|
6099 status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, |
|
|
6100 Ai, Ax, &result[iidx], &Bx[iidx], |
|
5164
|
6101 Numeric, control, info); |
|
|
6102 if (status < 0) |
|
|
6103 { |
|
|
6104 (*current_liboctave_error_handler) |
|
|
6105 ("SparseMatrix::solve solve failed"); |
|
|
6106 |
|
5322
|
6107 UMFPACK_DNAME (report_status) (control, status); |
|
5164
|
6108 |
|
|
6109 err = -1; |
|
|
6110 |
|
|
6111 break; |
|
|
6112 } |
|
|
6113 } |
|
|
6114 |
|
5322
|
6115 UMFPACK_DNAME (report_info) (control, info); |
|
5164
|
6116 |
|
5322
|
6117 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
6118 } |
|
5681
|
6119 else |
|
|
6120 mattype.mark_as_rectangular (); |
|
|
6121 |
|
5203
|
6122 #else |
|
|
6123 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
6124 #endif |
|
5164
|
6125 } |
|
5785
|
6126 else if (typ != MatrixType::Hermitian) |
|
5164
|
6127 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
6128 } |
|
|
6129 |
|
|
6130 return retval; |
|
|
6131 } |
|
|
6132 |
|
|
6133 SparseMatrix |
|
5785
|
6134 SparseMatrix::fsolve (MatrixType &mattype, const SparseMatrix& b, |
|
5681
|
6135 octave_idx_type& err, double& rcond, |
|
|
6136 solve_singularity_handler sing_handler, |
|
|
6137 bool calc_cond) const |
|
5164
|
6138 { |
|
|
6139 SparseMatrix retval; |
|
|
6140 |
|
5275
|
6141 octave_idx_type nr = rows (); |
|
|
6142 octave_idx_type nc = cols (); |
|
5164
|
6143 err = 0; |
|
|
6144 |
|
|
6145 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
6146 (*current_liboctave_error_handler) |
|
|
6147 ("matrix dimension mismatch solution of linear equations"); |
|
|
6148 else |
|
|
6149 { |
|
|
6150 // Print spparms("spumoni") info if requested |
|
5506
|
6151 volatile int typ = mattype.type (); |
|
5164
|
6152 mattype.info (); |
|
|
6153 |
|
5785
|
6154 if (typ == MatrixType::Hermitian) |
|
5164
|
6155 { |
|
5506
|
6156 #ifdef HAVE_CHOLMOD |
|
|
6157 cholmod_common Common; |
|
|
6158 cholmod_common *cm = &Common; |
|
|
6159 |
|
|
6160 // Setup initial parameters |
|
|
6161 CHOLMOD_NAME(start) (cm); |
|
5526
|
6162 cm->prefer_zomplex = false; |
|
5506
|
6163 |
|
5893
|
6164 double spu = octave_sparse_params::get_key ("spumoni"); |
|
5506
|
6165 if (spu == 0.) |
|
|
6166 { |
|
|
6167 cm->print = -1; |
|
|
6168 cm->print_function = NULL; |
|
|
6169 } |
|
|
6170 else |
|
|
6171 { |
|
5760
|
6172 cm->print = static_cast<int> (spu) + 2; |
|
5506
|
6173 cm->print_function =&SparseCholPrint; |
|
|
6174 } |
|
|
6175 |
|
|
6176 cm->error_handler = &SparseCholError; |
|
|
6177 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
|
|
6178 cm->hypotenuse = CHOLMOD_NAME(hypot); |
|
|
6179 |
|
|
6180 #ifdef HAVE_METIS |
|
|
6181 // METIS 4.0.1 uses malloc and free, and will terminate MATLAB if |
|
|
6182 // it runs out of memory. Use CHOLMOD's memory guard for METIS, |
|
|
6183 // which mxMalloc's a huge block of memory (and then immediately |
|
|
6184 // mxFree's it) before calling METIS |
|
|
6185 cm->metis_memory = 2.0; |
|
|
6186 |
|
|
6187 #if defined(METIS_VERSION) |
|
|
6188 #if (METIS_VERSION >= METIS_VER(4,0,2)) |
|
|
6189 // METIS 4.0.2 uses function pointers for malloc and free |
|
|
6190 METIS_malloc = cm->malloc_memory; |
|
|
6191 METIS_free = cm->free_memory; |
|
|
6192 // Turn off METIS memory guard. It is not needed, because mxMalloc |
|
|
6193 // will safely terminate the mexFunction and free any workspace |
|
|
6194 // without killing all of octave. |
|
|
6195 cm->metis_memory = 0.0; |
|
|
6196 #endif |
|
|
6197 #endif |
|
|
6198 #endif |
|
|
6199 |
|
5526
|
6200 cm->final_ll = true; |
|
5506
|
6201 |
|
|
6202 cholmod_sparse Astore; |
|
|
6203 cholmod_sparse *A = &Astore; |
|
|
6204 double dummy; |
|
|
6205 A->nrow = nr; |
|
|
6206 A->ncol = nc; |
|
|
6207 |
|
|
6208 A->p = cidx(); |
|
|
6209 A->i = ridx(); |
|
5604
|
6210 A->nzmax = nnz(); |
|
5526
|
6211 A->packed = true; |
|
|
6212 A->sorted = true; |
|
5506
|
6213 A->nz = NULL; |
|
|
6214 #ifdef IDX_TYPE_LONG |
|
|
6215 A->itype = CHOLMOD_LONG; |
|
|
6216 #else |
|
|
6217 A->itype = CHOLMOD_INT; |
|
|
6218 #endif |
|
|
6219 A->dtype = CHOLMOD_DOUBLE; |
|
|
6220 A->stype = 1; |
|
|
6221 A->xtype = CHOLMOD_REAL; |
|
|
6222 |
|
|
6223 if (nr < 1) |
|
|
6224 A->x = &dummy; |
|
|
6225 else |
|
|
6226 A->x = data(); |
|
|
6227 |
|
|
6228 cholmod_sparse Bstore; |
|
|
6229 cholmod_sparse *B = &Bstore; |
|
|
6230 B->nrow = b.rows(); |
|
|
6231 B->ncol = b.cols(); |
|
|
6232 B->p = b.cidx(); |
|
|
6233 B->i = b.ridx(); |
|
5604
|
6234 B->nzmax = b.nnz(); |
|
5526
|
6235 B->packed = true; |
|
|
6236 B->sorted = true; |
|
5506
|
6237 B->nz = NULL; |
|
|
6238 #ifdef IDX_TYPE_LONG |
|
|
6239 B->itype = CHOLMOD_LONG; |
|
|
6240 #else |
|
|
6241 B->itype = CHOLMOD_INT; |
|
|
6242 #endif |
|
|
6243 B->dtype = CHOLMOD_DOUBLE; |
|
|
6244 B->stype = 0; |
|
|
6245 B->xtype = CHOLMOD_REAL; |
|
|
6246 |
|
|
6247 if (b.rows() < 1 || b.cols() < 1) |
|
|
6248 B->x = &dummy; |
|
|
6249 else |
|
|
6250 B->x = b.data(); |
|
|
6251 |
|
|
6252 cholmod_factor *L; |
|
|
6253 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6254 L = CHOLMOD_NAME(analyze) (A, cm); |
|
|
6255 CHOLMOD_NAME(factorize) (A, L, cm); |
|
5681
|
6256 if (calc_cond) |
|
|
6257 rcond = CHOLMOD_NAME(rcond)(L, cm); |
|
|
6258 else |
|
|
6259 rcond = 1.; |
|
5506
|
6260 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6261 |
|
|
6262 if (rcond == 0.0) |
|
|
6263 { |
|
|
6264 // Either its indefinite or singular. Try UMFPACK |
|
|
6265 mattype.mark_as_unsymmetric (); |
|
5785
|
6266 typ = MatrixType::Full; |
|
5506
|
6267 } |
|
|
6268 else |
|
|
6269 { |
|
|
6270 volatile double rcond_plus_one = rcond + 1.0; |
|
|
6271 |
|
|
6272 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
6273 { |
|
|
6274 err = -2; |
|
|
6275 |
|
|
6276 if (sing_handler) |
|
5681
|
6277 { |
|
|
6278 sing_handler (rcond); |
|
|
6279 mattype.mark_as_rectangular (); |
|
|
6280 } |
|
5506
|
6281 else |
|
|
6282 (*current_liboctave_error_handler) |
|
|
6283 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
6284 rcond); |
|
|
6285 |
|
|
6286 return retval; |
|
|
6287 } |
|
|
6288 |
|
|
6289 cholmod_sparse *X; |
|
|
6290 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6291 X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); |
|
|
6292 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6293 |
|
|
6294 retval = SparseMatrix (static_cast<octave_idx_type>(X->nrow), |
|
|
6295 static_cast<octave_idx_type>(X->ncol), |
|
|
6296 static_cast<octave_idx_type>(X->nzmax)); |
|
|
6297 for (octave_idx_type j = 0; |
|
|
6298 j <= static_cast<octave_idx_type>(X->ncol); j++) |
|
|
6299 retval.xcidx(j) = static_cast<octave_idx_type *>(X->p)[j]; |
|
|
6300 for (octave_idx_type j = 0; |
|
|
6301 j < static_cast<octave_idx_type>(X->nzmax); j++) |
|
|
6302 { |
|
|
6303 retval.xridx(j) = static_cast<octave_idx_type *>(X->i)[j]; |
|
|
6304 retval.xdata(j) = static_cast<double *>(X->x)[j]; |
|
|
6305 } |
|
|
6306 |
|
|
6307 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6308 CHOLMOD_NAME(free_sparse) (&X, cm); |
|
|
6309 CHOLMOD_NAME(free_factor) (&L, cm); |
|
|
6310 CHOLMOD_NAME(finish) (cm); |
|
6482
|
6311 static char tmp[] = " "; |
|
|
6312 CHOLMOD_NAME(print_common) (tmp, cm); |
|
5506
|
6313 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6314 } |
|
|
6315 #else |
|
5164
|
6316 (*current_liboctave_warning_handler) |
|
5506
|
6317 ("CHOLMOD not installed"); |
|
5164
|
6318 |
|
|
6319 mattype.mark_as_unsymmetric (); |
|
5785
|
6320 typ = MatrixType::Full; |
|
5506
|
6321 #endif |
|
5164
|
6322 } |
|
|
6323 |
|
5785
|
6324 if (typ == MatrixType::Full) |
|
5164
|
6325 { |
|
5203
|
6326 #ifdef HAVE_UMFPACK |
|
5164
|
6327 Matrix Control, Info; |
|
|
6328 void *Numeric = factorize (err, rcond, Control, Info, |
|
5681
|
6329 sing_handler, calc_cond); |
|
5164
|
6330 |
|
|
6331 if (err == 0) |
|
|
6332 { |
|
5275
|
6333 octave_idx_type b_nr = b.rows (); |
|
|
6334 octave_idx_type b_nc = b.cols (); |
|
5164
|
6335 int status = 0; |
|
|
6336 double *control = Control.fortran_vec (); |
|
|
6337 double *info = Info.fortran_vec (); |
|
5275
|
6338 const octave_idx_type *Ap = cidx (); |
|
|
6339 const octave_idx_type *Ai = ridx (); |
|
5164
|
6340 const double *Ax = data (); |
|
|
6341 |
|
|
6342 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
6343 OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); |
|
|
6344 |
|
|
6345 // Take a first guess that the number of non-zero terms |
|
|
6346 // will be as many as in b |
|
5681
|
6347 octave_idx_type x_nz = b.nnz (); |
|
5275
|
6348 octave_idx_type ii = 0; |
|
5164
|
6349 retval = SparseMatrix (b_nr, b_nc, x_nz); |
|
|
6350 |
|
|
6351 retval.xcidx(0) = 0; |
|
5275
|
6352 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
6353 { |
|
|
6354 |
|
5275
|
6355 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6356 Bx[i] = b.elem (i, j); |
|
|
6357 |
|
5322
|
6358 status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, |
|
|
6359 Ai, Ax, Xx, Bx, Numeric, control, |
|
5164
|
6360 info); |
|
|
6361 if (status < 0) |
|
|
6362 { |
|
|
6363 (*current_liboctave_error_handler) |
|
|
6364 ("SparseMatrix::solve solve failed"); |
|
|
6365 |
|
5322
|
6366 UMFPACK_DNAME (report_status) (control, status); |
|
5164
|
6367 |
|
|
6368 err = -1; |
|
|
6369 |
|
|
6370 break; |
|
|
6371 } |
|
|
6372 |
|
5275
|
6373 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6374 { |
|
|
6375 double tmp = Xx[i]; |
|
|
6376 if (tmp != 0.0) |
|
|
6377 { |
|
|
6378 if (ii == x_nz) |
|
|
6379 { |
|
|
6380 // Resize the sparse matrix |
|
5275
|
6381 octave_idx_type sz = x_nz * (b_nc - j) / b_nc; |
|
5164
|
6382 sz = (sz > 10 ? sz : 10) + x_nz; |
|
|
6383 retval.change_capacity (sz); |
|
|
6384 x_nz = sz; |
|
|
6385 } |
|
|
6386 retval.xdata(ii) = tmp; |
|
|
6387 retval.xridx(ii++) = i; |
|
|
6388 } |
|
|
6389 } |
|
|
6390 retval.xcidx(j+1) = ii; |
|
|
6391 } |
|
|
6392 |
|
|
6393 retval.maybe_compress (); |
|
|
6394 |
|
5322
|
6395 UMFPACK_DNAME (report_info) (control, info); |
|
|
6396 |
|
|
6397 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
6398 } |
|
5681
|
6399 else |
|
|
6400 mattype.mark_as_rectangular (); |
|
|
6401 |
|
5203
|
6402 #else |
|
|
6403 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
6404 #endif |
|
5164
|
6405 } |
|
5785
|
6406 else if (typ != MatrixType::Hermitian) |
|
5164
|
6407 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
6408 } |
|
|
6409 |
|
|
6410 return retval; |
|
|
6411 } |
|
|
6412 |
|
|
6413 ComplexMatrix |
|
5785
|
6414 SparseMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
5681
|
6415 octave_idx_type& err, double& rcond, |
|
|
6416 solve_singularity_handler sing_handler, |
|
|
6417 bool calc_cond) const |
|
5164
|
6418 { |
|
|
6419 ComplexMatrix retval; |
|
|
6420 |
|
5275
|
6421 octave_idx_type nr = rows (); |
|
|
6422 octave_idx_type nc = cols (); |
|
5164
|
6423 err = 0; |
|
|
6424 |
|
|
6425 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
6426 (*current_liboctave_error_handler) |
|
|
6427 ("matrix dimension mismatch solution of linear equations"); |
|
|
6428 else |
|
|
6429 { |
|
|
6430 // Print spparms("spumoni") info if requested |
|
5506
|
6431 volatile int typ = mattype.type (); |
|
5164
|
6432 mattype.info (); |
|
|
6433 |
|
5785
|
6434 if (typ == MatrixType::Hermitian) |
|
5164
|
6435 { |
|
5506
|
6436 #ifdef HAVE_CHOLMOD |
|
|
6437 cholmod_common Common; |
|
|
6438 cholmod_common *cm = &Common; |
|
|
6439 |
|
|
6440 // Setup initial parameters |
|
|
6441 CHOLMOD_NAME(start) (cm); |
|
5526
|
6442 cm->prefer_zomplex = false; |
|
5506
|
6443 |
|
5893
|
6444 double spu = octave_sparse_params::get_key ("spumoni"); |
|
5506
|
6445 if (spu == 0.) |
|
|
6446 { |
|
|
6447 cm->print = -1; |
|
|
6448 cm->print_function = NULL; |
|
|
6449 } |
|
|
6450 else |
|
|
6451 { |
|
5760
|
6452 cm->print = static_cast<int> (spu) + 2; |
|
5506
|
6453 cm->print_function =&SparseCholPrint; |
|
|
6454 } |
|
|
6455 |
|
|
6456 cm->error_handler = &SparseCholError; |
|
|
6457 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
|
|
6458 cm->hypotenuse = CHOLMOD_NAME(hypot); |
|
|
6459 |
|
|
6460 #ifdef HAVE_METIS |
|
|
6461 // METIS 4.0.1 uses malloc and free, and will terminate MATLAB if |
|
|
6462 // it runs out of memory. Use CHOLMOD's memory guard for METIS, |
|
|
6463 // which mxMalloc's a huge block of memory (and then immediately |
|
|
6464 // mxFree's it) before calling METIS |
|
|
6465 cm->metis_memory = 2.0; |
|
|
6466 |
|
|
6467 #if defined(METIS_VERSION) |
|
|
6468 #if (METIS_VERSION >= METIS_VER(4,0,2)) |
|
|
6469 // METIS 4.0.2 uses function pointers for malloc and free |
|
|
6470 METIS_malloc = cm->malloc_memory; |
|
|
6471 METIS_free = cm->free_memory; |
|
|
6472 // Turn off METIS memory guard. It is not needed, because mxMalloc |
|
|
6473 // will safely terminate the mexFunction and free any workspace |
|
|
6474 // without killing all of octave. |
|
|
6475 cm->metis_memory = 0.0; |
|
|
6476 #endif |
|
|
6477 #endif |
|
|
6478 #endif |
|
|
6479 |
|
5526
|
6480 cm->final_ll = true; |
|
5506
|
6481 |
|
|
6482 cholmod_sparse Astore; |
|
|
6483 cholmod_sparse *A = &Astore; |
|
|
6484 double dummy; |
|
|
6485 A->nrow = nr; |
|
|
6486 A->ncol = nc; |
|
|
6487 |
|
|
6488 A->p = cidx(); |
|
|
6489 A->i = ridx(); |
|
5604
|
6490 A->nzmax = nnz(); |
|
5526
|
6491 A->packed = true; |
|
|
6492 A->sorted = true; |
|
5506
|
6493 A->nz = NULL; |
|
|
6494 #ifdef IDX_TYPE_LONG |
|
|
6495 A->itype = CHOLMOD_LONG; |
|
|
6496 #else |
|
|
6497 A->itype = CHOLMOD_INT; |
|
|
6498 #endif |
|
|
6499 A->dtype = CHOLMOD_DOUBLE; |
|
|
6500 A->stype = 1; |
|
|
6501 A->xtype = CHOLMOD_REAL; |
|
|
6502 |
|
|
6503 if (nr < 1) |
|
|
6504 A->x = &dummy; |
|
|
6505 else |
|
|
6506 A->x = data(); |
|
|
6507 |
|
|
6508 cholmod_dense Bstore; |
|
|
6509 cholmod_dense *B = &Bstore; |
|
|
6510 B->nrow = b.rows(); |
|
|
6511 B->ncol = b.cols(); |
|
|
6512 B->d = B->nrow; |
|
|
6513 B->nzmax = B->nrow * B->ncol; |
|
|
6514 B->dtype = CHOLMOD_DOUBLE; |
|
|
6515 B->xtype = CHOLMOD_COMPLEX; |
|
|
6516 if (nc < 1 || b.cols() < 1) |
|
|
6517 B->x = &dummy; |
|
|
6518 else |
|
|
6519 // We won't alter it, honest :-) |
|
|
6520 B->x = const_cast<Complex *>(b.fortran_vec()); |
|
|
6521 |
|
|
6522 cholmod_factor *L; |
|
|
6523 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6524 L = CHOLMOD_NAME(analyze) (A, cm); |
|
|
6525 CHOLMOD_NAME(factorize) (A, L, cm); |
|
5681
|
6526 if (calc_cond) |
|
|
6527 rcond = CHOLMOD_NAME(rcond)(L, cm); |
|
|
6528 else |
|
|
6529 rcond = 1.0; |
|
5506
|
6530 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6531 |
|
|
6532 if (rcond == 0.0) |
|
|
6533 { |
|
|
6534 // Either its indefinite or singular. Try UMFPACK |
|
|
6535 mattype.mark_as_unsymmetric (); |
|
5785
|
6536 typ = MatrixType::Full; |
|
5506
|
6537 } |
|
|
6538 else |
|
|
6539 { |
|
|
6540 volatile double rcond_plus_one = rcond + 1.0; |
|
|
6541 |
|
|
6542 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
6543 { |
|
|
6544 err = -2; |
|
|
6545 |
|
|
6546 if (sing_handler) |
|
5681
|
6547 { |
|
|
6548 sing_handler (rcond); |
|
|
6549 mattype.mark_as_rectangular (); |
|
|
6550 } |
|
5506
|
6551 else |
|
|
6552 (*current_liboctave_error_handler) |
|
|
6553 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
6554 rcond); |
|
|
6555 |
|
|
6556 return retval; |
|
|
6557 } |
|
|
6558 |
|
|
6559 cholmod_dense *X; |
|
|
6560 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6561 X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); |
|
|
6562 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6563 |
|
|
6564 retval.resize (b.rows (), b.cols()); |
|
|
6565 for (octave_idx_type j = 0; j < b.cols(); j++) |
|
|
6566 { |
|
|
6567 octave_idx_type jr = j * b.rows(); |
|
|
6568 for (octave_idx_type i = 0; i < b.rows(); i++) |
|
|
6569 retval.xelem(i,j) = static_cast<Complex *>(X->x)[jr + i]; |
|
|
6570 } |
|
|
6571 |
|
|
6572 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6573 CHOLMOD_NAME(free_dense) (&X, cm); |
|
|
6574 CHOLMOD_NAME(free_factor) (&L, cm); |
|
|
6575 CHOLMOD_NAME(finish) (cm); |
|
6482
|
6576 static char tmp[] = " "; |
|
|
6577 CHOLMOD_NAME(print_common) (tmp, cm); |
|
5506
|
6578 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6579 } |
|
|
6580 #else |
|
5164
|
6581 (*current_liboctave_warning_handler) |
|
5506
|
6582 ("CHOLMOD not installed"); |
|
5164
|
6583 |
|
|
6584 mattype.mark_as_unsymmetric (); |
|
5785
|
6585 typ = MatrixType::Full; |
|
5506
|
6586 #endif |
|
5164
|
6587 } |
|
|
6588 |
|
5785
|
6589 if (typ == MatrixType::Full) |
|
5164
|
6590 { |
|
5203
|
6591 #ifdef HAVE_UMFPACK |
|
5164
|
6592 Matrix Control, Info; |
|
|
6593 void *Numeric = factorize (err, rcond, Control, Info, |
|
5681
|
6594 sing_handler, calc_cond); |
|
5164
|
6595 |
|
|
6596 if (err == 0) |
|
|
6597 { |
|
5275
|
6598 octave_idx_type b_nr = b.rows (); |
|
|
6599 octave_idx_type b_nc = b.cols (); |
|
5164
|
6600 int status = 0; |
|
|
6601 double *control = Control.fortran_vec (); |
|
|
6602 double *info = Info.fortran_vec (); |
|
5275
|
6603 const octave_idx_type *Ap = cidx (); |
|
|
6604 const octave_idx_type *Ai = ridx (); |
|
5164
|
6605 const double *Ax = data (); |
|
|
6606 |
|
|
6607 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
6608 OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); |
|
|
6609 |
|
|
6610 retval.resize (b_nr, b_nc); |
|
|
6611 |
|
|
6612 OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); |
|
|
6613 OCTAVE_LOCAL_BUFFER (double, Xz, b_nr); |
|
|
6614 |
|
5275
|
6615 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
6616 { |
|
5275
|
6617 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6618 { |
|
|
6619 Complex c = b (i,j); |
|
5261
|
6620 Bx[i] = std::real (c); |
|
|
6621 Bz[i] = std::imag (c); |
|
5164
|
6622 } |
|
|
6623 |
|
5322
|
6624 status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, |
|
|
6625 Ai, Ax, Xx, Bx, Numeric, control, |
|
5164
|
6626 info); |
|
5322
|
6627 int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, |
|
|
6628 Ap, Ai, Ax, Xz, Bz, Numeric, |
|
5164
|
6629 control, info) ; |
|
|
6630 |
|
|
6631 if (status < 0 || status2 < 0) |
|
|
6632 { |
|
|
6633 (*current_liboctave_error_handler) |
|
|
6634 ("SparseMatrix::solve solve failed"); |
|
|
6635 |
|
5322
|
6636 UMFPACK_DNAME (report_status) (control, status); |
|
5164
|
6637 |
|
|
6638 err = -1; |
|
|
6639 |
|
|
6640 break; |
|
|
6641 } |
|
|
6642 |
|
5275
|
6643 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6644 retval (i, j) = Complex (Xx[i], Xz[i]); |
|
|
6645 } |
|
|
6646 |
|
5322
|
6647 UMFPACK_DNAME (report_info) (control, info); |
|
|
6648 |
|
|
6649 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
6650 } |
|
5681
|
6651 else |
|
|
6652 mattype.mark_as_rectangular (); |
|
|
6653 |
|
5203
|
6654 #else |
|
|
6655 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
6656 #endif |
|
5164
|
6657 } |
|
5785
|
6658 else if (typ != MatrixType::Hermitian) |
|
5164
|
6659 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
6660 } |
|
|
6661 |
|
|
6662 return retval; |
|
|
6663 } |
|
|
6664 |
|
|
6665 SparseComplexMatrix |
|
5785
|
6666 SparseMatrix::fsolve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5275
|
6667 octave_idx_type& err, double& rcond, |
|
5681
|
6668 solve_singularity_handler sing_handler, |
|
|
6669 bool calc_cond) const |
|
5164
|
6670 { |
|
|
6671 SparseComplexMatrix retval; |
|
|
6672 |
|
5275
|
6673 octave_idx_type nr = rows (); |
|
|
6674 octave_idx_type nc = cols (); |
|
5164
|
6675 err = 0; |
|
|
6676 |
|
|
6677 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
6678 (*current_liboctave_error_handler) |
|
|
6679 ("matrix dimension mismatch solution of linear equations"); |
|
|
6680 else |
|
|
6681 { |
|
|
6682 // Print spparms("spumoni") info if requested |
|
5506
|
6683 volatile int typ = mattype.type (); |
|
5164
|
6684 mattype.info (); |
|
|
6685 |
|
5785
|
6686 if (typ == MatrixType::Hermitian) |
|
5164
|
6687 { |
|
5506
|
6688 #ifdef HAVE_CHOLMOD |
|
|
6689 cholmod_common Common; |
|
|
6690 cholmod_common *cm = &Common; |
|
|
6691 |
|
|
6692 // Setup initial parameters |
|
|
6693 CHOLMOD_NAME(start) (cm); |
|
5526
|
6694 cm->prefer_zomplex = false; |
|
5506
|
6695 |
|
5893
|
6696 double spu = octave_sparse_params::get_key ("spumoni"); |
|
5506
|
6697 if (spu == 0.) |
|
|
6698 { |
|
|
6699 cm->print = -1; |
|
|
6700 cm->print_function = NULL; |
|
|
6701 } |
|
|
6702 else |
|
|
6703 { |
|
5760
|
6704 cm->print = static_cast<int> (spu) + 2; |
|
5506
|
6705 cm->print_function =&SparseCholPrint; |
|
|
6706 } |
|
|
6707 |
|
|
6708 cm->error_handler = &SparseCholError; |
|
|
6709 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
|
|
6710 cm->hypotenuse = CHOLMOD_NAME(hypot); |
|
|
6711 |
|
|
6712 #ifdef HAVE_METIS |
|
|
6713 // METIS 4.0.1 uses malloc and free, and will terminate MATLAB if |
|
|
6714 // it runs out of memory. Use CHOLMOD's memory guard for METIS, |
|
|
6715 // which mxMalloc's a huge block of memory (and then immediately |
|
|
6716 // mxFree's it) before calling METIS |
|
|
6717 cm->metis_memory = 2.0; |
|
|
6718 |
|
|
6719 #if defined(METIS_VERSION) |
|
|
6720 #if (METIS_VERSION >= METIS_VER(4,0,2)) |
|
|
6721 // METIS 4.0.2 uses function pointers for malloc and free |
|
|
6722 METIS_malloc = cm->malloc_memory; |
|
|
6723 METIS_free = cm->free_memory; |
|
|
6724 // Turn off METIS memory guard. It is not needed, because mxMalloc |
|
|
6725 // will safely terminate the mexFunction and free any workspace |
|
|
6726 // without killing all of octave. |
|
|
6727 cm->metis_memory = 0.0; |
|
|
6728 #endif |
|
|
6729 #endif |
|
|
6730 #endif |
|
|
6731 |
|
5526
|
6732 cm->final_ll = true; |
|
5506
|
6733 |
|
|
6734 cholmod_sparse Astore; |
|
|
6735 cholmod_sparse *A = &Astore; |
|
|
6736 double dummy; |
|
|
6737 A->nrow = nr; |
|
|
6738 A->ncol = nc; |
|
|
6739 |
|
|
6740 A->p = cidx(); |
|
|
6741 A->i = ridx(); |
|
5604
|
6742 A->nzmax = nnz(); |
|
5526
|
6743 A->packed = true; |
|
|
6744 A->sorted = true; |
|
5506
|
6745 A->nz = NULL; |
|
|
6746 #ifdef IDX_TYPE_LONG |
|
|
6747 A->itype = CHOLMOD_LONG; |
|
|
6748 #else |
|
|
6749 A->itype = CHOLMOD_INT; |
|
|
6750 #endif |
|
|
6751 A->dtype = CHOLMOD_DOUBLE; |
|
|
6752 A->stype = 1; |
|
|
6753 A->xtype = CHOLMOD_REAL; |
|
|
6754 |
|
|
6755 if (nr < 1) |
|
|
6756 A->x = &dummy; |
|
|
6757 else |
|
|
6758 A->x = data(); |
|
|
6759 |
|
|
6760 cholmod_sparse Bstore; |
|
|
6761 cholmod_sparse *B = &Bstore; |
|
|
6762 B->nrow = b.rows(); |
|
|
6763 B->ncol = b.cols(); |
|
|
6764 B->p = b.cidx(); |
|
|
6765 B->i = b.ridx(); |
|
5604
|
6766 B->nzmax = b.nnz(); |
|
5526
|
6767 B->packed = true; |
|
|
6768 B->sorted = true; |
|
5506
|
6769 B->nz = NULL; |
|
|
6770 #ifdef IDX_TYPE_LONG |
|
|
6771 B->itype = CHOLMOD_LONG; |
|
|
6772 #else |
|
|
6773 B->itype = CHOLMOD_INT; |
|
|
6774 #endif |
|
|
6775 B->dtype = CHOLMOD_DOUBLE; |
|
|
6776 B->stype = 0; |
|
|
6777 B->xtype = CHOLMOD_COMPLEX; |
|
|
6778 |
|
|
6779 if (b.rows() < 1 || b.cols() < 1) |
|
|
6780 B->x = &dummy; |
|
|
6781 else |
|
|
6782 B->x = b.data(); |
|
|
6783 |
|
|
6784 cholmod_factor *L; |
|
|
6785 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6786 L = CHOLMOD_NAME(analyze) (A, cm); |
|
|
6787 CHOLMOD_NAME(factorize) (A, L, cm); |
|
5681
|
6788 if (calc_cond) |
|
|
6789 rcond = CHOLMOD_NAME(rcond)(L, cm); |
|
|
6790 else |
|
|
6791 rcond = 1.0; |
|
5506
|
6792 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6793 |
|
|
6794 if (rcond == 0.0) |
|
|
6795 { |
|
|
6796 // Either its indefinite or singular. Try UMFPACK |
|
|
6797 mattype.mark_as_unsymmetric (); |
|
5785
|
6798 typ = MatrixType::Full; |
|
5506
|
6799 } |
|
|
6800 else |
|
|
6801 { |
|
|
6802 volatile double rcond_plus_one = rcond + 1.0; |
|
|
6803 |
|
|
6804 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
6805 { |
|
|
6806 err = -2; |
|
|
6807 |
|
|
6808 if (sing_handler) |
|
5681
|
6809 { |
|
|
6810 sing_handler (rcond); |
|
|
6811 mattype.mark_as_rectangular (); |
|
|
6812 } |
|
5506
|
6813 else |
|
|
6814 (*current_liboctave_error_handler) |
|
|
6815 ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", |
|
|
6816 rcond); |
|
|
6817 |
|
|
6818 return retval; |
|
|
6819 } |
|
|
6820 |
|
|
6821 cholmod_sparse *X; |
|
|
6822 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6823 X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); |
|
|
6824 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6825 |
|
|
6826 retval = SparseComplexMatrix |
|
|
6827 (static_cast<octave_idx_type>(X->nrow), |
|
|
6828 static_cast<octave_idx_type>(X->ncol), |
|
|
6829 static_cast<octave_idx_type>(X->nzmax)); |
|
|
6830 for (octave_idx_type j = 0; |
|
|
6831 j <= static_cast<octave_idx_type>(X->ncol); j++) |
|
|
6832 retval.xcidx(j) = static_cast<octave_idx_type *>(X->p)[j]; |
|
|
6833 for (octave_idx_type j = 0; |
|
|
6834 j < static_cast<octave_idx_type>(X->nzmax); j++) |
|
|
6835 { |
|
|
6836 retval.xridx(j) = static_cast<octave_idx_type *>(X->i)[j]; |
|
|
6837 retval.xdata(j) = static_cast<Complex *>(X->x)[j]; |
|
|
6838 } |
|
|
6839 |
|
|
6840 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6841 CHOLMOD_NAME(free_sparse) (&X, cm); |
|
|
6842 CHOLMOD_NAME(free_factor) (&L, cm); |
|
|
6843 CHOLMOD_NAME(finish) (cm); |
|
6482
|
6844 static char tmp[] = " "; |
|
|
6845 CHOLMOD_NAME(print_common) (tmp, cm); |
|
5506
|
6846 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
|
6847 } |
|
|
6848 #else |
|
5164
|
6849 (*current_liboctave_warning_handler) |
|
5506
|
6850 ("CHOLMOD not installed"); |
|
5164
|
6851 |
|
|
6852 mattype.mark_as_unsymmetric (); |
|
5785
|
6853 typ = MatrixType::Full; |
|
5506
|
6854 #endif |
|
5164
|
6855 } |
|
|
6856 |
|
5785
|
6857 if (typ == MatrixType::Full) |
|
5164
|
6858 { |
|
5203
|
6859 #ifdef HAVE_UMFPACK |
|
5164
|
6860 Matrix Control, Info; |
|
|
6861 void *Numeric = factorize (err, rcond, Control, Info, |
|
5681
|
6862 sing_handler, calc_cond); |
|
5164
|
6863 |
|
|
6864 if (err == 0) |
|
|
6865 { |
|
5275
|
6866 octave_idx_type b_nr = b.rows (); |
|
|
6867 octave_idx_type b_nc = b.cols (); |
|
5164
|
6868 int status = 0; |
|
|
6869 double *control = Control.fortran_vec (); |
|
|
6870 double *info = Info.fortran_vec (); |
|
5275
|
6871 const octave_idx_type *Ap = cidx (); |
|
|
6872 const octave_idx_type *Ai = ridx (); |
|
5164
|
6873 const double *Ax = data (); |
|
|
6874 |
|
|
6875 OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); |
|
|
6876 OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); |
|
|
6877 |
|
|
6878 // Take a first guess that the number of non-zero terms |
|
|
6879 // will be as many as in b |
|
5681
|
6880 octave_idx_type x_nz = b.nnz (); |
|
5275
|
6881 octave_idx_type ii = 0; |
|
5164
|
6882 retval = SparseComplexMatrix (b_nr, b_nc, x_nz); |
|
|
6883 |
|
|
6884 OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); |
|
|
6885 OCTAVE_LOCAL_BUFFER (double, Xz, b_nr); |
|
|
6886 |
|
|
6887 retval.xcidx(0) = 0; |
|
5275
|
6888 for (octave_idx_type j = 0; j < b_nc; j++) |
|
5164
|
6889 { |
|
5275
|
6890 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6891 { |
|
|
6892 Complex c = b (i,j); |
|
5261
|
6893 Bx[i] = std::real (c); |
|
|
6894 Bz[i] = std::imag (c); |
|
5164
|
6895 } |
|
|
6896 |
|
5322
|
6897 status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, |
|
|
6898 Ai, Ax, Xx, Bx, Numeric, control, |
|
5164
|
6899 info); |
|
5322
|
6900 int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, |
|
|
6901 Ap, Ai, Ax, Xz, Bz, Numeric, |
|
5164
|
6902 control, info) ; |
|
|
6903 |
|
|
6904 if (status < 0 || status2 < 0) |
|
|
6905 { |
|
|
6906 (*current_liboctave_error_handler) |
|
|
6907 ("SparseMatrix::solve solve failed"); |
|
|
6908 |
|
5322
|
6909 UMFPACK_DNAME (report_status) (control, status); |
|
5164
|
6910 |
|
|
6911 err = -1; |
|
|
6912 |
|
|
6913 break; |
|
|
6914 } |
|
|
6915 |
|
5275
|
6916 for (octave_idx_type i = 0; i < b_nr; i++) |
|
5164
|
6917 { |
|
|
6918 Complex tmp = Complex (Xx[i], Xz[i]); |
|
|
6919 if (tmp != 0.0) |
|
|
6920 { |
|
|
6921 if (ii == x_nz) |
|
|
6922 { |
|
|
6923 // Resize the sparse matrix |
|
5275
|
6924 octave_idx_type sz = x_nz * (b_nc - j) / b_nc; |
|
5164
|
6925 sz = (sz > 10 ? sz : 10) + x_nz; |
|
|
6926 retval.change_capacity (sz); |
|
|
6927 x_nz = sz; |
|
|
6928 } |
|
|
6929 retval.xdata(ii) = tmp; |
|
|
6930 retval.xridx(ii++) = i; |
|
|
6931 } |
|
|
6932 } |
|
|
6933 retval.xcidx(j+1) = ii; |
|
|
6934 } |
|
|
6935 |
|
|
6936 retval.maybe_compress (); |
|
|
6937 |
|
5322
|
6938 UMFPACK_DNAME (report_info) (control, info); |
|
|
6939 |
|
|
6940 UMFPACK_DNAME (free_numeric) (&Numeric); |
|
5164
|
6941 } |
|
5681
|
6942 else |
|
|
6943 mattype.mark_as_rectangular (); |
|
5203
|
6944 #else |
|
|
6945 (*current_liboctave_error_handler) ("UMFPACK not installed"); |
|
|
6946 #endif |
|
5164
|
6947 } |
|
5785
|
6948 else if (typ != MatrixType::Hermitian) |
|
5164
|
6949 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
6950 } |
|
|
6951 |
|
|
6952 return retval; |
|
|
6953 } |
|
|
6954 |
|
|
6955 Matrix |
|
5785
|
6956 SparseMatrix::solve (MatrixType &mattype, const Matrix& b) const |
|
5164
|
6957 { |
|
5275
|
6958 octave_idx_type info; |
|
5164
|
6959 double rcond; |
|
|
6960 return solve (mattype, b, info, rcond, 0); |
|
|
6961 } |
|
|
6962 |
|
|
6963 Matrix |
|
5785
|
6964 SparseMatrix::solve (MatrixType &mattype, const Matrix& b, |
|
5697
|
6965 octave_idx_type& info) const |
|
5164
|
6966 { |
|
|
6967 double rcond; |
|
|
6968 return solve (mattype, b, info, rcond, 0); |
|
|
6969 } |
|
|
6970 |
|
|
6971 Matrix |
|
5785
|
6972 SparseMatrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
5164
|
6973 double& rcond) const |
|
|
6974 { |
|
|
6975 return solve (mattype, b, info, rcond, 0); |
|
|
6976 } |
|
|
6977 |
|
|
6978 Matrix |
|
5785
|
6979 SparseMatrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& err, |
|
5697
|
6980 double& rcond, solve_singularity_handler sing_handler, |
|
|
6981 bool singular_fallback) const |
|
5164
|
6982 { |
|
5681
|
6983 Matrix retval; |
|
5322
|
6984 int typ = mattype.type (false); |
|
5164
|
6985 |
|
5785
|
6986 if (typ == MatrixType::Unknown) |
|
5164
|
6987 typ = mattype.type (*this); |
|
|
6988 |
|
5681
|
6989 // Only calculate the condition number for CHOLMOD/UMFPACK |
|
5785
|
6990 if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) |
|
5681
|
6991 retval = dsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
6992 else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
5681
|
6993 retval = utsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
6994 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
5681
|
6995 retval = ltsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
6996 else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) |
|
5681
|
6997 retval = bsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
6998 else if (typ == MatrixType::Tridiagonal || |
|
|
6999 typ == MatrixType::Tridiagonal_Hermitian) |
|
5681
|
7000 retval = trisolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7001 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
5681
|
7002 retval = fsolve (mattype, b, err, rcond, sing_handler, true); |
|
5785
|
7003 else if (typ != MatrixType::Rectangular) |
|
5164
|
7004 { |
|
5681
|
7005 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
5164
|
7006 return Matrix (); |
|
|
7007 } |
|
5681
|
7008 |
|
|
7009 // Rectangular or one of the above solvers flags a singular matrix |
|
5785
|
7010 if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) |
|
5681
|
7011 { |
|
|
7012 rcond = 1.; |
|
|
7013 #ifdef USE_QRSOLVE |
|
|
7014 retval = qrsolve (*this, b, err); |
|
|
7015 #else |
|
|
7016 retval = dmsolve<Matrix, SparseMatrix, Matrix> (*this, b, err); |
|
|
7017 #endif |
|
|
7018 } |
|
|
7019 |
|
|
7020 return retval; |
|
5164
|
7021 } |
|
|
7022 |
|
|
7023 SparseMatrix |
|
5785
|
7024 SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b) const |
|
5164
|
7025 { |
|
5275
|
7026 octave_idx_type info; |
|
5164
|
7027 double rcond; |
|
|
7028 return solve (mattype, b, info, rcond, 0); |
|
|
7029 } |
|
|
7030 |
|
|
7031 SparseMatrix |
|
5785
|
7032 SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b, |
|
5275
|
7033 octave_idx_type& info) const |
|
5164
|
7034 { |
|
|
7035 double rcond; |
|
|
7036 return solve (mattype, b, info, rcond, 0); |
|
|
7037 } |
|
|
7038 |
|
|
7039 SparseMatrix |
|
5785
|
7040 SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b, |
|
5275
|
7041 octave_idx_type& info, double& rcond) const |
|
5164
|
7042 { |
|
|
7043 return solve (mattype, b, info, rcond, 0); |
|
|
7044 } |
|
|
7045 |
|
|
7046 SparseMatrix |
|
5785
|
7047 SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b, |
|
5275
|
7048 octave_idx_type& err, double& rcond, |
|
5697
|
7049 solve_singularity_handler sing_handler, |
|
|
7050 bool singular_fallback) const |
|
5164
|
7051 { |
|
5681
|
7052 SparseMatrix retval; |
|
5322
|
7053 int typ = mattype.type (false); |
|
5164
|
7054 |
|
5785
|
7055 if (typ == MatrixType::Unknown) |
|
5164
|
7056 typ = mattype.type (*this); |
|
|
7057 |
|
5785
|
7058 if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) |
|
5681
|
7059 retval = dsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7060 else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
5681
|
7061 retval = utsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7062 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
5681
|
7063 retval = ltsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7064 else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) |
|
5681
|
7065 retval = bsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7066 else if (typ == MatrixType::Tridiagonal || |
|
|
7067 typ == MatrixType::Tridiagonal_Hermitian) |
|
5681
|
7068 retval = trisolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7069 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
5681
|
7070 retval = fsolve (mattype, b, err, rcond, sing_handler, true); |
|
5785
|
7071 else if (typ != MatrixType::Rectangular) |
|
5164
|
7072 { |
|
5681
|
7073 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
5164
|
7074 return SparseMatrix (); |
|
|
7075 } |
|
5681
|
7076 |
|
5785
|
7077 if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) |
|
5681
|
7078 { |
|
|
7079 rcond = 1.; |
|
|
7080 #ifdef USE_QRSOLVE |
|
|
7081 retval = qrsolve (*this, b, err); |
|
|
7082 #else |
|
|
7083 retval = dmsolve<SparseMatrix, SparseMatrix, |
|
|
7084 SparseMatrix> (*this, b, err); |
|
|
7085 #endif |
|
|
7086 } |
|
|
7087 |
|
|
7088 return retval; |
|
5164
|
7089 } |
|
|
7090 |
|
|
7091 ComplexMatrix |
|
5785
|
7092 SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b) const |
|
5164
|
7093 { |
|
5275
|
7094 octave_idx_type info; |
|
5164
|
7095 double rcond; |
|
|
7096 return solve (mattype, b, info, rcond, 0); |
|
|
7097 } |
|
|
7098 |
|
|
7099 ComplexMatrix |
|
5785
|
7100 SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, |
|
5275
|
7101 octave_idx_type& info) const |
|
5164
|
7102 { |
|
|
7103 double rcond; |
|
|
7104 return solve (mattype, b, info, rcond, 0); |
|
|
7105 } |
|
|
7106 |
|
|
7107 ComplexMatrix |
|
5785
|
7108 SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, |
|
5275
|
7109 octave_idx_type& info, double& rcond) const |
|
5164
|
7110 { |
|
|
7111 return solve (mattype, b, info, rcond, 0); |
|
|
7112 } |
|
|
7113 |
|
|
7114 ComplexMatrix |
|
5785
|
7115 SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, |
|
5275
|
7116 octave_idx_type& err, double& rcond, |
|
5697
|
7117 solve_singularity_handler sing_handler, |
|
|
7118 bool singular_fallback) const |
|
5164
|
7119 { |
|
5681
|
7120 ComplexMatrix retval; |
|
5322
|
7121 int typ = mattype.type (false); |
|
5164
|
7122 |
|
5785
|
7123 if (typ == MatrixType::Unknown) |
|
5164
|
7124 typ = mattype.type (*this); |
|
|
7125 |
|
5785
|
7126 if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) |
|
5681
|
7127 retval = dsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7128 else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
5681
|
7129 retval = utsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7130 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
5681
|
7131 retval = ltsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7132 else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) |
|
5681
|
7133 retval = bsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7134 else if (typ == MatrixType::Tridiagonal || |
|
|
7135 typ == MatrixType::Tridiagonal_Hermitian) |
|
5681
|
7136 retval = trisolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7137 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
5681
|
7138 retval = fsolve (mattype, b, err, rcond, sing_handler, true); |
|
5785
|
7139 else if (typ != MatrixType::Rectangular) |
|
5164
|
7140 { |
|
5681
|
7141 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
5164
|
7142 return ComplexMatrix (); |
|
|
7143 } |
|
5681
|
7144 |
|
5785
|
7145 if (singular_fallback && mattype.type(false) == MatrixType::Rectangular) |
|
5681
|
7146 { |
|
|
7147 rcond = 1.; |
|
|
7148 #ifdef USE_QRSOLVE |
|
|
7149 retval = qrsolve (*this, b, err); |
|
|
7150 #else |
|
|
7151 retval = dmsolve<ComplexMatrix, SparseMatrix, |
|
|
7152 ComplexMatrix> (*this, b, err); |
|
|
7153 #endif |
|
|
7154 } |
|
|
7155 |
|
|
7156 return retval; |
|
5164
|
7157 } |
|
|
7158 |
|
|
7159 SparseComplexMatrix |
|
5785
|
7160 SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b) const |
|
5164
|
7161 { |
|
5275
|
7162 octave_idx_type info; |
|
5164
|
7163 double rcond; |
|
|
7164 return solve (mattype, b, info, rcond, 0); |
|
|
7165 } |
|
|
7166 |
|
|
7167 SparseComplexMatrix |
|
5785
|
7168 SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5275
|
7169 octave_idx_type& info) const |
|
5164
|
7170 { |
|
|
7171 double rcond; |
|
|
7172 return solve (mattype, b, info, rcond, 0); |
|
|
7173 } |
|
|
7174 |
|
|
7175 SparseComplexMatrix |
|
5785
|
7176 SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5275
|
7177 octave_idx_type& info, double& rcond) const |
|
5164
|
7178 { |
|
|
7179 return solve (mattype, b, info, rcond, 0); |
|
|
7180 } |
|
|
7181 |
|
|
7182 SparseComplexMatrix |
|
5785
|
7183 SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b, |
|
5275
|
7184 octave_idx_type& err, double& rcond, |
|
5697
|
7185 solve_singularity_handler sing_handler, |
|
|
7186 bool singular_fallback) const |
|
5164
|
7187 { |
|
5681
|
7188 SparseComplexMatrix retval; |
|
5322
|
7189 int typ = mattype.type (false); |
|
5164
|
7190 |
|
5785
|
7191 if (typ == MatrixType::Unknown) |
|
5164
|
7192 typ = mattype.type (*this); |
|
|
7193 |
|
5785
|
7194 if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) |
|
5681
|
7195 retval = dsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7196 else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
5681
|
7197 retval = utsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7198 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
5681
|
7199 retval = ltsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7200 else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) |
|
5681
|
7201 retval = bsolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7202 else if (typ == MatrixType::Tridiagonal || |
|
|
7203 typ == MatrixType::Tridiagonal_Hermitian) |
|
5681
|
7204 retval = trisolve (mattype, b, err, rcond, sing_handler, false); |
|
5785
|
7205 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
5681
|
7206 retval = fsolve (mattype, b, err, rcond, sing_handler, true); |
|
5785
|
7207 else if (typ != MatrixType::Rectangular) |
|
5164
|
7208 { |
|
5681
|
7209 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
5164
|
7210 return SparseComplexMatrix (); |
|
|
7211 } |
|
5681
|
7212 |
|
5785
|
7213 if (singular_fallback && mattype.type(false) == MatrixType::Rectangular) |
|
5681
|
7214 { |
|
|
7215 rcond = 1.; |
|
|
7216 #ifdef USE_QRSOLVE |
|
|
7217 retval = qrsolve (*this, b, err); |
|
|
7218 #else |
|
|
7219 retval = dmsolve<SparseComplexMatrix, SparseMatrix, |
|
|
7220 SparseComplexMatrix> (*this, b, err); |
|
|
7221 #endif |
|
|
7222 } |
|
|
7223 |
|
|
7224 return retval; |
|
5164
|
7225 } |
|
|
7226 |
|
|
7227 ColumnVector |
|
5785
|
7228 SparseMatrix::solve (MatrixType &mattype, const ColumnVector& b) const |
|
5164
|
7229 { |
|
5275
|
7230 octave_idx_type info; double rcond; |
|
5164
|
7231 return solve (mattype, b, info, rcond); |
|
|
7232 } |
|
|
7233 |
|
|
7234 ColumnVector |
|
5785
|
7235 SparseMatrix::solve (MatrixType &mattype, const ColumnVector& b, octave_idx_type& info) const |
|
5164
|
7236 { |
|
|
7237 double rcond; |
|
|
7238 return solve (mattype, b, info, rcond); |
|
|
7239 } |
|
|
7240 |
|
|
7241 ColumnVector |
|
5785
|
7242 SparseMatrix::solve (MatrixType &mattype, const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
5164
|
7243 { |
|
|
7244 return solve (mattype, b, info, rcond, 0); |
|
|
7245 } |
|
|
7246 |
|
|
7247 ColumnVector |
|
5785
|
7248 SparseMatrix::solve (MatrixType &mattype, const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
5164
|
7249 solve_singularity_handler sing_handler) const |
|
|
7250 { |
|
|
7251 Matrix tmp (b); |
|
5275
|
7252 return solve (mattype, tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); |
|
5164
|
7253 } |
|
|
7254 |
|
|
7255 ComplexColumnVector |
|
5785
|
7256 SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b) const |
|
5164
|
7257 { |
|
5275
|
7258 octave_idx_type info; |
|
5164
|
7259 double rcond; |
|
|
7260 return solve (mattype, b, info, rcond, 0); |
|
|
7261 } |
|
|
7262 |
|
|
7263 ComplexColumnVector |
|
5785
|
7264 SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b, octave_idx_type& info) const |
|
5164
|
7265 { |
|
|
7266 double rcond; |
|
|
7267 return solve (mattype, b, info, rcond, 0); |
|
|
7268 } |
|
|
7269 |
|
|
7270 ComplexColumnVector |
|
5785
|
7271 SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b, octave_idx_type& info, |
|
5164
|
7272 double& rcond) const |
|
|
7273 { |
|
|
7274 return solve (mattype, b, info, rcond, 0); |
|
|
7275 } |
|
|
7276 |
|
|
7277 ComplexColumnVector |
|
5785
|
7278 SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
5164
|
7279 solve_singularity_handler sing_handler) const |
|
|
7280 { |
|
|
7281 ComplexMatrix tmp (b); |
|
5275
|
7282 return solve (mattype, tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); |
|
5164
|
7283 } |
|
|
7284 |
|
|
7285 Matrix |
|
|
7286 SparseMatrix::solve (const Matrix& b) const |
|
|
7287 { |
|
5275
|
7288 octave_idx_type info; |
|
5164
|
7289 double rcond; |
|
|
7290 return solve (b, info, rcond, 0); |
|
|
7291 } |
|
|
7292 |
|
|
7293 Matrix |
|
5275
|
7294 SparseMatrix::solve (const Matrix& b, octave_idx_type& info) const |
|
5164
|
7295 { |
|
|
7296 double rcond; |
|
|
7297 return solve (b, info, rcond, 0); |
|
|
7298 } |
|
|
7299 |
|
|
7300 Matrix |
|
5275
|
7301 SparseMatrix::solve (const Matrix& b, octave_idx_type& info, |
|
5164
|
7302 double& rcond) const |
|
|
7303 { |
|
|
7304 return solve (b, info, rcond, 0); |
|
|
7305 } |
|
|
7306 |
|
|
7307 Matrix |
|
5275
|
7308 SparseMatrix::solve (const Matrix& b, octave_idx_type& err, |
|
5164
|
7309 double& rcond, |
|
|
7310 solve_singularity_handler sing_handler) const |
|
|
7311 { |
|
5785
|
7312 MatrixType mattype (*this); |
|
5164
|
7313 return solve (mattype, b, err, rcond, sing_handler); |
|
|
7314 } |
|
|
7315 |
|
|
7316 SparseMatrix |
|
|
7317 SparseMatrix::solve (const SparseMatrix& b) const |
|
|
7318 { |
|
5275
|
7319 octave_idx_type info; |
|
5164
|
7320 double rcond; |
|
|
7321 return solve (b, info, rcond, 0); |
|
|
7322 } |
|
|
7323 |
|
|
7324 SparseMatrix |
|
|
7325 SparseMatrix::solve (const SparseMatrix& b, |
|
5275
|
7326 octave_idx_type& info) const |
|
5164
|
7327 { |
|
|
7328 double rcond; |
|
|
7329 return solve (b, info, rcond, 0); |
|
|
7330 } |
|
|
7331 |
|
|
7332 SparseMatrix |
|
|
7333 SparseMatrix::solve (const SparseMatrix& b, |
|
5275
|
7334 octave_idx_type& info, double& rcond) const |
|
5164
|
7335 { |
|
|
7336 return solve (b, info, rcond, 0); |
|
|
7337 } |
|
|
7338 |
|
|
7339 SparseMatrix |
|
|
7340 SparseMatrix::solve (const SparseMatrix& b, |
|
5275
|
7341 octave_idx_type& err, double& rcond, |
|
5164
|
7342 solve_singularity_handler sing_handler) const |
|
|
7343 { |
|
5785
|
7344 MatrixType mattype (*this); |
|
5164
|
7345 return solve (mattype, b, err, rcond, sing_handler); |
|
|
7346 } |
|
|
7347 |
|
|
7348 ComplexMatrix |
|
|
7349 SparseMatrix::solve (const ComplexMatrix& b, |
|
5275
|
7350 octave_idx_type& info) const |
|
5164
|
7351 { |
|
|
7352 double rcond; |
|
|
7353 return solve (b, info, rcond, 0); |
|
|
7354 } |
|
|
7355 |
|
|
7356 ComplexMatrix |
|
|
7357 SparseMatrix::solve (const ComplexMatrix& b, |
|
5275
|
7358 octave_idx_type& info, double& rcond) const |
|
5164
|
7359 { |
|
|
7360 return solve (b, info, rcond, 0); |
|
|
7361 } |
|
|
7362 |
|
|
7363 ComplexMatrix |
|
|
7364 SparseMatrix::solve (const ComplexMatrix& b, |
|
5275
|
7365 octave_idx_type& err, double& rcond, |
|
5164
|
7366 solve_singularity_handler sing_handler) const |
|
|
7367 { |
|
5785
|
7368 MatrixType mattype (*this); |
|
5164
|
7369 return solve (mattype, b, err, rcond, sing_handler); |
|
|
7370 } |
|
|
7371 |
|
|
7372 SparseComplexMatrix |
|
|
7373 SparseMatrix::solve (const SparseComplexMatrix& b) const |
|
|
7374 { |
|
5275
|
7375 octave_idx_type info; |
|
5164
|
7376 double rcond; |
|
|
7377 return solve (b, info, rcond, 0); |
|
|
7378 } |
|
|
7379 |
|
|
7380 SparseComplexMatrix |
|
|
7381 SparseMatrix::solve (const SparseComplexMatrix& b, |
|
5275
|
7382 octave_idx_type& info) const |
|
5164
|
7383 { |
|
|
7384 double rcond; |
|
|
7385 return solve (b, info, rcond, 0); |
|
|
7386 } |
|
|
7387 |
|
|
7388 SparseComplexMatrix |
|
|
7389 SparseMatrix::solve (const SparseComplexMatrix& b, |
|
5275
|
7390 octave_idx_type& info, double& rcond) const |
|
5164
|
7391 { |
|
|
7392 return solve (b, info, rcond, 0); |
|
|
7393 } |
|
|
7394 |
|
|
7395 SparseComplexMatrix |
|
|
7396 SparseMatrix::solve (const SparseComplexMatrix& b, |
|
5275
|
7397 octave_idx_type& err, double& rcond, |
|
5164
|
7398 solve_singularity_handler sing_handler) const |
|
|
7399 { |
|
5785
|
7400 MatrixType mattype (*this); |
|
5164
|
7401 return solve (mattype, b, err, rcond, sing_handler); |
|
|
7402 } |
|
|
7403 |
|
|
7404 ColumnVector |
|
|
7405 SparseMatrix::solve (const ColumnVector& b) const |
|
|
7406 { |
|
5275
|
7407 octave_idx_type info; double rcond; |
|
5164
|
7408 return solve (b, info, rcond); |
|
|
7409 } |
|
|
7410 |
|
|
7411 ColumnVector |
|
5275
|
7412 SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
5164
|
7413 { |
|
|
7414 double rcond; |
|
|
7415 return solve (b, info, rcond); |
|
|
7416 } |
|
|
7417 |
|
|
7418 ColumnVector |
|
5275
|
7419 SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
5164
|
7420 { |
|
|
7421 return solve (b, info, rcond, 0); |
|
|
7422 } |
|
|
7423 |
|
|
7424 ColumnVector |
|
5275
|
7425 SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
5164
|
7426 solve_singularity_handler sing_handler) const |
|
|
7427 { |
|
|
7428 Matrix tmp (b); |
|
5275
|
7429 return solve (tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); |
|
5164
|
7430 } |
|
|
7431 |
|
|
7432 ComplexColumnVector |
|
|
7433 SparseMatrix::solve (const ComplexColumnVector& b) const |
|
|
7434 { |
|
5275
|
7435 octave_idx_type info; |
|
5164
|
7436 double rcond; |
|
|
7437 return solve (b, info, rcond, 0); |
|
|
7438 } |
|
|
7439 |
|
|
7440 ComplexColumnVector |
|
5275
|
7441 SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
5164
|
7442 { |
|
|
7443 double rcond; |
|
|
7444 return solve (b, info, rcond, 0); |
|
|
7445 } |
|
|
7446 |
|
|
7447 ComplexColumnVector |
|
5275
|
7448 SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
5164
|
7449 double& rcond) const |
|
|
7450 { |
|
|
7451 return solve (b, info, rcond, 0); |
|
|
7452 } |
|
|
7453 |
|
|
7454 ComplexColumnVector |
|
5275
|
7455 SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
5164
|
7456 solve_singularity_handler sing_handler) const |
|
|
7457 { |
|
|
7458 ComplexMatrix tmp (b); |
|
5275
|
7459 return solve (tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); |
|
5164
|
7460 } |
|
|
7461 |
|
|
7462 // other operations. |
|
|
7463 |
|
|
7464 SparseMatrix |
|
|
7465 SparseMatrix::map (d_d_Mapper f) const |
|
|
7466 { |
|
5275
|
7467 octave_idx_type nr = rows (); |
|
|
7468 octave_idx_type nc = cols (); |
|
5681
|
7469 octave_idx_type nz = nnz (); |
|
5164
|
7470 bool f_zero = (f(0.0) == 0.0); |
|
|
7471 |
|
|
7472 // Count number of non-zero elements |
|
5275
|
7473 octave_idx_type nel = (f_zero ? 0 : nr*nc - nz); |
|
|
7474 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
7475 if (f (data(i)) != 0.0) |
|
|
7476 nel++; |
|
|
7477 |
|
|
7478 SparseMatrix retval (nr, nc, nel); |
|
|
7479 |
|
|
7480 if (f_zero) |
|
|
7481 { |
|
5275
|
7482 octave_idx_type ii = 0; |
|
|
7483 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
7484 { |
|
5275
|
7485 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
7486 { |
|
|
7487 double tmp = f (elem (i, j)); |
|
|
7488 if (tmp != 0.0) |
|
|
7489 { |
|
|
7490 retval.data(ii) = tmp; |
|
|
7491 retval.ridx(ii++) = i; |
|
|
7492 } |
|
|
7493 } |
|
|
7494 retval.cidx(j+1) = ii; |
|
|
7495 } |
|
|
7496 } |
|
|
7497 else |
|
|
7498 { |
|
5275
|
7499 octave_idx_type ii = 0; |
|
|
7500 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
7501 { |
|
5275
|
7502 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
7503 { |
|
|
7504 retval.data(ii) = f (elem(i)); |
|
|
7505 retval.ridx(ii++) = ridx(i); |
|
|
7506 } |
|
|
7507 retval.cidx(j+1) = ii; |
|
|
7508 } |
|
|
7509 } |
|
|
7510 |
|
|
7511 return retval; |
|
|
7512 } |
|
|
7513 |
|
|
7514 SparseBoolMatrix |
|
|
7515 SparseMatrix::map (b_d_Mapper f) const |
|
|
7516 { |
|
5275
|
7517 octave_idx_type nr = rows (); |
|
|
7518 octave_idx_type nc = cols (); |
|
5681
|
7519 octave_idx_type nz = nnz (); |
|
5164
|
7520 bool f_zero = f(0.0); |
|
|
7521 |
|
|
7522 // Count number of non-zero elements |
|
5275
|
7523 octave_idx_type nel = (f_zero ? 0 : nr*nc - nz); |
|
|
7524 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
7525 if (f (data(i)) != 0.0) |
|
|
7526 nel++; |
|
|
7527 |
|
|
7528 SparseBoolMatrix retval (nr, nc, nel); |
|
|
7529 |
|
|
7530 if (f_zero) |
|
|
7531 { |
|
5275
|
7532 octave_idx_type ii = 0; |
|
|
7533 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
7534 { |
|
5275
|
7535 for (octave_idx_type i = 0; i < nr; i++) |
|
5164
|
7536 { |
|
|
7537 bool tmp = f (elem (i, j)); |
|
|
7538 if (tmp) |
|
|
7539 { |
|
|
7540 retval.data(ii) = tmp; |
|
|
7541 retval.ridx(ii++) = i; |
|
|
7542 } |
|
|
7543 } |
|
|
7544 retval.cidx(j+1) = ii; |
|
|
7545 } |
|
|
7546 } |
|
|
7547 else |
|
|
7548 { |
|
5275
|
7549 octave_idx_type ii = 0; |
|
|
7550 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
7551 { |
|
5275
|
7552 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
7553 { |
|
|
7554 retval.data(ii) = f (elem(i)); |
|
|
7555 retval.ridx(ii++) = ridx(i); |
|
|
7556 } |
|
|
7557 retval.cidx(j+1) = ii; |
|
|
7558 } |
|
|
7559 } |
|
|
7560 |
|
|
7561 return retval; |
|
|
7562 } |
|
|
7563 |
|
|
7564 SparseMatrix& |
|
|
7565 SparseMatrix::apply (d_d_Mapper f) |
|
|
7566 { |
|
|
7567 *this = map (f); |
|
|
7568 return *this; |
|
|
7569 } |
|
|
7570 |
|
|
7571 bool |
|
|
7572 SparseMatrix::any_element_is_negative (bool neg_zero) const |
|
|
7573 { |
|
5681
|
7574 octave_idx_type nel = nnz (); |
|
5164
|
7575 |
|
|
7576 if (neg_zero) |
|
|
7577 { |
|
5275
|
7578 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7579 if (lo_ieee_signbit (data (i))) |
|
|
7580 return true; |
|
|
7581 } |
|
|
7582 else |
|
|
7583 { |
|
5275
|
7584 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7585 if (data (i) < 0) |
|
|
7586 return true; |
|
|
7587 } |
|
|
7588 |
|
|
7589 return false; |
|
|
7590 } |
|
|
7591 |
|
|
7592 bool |
|
|
7593 SparseMatrix::any_element_is_inf_or_nan (void) const |
|
|
7594 { |
|
5681
|
7595 octave_idx_type nel = nnz (); |
|
5275
|
7596 |
|
|
7597 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7598 { |
|
|
7599 double val = data (i); |
|
|
7600 if (xisinf (val) || xisnan (val)) |
|
|
7601 return true; |
|
|
7602 } |
|
|
7603 |
|
|
7604 return false; |
|
|
7605 } |
|
|
7606 |
|
|
7607 bool |
|
|
7608 SparseMatrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
7609 { |
|
5681
|
7610 octave_idx_type nel = nnz (); |
|
5275
|
7611 |
|
|
7612 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7613 { |
|
|
7614 double val = data (i); |
|
|
7615 if (xisnan (val) || D_NINT (val) == val) |
|
|
7616 continue; |
|
|
7617 else |
|
|
7618 return false; |
|
|
7619 } |
|
|
7620 |
|
|
7621 return true; |
|
|
7622 } |
|
|
7623 |
|
|
7624 // Return nonzero if any element of M is not an integer. Also extract |
|
|
7625 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
7626 |
|
|
7627 bool |
|
|
7628 SparseMatrix::all_integers (double& max_val, double& min_val) const |
|
|
7629 { |
|
5681
|
7630 octave_idx_type nel = nnz (); |
|
5164
|
7631 |
|
|
7632 if (nel == 0) |
|
|
7633 return false; |
|
|
7634 |
|
|
7635 max_val = data (0); |
|
|
7636 min_val = data (0); |
|
|
7637 |
|
5275
|
7638 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7639 { |
|
|
7640 double val = data (i); |
|
|
7641 |
|
|
7642 if (val > max_val) |
|
|
7643 max_val = val; |
|
|
7644 |
|
|
7645 if (val < min_val) |
|
|
7646 min_val = val; |
|
|
7647 |
|
|
7648 if (D_NINT (val) != val) |
|
|
7649 return false; |
|
|
7650 } |
|
|
7651 |
|
|
7652 return true; |
|
|
7653 } |
|
|
7654 |
|
|
7655 bool |
|
|
7656 SparseMatrix::too_large_for_float (void) const |
|
|
7657 { |
|
5681
|
7658 octave_idx_type nel = nnz (); |
|
5275
|
7659 |
|
|
7660 for (octave_idx_type i = 0; i < nel; i++) |
|
5164
|
7661 { |
|
|
7662 double val = data (i); |
|
|
7663 |
|
|
7664 if (val > FLT_MAX || val < FLT_MIN) |
|
|
7665 return true; |
|
|
7666 } |
|
|
7667 |
|
|
7668 return false; |
|
|
7669 } |
|
|
7670 |
|
|
7671 SparseBoolMatrix |
|
|
7672 SparseMatrix::operator ! (void) const |
|
|
7673 { |
|
5275
|
7674 octave_idx_type nr = rows (); |
|
|
7675 octave_idx_type nc = cols (); |
|
5681
|
7676 octave_idx_type nz1 = nnz (); |
|
5275
|
7677 octave_idx_type nz2 = nr*nc - nz1; |
|
5164
|
7678 |
|
|
7679 SparseBoolMatrix r (nr, nc, nz2); |
|
|
7680 |
|
5275
|
7681 octave_idx_type ii = 0; |
|
|
7682 octave_idx_type jj = 0; |
|
5164
|
7683 r.cidx (0) = 0; |
|
5275
|
7684 for (octave_idx_type i = 0; i < nc; i++) |
|
5164
|
7685 { |
|
5275
|
7686 for (octave_idx_type j = 0; j < nr; j++) |
|
5164
|
7687 { |
|
|
7688 if (jj < cidx(i+1) && ridx(jj) == j) |
|
|
7689 jj++; |
|
|
7690 else |
|
|
7691 { |
|
|
7692 r.data(ii) = true; |
|
|
7693 r.ridx(ii++) = j; |
|
|
7694 } |
|
|
7695 } |
|
|
7696 r.cidx (i+1) = ii; |
|
|
7697 } |
|
|
7698 |
|
|
7699 return r; |
|
|
7700 } |
|
|
7701 |
|
5775
|
7702 // FIXME Do these really belong here? Maybe they should be |
|
5164
|
7703 // in a base class? |
|
|
7704 |
|
|
7705 SparseBoolMatrix |
|
|
7706 SparseMatrix::all (int dim) const |
|
|
7707 { |
|
|
7708 SPARSE_ALL_OP (dim); |
|
|
7709 } |
|
|
7710 |
|
|
7711 SparseBoolMatrix |
|
|
7712 SparseMatrix::any (int dim) const |
|
|
7713 { |
|
|
7714 SPARSE_ANY_OP (dim); |
|
|
7715 } |
|
|
7716 |
|
|
7717 SparseMatrix |
|
|
7718 SparseMatrix::cumprod (int dim) const |
|
|
7719 { |
|
|
7720 SPARSE_CUMPROD (SparseMatrix, double, cumprod); |
|
|
7721 } |
|
|
7722 |
|
|
7723 SparseMatrix |
|
|
7724 SparseMatrix::cumsum (int dim) const |
|
|
7725 { |
|
|
7726 SPARSE_CUMSUM (SparseMatrix, double, cumsum); |
|
|
7727 } |
|
|
7728 |
|
|
7729 SparseMatrix |
|
|
7730 SparseMatrix::prod (int dim) const |
|
|
7731 { |
|
|
7732 SPARSE_REDUCTION_OP (SparseMatrix, double, *=, 1.0, 1.0); |
|
|
7733 } |
|
|
7734 |
|
|
7735 SparseMatrix |
|
|
7736 SparseMatrix::sum (int dim) const |
|
|
7737 { |
|
|
7738 SPARSE_REDUCTION_OP (SparseMatrix, double, +=, 0.0, 0.0); |
|
|
7739 } |
|
|
7740 |
|
|
7741 SparseMatrix |
|
|
7742 SparseMatrix::sumsq (int dim) const |
|
|
7743 { |
|
|
7744 #define ROW_EXPR \ |
|
|
7745 double d = elem (i, j); \ |
|
|
7746 tmp[i] += d * d |
|
|
7747 |
|
|
7748 #define COL_EXPR \ |
|
|
7749 double d = elem (i, j); \ |
|
|
7750 tmp[j] += d * d |
|
|
7751 |
|
|
7752 SPARSE_BASE_REDUCTION_OP (SparseMatrix, double, ROW_EXPR, COL_EXPR, |
|
|
7753 0.0, 0.0); |
|
|
7754 |
|
|
7755 #undef ROW_EXPR |
|
|
7756 #undef COL_EXPR |
|
|
7757 } |
|
|
7758 |
|
|
7759 SparseMatrix |
|
|
7760 SparseMatrix::abs (void) const |
|
|
7761 { |
|
5681
|
7762 octave_idx_type nz = nnz (); |
|
5164
|
7763 |
|
|
7764 SparseMatrix retval (*this); |
|
|
7765 |
|
5275
|
7766 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
7767 retval.data(i) = fabs(retval.data(i)); |
|
|
7768 |
|
|
7769 return retval; |
|
|
7770 } |
|
|
7771 |
|
|
7772 SparseMatrix |
|
5275
|
7773 SparseMatrix::diag (octave_idx_type k) const |
|
5164
|
7774 { |
|
5275
|
7775 octave_idx_type nnr = rows (); |
|
|
7776 octave_idx_type nnc = cols (); |
|
5164
|
7777 |
|
|
7778 if (k > 0) |
|
|
7779 nnc -= k; |
|
|
7780 else if (k < 0) |
|
|
7781 nnr += k; |
|
|
7782 |
|
|
7783 SparseMatrix d; |
|
|
7784 |
|
|
7785 if (nnr > 0 && nnc > 0) |
|
|
7786 { |
|
5275
|
7787 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
5164
|
7788 |
|
|
7789 // Count the number of non-zero elements |
|
5275
|
7790 octave_idx_type nel = 0; |
|
5164
|
7791 if (k > 0) |
|
|
7792 { |
|
5275
|
7793 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7794 if (elem (i, i+k) != 0.) |
|
|
7795 nel++; |
|
|
7796 } |
|
|
7797 else if ( k < 0) |
|
|
7798 { |
|
5275
|
7799 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7800 if (elem (i-k, i) != 0.) |
|
|
7801 nel++; |
|
|
7802 } |
|
|
7803 else |
|
|
7804 { |
|
5275
|
7805 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7806 if (elem (i, i) != 0.) |
|
|
7807 nel++; |
|
|
7808 } |
|
|
7809 |
|
|
7810 d = SparseMatrix (ndiag, 1, nel); |
|
|
7811 d.xcidx (0) = 0; |
|
|
7812 d.xcidx (1) = nel; |
|
|
7813 |
|
5275
|
7814 octave_idx_type ii = 0; |
|
5164
|
7815 if (k > 0) |
|
|
7816 { |
|
5275
|
7817 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7818 { |
|
|
7819 double tmp = elem (i, i+k); |
|
|
7820 if (tmp != 0.) |
|
|
7821 { |
|
|
7822 d.xdata (ii) = tmp; |
|
|
7823 d.xridx (ii++) = i; |
|
|
7824 } |
|
|
7825 } |
|
|
7826 } |
|
|
7827 else if ( k < 0) |
|
|
7828 { |
|
5275
|
7829 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7830 { |
|
|
7831 double tmp = elem (i-k, i); |
|
|
7832 if (tmp != 0.) |
|
|
7833 { |
|
|
7834 d.xdata (ii) = tmp; |
|
|
7835 d.xridx (ii++) = i; |
|
|
7836 } |
|
|
7837 } |
|
|
7838 } |
|
|
7839 else |
|
|
7840 { |
|
5275
|
7841 for (octave_idx_type i = 0; i < ndiag; i++) |
|
5164
|
7842 { |
|
|
7843 double tmp = elem (i, i); |
|
|
7844 if (tmp != 0.) |
|
|
7845 { |
|
|
7846 d.xdata (ii) = tmp; |
|
|
7847 d.xridx (ii++) = i; |
|
|
7848 } |
|
|
7849 } |
|
|
7850 } |
|
|
7851 } |
|
|
7852 else |
|
|
7853 (*current_liboctave_error_handler) |
|
|
7854 ("diag: requested diagonal out of range"); |
|
|
7855 |
|
|
7856 return d; |
|
|
7857 } |
|
|
7858 |
|
|
7859 Matrix |
|
|
7860 SparseMatrix::matrix_value (void) const |
|
|
7861 { |
|
5275
|
7862 octave_idx_type nr = rows (); |
|
|
7863 octave_idx_type nc = cols (); |
|
5164
|
7864 |
|
|
7865 Matrix retval (nr, nc, 0.0); |
|
5275
|
7866 for (octave_idx_type j = 0; j < nc; j++) |
|
|
7867 for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) |
|
5164
|
7868 retval.elem (ridx(i), j) = data (i); |
|
|
7869 |
|
|
7870 return retval; |
|
|
7871 } |
|
|
7872 |
|
|
7873 std::ostream& |
|
|
7874 operator << (std::ostream& os, const SparseMatrix& a) |
|
|
7875 { |
|
5275
|
7876 octave_idx_type nc = a.cols (); |
|
5164
|
7877 |
|
|
7878 // add one to the printed indices to go from |
|
|
7879 // zero-based to one-based arrays |
|
5275
|
7880 for (octave_idx_type j = 0; j < nc; j++) { |
|
5164
|
7881 OCTAVE_QUIT; |
|
5275
|
7882 for (octave_idx_type i = a.cidx(j); i < a.cidx(j+1); i++) { |
|
5164
|
7883 os << a.ridx(i) + 1 << " " << j + 1 << " "; |
|
|
7884 octave_write_double (os, a.data(i)); |
|
|
7885 os << "\n"; |
|
|
7886 } |
|
|
7887 } |
|
|
7888 |
|
|
7889 return os; |
|
|
7890 } |
|
|
7891 |
|
|
7892 std::istream& |
|
|
7893 operator >> (std::istream& is, SparseMatrix& a) |
|
|
7894 { |
|
5275
|
7895 octave_idx_type nr = a.rows (); |
|
|
7896 octave_idx_type nc = a.cols (); |
|
5604
|
7897 octave_idx_type nz = a.nzmax (); |
|
5164
|
7898 |
|
|
7899 if (nr < 1 || nc < 1) |
|
|
7900 is.clear (std::ios::badbit); |
|
|
7901 else |
|
|
7902 { |
|
5275
|
7903 octave_idx_type itmp, jtmp, jold = 0; |
|
5164
|
7904 double tmp; |
|
5275
|
7905 octave_idx_type ii = 0; |
|
5164
|
7906 |
|
|
7907 a.cidx (0) = 0; |
|
5275
|
7908 for (octave_idx_type i = 0; i < nz; i++) |
|
5164
|
7909 { |
|
|
7910 is >> itmp; |
|
|
7911 itmp--; |
|
|
7912 is >> jtmp; |
|
|
7913 jtmp--; |
|
|
7914 tmp = octave_read_double (is); |
|
|
7915 |
|
|
7916 if (is) |
|
|
7917 { |
|
|
7918 if (jold != jtmp) |
|
|
7919 { |
|
5275
|
7920 for (octave_idx_type j = jold; j < jtmp; j++) |
|
5164
|
7921 a.cidx(j+1) = ii; |
|
|
7922 |
|
|
7923 jold = jtmp; |
|
|
7924 } |
|
|
7925 a.data (ii) = tmp; |
|
|
7926 a.ridx (ii++) = itmp; |
|
|
7927 } |
|
|
7928 else |
|
|
7929 goto done; |
|
|
7930 } |
|
|
7931 |
|
5275
|
7932 for (octave_idx_type j = jold; j < nc; j++) |
|
5164
|
7933 a.cidx(j+1) = ii; |
|
|
7934 } |
|
|
7935 |
|
|
7936 done: |
|
|
7937 |
|
|
7938 return is; |
|
|
7939 } |
|
|
7940 |
|
|
7941 SparseMatrix |
|
|
7942 SparseMatrix::squeeze (void) const |
|
|
7943 { |
|
|
7944 return MSparse<double>::squeeze (); |
|
|
7945 } |
|
|
7946 |
|
|
7947 SparseMatrix |
|
|
7948 SparseMatrix::index (idx_vector& i, int resize_ok) const |
|
|
7949 { |
|
|
7950 return MSparse<double>::index (i, resize_ok); |
|
|
7951 } |
|
|
7952 |
|
|
7953 SparseMatrix |
|
|
7954 SparseMatrix::index (idx_vector& i, idx_vector& j, int resize_ok) const |
|
|
7955 { |
|
|
7956 return MSparse<double>::index (i, j, resize_ok); |
|
|
7957 } |
|
|
7958 |
|
|
7959 SparseMatrix |
|
|
7960 SparseMatrix::index (Array<idx_vector>& ra_idx, int resize_ok) const |
|
|
7961 { |
|
|
7962 return MSparse<double>::index (ra_idx, resize_ok); |
|
|
7963 } |
|
|
7964 |
|
|
7965 SparseMatrix |
|
|
7966 SparseMatrix::reshape (const dim_vector& new_dims) const |
|
|
7967 { |
|
|
7968 return MSparse<double>::reshape (new_dims); |
|
|
7969 } |
|
|
7970 |
|
|
7971 SparseMatrix |
|
5275
|
7972 SparseMatrix::permute (const Array<octave_idx_type>& vec, bool inv) const |
|
5164
|
7973 { |
|
|
7974 return MSparse<double>::permute (vec, inv); |
|
|
7975 } |
|
|
7976 |
|
|
7977 SparseMatrix |
|
5275
|
7978 SparseMatrix::ipermute (const Array<octave_idx_type>& vec) const |
|
5164
|
7979 { |
|
|
7980 return MSparse<double>::ipermute (vec); |
|
|
7981 } |
|
|
7982 |
|
|
7983 // matrix by matrix -> matrix operations |
|
|
7984 |
|
|
7985 SparseMatrix |
|
|
7986 operator * (const SparseMatrix& m, const SparseMatrix& a) |
|
|
7987 { |
|
5681
|
7988 SPARSE_SPARSE_MUL (SparseMatrix, double, double); |
|
5164
|
7989 } |
|
|
7990 |
|
5429
|
7991 Matrix |
|
|
7992 operator * (const Matrix& m, const SparseMatrix& a) |
|
|
7993 { |
|
5681
|
7994 FULL_SPARSE_MUL (Matrix, double, 0.); |
|
5429
|
7995 } |
|
|
7996 |
|
|
7997 Matrix |
|
|
7998 operator * (const SparseMatrix& m, const Matrix& a) |
|
|
7999 { |
|
5681
|
8000 SPARSE_FULL_MUL (Matrix, double, 0.); |
|
5429
|
8001 } |
|
|
8002 |
|
5775
|
8003 // FIXME -- it would be nice to share code among the min/max |
|
5164
|
8004 // functions below. |
|
|
8005 |
|
|
8006 #define EMPTY_RETURN_CHECK(T) \ |
|
|
8007 if (nr == 0 || nc == 0) \ |
|
|
8008 return T (nr, nc); |
|
|
8009 |
|
|
8010 SparseMatrix |
|
|
8011 min (double d, const SparseMatrix& m) |
|
|
8012 { |
|
|
8013 SparseMatrix result; |
|
|
8014 |
|
5275
|
8015 octave_idx_type nr = m.rows (); |
|
|
8016 octave_idx_type nc = m.columns (); |
|
5164
|
8017 |
|
|
8018 EMPTY_RETURN_CHECK (SparseMatrix); |
|
|
8019 |
|
|
8020 // Count the number of non-zero elements |
|
|
8021 if (d < 0.) |
|
|
8022 { |
|
|
8023 result = SparseMatrix (nr, nc, d); |
|
5275
|
8024 for (octave_idx_type j = 0; j < nc; j++) |
|
|
8025 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8026 { |
|
|
8027 double tmp = xmin (d, m.data (i)); |
|
|
8028 if (tmp != 0.) |
|
|
8029 { |
|
5275
|
8030 octave_idx_type idx = m.ridx(i) + j * nr; |
|
5164
|
8031 result.xdata(idx) = tmp; |
|
|
8032 result.xridx(idx) = m.ridx(i); |
|
|
8033 } |
|
|
8034 } |
|
|
8035 } |
|
|
8036 else |
|
|
8037 { |
|
5275
|
8038 octave_idx_type nel = 0; |
|
|
8039 for (octave_idx_type j = 0; j < nc; j++) |
|
|
8040 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8041 if (xmin (d, m.data (i)) != 0.) |
|
|
8042 nel++; |
|
|
8043 |
|
|
8044 result = SparseMatrix (nr, nc, nel); |
|
|
8045 |
|
5275
|
8046 octave_idx_type ii = 0; |
|
5164
|
8047 result.xcidx(0) = 0; |
|
5275
|
8048 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
8049 { |
|
5275
|
8050 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8051 { |
|
|
8052 double tmp = xmin (d, m.data (i)); |
|
|
8053 |
|
|
8054 if (tmp != 0.) |
|
|
8055 { |
|
|
8056 result.xdata(ii) = tmp; |
|
|
8057 result.xridx(ii++) = m.ridx(i); |
|
|
8058 } |
|
|
8059 } |
|
|
8060 result.xcidx(j+1) = ii; |
|
|
8061 } |
|
|
8062 } |
|
|
8063 |
|
|
8064 return result; |
|
|
8065 } |
|
|
8066 |
|
|
8067 SparseMatrix |
|
|
8068 min (const SparseMatrix& m, double d) |
|
|
8069 { |
|
|
8070 return min (d, m); |
|
|
8071 } |
|
|
8072 |
|
|
8073 SparseMatrix |
|
|
8074 min (const SparseMatrix& a, const SparseMatrix& b) |
|
|
8075 { |
|
|
8076 SparseMatrix r; |
|
|
8077 |
|
|
8078 if ((a.rows() == b.rows()) && (a.cols() == b.cols())) |
|
|
8079 { |
|
5275
|
8080 octave_idx_type a_nr = a.rows (); |
|
|
8081 octave_idx_type a_nc = a.cols (); |
|
|
8082 |
|
|
8083 octave_idx_type b_nr = b.rows (); |
|
|
8084 octave_idx_type b_nc = b.cols (); |
|
5164
|
8085 |
|
|
8086 if (a_nr != b_nr || a_nc != b_nc) |
|
|
8087 gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc); |
|
|
8088 else |
|
|
8089 { |
|
5681
|
8090 r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ())); |
|
5164
|
8091 |
|
5275
|
8092 octave_idx_type jx = 0; |
|
5164
|
8093 r.cidx (0) = 0; |
|
5275
|
8094 for (octave_idx_type i = 0 ; i < a_nc ; i++) |
|
5164
|
8095 { |
|
5275
|
8096 octave_idx_type ja = a.cidx(i); |
|
|
8097 octave_idx_type ja_max = a.cidx(i+1); |
|
5164
|
8098 bool ja_lt_max= ja < ja_max; |
|
|
8099 |
|
5275
|
8100 octave_idx_type jb = b.cidx(i); |
|
|
8101 octave_idx_type jb_max = b.cidx(i+1); |
|
5164
|
8102 bool jb_lt_max = jb < jb_max; |
|
|
8103 |
|
|
8104 while (ja_lt_max || jb_lt_max ) |
|
|
8105 { |
|
|
8106 OCTAVE_QUIT; |
|
|
8107 if ((! jb_lt_max) || |
|
|
8108 (ja_lt_max && (a.ridx(ja) < b.ridx(jb)))) |
|
|
8109 { |
|
|
8110 double tmp = xmin (a.data(ja), 0.); |
|
|
8111 if (tmp != 0.) |
|
|
8112 { |
|
|
8113 r.ridx(jx) = a.ridx(ja); |
|
|
8114 r.data(jx) = tmp; |
|
|
8115 jx++; |
|
|
8116 } |
|
|
8117 ja++; |
|
|
8118 ja_lt_max= ja < ja_max; |
|
|
8119 } |
|
|
8120 else if (( !ja_lt_max ) || |
|
|
8121 (jb_lt_max && (b.ridx(jb) < a.ridx(ja)) ) ) |
|
|
8122 { |
|
|
8123 double tmp = xmin (0., b.data(jb)); |
|
|
8124 if (tmp != 0.) |
|
|
8125 { |
|
|
8126 r.ridx(jx) = b.ridx(jb); |
|
|
8127 r.data(jx) = tmp; |
|
|
8128 jx++; |
|
|
8129 } |
|
|
8130 jb++; |
|
|
8131 jb_lt_max= jb < jb_max; |
|
|
8132 } |
|
|
8133 else |
|
|
8134 { |
|
|
8135 double tmp = xmin (a.data(ja), b.data(jb)); |
|
|
8136 if (tmp != 0.) |
|
|
8137 { |
|
|
8138 r.data(jx) = tmp; |
|
|
8139 r.ridx(jx) = a.ridx(ja); |
|
|
8140 jx++; |
|
|
8141 } |
|
|
8142 ja++; |
|
|
8143 ja_lt_max= ja < ja_max; |
|
|
8144 jb++; |
|
|
8145 jb_lt_max= jb < jb_max; |
|
|
8146 } |
|
|
8147 } |
|
|
8148 r.cidx(i+1) = jx; |
|
|
8149 } |
|
|
8150 |
|
|
8151 r.maybe_compress (); |
|
|
8152 } |
|
|
8153 } |
|
|
8154 else |
|
|
8155 (*current_liboctave_error_handler) ("matrix size mismatch"); |
|
|
8156 |
|
|
8157 return r; |
|
|
8158 } |
|
|
8159 |
|
|
8160 SparseMatrix |
|
|
8161 max (double d, const SparseMatrix& m) |
|
|
8162 { |
|
|
8163 SparseMatrix result; |
|
|
8164 |
|
5275
|
8165 octave_idx_type nr = m.rows (); |
|
|
8166 octave_idx_type nc = m.columns (); |
|
5164
|
8167 |
|
|
8168 EMPTY_RETURN_CHECK (SparseMatrix); |
|
|
8169 |
|
|
8170 // Count the number of non-zero elements |
|
|
8171 if (d > 0.) |
|
|
8172 { |
|
|
8173 result = SparseMatrix (nr, nc, d); |
|
5275
|
8174 for (octave_idx_type j = 0; j < nc; j++) |
|
|
8175 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8176 { |
|
|
8177 double tmp = xmax (d, m.data (i)); |
|
|
8178 |
|
|
8179 if (tmp != 0.) |
|
|
8180 { |
|
5275
|
8181 octave_idx_type idx = m.ridx(i) + j * nr; |
|
5164
|
8182 result.xdata(idx) = tmp; |
|
|
8183 result.xridx(idx) = m.ridx(i); |
|
|
8184 } |
|
|
8185 } |
|
|
8186 } |
|
|
8187 else |
|
|
8188 { |
|
5275
|
8189 octave_idx_type nel = 0; |
|
|
8190 for (octave_idx_type j = 0; j < nc; j++) |
|
|
8191 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8192 if (xmax (d, m.data (i)) != 0.) |
|
|
8193 nel++; |
|
|
8194 |
|
|
8195 result = SparseMatrix (nr, nc, nel); |
|
|
8196 |
|
5275
|
8197 octave_idx_type ii = 0; |
|
5164
|
8198 result.xcidx(0) = 0; |
|
5275
|
8199 for (octave_idx_type j = 0; j < nc; j++) |
|
5164
|
8200 { |
|
5275
|
8201 for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) |
|
5164
|
8202 { |
|
|
8203 double tmp = xmax (d, m.data (i)); |
|
|
8204 if (tmp != 0.) |
|
|
8205 { |
|
|
8206 result.xdata(ii) = tmp; |
|
|
8207 result.xridx(ii++) = m.ridx(i); |
|
|
8208 } |
|
|
8209 } |
|
|
8210 result.xcidx(j+1) = ii; |
|
|
8211 } |
|
|
8212 } |
|
|
8213 |
|
|
8214 return result; |
|
|
8215 } |
|
|
8216 |
|
|
8217 SparseMatrix |
|
|
8218 max (const SparseMatrix& m, double d) |
|
|
8219 { |
|
|
8220 return max (d, m); |
|
|
8221 } |
|
|
8222 |
|
|
8223 SparseMatrix |
|
|
8224 max (const SparseMatrix& a, const SparseMatrix& b) |
|
|
8225 { |
|
|
8226 SparseMatrix r; |
|
|
8227 |
|
|
8228 if ((a.rows() == b.rows()) && (a.cols() == b.cols())) |
|
|
8229 { |
|
5275
|
8230 octave_idx_type a_nr = a.rows (); |
|
|
8231 octave_idx_type a_nc = a.cols (); |
|
|
8232 |
|
|
8233 octave_idx_type b_nr = b.rows (); |
|
|
8234 octave_idx_type b_nc = b.cols (); |
|
5164
|
8235 |
|
|
8236 if (a_nr != b_nr || a_nc != b_nc) |
|
|
8237 gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc); |
|
|
8238 else |
|
|
8239 { |
|
5681
|
8240 r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ())); |
|
5164
|
8241 |
|
5275
|
8242 octave_idx_type jx = 0; |
|
5164
|
8243 r.cidx (0) = 0; |
|
5275
|
8244 for (octave_idx_type i = 0 ; i < a_nc ; i++) |
|
5164
|
8245 { |
|
5275
|
8246 octave_idx_type ja = a.cidx(i); |
|
|
8247 octave_idx_type ja_max = a.cidx(i+1); |
|
5164
|
8248 bool ja_lt_max= ja < ja_max; |
|
|
8249 |
|
5275
|
8250 octave_idx_type jb = b.cidx(i); |
|
|
8251 octave_idx_type jb_max = b.cidx(i+1); |
|
5164
|
8252 bool jb_lt_max = jb < jb_max; |
|
|
8253 |
|
|
8254 while (ja_lt_max || jb_lt_max ) |
|
|
8255 { |
|
|
8256 OCTAVE_QUIT; |
|
|
8257 if ((! jb_lt_max) || |
|
|
8258 (ja_lt_max && (a.ridx(ja) < b.ridx(jb)))) |
|
|
8259 { |
|
|
8260 double tmp = xmax (a.data(ja), 0.); |
|
|
8261 if (tmp != 0.) |
|
|
8262 { |
|
|
8263 r.ridx(jx) = a.ridx(ja); |
|
|
8264 r.data(jx) = tmp; |
|
|
8265 jx++; |
|
|
8266 } |
|
|
8267 ja++; |
|
|
8268 ja_lt_max= ja < ja_max; |
|
|
8269 } |
|
|
8270 else if (( !ja_lt_max ) || |
|
|
8271 (jb_lt_max && (b.ridx(jb) < a.ridx(ja)) ) ) |
|
|
8272 { |
|
|
8273 double tmp = xmax (0., b.data(jb)); |
|
|
8274 if (tmp != 0.) |
|
|
8275 { |
|
|
8276 r.ridx(jx) = b.ridx(jb); |
|
|
8277 r.data(jx) = tmp; |
|
|
8278 jx++; |
|
|
8279 } |
|
|
8280 jb++; |
|
|
8281 jb_lt_max= jb < jb_max; |
|
|
8282 } |
|
|
8283 else |
|
|
8284 { |
|
|
8285 double tmp = xmax (a.data(ja), b.data(jb)); |
|
|
8286 if (tmp != 0.) |
|
|
8287 { |
|
|
8288 r.data(jx) = tmp; |
|
|
8289 r.ridx(jx) = a.ridx(ja); |
|
|
8290 jx++; |
|
|
8291 } |
|
|
8292 ja++; |
|
|
8293 ja_lt_max= ja < ja_max; |
|
|
8294 jb++; |
|
|
8295 jb_lt_max= jb < jb_max; |
|
|
8296 } |
|
|
8297 } |
|
|
8298 r.cidx(i+1) = jx; |
|
|
8299 } |
|
|
8300 |
|
|
8301 r.maybe_compress (); |
|
|
8302 } |
|
|
8303 } |
|
|
8304 else |
|
|
8305 (*current_liboctave_error_handler) ("matrix size mismatch"); |
|
|
8306 |
|
|
8307 return r; |
|
|
8308 } |
|
|
8309 |
|
|
8310 SPARSE_SMS_CMP_OPS (SparseMatrix, 0.0, , double, 0.0, ) |
|
|
8311 SPARSE_SMS_BOOL_OPS (SparseMatrix, double, 0.0) |
|
|
8312 |
|
|
8313 SPARSE_SSM_CMP_OPS (double, 0.0, , SparseMatrix, 0.0, ) |
|
|
8314 SPARSE_SSM_BOOL_OPS (double, SparseMatrix, 0.0) |
|
|
8315 |
|
|
8316 SPARSE_SMSM_CMP_OPS (SparseMatrix, 0.0, , SparseMatrix, 0.0, ) |
|
|
8317 SPARSE_SMSM_BOOL_OPS (SparseMatrix, SparseMatrix, 0.0) |
|
|
8318 |
|
|
8319 /* |
|
|
8320 ;;; Local Variables: *** |
|
|
8321 ;;; mode: C++ *** |
|
|
8322 ;;; End: *** |
|
|
8323 */ |
