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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 Free |
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18 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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19 |
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20 */ |
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21 |
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22 #ifdef HAVE_CONFIG_H |
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23 #include <config.h> |
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24 #endif |
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25 |
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26 #include <cassert> |
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27 |
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28 #include "Array-util.h" |
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29 #include "oct-cmplx.h" |
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30 #include "quit.h" |
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31 #include "error.h" |
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32 |
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33 #include "dSparse.h" |
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34 #include "CSparse.h" |
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35 #include "oct-spparms.h" |
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36 #include "sparse-xdiv.h" |
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37 |
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38 static inline bool |
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39 result_ok (octave_idx_type info) |
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40 { |
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41 #ifdef HAVE_LSSOLVE |
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42 return (info != -2 && info != -1); |
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43 #else |
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44 // If the matrix is singular, who cares as we don't have QR based solver yet |
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45 return (info != -1); |
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46 #endif |
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47 } |
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48 |
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49 static void |
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50 solve_singularity_warning (double rcond) |
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51 { |
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52 warning ("matrix singular to machine precision, rcond = %g", rcond); |
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53 warning ("attempting to find minimum norm solution"); |
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54 } |
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55 |
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56 template <class T1, class T2> |
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57 bool |
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58 mx_leftdiv_conform (const T1& a, const T2& b) |
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59 { |
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60 octave_idx_type a_nr = a.rows (); |
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61 octave_idx_type b_nr = b.rows (); |
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62 |
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63 if (a_nr != b_nr) |
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64 { |
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65 octave_idx_type a_nc = a.cols (); |
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66 octave_idx_type b_nc = b.cols (); |
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67 |
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68 gripe_nonconformant ("operator \\", a_nr, a_nc, b_nr, b_nc); |
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69 return false; |
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70 } |
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71 |
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72 return true; |
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73 } |
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74 |
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75 #define INSTANTIATE_MX_LEFTDIV_CONFORM(T1, T2) \ |
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76 template bool mx_leftdiv_conform (const T1&, const T2&) |
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77 |
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78 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, SparseMatrix); |
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79 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, SparseComplexMatrix); |
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80 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, SparseMatrix); |
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81 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, SparseComplexMatrix); |
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82 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, Matrix); |
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83 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, ComplexMatrix); |
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84 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, Matrix); |
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85 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, ComplexMatrix); |
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86 |
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87 template <class T1, class T2> |
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88 bool |
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89 mx_div_conform (const T1& a, const T2& b) |
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90 { |
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91 octave_idx_type a_nc = a.cols (); |
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92 octave_idx_type b_nc = b.cols (); |
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93 |
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94 if (a_nc != b_nc) |
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95 { |
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96 octave_idx_type a_nr = a.rows (); |
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97 octave_idx_type b_nr = b.rows (); |
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98 |
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99 gripe_nonconformant ("operator /", a_nr, a_nc, b_nr, b_nc); |
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100 return false; |
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101 } |
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102 |
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103 return true; |
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104 } |
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105 |
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106 #define INSTANTIATE_MX_DIV_CONFORM(T1, T2) \ |
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107 template bool mx_div_conform (const T1&, const T2&) |
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108 |
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109 INSTANTIATE_MX_DIV_CONFORM (SparseMatrix, SparseMatrix); |
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110 INSTANTIATE_MX_DIV_CONFORM (SparseMatrix, SparseComplexMatrix); |
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111 INSTANTIATE_MX_DIV_CONFORM (SparseComplexMatrix, SparseMatrix); |
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112 INSTANTIATE_MX_DIV_CONFORM (SparseComplexMatrix, SparseComplexMatrix); |
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113 INSTANTIATE_MX_DIV_CONFORM (Matrix, SparseMatrix); |
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114 INSTANTIATE_MX_DIV_CONFORM (Matrix, SparseComplexMatrix); |
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115 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, SparseMatrix); |
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116 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, SparseComplexMatrix); |
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117 |
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118 // Right division functions. |
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119 // |
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120 // op2 / op1: m cm sm scm |
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121 // +-- +---+----+----+----+ |
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122 // sparse matrix | 1 | 3 | 5 | 7 | |
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123 // +---+----+----+----+ |
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124 // sparse complex_matrix | 2 | 4 | 6 | 8 | |
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125 // +---+----+----+----+ |
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126 |
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127 // -*- 1 -*- |
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128 Matrix |
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129 xdiv (const Matrix& a, const SparseMatrix& b) |
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130 { |
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131 if (! mx_div_conform (a, b)) |
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132 return Matrix (); |
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133 |
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134 Matrix atmp = a.transpose (); |
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135 SparseMatrix btmp = b.transpose (); |
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136 |
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137 octave_idx_type info; |
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138 if (btmp.rows () == btmp.columns ()) |
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139 { |
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140 double rcond = 0.0; |
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141 |
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142 Matrix result = btmp.solve (atmp, info, rcond, |
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143 solve_singularity_warning); |
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144 |
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145 if (result_ok (info)) |
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146 return Matrix (result.transpose ()); |
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147 } |
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148 |
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149 octave_idx_type rank; |
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150 Matrix result = btmp.lssolve (atmp, info, rank); |
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151 |
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152 return result.transpose (); |
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153 } |
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154 |
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155 // -*- 2 -*- |
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156 ComplexMatrix |
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157 xdiv (const Matrix& a, const SparseComplexMatrix& b) |
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158 { |
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159 if (! mx_div_conform (a, b)) |
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160 return ComplexMatrix (); |
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161 |
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162 Matrix atmp = a.transpose (); |
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163 SparseComplexMatrix btmp = b.hermitian (); |
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164 |
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165 octave_idx_type info; |
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166 if (btmp.rows () == btmp.columns ()) |
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167 { |
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168 double rcond = 0.0; |
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169 |
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170 ComplexMatrix result |
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171 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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172 |
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173 if (result_ok (info)) |
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174 return result.hermitian (); |
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175 } |
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176 |
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177 octave_idx_type rank; |
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178 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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179 |
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180 return result.hermitian (); |
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181 } |
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182 |
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183 // -*- 3 -*- |
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184 ComplexMatrix |
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185 xdiv (const ComplexMatrix& a, const SparseMatrix& b) |
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186 { |
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187 if (! mx_div_conform (a, b)) |
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188 return ComplexMatrix (); |
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189 |
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190 ComplexMatrix atmp = a.hermitian (); |
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191 SparseMatrix btmp = b.transpose (); |
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192 |
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193 octave_idx_type info; |
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194 if (btmp.rows () == btmp.columns ()) |
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195 { |
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196 double rcond = 0.0; |
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197 |
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198 ComplexMatrix result |
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199 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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200 |
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201 if (result_ok (info)) |
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202 return result.hermitian (); |
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203 } |
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204 |
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205 octave_idx_type rank; |
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206 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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207 |
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208 return result.hermitian (); |
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209 } |
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210 |
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211 // -*- 4 -*- |
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212 ComplexMatrix |
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213 xdiv (const ComplexMatrix& a, const SparseComplexMatrix& b) |
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214 { |
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215 if (! mx_div_conform (a, b)) |
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216 return ComplexMatrix (); |
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217 |
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218 ComplexMatrix atmp = a.hermitian (); |
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219 SparseComplexMatrix btmp = b.hermitian (); |
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220 |
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221 octave_idx_type info; |
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222 if (btmp.rows () == btmp.columns ()) |
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223 { |
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224 double rcond = 0.0; |
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225 |
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226 ComplexMatrix result |
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227 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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228 |
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229 if (result_ok (info)) |
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230 return result.hermitian (); |
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231 } |
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232 |
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233 octave_idx_type rank; |
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234 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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235 |
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236 return result.hermitian (); |
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237 } |
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238 |
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239 // -*- 5 -*- |
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240 SparseMatrix |
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241 xdiv (const SparseMatrix& a, const SparseMatrix& b) |
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242 { |
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243 if (! mx_div_conform (a, b)) |
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244 return SparseMatrix (); |
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245 |
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246 SparseMatrix atmp = a.transpose (); |
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247 SparseMatrix btmp = b.transpose (); |
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248 |
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249 octave_idx_type info; |
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250 if (btmp.rows () == btmp.columns ()) |
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251 { |
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252 double rcond = 0.0; |
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253 |
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254 SparseMatrix result = btmp.solve (atmp, info, rcond, |
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255 solve_singularity_warning); |
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256 |
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257 if (result_ok (info)) |
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258 return SparseMatrix (result.transpose ()); |
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259 } |
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260 |
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261 octave_idx_type rank; |
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262 SparseMatrix result = btmp.lssolve (atmp, info, rank); |
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263 |
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264 return result.transpose (); |
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265 } |
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266 |
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267 // -*- 6 -*- |
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268 SparseComplexMatrix |
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269 xdiv (const SparseMatrix& a, const SparseComplexMatrix& b) |
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270 { |
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271 if (! mx_div_conform (a, b)) |
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272 return SparseComplexMatrix (); |
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273 |
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274 SparseMatrix atmp = a.transpose (); |
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275 SparseComplexMatrix btmp = b.hermitian (); |
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276 |
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277 octave_idx_type info; |
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278 if (btmp.rows () == btmp.columns ()) |
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279 { |
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280 double rcond = 0.0; |
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281 |
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282 SparseComplexMatrix result |
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283 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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284 |
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285 if (result_ok (info)) |
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286 return result.hermitian (); |
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287 } |
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288 |
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289 octave_idx_type rank; |
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290 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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291 |
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292 return result.hermitian (); |
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293 } |
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294 |
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295 // -*- 7 -*- |
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296 SparseComplexMatrix |
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297 xdiv (const SparseComplexMatrix& a, const SparseMatrix& b) |
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298 { |
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299 if (! mx_div_conform (a, b)) |
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300 return SparseComplexMatrix (); |
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301 |
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302 SparseComplexMatrix atmp = a.hermitian (); |
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303 SparseMatrix btmp = b.transpose (); |
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304 |
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305 octave_idx_type info; |
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306 if (btmp.rows () == btmp.columns ()) |
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307 { |
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308 double rcond = 0.0; |
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309 |
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310 SparseComplexMatrix result |
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311 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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312 |
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313 if (result_ok (info)) |
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314 return result.hermitian (); |
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315 } |
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316 |
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317 octave_idx_type rank; |
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318 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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319 |
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320 return result.hermitian (); |
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321 } |
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322 |
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323 // -*- 8 -*- |
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324 SparseComplexMatrix |
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325 xdiv (const SparseComplexMatrix& a, const SparseComplexMatrix& b) |
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326 { |
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327 if (! mx_div_conform (a, b)) |
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328 return SparseComplexMatrix (); |
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329 |
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330 SparseComplexMatrix atmp = a.hermitian (); |
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331 SparseComplexMatrix btmp = b.hermitian (); |
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332 |
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333 octave_idx_type info; |
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334 if (btmp.rows () == btmp.columns ()) |
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335 { |
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336 double rcond = 0.0; |
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337 |
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338 SparseComplexMatrix result |
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339 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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340 |
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341 if (result_ok (info)) |
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342 return result.hermitian (); |
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343 } |
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344 |
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345 octave_idx_type rank; |
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346 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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347 |
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348 return result.hermitian (); |
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349 } |
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350 |
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351 // Funny element by element division operations. |
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352 // |
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353 // op2 \ op1: s cs |
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354 // +-- +---+----+ |
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355 // matrix | 1 | 3 | |
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356 // +---+----+ |
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357 // complex_matrix | 2 | 4 | |
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358 // +---+----+ |
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359 |
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360 Matrix |
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361 x_el_div (double a, const SparseMatrix& b) |
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362 { |
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363 octave_idx_type nr = b.rows (); |
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364 octave_idx_type nc = b.cols (); |
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365 |
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366 Matrix result; |
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367 if (a == 0.) |
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368 result = Matrix (nr, nc, octave_NaN); |
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369 else if (a > 0.) |
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370 result = Matrix (nr, nc, octave_Inf); |
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371 else |
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372 result = Matrix (nr, nc, -octave_Inf); |
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373 |
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374 |
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375 for (octave_idx_type j = 0; j < nc; j++) |
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376 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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377 { |
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378 OCTAVE_QUIT; |
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379 result.elem (b.ridx(i), j) = a / b.data (i); |
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380 } |
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381 |
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382 return result; |
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383 } |
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384 |
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385 ComplexMatrix |
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386 x_el_div (double a, const SparseComplexMatrix& b) |
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387 { |
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388 octave_idx_type nr = b.rows (); |
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389 octave_idx_type nc = b.cols (); |
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390 |
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391 ComplexMatrix result (nr, nc, Complex(octave_NaN, octave_NaN)); |
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392 |
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393 for (octave_idx_type j = 0; j < nc; j++) |
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394 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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395 { |
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396 OCTAVE_QUIT; |
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397 result.elem (b.ridx(i), j) = a / b.data (i); |
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398 } |
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399 |
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400 return result; |
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401 } |
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402 |
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403 ComplexMatrix |
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404 x_el_div (const Complex a, const SparseMatrix& b) |
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405 { |
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406 octave_idx_type nr = b.rows (); |
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407 octave_idx_type nc = b.cols (); |
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408 |
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409 ComplexMatrix result (nr, nc, (a / 0.0)); |
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410 |
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411 for (octave_idx_type j = 0; j < nc; j++) |
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412 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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413 { |
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414 OCTAVE_QUIT; |
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415 result.elem (b.ridx(i), j) = a / b.data (i); |
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416 } |
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417 |
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418 return result; |
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419 } |
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420 |
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421 ComplexMatrix |
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422 x_el_div (const Complex a, const SparseComplexMatrix& b) |
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423 { |
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424 octave_idx_type nr = b.rows (); |
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425 octave_idx_type nc = b.cols (); |
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426 |
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427 ComplexMatrix result (nr, nc, (a / 0.0)); |
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428 |
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429 for (octave_idx_type j = 0; j < nc; j++) |
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430 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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431 { |
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432 OCTAVE_QUIT; |
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433 result.elem (b.ridx(i), j) = a / b.data (i); |
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434 } |
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435 |
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436 return result; |
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437 } |
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438 |
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439 // Left division functions. |
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440 // |
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441 // op2 \ op1: m cm |
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442 // +-- +---+----+ |
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443 // matrix | 1 | 5 | |
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444 // +---+----+ |
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445 // complex_matrix | 2 | 6 | |
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446 // +---+----+ |
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447 // sparse matrix | 3 | 7 | |
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448 // +---+----+ |
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449 // sparse complex_matrix | 4 | 8 | |
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450 // +---+----+ |
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451 |
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452 // -*- 1 -*- |
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453 Matrix |
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454 xleftdiv (const SparseMatrix& a, const Matrix& b) |
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455 { |
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456 if (! mx_leftdiv_conform (a, b)) |
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457 return Matrix (); |
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458 |
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459 octave_idx_type info; |
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5164
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460 if (a.rows () == a.columns ()) |
|
|
461 { |
|
|
462 double rcond = 0.0; |
|
|
463 |
|
|
464 Matrix result |
|
|
465 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
466 |
|
|
467 if (result_ok (info)) |
|
|
468 return result; |
|
|
469 } |
|
|
470 |
|
5275
|
471 octave_idx_type rank; |
|
5164
|
472 return a.lssolve (b, info, rank); |
|
|
473 } |
|
|
474 |
|
|
475 // -*- 2 -*- |
|
|
476 ComplexMatrix |
|
|
477 xleftdiv (const SparseMatrix& a, const ComplexMatrix& b) |
|
|
478 { |
|
|
479 if (! mx_leftdiv_conform (a, b)) |
|
|
480 return ComplexMatrix (); |
|
|
481 |
|
5275
|
482 octave_idx_type info; |
|
5164
|
483 if (a.rows () == a.columns ()) |
|
|
484 { |
|
|
485 double rcond = 0.0; |
|
|
486 |
|
|
487 ComplexMatrix result |
|
|
488 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
489 |
|
|
490 if (result_ok (info)) |
|
|
491 return result; |
|
|
492 } |
|
|
493 |
|
5275
|
494 octave_idx_type rank; |
|
5164
|
495 return a.lssolve (b, info, rank); |
|
|
496 } |
|
|
497 |
|
|
498 // -*- 3 -*- |
|
|
499 SparseMatrix |
|
|
500 xleftdiv (const SparseMatrix& a, const SparseMatrix& b) |
|
|
501 { |
|
|
502 if (! mx_leftdiv_conform (a, b)) |
|
|
503 return SparseMatrix (); |
|
|
504 |
|
5275
|
505 octave_idx_type info; |
|
5164
|
506 if (a.rows () == a.columns ()) |
|
|
507 { |
|
|
508 double rcond = 0.0; |
|
|
509 |
|
|
510 SparseMatrix result |
|
|
511 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
512 |
|
|
513 if (result_ok (info)) |
|
|
514 return result; |
|
|
515 } |
|
|
516 |
|
5275
|
517 octave_idx_type rank; |
|
5164
|
518 return a.lssolve (b, info, rank); |
|
|
519 } |
|
|
520 |
|
|
521 // -*- 4 -*- |
|
|
522 SparseComplexMatrix |
|
|
523 xleftdiv (const SparseMatrix& a, const SparseComplexMatrix& b) |
|
|
524 { |
|
|
525 if (! mx_leftdiv_conform (a, b)) |
|
|
526 return SparseComplexMatrix (); |
|
|
527 |
|
5275
|
528 octave_idx_type info; |
|
5164
|
529 if (a.rows () == a.columns ()) |
|
|
530 { |
|
|
531 double rcond = 0.0; |
|
|
532 |
|
|
533 SparseComplexMatrix result |
|
|
534 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
535 |
|
|
536 if (result_ok (info)) |
|
|
537 return result; |
|
|
538 } |
|
|
539 |
|
5275
|
540 octave_idx_type rank; |
|
5164
|
541 return a.lssolve (b, info, rank); |
|
|
542 } |
|
|
543 |
|
|
544 // -*- 5 -*- |
|
|
545 ComplexMatrix |
|
|
546 xleftdiv (const SparseComplexMatrix& a, const Matrix& b) |
|
|
547 { |
|
|
548 if (! mx_leftdiv_conform (a, b)) |
|
|
549 return ComplexMatrix (); |
|
|
550 |
|
5275
|
551 octave_idx_type info; |
|
5164
|
552 if (a.rows () == a.columns ()) |
|
|
553 { |
|
|
554 double rcond = 0.0; |
|
|
555 |
|
|
556 ComplexMatrix result |
|
|
557 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
558 |
|
|
559 if (result_ok (info)) |
|
|
560 return result; |
|
|
561 } |
|
|
562 |
|
5275
|
563 octave_idx_type rank; |
|
5164
|
564 return a.lssolve (b, info, rank); |
|
|
565 } |
|
|
566 |
|
|
567 // -*- 6 -*- |
|
|
568 ComplexMatrix |
|
|
569 xleftdiv (const SparseComplexMatrix& a, const ComplexMatrix& b) |
|
|
570 { |
|
|
571 if (! mx_leftdiv_conform (a, b)) |
|
|
572 return ComplexMatrix (); |
|
|
573 |
|
5275
|
574 octave_idx_type info; |
|
5164
|
575 if (a.rows () == a.columns ()) |
|
|
576 { |
|
|
577 double rcond = 0.0; |
|
|
578 |
|
|
579 ComplexMatrix result |
|
|
580 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
581 |
|
|
582 if (result_ok (info)) |
|
|
583 return result; |
|
|
584 } |
|
|
585 |
|
5275
|
586 octave_idx_type rank; |
|
5164
|
587 return a.lssolve (b, info, rank); |
|
|
588 } |
|
|
589 |
|
|
590 // -*- 7 -*- |
|
|
591 SparseComplexMatrix |
|
|
592 xleftdiv (const SparseComplexMatrix& a, const SparseMatrix& b) |
|
|
593 { |
|
|
594 if (! mx_leftdiv_conform (a, b)) |
|
|
595 return SparseComplexMatrix (); |
|
|
596 |
|
5275
|
597 octave_idx_type info; |
|
5164
|
598 if (a.rows () == a.columns ()) |
|
|
599 { |
|
|
600 double rcond = 0.0; |
|
|
601 |
|
|
602 SparseComplexMatrix result |
|
|
603 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
604 |
|
|
605 if (result_ok (info)) |
|
|
606 return result; |
|
|
607 } |
|
|
608 |
|
5275
|
609 octave_idx_type rank; |
|
5164
|
610 return a.lssolve (b, info, rank); |
|
|
611 } |
|
|
612 |
|
|
613 // -*- 8 -*- |
|
|
614 SparseComplexMatrix |
|
|
615 xleftdiv (const SparseComplexMatrix& a, const SparseComplexMatrix& b) |
|
|
616 { |
|
|
617 if (! mx_leftdiv_conform (a, b)) |
|
|
618 return SparseComplexMatrix (); |
|
|
619 |
|
5275
|
620 octave_idx_type info; |
|
5164
|
621 if (a.rows () == a.columns ()) |
|
|
622 { |
|
|
623 double rcond = 0.0; |
|
|
624 |
|
|
625 SparseComplexMatrix result |
|
|
626 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
627 |
|
|
628 if (result_ok (info)) |
|
|
629 return result; |
|
|
630 } |
|
|
631 |
|
5275
|
632 octave_idx_type rank; |
|
5164
|
633 return a.lssolve (b, info, rank); |
|
|
634 } |
|
|
635 |
|
|
636 /* |
|
|
637 ;;; Local Variables: *** |
|
|
638 ;;; mode: C++ *** |
|
|
639 ;;; End: *** |
|
|
640 */ |
