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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 <cassert> |
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28 |
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29 #include "Array-util.h" |
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30 #include "oct-cmplx.h" |
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31 #include "quit.h" |
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32 #include "error.h" |
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33 |
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34 #include "dSparse.h" |
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35 #include "CSparse.h" |
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36 #include "oct-spparms.h" |
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37 #include "sparse-xdiv.h" |
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38 |
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39 static inline bool |
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40 result_ok (octave_idx_type info) |
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41 { |
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42 #ifdef HAVE_LSSOLVE |
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43 return (info != -2 && info != -1); |
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44 #else |
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45 // If the matrix is singular, who cares as we don't have QR based solver yet |
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46 return (info != -1); |
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47 #endif |
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48 } |
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49 |
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50 static void |
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51 solve_singularity_warning (double rcond) |
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52 { |
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53 warning ("matrix singular to machine precision, rcond = %g", rcond); |
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54 warning ("attempting to find minimum norm solution"); |
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55 } |
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56 |
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57 template <class T1, class T2> |
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58 bool |
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59 mx_leftdiv_conform (const T1& a, const T2& b) |
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60 { |
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61 octave_idx_type a_nr = a.rows (); |
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62 octave_idx_type b_nr = b.rows (); |
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63 |
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64 if (a_nr != b_nr) |
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65 { |
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66 octave_idx_type a_nc = a.cols (); |
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67 octave_idx_type b_nc = b.cols (); |
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68 |
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69 gripe_nonconformant ("operator \\", a_nr, a_nc, b_nr, b_nc); |
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70 return false; |
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71 } |
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72 |
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73 return true; |
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74 } |
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75 |
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76 #define INSTANTIATE_MX_LEFTDIV_CONFORM(T1, T2) \ |
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77 template bool mx_leftdiv_conform (const T1&, const T2&) |
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78 |
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79 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, SparseMatrix); |
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80 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, SparseComplexMatrix); |
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81 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, SparseMatrix); |
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82 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, SparseComplexMatrix); |
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83 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, Matrix); |
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84 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseMatrix, ComplexMatrix); |
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85 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, Matrix); |
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86 INSTANTIATE_MX_LEFTDIV_CONFORM (SparseComplexMatrix, ComplexMatrix); |
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87 |
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88 template <class T1, class T2> |
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89 bool |
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90 mx_div_conform (const T1& a, const T2& b) |
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91 { |
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92 octave_idx_type a_nc = a.cols (); |
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93 octave_idx_type b_nc = b.cols (); |
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94 |
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95 if (a_nc != b_nc) |
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96 { |
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97 octave_idx_type a_nr = a.rows (); |
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98 octave_idx_type b_nr = b.rows (); |
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99 |
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100 gripe_nonconformant ("operator /", a_nr, a_nc, b_nr, b_nc); |
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101 return false; |
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102 } |
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103 |
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104 return true; |
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105 } |
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106 |
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107 #define INSTANTIATE_MX_DIV_CONFORM(T1, T2) \ |
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108 template bool mx_div_conform (const T1&, const T2&) |
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109 |
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110 INSTANTIATE_MX_DIV_CONFORM (SparseMatrix, SparseMatrix); |
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111 INSTANTIATE_MX_DIV_CONFORM (SparseMatrix, SparseComplexMatrix); |
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112 INSTANTIATE_MX_DIV_CONFORM (SparseComplexMatrix, SparseMatrix); |
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113 INSTANTIATE_MX_DIV_CONFORM (SparseComplexMatrix, SparseComplexMatrix); |
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114 INSTANTIATE_MX_DIV_CONFORM (Matrix, SparseMatrix); |
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115 INSTANTIATE_MX_DIV_CONFORM (Matrix, SparseComplexMatrix); |
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116 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, SparseMatrix); |
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117 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, SparseComplexMatrix); |
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118 |
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119 // Right division functions. |
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120 // |
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121 // op2 / op1: m cm sm scm |
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122 // +-- +---+----+----+----+ |
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123 // sparse matrix | 1 | 3 | 5 | 7 | |
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124 // +---+----+----+----+ |
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125 // sparse complex_matrix | 2 | 4 | 6 | 8 | |
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126 // +---+----+----+----+ |
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127 |
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128 // -*- 1 -*- |
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129 Matrix |
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130 xdiv (const Matrix& a, const SparseMatrix& b) |
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131 { |
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132 if (! mx_div_conform (a, b)) |
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133 return Matrix (); |
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134 |
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135 Matrix atmp = a.transpose (); |
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136 SparseMatrix btmp = b.transpose (); |
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137 |
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138 octave_idx_type info; |
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139 if (btmp.rows () == btmp.columns ()) |
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140 { |
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141 double rcond = 0.0; |
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142 |
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143 Matrix result = btmp.solve (atmp, info, rcond, |
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144 solve_singularity_warning); |
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145 |
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146 if (result_ok (info)) |
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147 return Matrix (result.transpose ()); |
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148 } |
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149 |
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150 octave_idx_type rank; |
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151 Matrix result = btmp.lssolve (atmp, info, rank); |
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152 |
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153 return result.transpose (); |
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154 } |
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155 |
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156 // -*- 2 -*- |
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157 ComplexMatrix |
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158 xdiv (const Matrix& a, const SparseComplexMatrix& b) |
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159 { |
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160 if (! mx_div_conform (a, b)) |
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161 return ComplexMatrix (); |
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162 |
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163 Matrix atmp = a.transpose (); |
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164 SparseComplexMatrix btmp = b.hermitian (); |
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165 |
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166 octave_idx_type info; |
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167 if (btmp.rows () == btmp.columns ()) |
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168 { |
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169 double rcond = 0.0; |
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170 |
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171 ComplexMatrix result |
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172 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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173 |
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174 if (result_ok (info)) |
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175 return result.hermitian (); |
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176 } |
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177 |
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178 octave_idx_type rank; |
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179 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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180 |
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181 return result.hermitian (); |
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182 } |
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183 |
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184 // -*- 3 -*- |
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185 ComplexMatrix |
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186 xdiv (const ComplexMatrix& a, const SparseMatrix& b) |
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187 { |
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188 if (! mx_div_conform (a, b)) |
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189 return ComplexMatrix (); |
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190 |
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191 ComplexMatrix atmp = a.hermitian (); |
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192 SparseMatrix btmp = b.transpose (); |
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193 |
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194 octave_idx_type info; |
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195 if (btmp.rows () == btmp.columns ()) |
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196 { |
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197 double rcond = 0.0; |
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198 |
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199 ComplexMatrix result |
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200 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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201 |
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202 if (result_ok (info)) |
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203 return result.hermitian (); |
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204 } |
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205 |
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206 octave_idx_type rank; |
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207 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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208 |
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209 return result.hermitian (); |
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210 } |
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211 |
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212 // -*- 4 -*- |
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213 ComplexMatrix |
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214 xdiv (const ComplexMatrix& a, const SparseComplexMatrix& b) |
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215 { |
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216 if (! mx_div_conform (a, b)) |
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217 return ComplexMatrix (); |
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218 |
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219 ComplexMatrix atmp = a.hermitian (); |
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220 SparseComplexMatrix btmp = b.hermitian (); |
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221 |
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222 octave_idx_type info; |
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223 if (btmp.rows () == btmp.columns ()) |
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224 { |
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225 double rcond = 0.0; |
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226 |
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227 ComplexMatrix result |
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228 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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229 |
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230 if (result_ok (info)) |
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231 return result.hermitian (); |
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232 } |
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233 |
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234 octave_idx_type rank; |
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235 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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236 |
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237 return result.hermitian (); |
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238 } |
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239 |
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240 // -*- 5 -*- |
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241 SparseMatrix |
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242 xdiv (const SparseMatrix& a, const SparseMatrix& b) |
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243 { |
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244 if (! mx_div_conform (a, b)) |
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245 return SparseMatrix (); |
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246 |
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247 SparseMatrix atmp = a.transpose (); |
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248 SparseMatrix btmp = b.transpose (); |
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249 |
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250 octave_idx_type info; |
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251 if (btmp.rows () == btmp.columns ()) |
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252 { |
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253 double rcond = 0.0; |
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254 |
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255 SparseMatrix result = btmp.solve (atmp, info, rcond, |
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256 solve_singularity_warning); |
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257 |
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258 if (result_ok (info)) |
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259 return SparseMatrix (result.transpose ()); |
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260 } |
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261 |
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262 octave_idx_type rank; |
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263 SparseMatrix result = btmp.lssolve (atmp, info, rank); |
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264 |
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265 return result.transpose (); |
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266 } |
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267 |
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268 // -*- 6 -*- |
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269 SparseComplexMatrix |
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270 xdiv (const SparseMatrix& a, const SparseComplexMatrix& b) |
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271 { |
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272 if (! mx_div_conform (a, b)) |
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273 return SparseComplexMatrix (); |
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274 |
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275 SparseMatrix atmp = a.transpose (); |
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276 SparseComplexMatrix btmp = b.hermitian (); |
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277 |
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278 octave_idx_type info; |
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279 if (btmp.rows () == btmp.columns ()) |
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280 { |
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281 double rcond = 0.0; |
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282 |
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283 SparseComplexMatrix result |
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284 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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285 |
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286 if (result_ok (info)) |
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287 return result.hermitian (); |
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288 } |
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289 |
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290 octave_idx_type rank; |
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291 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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292 |
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293 return result.hermitian (); |
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294 } |
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295 |
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296 // -*- 7 -*- |
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297 SparseComplexMatrix |
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298 xdiv (const SparseComplexMatrix& a, const SparseMatrix& b) |
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299 { |
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300 if (! mx_div_conform (a, b)) |
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301 return SparseComplexMatrix (); |
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302 |
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303 SparseComplexMatrix atmp = a.hermitian (); |
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304 SparseMatrix btmp = b.transpose (); |
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305 |
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306 octave_idx_type info; |
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307 if (btmp.rows () == btmp.columns ()) |
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308 { |
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309 double rcond = 0.0; |
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310 |
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311 SparseComplexMatrix result |
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312 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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313 |
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314 if (result_ok (info)) |
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315 return result.hermitian (); |
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316 } |
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317 |
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318 octave_idx_type rank; |
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319 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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320 |
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321 return result.hermitian (); |
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322 } |
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323 |
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324 // -*- 8 -*- |
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325 SparseComplexMatrix |
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326 xdiv (const SparseComplexMatrix& a, const SparseComplexMatrix& b) |
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327 { |
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328 if (! mx_div_conform (a, b)) |
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329 return SparseComplexMatrix (); |
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330 |
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331 SparseComplexMatrix atmp = a.hermitian (); |
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332 SparseComplexMatrix btmp = b.hermitian (); |
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333 |
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334 octave_idx_type info; |
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335 if (btmp.rows () == btmp.columns ()) |
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336 { |
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337 double rcond = 0.0; |
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338 |
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339 SparseComplexMatrix result |
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340 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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341 |
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342 if (result_ok (info)) |
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343 return result.hermitian (); |
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344 } |
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345 |
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346 octave_idx_type rank; |
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347 SparseComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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348 |
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349 return result.hermitian (); |
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350 } |
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351 |
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352 // Funny element by element division operations. |
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353 // |
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354 // op2 \ op1: s cs |
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355 // +-- +---+----+ |
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356 // matrix | 1 | 3 | |
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357 // +---+----+ |
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358 // complex_matrix | 2 | 4 | |
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359 // +---+----+ |
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360 |
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361 Matrix |
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362 x_el_div (double a, const SparseMatrix& b) |
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363 { |
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364 octave_idx_type nr = b.rows (); |
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365 octave_idx_type nc = b.cols (); |
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366 |
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367 Matrix result; |
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368 if (a == 0.) |
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369 result = Matrix (nr, nc, octave_NaN); |
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370 else if (a > 0.) |
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371 result = Matrix (nr, nc, octave_Inf); |
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372 else |
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373 result = Matrix (nr, nc, -octave_Inf); |
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374 |
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375 |
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376 for (octave_idx_type j = 0; j < nc; j++) |
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377 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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378 { |
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379 OCTAVE_QUIT; |
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380 result.elem (b.ridx(i), j) = a / b.data (i); |
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381 } |
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382 |
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383 return result; |
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384 } |
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385 |
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386 ComplexMatrix |
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387 x_el_div (double a, const SparseComplexMatrix& b) |
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388 { |
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389 octave_idx_type nr = b.rows (); |
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390 octave_idx_type nc = b.cols (); |
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391 |
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392 ComplexMatrix result (nr, nc, Complex(octave_NaN, octave_NaN)); |
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393 |
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394 for (octave_idx_type j = 0; j < nc; j++) |
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395 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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396 { |
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397 OCTAVE_QUIT; |
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398 result.elem (b.ridx(i), j) = a / b.data (i); |
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399 } |
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400 |
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401 return result; |
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402 } |
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403 |
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404 ComplexMatrix |
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405 x_el_div (const Complex a, const SparseMatrix& b) |
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406 { |
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407 octave_idx_type nr = b.rows (); |
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408 octave_idx_type nc = b.cols (); |
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409 |
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410 ComplexMatrix result (nr, nc, (a / 0.0)); |
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411 |
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412 for (octave_idx_type j = 0; j < nc; j++) |
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413 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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414 { |
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415 OCTAVE_QUIT; |
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416 result.elem (b.ridx(i), j) = a / b.data (i); |
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417 } |
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418 |
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419 return result; |
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420 } |
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421 |
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422 ComplexMatrix |
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423 x_el_div (const Complex a, const SparseComplexMatrix& b) |
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424 { |
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425 octave_idx_type nr = b.rows (); |
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426 octave_idx_type nc = b.cols (); |
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427 |
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428 ComplexMatrix result (nr, nc, (a / 0.0)); |
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429 |
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430 for (octave_idx_type j = 0; j < nc; j++) |
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431 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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432 { |
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433 OCTAVE_QUIT; |
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434 result.elem (b.ridx(i), j) = a / b.data (i); |
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435 } |
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436 |
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437 return result; |
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438 } |
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439 |
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440 // Left division functions. |
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441 // |
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442 // op2 \ op1: m cm |
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443 // +-- +---+----+ |
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444 // matrix | 1 | 5 | |
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445 // +---+----+ |
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446 // complex_matrix | 2 | 6 | |
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447 // +---+----+ |
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448 // sparse matrix | 3 | 7 | |
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449 // +---+----+ |
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450 // sparse complex_matrix | 4 | 8 | |
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451 // +---+----+ |
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452 |
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453 // -*- 1 -*- |
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454 Matrix |
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455 xleftdiv (const SparseMatrix& a, const Matrix& b) |
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456 { |
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457 if (! mx_leftdiv_conform (a, b)) |
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458 return Matrix (); |
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459 |
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460 octave_idx_type info; |
|
5164
|
461 if (a.rows () == a.columns ()) |
|
|
462 { |
|
|
463 double rcond = 0.0; |
|
|
464 |
|
|
465 Matrix result |
|
|
466 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
467 |
|
|
468 if (result_ok (info)) |
|
|
469 return result; |
|
|
470 } |
|
|
471 |
|
5275
|
472 octave_idx_type rank; |
|
5164
|
473 return a.lssolve (b, info, rank); |
|
|
474 } |
|
|
475 |
|
|
476 // -*- 2 -*- |
|
|
477 ComplexMatrix |
|
|
478 xleftdiv (const SparseMatrix& a, const ComplexMatrix& b) |
|
|
479 { |
|
|
480 if (! mx_leftdiv_conform (a, b)) |
|
|
481 return ComplexMatrix (); |
|
|
482 |
|
5275
|
483 octave_idx_type info; |
|
5164
|
484 if (a.rows () == a.columns ()) |
|
|
485 { |
|
|
486 double rcond = 0.0; |
|
|
487 |
|
|
488 ComplexMatrix result |
|
|
489 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
490 |
|
|
491 if (result_ok (info)) |
|
|
492 return result; |
|
|
493 } |
|
|
494 |
|
5275
|
495 octave_idx_type rank; |
|
5164
|
496 return a.lssolve (b, info, rank); |
|
|
497 } |
|
|
498 |
|
|
499 // -*- 3 -*- |
|
|
500 SparseMatrix |
|
|
501 xleftdiv (const SparseMatrix& a, const SparseMatrix& b) |
|
|
502 { |
|
|
503 if (! mx_leftdiv_conform (a, b)) |
|
|
504 return SparseMatrix (); |
|
|
505 |
|
5275
|
506 octave_idx_type info; |
|
5164
|
507 if (a.rows () == a.columns ()) |
|
|
508 { |
|
|
509 double rcond = 0.0; |
|
|
510 |
|
|
511 SparseMatrix result |
|
|
512 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
513 |
|
|
514 if (result_ok (info)) |
|
|
515 return result; |
|
|
516 } |
|
|
517 |
|
5275
|
518 octave_idx_type rank; |
|
5164
|
519 return a.lssolve (b, info, rank); |
|
|
520 } |
|
|
521 |
|
|
522 // -*- 4 -*- |
|
|
523 SparseComplexMatrix |
|
|
524 xleftdiv (const SparseMatrix& a, const SparseComplexMatrix& b) |
|
|
525 { |
|
|
526 if (! mx_leftdiv_conform (a, b)) |
|
|
527 return SparseComplexMatrix (); |
|
|
528 |
|
5275
|
529 octave_idx_type info; |
|
5164
|
530 if (a.rows () == a.columns ()) |
|
|
531 { |
|
|
532 double rcond = 0.0; |
|
|
533 |
|
|
534 SparseComplexMatrix result |
|
|
535 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
536 |
|
|
537 if (result_ok (info)) |
|
|
538 return result; |
|
|
539 } |
|
|
540 |
|
5275
|
541 octave_idx_type rank; |
|
5164
|
542 return a.lssolve (b, info, rank); |
|
|
543 } |
|
|
544 |
|
|
545 // -*- 5 -*- |
|
|
546 ComplexMatrix |
|
|
547 xleftdiv (const SparseComplexMatrix& a, const Matrix& b) |
|
|
548 { |
|
|
549 if (! mx_leftdiv_conform (a, b)) |
|
|
550 return ComplexMatrix (); |
|
|
551 |
|
5275
|
552 octave_idx_type info; |
|
5164
|
553 if (a.rows () == a.columns ()) |
|
|
554 { |
|
|
555 double rcond = 0.0; |
|
|
556 |
|
|
557 ComplexMatrix result |
|
|
558 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
559 |
|
|
560 if (result_ok (info)) |
|
|
561 return result; |
|
|
562 } |
|
|
563 |
|
5275
|
564 octave_idx_type rank; |
|
5164
|
565 return a.lssolve (b, info, rank); |
|
|
566 } |
|
|
567 |
|
|
568 // -*- 6 -*- |
|
|
569 ComplexMatrix |
|
|
570 xleftdiv (const SparseComplexMatrix& a, const ComplexMatrix& b) |
|
|
571 { |
|
|
572 if (! mx_leftdiv_conform (a, b)) |
|
|
573 return ComplexMatrix (); |
|
|
574 |
|
5275
|
575 octave_idx_type info; |
|
5164
|
576 if (a.rows () == a.columns ()) |
|
|
577 { |
|
|
578 double rcond = 0.0; |
|
|
579 |
|
|
580 ComplexMatrix result |
|
|
581 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
582 |
|
|
583 if (result_ok (info)) |
|
|
584 return result; |
|
|
585 } |
|
|
586 |
|
5275
|
587 octave_idx_type rank; |
|
5164
|
588 return a.lssolve (b, info, rank); |
|
|
589 } |
|
|
590 |
|
|
591 // -*- 7 -*- |
|
|
592 SparseComplexMatrix |
|
|
593 xleftdiv (const SparseComplexMatrix& a, const SparseMatrix& b) |
|
|
594 { |
|
|
595 if (! mx_leftdiv_conform (a, b)) |
|
|
596 return SparseComplexMatrix (); |
|
|
597 |
|
5275
|
598 octave_idx_type info; |
|
5164
|
599 if (a.rows () == a.columns ()) |
|
|
600 { |
|
|
601 double rcond = 0.0; |
|
|
602 |
|
|
603 SparseComplexMatrix result |
|
|
604 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
605 |
|
|
606 if (result_ok (info)) |
|
|
607 return result; |
|
|
608 } |
|
|
609 |
|
5275
|
610 octave_idx_type rank; |
|
5164
|
611 return a.lssolve (b, info, rank); |
|
|
612 } |
|
|
613 |
|
|
614 // -*- 8 -*- |
|
|
615 SparseComplexMatrix |
|
|
616 xleftdiv (const SparseComplexMatrix& a, const SparseComplexMatrix& b) |
|
|
617 { |
|
|
618 if (! mx_leftdiv_conform (a, b)) |
|
|
619 return SparseComplexMatrix (); |
|
|
620 |
|
5275
|
621 octave_idx_type info; |
|
5164
|
622 if (a.rows () == a.columns ()) |
|
|
623 { |
|
|
624 double rcond = 0.0; |
|
|
625 |
|
|
626 SparseComplexMatrix result |
|
|
627 = a.solve (b, info, rcond, solve_singularity_warning); |
|
|
628 |
|
|
629 if (result_ok (info)) |
|
|
630 return result; |
|
|
631 } |
|
|
632 |
|
5275
|
633 octave_idx_type rank; |
|
5164
|
634 return a.lssolve (b, info, rank); |
|
|
635 } |
|
|
636 |
|
|
637 /* |
|
|
638 ;;; Local Variables: *** |
|
|
639 ;;; mode: C++ *** |
|
|
640 ;;; End: *** |
|
|
641 */ |
