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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, write to the Free |
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19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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240
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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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1343
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27 #include <cassert> |
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28 |
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1352
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29 #include "CMatrix.h" |
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453
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30 #include "dMatrix.h" |
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4543
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31 #include "CNDArray.h" |
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32 #include "dNDArray.h" |
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1651
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33 #include "oct-cmplx.h" |
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4153
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34 #include "quit.h" |
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35 |
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36 #include "error.h" |
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37 #include "xdiv.h" |
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38 |
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39 static inline bool |
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40 result_ok (int info) |
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41 { |
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42 assert (info != -1); |
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43 |
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44 return (info != -2); |
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45 } |
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46 |
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47 static void |
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48 solve_singularity_warning (double rcond) |
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49 { |
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50 warning ("matrix singular to machine precision, rcond = %g", rcond); |
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51 warning ("attempting to find minimum norm solution"); |
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52 } |
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53 |
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54 template <class T1, class T2> |
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55 bool |
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56 mx_leftdiv_conform (const T1& a, const T2& b) |
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57 { |
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2364
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58 int a_nr = a.rows (); |
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59 int b_nr = b.rows (); |
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60 |
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61 if (a_nr != b_nr) |
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62 { |
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63 int a_nc = a.cols (); |
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64 int b_nc = b.cols (); |
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65 |
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66 gripe_nonconformant ("operator \\", a_nr, a_nc, b_nr, b_nc); |
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67 return false; |
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68 } |
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69 |
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70 return true; |
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71 } |
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72 |
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73 #define INSTANTIATE_MX_LEFTDIV_CONFORM(T1, T2) \ |
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74 template bool mx_leftdiv_conform (const T1&, const T2&) |
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75 |
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76 INSTANTIATE_MX_LEFTDIV_CONFORM (Matrix, Matrix); |
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77 INSTANTIATE_MX_LEFTDIV_CONFORM (Matrix, ComplexMatrix); |
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78 INSTANTIATE_MX_LEFTDIV_CONFORM (ComplexMatrix, Matrix); |
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79 INSTANTIATE_MX_LEFTDIV_CONFORM (ComplexMatrix, ComplexMatrix); |
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80 |
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81 template <class T1, class T2> |
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82 bool |
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83 mx_div_conform (const T1& a, const T2& b) |
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84 { |
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85 int a_nc = a.cols (); |
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86 int b_nc = b.cols (); |
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87 |
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88 if (a_nc != b_nc) |
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89 { |
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90 int a_nr = a.rows (); |
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91 int b_nr = b.rows (); |
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92 |
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93 gripe_nonconformant ("operator /", a_nr, a_nc, b_nr, b_nc); |
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94 return false; |
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95 } |
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96 |
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97 return true; |
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98 } |
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99 |
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100 #define INSTANTIATE_MX_DIV_CONFORM(T1, T2) \ |
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101 template bool mx_div_conform (const T1&, const T2&) |
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102 |
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103 INSTANTIATE_MX_DIV_CONFORM (Matrix, Matrix); |
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104 INSTANTIATE_MX_DIV_CONFORM (Matrix, ComplexMatrix); |
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105 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, Matrix); |
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106 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, ComplexMatrix); |
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107 |
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767
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108 // Right division functions. |
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109 // |
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110 // op2 / op1: m cm |
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111 // +-- +---+----+ |
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112 // matrix | 1 | 3 | |
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113 // +---+----+ |
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114 // complex_matrix | 2 | 4 | |
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115 // +---+----+ |
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116 |
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767
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117 // -*- 1 -*- |
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118 Matrix |
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164
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119 xdiv (const Matrix& a, const Matrix& b) |
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120 { |
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121 if (! mx_div_conform (a, b)) |
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122 return Matrix (); |
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123 |
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124 Matrix atmp = a.transpose (); |
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125 Matrix btmp = b.transpose (); |
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126 |
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127 int info; |
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128 if (btmp.rows () == btmp.columns ()) |
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129 { |
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130 double rcond = 0.0; |
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131 |
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132 Matrix result |
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133 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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134 |
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135 if (result_ok (info)) |
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136 return Matrix (result.transpose ()); |
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137 } |
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138 |
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139 int rank; |
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140 Matrix result = btmp.lssolve (atmp, info, rank); |
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141 |
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142 return result.transpose (); |
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143 } |
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144 |
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145 // -*- 2 -*- |
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1800
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146 ComplexMatrix |
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164
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147 xdiv (const Matrix& a, const ComplexMatrix& b) |
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148 { |
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149 if (! mx_div_conform (a, b)) |
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150 return ComplexMatrix (); |
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151 |
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152 Matrix atmp = a.transpose (); |
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153 ComplexMatrix btmp = b.hermitian (); |
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154 |
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155 int info; |
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156 if (btmp.rows () == btmp.columns ()) |
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157 { |
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158 double rcond = 0.0; |
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159 |
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160 ComplexMatrix result |
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161 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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162 |
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163 if (result_ok (info)) |
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164 return result.hermitian (); |
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165 } |
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166 |
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167 int rank; |
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168 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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169 |
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170 return result.hermitian (); |
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171 } |
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172 |
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173 // -*- 3 -*- |
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1800
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174 ComplexMatrix |
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164
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175 xdiv (const ComplexMatrix& a, const Matrix& b) |
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176 { |
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177 if (! mx_div_conform (a, b)) |
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178 return ComplexMatrix (); |
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179 |
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180 ComplexMatrix atmp = a.hermitian (); |
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181 Matrix btmp = b.transpose (); |
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182 |
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183 int info; |
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184 if (btmp.rows () == btmp.columns ()) |
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185 { |
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186 double rcond = 0.0; |
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187 |
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188 ComplexMatrix result |
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189 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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190 |
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191 if (result_ok (info)) |
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192 return result.hermitian (); |
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193 } |
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194 |
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195 int rank; |
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196 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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197 |
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198 return result.hermitian (); |
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199 } |
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200 |
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201 // -*- 4 -*- |
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1800
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202 ComplexMatrix |
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203 xdiv (const ComplexMatrix& a, const ComplexMatrix& b) |
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204 { |
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205 if (! mx_div_conform (a, b)) |
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206 return ComplexMatrix (); |
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207 |
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208 ComplexMatrix atmp = a.hermitian (); |
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209 ComplexMatrix btmp = b.hermitian (); |
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210 |
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211 int info; |
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212 if (btmp.rows () == btmp.columns ()) |
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213 { |
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214 double rcond = 0.0; |
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215 |
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216 ComplexMatrix result |
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217 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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218 |
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219 if (result_ok (info)) |
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220 return result.hermitian (); |
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221 } |
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222 |
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223 int rank; |
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224 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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225 |
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226 return result.hermitian (); |
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227 } |
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228 |
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767
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229 // Funny element by element division operations. |
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230 // |
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231 // op2 \ op1: s cs |
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232 // +-- +---+----+ |
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233 // matrix | 1 | 3 | |
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234 // +---+----+ |
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235 // complex_matrix | 2 | 4 | |
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236 // +---+----+ |
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237 |
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238 Matrix |
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239 x_el_div (double a, const Matrix& b) |
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240 { |
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241 int nr = b.rows (); |
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242 int nc = b.columns (); |
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243 |
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244 Matrix result (nr, nc); |
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245 |
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246 for (int j = 0; j < nc; j++) |
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247 for (int i = 0; i < nr; i++) |
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248 { |
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249 OCTAVE_QUIT; |
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250 result (i, j) = a / b (i, j); |
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251 } |
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252 |
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253 return result; |
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254 } |
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255 |
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256 ComplexMatrix |
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257 x_el_div (double a, const ComplexMatrix& b) |
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258 { |
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259 int nr = b.rows (); |
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260 int nc = b.columns (); |
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261 |
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262 ComplexMatrix result (nr, nc); |
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263 |
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264 for (int j = 0; j < nc; j++) |
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265 for (int i = 0; i < nr; i++) |
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266 { |
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267 OCTAVE_QUIT; |
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268 result (i, j) = a / b (i, j); |
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269 } |
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270 |
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271 return result; |
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272 } |
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273 |
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274 ComplexMatrix |
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275 x_el_div (const Complex a, const Matrix& b) |
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276 { |
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277 int nr = b.rows (); |
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278 int nc = b.columns (); |
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279 |
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280 ComplexMatrix result (nr, nc); |
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281 |
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282 for (int j = 0; j < nc; j++) |
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283 for (int i = 0; i < nr; i++) |
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284 { |
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285 OCTAVE_QUIT; |
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286 result (i, j) = a / b (i, j); |
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287 } |
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288 |
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289 return result; |
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290 } |
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291 |
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292 ComplexMatrix |
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293 x_el_div (const Complex a, const ComplexMatrix& b) |
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294 { |
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295 int nr = b.rows (); |
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296 int nc = b.columns (); |
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297 |
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298 ComplexMatrix result (nr, nc); |
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299 |
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300 for (int j = 0; j < nc; j++) |
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301 for (int i = 0; i < nr; i++) |
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302 { |
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303 OCTAVE_QUIT; |
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304 result (i, j) = a / b (i, j); |
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305 } |
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306 |
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307 return result; |
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308 } |
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309 |
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310 // Funny element by element division operations. |
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311 // |
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312 // op2 \ op1: s cs |
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313 // +-- +---+----+ |
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314 // N-d array | 1 | 3 | |
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315 // +---+----+ |
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316 // complex N-d array | 2 | 4 | |
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317 // +---+----+ |
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318 |
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319 NDArray |
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320 x_el_div (double a, const NDArray& b) |
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321 { |
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322 NDArray result (b.dims ()); |
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323 |
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324 for (int i = 0; i < b.length (); i++) |
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325 { |
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326 OCTAVE_QUIT; |
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327 result (i) = a / b (i); |
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328 } |
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329 |
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330 return result; |
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331 } |
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332 |
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333 ComplexNDArray |
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334 x_el_div (double a, const ComplexNDArray& b) |
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335 { |
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336 ComplexNDArray result (b.dims ()); |
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337 |
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338 for (int i = 0; i < b.length (); i++) |
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339 { |
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340 OCTAVE_QUIT; |
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341 result (i) = a / b (i); |
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342 } |
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343 |
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344 return result; |
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345 } |
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346 |
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347 ComplexNDArray |
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348 x_el_div (const Complex a, const NDArray& b) |
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349 { |
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350 ComplexNDArray result (b.dims ()); |
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351 |
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352 for (int i = 0; i < b.length (); i++) |
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353 { |
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354 OCTAVE_QUIT; |
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355 result (i) = a / b (i); |
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356 } |
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357 |
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358 return result; |
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359 } |
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360 |
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361 ComplexNDArray |
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362 x_el_div (const Complex a, const ComplexNDArray& b) |
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363 { |
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364 ComplexNDArray result (b.dims ()); |
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365 |
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366 for (int i = 0; i < b.length (); i++) |
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367 { |
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368 OCTAVE_QUIT; |
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369 result (i) = a / b (i); |
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370 } |
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371 |
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372 return result; |
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373 } |
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374 |
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767
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375 // Left division functions. |
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376 // |
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377 // op2 \ op1: m cm |
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378 // +-- +---+----+ |
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379 // matrix | 1 | 3 | |
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380 // +---+----+ |
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381 // complex_matrix | 2 | 4 | |
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382 // +---+----+ |
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383 |
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767
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384 // -*- 1 -*- |
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1800
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385 Matrix |
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164
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386 xleftdiv (const Matrix& a, const Matrix& b) |
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1
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387 { |
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2364
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388 if (! mx_leftdiv_conform (a, b)) |
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1800
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389 return Matrix (); |
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390 |
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391 int info; |
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392 if (a.rows () == a.columns ()) |
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393 { |
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394 double rcond = 0.0; |
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395 |
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396 Matrix result |
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397 = a.solve (b, info, rcond, solve_singularity_warning); |
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398 |
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399 if (result_ok (info)) |
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1800
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400 return result; |
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1
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401 } |
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402 |
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403 int rank; |
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1800
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404 return a.lssolve (b, info, rank); |
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1
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405 } |
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406 |
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767
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407 // -*- 2 -*- |
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1800
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408 ComplexMatrix |
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164
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409 xleftdiv (const Matrix& a, const ComplexMatrix& b) |
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1
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410 { |
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2364
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411 if (! mx_leftdiv_conform (a, b)) |
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1800
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412 return ComplexMatrix (); |
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413 |
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414 int info; |
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415 if (a.rows () == a.columns ()) |
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416 { |
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417 double rcond = 0.0; |
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3480
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418 |
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419 ComplexMatrix result |
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420 = a.solve (b, info, rcond, solve_singularity_warning); |
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421 |
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422 if (result_ok (info)) |
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1800
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423 return result; |
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1
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424 } |
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425 |
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426 int rank; |
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1800
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427 return a.lssolve (b, info, rank); |
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1
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428 } |
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429 |
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767
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430 // -*- 3 -*- |
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1800
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431 ComplexMatrix |
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164
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432 xleftdiv (const ComplexMatrix& a, const Matrix& b) |
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1
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433 { |
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2364
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434 if (! mx_leftdiv_conform (a, b)) |
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1800
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435 return ComplexMatrix (); |
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1
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436 |
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437 int info; |
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438 if (a.rows () == a.columns ()) |
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439 { |
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440 double rcond = 0.0; |
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3480
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441 |
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442 ComplexMatrix result |
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443 = a.solve (b, info, rcond, solve_singularity_warning); |
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444 |
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445 if (result_ok (info)) |
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1800
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446 return result; |
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1
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447 } |
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448 |
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449 int rank; |
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1800
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450 return a.lssolve (b, info, rank); |
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1
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451 } |
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452 |
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767
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453 // -*- 4 -*- |
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1800
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454 ComplexMatrix |
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164
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455 xleftdiv (const ComplexMatrix& a, const ComplexMatrix& b) |
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1
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456 { |
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2364
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457 if (! mx_leftdiv_conform (a, b)) |
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1800
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458 return ComplexMatrix (); |
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1
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459 |
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460 int info; |
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461 if (a.rows () == a.columns ()) |
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462 { |
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463 double rcond = 0.0; |
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3480
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464 |
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465 ComplexMatrix result |
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466 = a.solve (b, info, rcond, solve_singularity_warning); |
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467 |
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468 if (result_ok (info)) |
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1800
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469 return result; |
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1
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470 } |
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471 |
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472 int rank; |
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1800
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473 return a.lssolve (b, info, rank); |
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1
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474 } |
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475 |
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476 /* |
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477 ;;; Local Variables: *** |
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478 ;;; mode: C++ *** |
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479 ;;; End: *** |
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480 */ |
