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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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27 #include <cassert> |
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28 |
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4669
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29 #include "Array-util.h" |
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1352
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30 #include "CMatrix.h" |
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453
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31 #include "dMatrix.h" |
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4543
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32 #include "CNDArray.h" |
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33 #include "dNDArray.h" |
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1651
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34 #include "oct-cmplx.h" |
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4153
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35 #include "quit.h" |
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36 |
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37 #include "error.h" |
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38 #include "xdiv.h" |
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39 |
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3480
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40 static inline bool |
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41 result_ok (int info) |
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42 { |
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43 assert (info != -1); |
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44 |
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3480
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45 return (info != -2); |
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46 } |
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47 |
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48 static void |
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49 solve_singularity_warning (double rcond) |
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50 { |
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51 warning ("matrix singular to machine precision, rcond = %g", rcond); |
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52 warning ("attempting to find minimum norm solution"); |
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53 } |
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54 |
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55 template <class T1, class T2> |
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56 bool |
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57 mx_leftdiv_conform (const T1& a, const T2& b) |
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58 { |
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59 int a_nr = a.rows (); |
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60 int b_nr = b.rows (); |
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61 |
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62 if (a_nr != b_nr) |
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63 { |
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2364
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64 int a_nc = a.cols (); |
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65 int b_nc = b.cols (); |
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66 |
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67 gripe_nonconformant ("operator \\", a_nr, a_nc, b_nr, b_nc); |
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68 return false; |
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69 } |
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70 |
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71 return true; |
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72 } |
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73 |
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74 #define INSTANTIATE_MX_LEFTDIV_CONFORM(T1, T2) \ |
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75 template bool mx_leftdiv_conform (const T1&, const T2&) |
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76 |
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77 INSTANTIATE_MX_LEFTDIV_CONFORM (Matrix, Matrix); |
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78 INSTANTIATE_MX_LEFTDIV_CONFORM (Matrix, ComplexMatrix); |
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79 INSTANTIATE_MX_LEFTDIV_CONFORM (ComplexMatrix, Matrix); |
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80 INSTANTIATE_MX_LEFTDIV_CONFORM (ComplexMatrix, ComplexMatrix); |
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81 |
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82 template <class T1, class T2> |
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83 bool |
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84 mx_div_conform (const T1& a, const T2& b) |
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85 { |
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86 int a_nc = a.cols (); |
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87 int b_nc = b.cols (); |
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88 |
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89 if (a_nc != b_nc) |
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90 { |
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91 int a_nr = a.rows (); |
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92 int b_nr = b.rows (); |
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93 |
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94 gripe_nonconformant ("operator /", a_nr, a_nc, b_nr, b_nc); |
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95 return false; |
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96 } |
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97 |
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98 return true; |
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99 } |
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100 |
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101 #define INSTANTIATE_MX_DIV_CONFORM(T1, T2) \ |
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102 template bool mx_div_conform (const T1&, const T2&) |
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103 |
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104 INSTANTIATE_MX_DIV_CONFORM (Matrix, Matrix); |
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105 INSTANTIATE_MX_DIV_CONFORM (Matrix, ComplexMatrix); |
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106 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, Matrix); |
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107 INSTANTIATE_MX_DIV_CONFORM (ComplexMatrix, ComplexMatrix); |
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108 |
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109 // Right division functions. |
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110 // |
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111 // op2 / op1: m cm |
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112 // +-- +---+----+ |
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113 // matrix | 1 | 3 | |
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114 // +---+----+ |
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115 // complex_matrix | 2 | 4 | |
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116 // +---+----+ |
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117 |
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767
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118 // -*- 1 -*- |
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119 Matrix |
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164
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120 xdiv (const Matrix& a, const Matrix& b) |
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121 { |
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122 if (! mx_div_conform (a, b)) |
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123 return Matrix (); |
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124 |
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125 Matrix atmp = a.transpose (); |
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126 Matrix btmp = b.transpose (); |
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127 |
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128 int info; |
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129 if (btmp.rows () == btmp.columns ()) |
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130 { |
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131 double rcond = 0.0; |
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132 |
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133 Matrix result |
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134 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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135 |
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136 if (result_ok (info)) |
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137 return Matrix (result.transpose ()); |
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138 } |
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139 |
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140 int rank; |
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141 Matrix result = btmp.lssolve (atmp, info, rank); |
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142 |
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143 return result.transpose (); |
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144 } |
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145 |
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767
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146 // -*- 2 -*- |
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1800
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147 ComplexMatrix |
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164
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148 xdiv (const Matrix& a, const ComplexMatrix& b) |
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149 { |
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150 if (! mx_div_conform (a, b)) |
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151 return ComplexMatrix (); |
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152 |
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153 Matrix atmp = a.transpose (); |
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154 ComplexMatrix btmp = b.hermitian (); |
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155 |
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156 int info; |
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157 if (btmp.rows () == btmp.columns ()) |
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158 { |
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159 double rcond = 0.0; |
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160 |
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161 ComplexMatrix result |
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162 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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163 |
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164 if (result_ok (info)) |
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165 return result.hermitian (); |
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166 } |
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167 |
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168 int rank; |
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169 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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170 |
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1800
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171 return result.hermitian (); |
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172 } |
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173 |
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767
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174 // -*- 3 -*- |
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1800
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175 ComplexMatrix |
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164
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176 xdiv (const ComplexMatrix& a, const Matrix& b) |
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177 { |
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178 if (! mx_div_conform (a, b)) |
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1800
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179 return ComplexMatrix (); |
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180 |
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181 ComplexMatrix atmp = a.hermitian (); |
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182 Matrix btmp = b.transpose (); |
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183 |
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184 int info; |
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185 if (btmp.rows () == btmp.columns ()) |
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186 { |
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187 double rcond = 0.0; |
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188 |
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189 ComplexMatrix result |
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190 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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191 |
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192 if (result_ok (info)) |
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193 return result.hermitian (); |
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194 } |
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195 |
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196 int rank; |
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197 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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198 |
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199 return result.hermitian (); |
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200 } |
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201 |
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202 // -*- 4 -*- |
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1800
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203 ComplexMatrix |
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204 xdiv (const ComplexMatrix& a, const ComplexMatrix& b) |
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205 { |
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206 if (! mx_div_conform (a, b)) |
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207 return ComplexMatrix (); |
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208 |
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209 ComplexMatrix atmp = a.hermitian (); |
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210 ComplexMatrix btmp = b.hermitian (); |
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211 |
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212 int info; |
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213 if (btmp.rows () == btmp.columns ()) |
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214 { |
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215 double rcond = 0.0; |
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216 |
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217 ComplexMatrix result |
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218 = btmp.solve (atmp, info, rcond, solve_singularity_warning); |
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219 |
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220 if (result_ok (info)) |
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221 return result.hermitian (); |
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222 } |
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223 |
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224 int rank; |
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225 ComplexMatrix result = btmp.lssolve (atmp, info, rank); |
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226 |
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227 return result.hermitian (); |
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228 } |
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229 |
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767
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230 // Funny element by element division operations. |
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231 // |
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232 // op2 \ op1: s cs |
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233 // +-- +---+----+ |
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234 // matrix | 1 | 3 | |
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235 // +---+----+ |
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236 // complex_matrix | 2 | 4 | |
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237 // +---+----+ |
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238 |
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239 Matrix |
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240 x_el_div (double a, const Matrix& b) |
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241 { |
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242 int nr = b.rows (); |
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243 int nc = b.columns (); |
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244 |
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245 Matrix result (nr, nc); |
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246 |
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247 for (int j = 0; j < nc; j++) |
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248 for (int i = 0; i < nr; i++) |
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249 { |
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250 OCTAVE_QUIT; |
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251 result (i, j) = a / b (i, j); |
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252 } |
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253 |
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254 return result; |
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255 } |
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256 |
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257 ComplexMatrix |
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258 x_el_div (double a, const ComplexMatrix& b) |
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259 { |
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260 int nr = b.rows (); |
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261 int nc = b.columns (); |
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262 |
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263 ComplexMatrix result (nr, nc); |
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264 |
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265 for (int j = 0; j < nc; j++) |
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266 for (int i = 0; i < nr; i++) |
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267 { |
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268 OCTAVE_QUIT; |
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269 result (i, j) = a / b (i, j); |
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270 } |
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271 |
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272 return result; |
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273 } |
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274 |
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275 ComplexMatrix |
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276 x_el_div (const Complex a, const Matrix& b) |
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277 { |
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278 int nr = b.rows (); |
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279 int nc = b.columns (); |
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280 |
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281 ComplexMatrix result (nr, nc); |
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282 |
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283 for (int j = 0; j < nc; j++) |
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284 for (int i = 0; i < nr; i++) |
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285 { |
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286 OCTAVE_QUIT; |
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287 result (i, j) = a / b (i, j); |
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288 } |
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289 |
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290 return result; |
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291 } |
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292 |
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293 ComplexMatrix |
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294 x_el_div (const Complex a, const ComplexMatrix& b) |
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295 { |
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296 int nr = b.rows (); |
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297 int nc = b.columns (); |
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298 |
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299 ComplexMatrix result (nr, nc); |
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300 |
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301 for (int j = 0; j < nc; j++) |
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302 for (int i = 0; i < nr; i++) |
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303 { |
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304 OCTAVE_QUIT; |
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305 result (i, j) = a / b (i, j); |
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306 } |
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307 |
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308 return result; |
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309 } |
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310 |
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311 // Funny element by element division operations. |
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312 // |
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313 // op2 \ op1: s cs |
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314 // +-- +---+----+ |
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315 // N-d array | 1 | 3 | |
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316 // +---+----+ |
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317 // complex N-d array | 2 | 4 | |
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318 // +---+----+ |
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319 |
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320 NDArray |
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321 x_el_div (double a, const NDArray& b) |
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322 { |
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323 NDArray result (b.dims ()); |
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324 |
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325 for (int i = 0; i < b.length (); i++) |
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326 { |
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327 OCTAVE_QUIT; |
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328 result (i) = a / b (i); |
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329 } |
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330 |
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331 return result; |
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332 } |
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333 |
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334 ComplexNDArray |
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335 x_el_div (double a, const ComplexNDArray& b) |
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336 { |
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337 ComplexNDArray result (b.dims ()); |
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338 |
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339 for (int i = 0; i < b.length (); i++) |
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340 { |
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341 OCTAVE_QUIT; |
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342 result (i) = a / b (i); |
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343 } |
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344 |
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345 return result; |
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346 } |
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347 |
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348 ComplexNDArray |
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349 x_el_div (const Complex a, const NDArray& b) |
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350 { |
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351 ComplexNDArray result (b.dims ()); |
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352 |
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353 for (int i = 0; i < b.length (); i++) |
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354 { |
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355 OCTAVE_QUIT; |
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356 result (i) = a / b (i); |
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357 } |
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358 |
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359 return result; |
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360 } |
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361 |
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362 ComplexNDArray |
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363 x_el_div (const Complex a, const ComplexNDArray& b) |
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364 { |
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365 ComplexNDArray result (b.dims ()); |
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366 |
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367 for (int i = 0; i < b.length (); i++) |
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368 { |
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369 OCTAVE_QUIT; |
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370 result (i) = a / b (i); |
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371 } |
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372 |
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373 return result; |
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374 } |
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375 |
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767
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376 // Left division functions. |
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377 // |
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378 // op2 \ op1: m cm |
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379 // +-- +---+----+ |
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380 // matrix | 1 | 3 | |
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381 // +---+----+ |
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382 // complex_matrix | 2 | 4 | |
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383 // +---+----+ |
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384 |
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767
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385 // -*- 1 -*- |
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1800
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386 Matrix |
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164
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387 xleftdiv (const Matrix& a, const Matrix& b) |
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1
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388 { |
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2364
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389 if (! mx_leftdiv_conform (a, b)) |
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1800
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390 return Matrix (); |
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391 |
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392 int info; |
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393 if (a.rows () == a.columns ()) |
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394 { |
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395 double rcond = 0.0; |
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396 |
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397 Matrix result |
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398 = a.solve (b, info, rcond, solve_singularity_warning); |
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399 |
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400 if (result_ok (info)) |
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1800
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401 return result; |
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1
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402 } |
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403 |
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404 int rank; |
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1800
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405 return a.lssolve (b, info, rank); |
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1
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406 } |
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407 |
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767
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408 // -*- 2 -*- |
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1800
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409 ComplexMatrix |
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164
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410 xleftdiv (const Matrix& a, const ComplexMatrix& b) |
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1
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411 { |
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2364
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412 if (! mx_leftdiv_conform (a, b)) |
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1800
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413 return ComplexMatrix (); |
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1
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414 |
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415 int info; |
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416 if (a.rows () == a.columns ()) |
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417 { |
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418 double rcond = 0.0; |
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3480
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419 |
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420 ComplexMatrix result |
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421 = a.solve (b, info, rcond, solve_singularity_warning); |
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422 |
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423 if (result_ok (info)) |
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1800
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424 return result; |
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1
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425 } |
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426 |
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427 int rank; |
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1800
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428 return a.lssolve (b, info, rank); |
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1
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429 } |
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430 |
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767
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431 // -*- 3 -*- |
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1800
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432 ComplexMatrix |
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164
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433 xleftdiv (const ComplexMatrix& a, const Matrix& b) |
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1
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434 { |
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2364
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435 if (! mx_leftdiv_conform (a, b)) |
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1800
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436 return ComplexMatrix (); |
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1
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437 |
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438 int info; |
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439 if (a.rows () == a.columns ()) |
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440 { |
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441 double rcond = 0.0; |
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3480
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442 |
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443 ComplexMatrix result |
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444 = a.solve (b, info, rcond, solve_singularity_warning); |
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445 |
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446 if (result_ok (info)) |
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1800
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447 return result; |
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1
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448 } |
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449 |
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450 int rank; |
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1800
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451 return a.lssolve (b, info, rank); |
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1
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452 } |
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453 |
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767
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454 // -*- 4 -*- |
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1800
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455 ComplexMatrix |
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164
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456 xleftdiv (const ComplexMatrix& a, const ComplexMatrix& b) |
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1
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457 { |
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2364
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458 if (! mx_leftdiv_conform (a, b)) |
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1800
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459 return ComplexMatrix (); |
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1
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460 |
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461 int info; |
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462 if (a.rows () == a.columns ()) |
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463 { |
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464 double rcond = 0.0; |
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3480
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465 |
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466 ComplexMatrix result |
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467 = a.solve (b, info, rcond, solve_singularity_warning); |
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468 |
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469 if (result_ok (info)) |
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1800
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470 return result; |
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1
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471 } |
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472 |
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473 int rank; |
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1800
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474 return a.lssolve (b, info, rank); |
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1
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475 } |
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476 |
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477 /* |
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478 ;;; Local Variables: *** |
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479 ;;; mode: C++ *** |
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480 ;;; End: *** |
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481 */ |
