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1 // Matrix manipulations. -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include <sys/types.h> |
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29 #include <iostream.h> |
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30 #include <float.h> |
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31 |
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32 #include <Complex.h> |
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33 |
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34 #include "mx-base.h" |
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35 #include "CmplxDET.h" |
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36 #include "CmplxSVD.h" |
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37 #include "mx-inlines.cc" |
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38 #include "lo-error.h" |
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39 #include "f77-uscore.h" |
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40 |
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41 // Fortran functions we call. |
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42 |
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43 extern "C" |
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44 { |
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45 int F77_FCN (zgemm) (const char*, const char*, const int*, |
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46 const int*, const int*, const Complex*, |
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47 const Complex*, const int*, const Complex*, |
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48 const int*, const Complex*, Complex*, const int*, |
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49 long, long); |
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50 |
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51 int F77_FCN (zgemv) (const char*, const int*, const int*, |
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52 const Complex*, const Complex*, const int*, |
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53 const Complex*, const int*, const Complex*, |
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54 Complex*, const int*, long); |
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55 |
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56 int F77_FCN (zgeco) (Complex*, const int*, const int*, int*, |
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57 double*, Complex*); |
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58 |
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59 int F77_FCN (zgedi) (Complex*, const int*, const int*, int*, |
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60 Complex*, Complex*, const int*); |
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61 |
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62 int F77_FCN (zgesl) (Complex*, const int*, const int*, int*, |
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63 Complex*, const int*); |
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64 |
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65 int F77_FCN (zgelss) (const int*, const int*, const int*, Complex*, |
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66 const int*, Complex*, const int*, double*, |
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67 const double*, int*, Complex*, const int*, |
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68 double*, int*); |
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69 |
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70 // Note that the original complex fft routines were not written for |
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71 // double complex arguments. They have been modified by adding an |
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72 // implicit double precision (a-h,o-z) statement at the beginning of |
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73 // each subroutine. |
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74 |
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75 int F77_FCN (cffti) (const int*, Complex*); |
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76 |
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77 int F77_FCN (cfftf) (const int*, Complex*, Complex*); |
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78 |
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79 int F77_FCN (cfftb) (const int*, Complex*, Complex*); |
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80 } |
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81 |
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82 #define KLUDGE_MATRICES |
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83 #define TYPE Complex |
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84 #define KL_MAT_TYPE ComplexMatrix |
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85 #include "mx-kludge.cc" |
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86 #undef KLUDGE_MATRICES |
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87 #undef TYPE |
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88 #undef KL_MAT_TYPE |
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89 |
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90 /* |
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91 * Complex Matrix class |
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92 */ |
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93 |
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94 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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95 : Array2<Complex> (a.rows (), a.cols ()) |
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96 { |
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97 for (int j = 0; j < cols (); j++) |
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98 for (int i = 0; i < rows (); i++) |
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99 elem (i, j) = a.elem (i, j); |
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100 } |
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101 |
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102 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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103 : Array2<Complex> (a.rows (), a.cols (), 0.0) |
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104 { |
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105 for (int i = 0; i < a.length (); i++) |
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106 elem (i, i) = a.elem (i, i); |
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107 } |
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108 |
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109 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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110 : Array2<Complex> (a.rows (), a.cols (), 0.0) |
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111 { |
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112 for (int i = 0; i < a.length (); i++) |
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113 elem (i, i) = a.elem (i, i); |
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114 } |
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115 |
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116 #if 0 |
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117 ComplexMatrix& |
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118 ComplexMatrix::resize (int r, int c) |
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119 { |
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120 if (r < 0 || c < 0) |
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121 { |
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122 (*current_liboctave_error_handler) |
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123 ("can't resize to negative dimensions"); |
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124 return *this; |
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125 } |
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126 |
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127 int new_len = r * c; |
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128 Complex* new_data = 0; |
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129 if (new_len > 0) |
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130 { |
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131 new_data = new Complex [new_len]; |
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132 |
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133 int min_r = nr < r ? nr : r; |
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134 int min_c = nc < c ? nc : c; |
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135 |
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136 for (int j = 0; j < min_c; j++) |
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137 for (int i = 0; i < min_r; i++) |
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138 new_data[r*j+i] = elem (i, j); |
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139 } |
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140 |
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141 delete [] data; |
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142 nr = r; |
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143 nc = c; |
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144 len = new_len; |
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145 data = new_data; |
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146 |
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147 return *this; |
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148 } |
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149 |
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150 ComplexMatrix& |
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151 ComplexMatrix::resize (int r, int c, double val) |
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152 { |
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153 if (r < 0 || c < 0) |
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154 { |
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155 (*current_liboctave_error_handler) |
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156 ("can't resize to negative dimensions"); |
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157 return *this; |
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158 } |
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159 |
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160 int new_len = r * c; |
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161 Complex *new_data = 0; |
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162 if (new_len > 0) |
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163 { |
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164 new_data = new Complex [new_len]; |
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165 |
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166 // There may be faster or cleaner ways to do this. |
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167 |
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168 if (r > nr || c > nc) |
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169 copy (new_data, new_len, val); |
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170 |
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171 int min_r = nr < r ? nr : r; |
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172 int min_c = nc < c ? nc : c; |
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173 |
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174 for (int j = 0; j < min_c; j++) |
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175 for (int i = 0; i < min_r; i++) |
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176 new_data[r*j+i] = elem (i, j); |
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177 } |
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178 |
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179 delete [] data; |
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180 nr = r; |
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181 nc = c; |
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182 len = new_len; |
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183 data = new_data; |
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184 |
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185 return *this; |
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186 } |
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187 |
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188 ComplexMatrix& |
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189 ComplexMatrix::resize (int r, int c, const Complex& val) |
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190 { |
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191 if (r < 0 || c < 0) |
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192 { |
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193 (*current_liboctave_error_handler) |
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194 ("can't resize to negative dimensions"); |
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195 return *this; |
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196 } |
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197 |
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198 int new_len = r * c; |
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199 Complex *new_data = 0; |
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200 if (new_len > 0) |
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201 { |
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202 new_data = new Complex [new_len]; |
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203 |
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204 // There may be faster or cleaner ways to do this. |
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205 |
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206 if (r > nr || c > nc) |
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207 copy (new_data, new_len, val); |
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208 |
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209 int min_r = nr < r ? nr : r; |
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210 int min_c = nc < c ? nc : c; |
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211 |
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212 for (int j = 0; j < min_c; j++) |
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213 for (int i = 0; i < min_r; i++) |
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214 new_data[r*j+i] = elem (i, j); |
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215 } |
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216 |
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217 delete [] data; |
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218 nr = r; |
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219 nc = c; |
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220 len = new_len; |
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221 data = new_data; |
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222 |
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223 return *this; |
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224 } |
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225 #endif |
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226 |
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227 int |
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228 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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229 { |
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230 if (rows () != a.rows () || cols () != a.cols ()) |
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231 return 0; |
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232 |
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233 return equal (data (), a.data (), length ()); |
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234 } |
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235 |
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236 int |
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237 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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238 { |
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239 return !(*this == a); |
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240 } |
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241 |
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242 // destructive insert/delete/reorder operations |
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243 |
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244 ComplexMatrix& |
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245 ComplexMatrix::insert (const Matrix& a, int r, int c) |
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246 { |
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247 int a_nr = a.rows (); |
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248 int a_nc = a.cols (); |
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249 if (r < 0 || r + a_nr - 1 > rows () || c < 0 || c + a_nc - 1 > cols ()) |
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250 { |
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251 (*current_liboctave_error_handler) ("range error for insert"); |
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252 return *this; |
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253 } |
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254 |
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255 for (int j = 0; j < a_nc; j++) |
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256 for (int i = 0; i < a_nr; i++) |
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257 elem (r+i, c+j) = a.elem (i, j); |
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258 |
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259 return *this; |
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260 } |
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261 |
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262 ComplexMatrix& |
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263 ComplexMatrix::insert (const RowVector& a, int r, int c) |
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264 { |
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265 int a_len = a.length (); |
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266 if (r < 0 || r >= rows () || c < 0 || c + a_len - 1 > cols ()) |
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267 { |
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268 (*current_liboctave_error_handler) ("range error for insert"); |
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269 return *this; |
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270 } |
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271 |
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272 for (int i = 0; i < a_len; i++) |
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273 elem (r, c+i) = a.elem (i); |
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274 |
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275 return *this; |
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276 } |
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277 |
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278 ComplexMatrix& |
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279 ComplexMatrix::insert (const ColumnVector& a, int r, int c) |
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280 { |
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281 int a_len = a.length (); |
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282 if (r < 0 || r + a_len - 1 > rows () || c < 0 || c >= cols ()) |
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283 { |
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284 (*current_liboctave_error_handler) ("range error for insert"); |
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285 return *this; |
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286 } |
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287 |
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288 for (int i = 0; i < a_len; i++) |
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289 elem (r+i, c) = a.elem (i); |
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290 |
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291 return *this; |
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292 } |
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293 |
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294 ComplexMatrix& |
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295 ComplexMatrix::insert (const DiagMatrix& a, int r, int c) |
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296 { |
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297 if (r < 0 || r + a.rows () - 1 > rows () |
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298 || c < 0 || c + a.cols () - 1 > cols ()) |
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299 { |
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300 (*current_liboctave_error_handler) ("range error for insert"); |
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301 return *this; |
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302 } |
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303 |
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304 for (int i = 0; i < a.length (); i++) |
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305 elem (r+i, c+i) = a.elem (i, i); |
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306 |
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307 return *this; |
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308 } |
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309 |
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310 ComplexMatrix& |
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311 ComplexMatrix::insert (const ComplexMatrix& a, int r, int c) |
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312 { |
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313 int a_nr = a.rows (); |
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314 int a_nc = a.cols (); |
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315 if (r < 0 || r + a_nr - 1 > rows () || c < 0 || c + a_nc - 1 > cols ()) |
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316 { |
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317 (*current_liboctave_error_handler) ("range error for insert"); |
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318 return *this; |
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319 } |
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320 |
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321 for (int j = 0; j < a_nc; j++) |
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322 for (int i = 0; i < a_nr; i++) |
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323 elem (r+i, c+j) = a.elem (i, j); |
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324 |
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325 return *this; |
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326 } |
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327 |
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328 ComplexMatrix& |
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329 ComplexMatrix::insert (const ComplexRowVector& a, int r, int c) |
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330 { |
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331 int a_len = a.length (); |
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332 if (r < 0 || r >= rows () || c < 0 || c + a_len - 1 > cols ()) |
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333 { |
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334 (*current_liboctave_error_handler) ("range error for insert"); |
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335 return *this; |
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336 } |
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337 |
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338 for (int i = 0; i < a_len; i++) |
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339 elem (r, c+i) = a.elem (i); |
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340 |
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341 return *this; |
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342 } |
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343 |
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344 ComplexMatrix& |
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345 ComplexMatrix::insert (const ComplexColumnVector& a, int r, int c) |
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346 { |
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347 int a_len = a.length (); |
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348 if (r < 0 || r + a_len - 1 > rows () || c < 0 || c >= cols ()) |
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349 { |
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350 (*current_liboctave_error_handler) ("range error for insert"); |
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351 return *this; |
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352 } |
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353 |
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354 for (int i = 0; i < a_len; i++) |
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355 elem (r+i, c) = a.elem (i); |
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356 |
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357 return *this; |
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358 } |
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359 |
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360 ComplexMatrix& |
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361 ComplexMatrix::insert (const ComplexDiagMatrix& a, int r, int c) |
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362 { |
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363 if (r < 0 || r + a.rows () - 1 > rows () |
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364 || c < 0 || c + a.cols () - 1 > cols ()) |
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365 { |
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366 (*current_liboctave_error_handler) ("range error for insert"); |
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367 return *this; |
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368 } |
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369 |
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370 for (int i = 0; i < a.length (); i++) |
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371 elem (r+i, c+i) = a.elem (i, i); |
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372 |
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373 return *this; |
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374 } |
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375 |
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376 ComplexMatrix& |
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377 ComplexMatrix::fill (double val) |
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378 { |
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379 int nr = rows (); |
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380 int nc = cols (); |
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381 if (nr > 0 && nc > 0) |
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382 for (int j = 0; j < nc; j++) |
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383 for (int i = 0; i < nr; i++) |
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384 elem (i, j) = val; |
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385 |
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386 return *this; |
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387 } |
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388 |
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389 ComplexMatrix& |
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390 ComplexMatrix::fill (const Complex& val) |
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391 { |
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392 int nr = rows (); |
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393 int nc = cols (); |
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394 if (nr > 0 && nc > 0) |
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395 for (int j = 0; j < nc; j++) |
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396 for (int i = 0; i < nr; i++) |
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397 elem (i, j) = val; |
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398 |
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399 return *this; |
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400 } |
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401 |
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402 ComplexMatrix& |
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403 ComplexMatrix::fill (double val, int r1, int c1, int r2, int c2) |
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404 { |
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405 int nr = rows (); |
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406 int nc = cols (); |
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407 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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408 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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409 { |
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410 (*current_liboctave_error_handler) ("range error for fill"); |
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411 return *this; |
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412 } |
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413 |
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414 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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415 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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416 |
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417 for (int j = c1; j <= c2; j++) |
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418 for (int i = r1; i <= r2; i++) |
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419 elem (i, j) = val; |
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420 |
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421 return *this; |
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422 } |
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423 |
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424 ComplexMatrix& |
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425 ComplexMatrix::fill (const Complex& val, int r1, int c1, int r2, int c2) |
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426 { |
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427 int nr = rows (); |
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428 int nc = cols (); |
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429 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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430 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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431 { |
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432 (*current_liboctave_error_handler) ("range error for fill"); |
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433 return *this; |
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434 } |
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435 |
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436 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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437 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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438 |
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439 for (int j = c1; j <= c2; j++) |
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440 for (int i = r1; i <= r2; i++) |
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441 elem (i, j) = val; |
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442 |
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443 return *this; |
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444 } |
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445 |
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446 ComplexMatrix |
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447 ComplexMatrix::append (const Matrix& a) const |
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448 { |
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449 int nr = rows (); |
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450 int nc = cols (); |
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451 if (nr != a.rows ()) |
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452 { |
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453 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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454 return *this; |
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455 } |
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456 |
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457 int nc_insert = nc; |
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458 ComplexMatrix retval (nr, nc + a.cols ()); |
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459 retval.insert (*this, 0, 0); |
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460 retval.insert (a, 0, nc_insert); |
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461 return retval; |
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462 } |
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463 |
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464 ComplexMatrix |
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465 ComplexMatrix::append (const RowVector& a) const |
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466 { |
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467 int nr = rows (); |
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468 int nc = cols (); |
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469 if (nr != 1) |
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470 { |
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471 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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472 return *this; |
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473 } |
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474 |
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475 int nc_insert = nc; |
|
|
476 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
477 retval.insert (*this, 0, 0); |
|
|
478 retval.insert (a, 0, nc_insert); |
|
|
479 return retval; |
|
|
480 } |
|
|
481 |
|
|
482 ComplexMatrix |
|
|
483 ComplexMatrix::append (const ColumnVector& a) const |
|
|
484 { |
|
|
485 int nr = rows (); |
|
|
486 int nc = cols (); |
|
|
487 if (nr != a.length ()) |
|
|
488 { |
|
|
489 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
490 return *this; |
|
|
491 } |
|
|
492 |
|
|
493 int nc_insert = nc; |
|
|
494 ComplexMatrix retval (nr, nc + 1); |
|
|
495 retval.insert (*this, 0, 0); |
|
|
496 retval.insert (a, 0, nc_insert); |
|
|
497 return retval; |
|
|
498 } |
|
|
499 |
|
|
500 ComplexMatrix |
|
|
501 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
502 { |
|
|
503 int nr = rows (); |
|
|
504 int nc = cols (); |
|
|
505 if (nr != a.rows ()) |
|
|
506 { |
|
|
507 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
508 return *this; |
|
|
509 } |
|
|
510 |
|
|
511 int nc_insert = nc; |
|
|
512 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
513 retval.insert (*this, 0, 0); |
|
|
514 retval.insert (a, 0, nc_insert); |
|
|
515 return retval; |
|
|
516 } |
|
|
517 |
|
|
518 ComplexMatrix |
|
|
519 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
520 { |
|
|
521 int nr = rows (); |
|
|
522 int nc = cols (); |
|
|
523 if (nr != a.rows ()) |
|
|
524 { |
|
|
525 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
526 return *this; |
|
|
527 } |
|
|
528 |
|
|
529 int nc_insert = nc; |
|
|
530 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
531 retval.insert (*this, 0, 0); |
|
|
532 retval.insert (a, 0, nc_insert); |
|
|
533 return retval; |
|
|
534 } |
|
|
535 |
|
|
536 ComplexMatrix |
|
|
537 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
538 { |
|
|
539 int nr = rows (); |
|
|
540 int nc = cols (); |
|
|
541 if (nr != 1) |
|
|
542 { |
|
|
543 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
544 return *this; |
|
|
545 } |
|
|
546 |
|
|
547 int nc_insert = nc; |
|
|
548 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
549 retval.insert (*this, 0, 0); |
|
|
550 retval.insert (a, 0, nc_insert); |
|
|
551 return retval; |
|
|
552 } |
|
|
553 |
|
|
554 ComplexMatrix |
|
|
555 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
556 { |
|
|
557 int nr = rows (); |
|
|
558 int nc = cols (); |
|
|
559 if (nr != a.length ()) |
|
|
560 { |
|
|
561 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
562 return *this; |
|
|
563 } |
|
|
564 |
|
|
565 int nc_insert = nc; |
|
|
566 ComplexMatrix retval (nr, nc + 1); |
|
|
567 retval.insert (*this, 0, 0); |
|
|
568 retval.insert (a, 0, nc_insert); |
|
|
569 return retval; |
|
|
570 } |
|
|
571 |
|
|
572 ComplexMatrix |
|
|
573 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
574 { |
|
|
575 int nr = rows (); |
|
|
576 int nc = cols (); |
|
|
577 if (nr != a.rows ()) |
|
|
578 { |
|
|
579 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
580 return *this; |
|
|
581 } |
|
|
582 |
|
|
583 int nc_insert = nc; |
|
|
584 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
585 retval.insert (*this, 0, 0); |
|
|
586 retval.insert (a, 0, nc_insert); |
|
|
587 return retval; |
|
|
588 } |
|
|
589 |
|
|
590 ComplexMatrix |
|
|
591 ComplexMatrix::stack (const Matrix& a) const |
|
|
592 { |
|
|
593 int nr = rows (); |
|
|
594 int nc = cols (); |
|
|
595 if (nc != a.cols ()) |
|
|
596 { |
|
|
597 (*current_liboctave_error_handler) |
|
|
598 ("column dimension mismatch for stack"); |
|
|
599 return *this; |
|
|
600 } |
|
|
601 |
|
|
602 int nr_insert = nr; |
|
|
603 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
604 retval.insert (*this, 0, 0); |
|
|
605 retval.insert (a, nr_insert, 0); |
|
|
606 return retval; |
|
|
607 } |
|
|
608 |
|
|
609 ComplexMatrix |
|
|
610 ComplexMatrix::stack (const RowVector& a) const |
|
|
611 { |
|
|
612 int nr = rows (); |
|
|
613 int nc = cols (); |
|
|
614 if (nc != a.length ()) |
|
|
615 { |
|
|
616 (*current_liboctave_error_handler) |
|
|
617 ("column dimension mismatch for stack"); |
|
|
618 return *this; |
|
|
619 } |
|
|
620 |
|
|
621 int nr_insert = nr; |
|
|
622 ComplexMatrix retval (nr + 1, nc); |
|
|
623 retval.insert (*this, 0, 0); |
|
|
624 retval.insert (a, nr_insert, 0); |
|
|
625 return retval; |
|
|
626 } |
|
|
627 |
|
|
628 ComplexMatrix |
|
|
629 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
630 { |
|
|
631 int nr = rows (); |
|
|
632 int nc = cols (); |
|
|
633 if (nc != 1) |
|
|
634 { |
|
|
635 (*current_liboctave_error_handler) |
|
|
636 ("column dimension mismatch for stack"); |
|
|
637 return *this; |
|
|
638 } |
|
|
639 |
|
|
640 int nr_insert = nr; |
|
|
641 ComplexMatrix retval (nr + a.length (), nc); |
|
|
642 retval.insert (*this, 0, 0); |
|
|
643 retval.insert (a, nr_insert, 0); |
|
|
644 return retval; |
|
|
645 } |
|
|
646 |
|
|
647 ComplexMatrix |
|
|
648 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
649 { |
|
|
650 int nr = rows (); |
|
|
651 int nc = cols (); |
|
|
652 if (nc != a.cols ()) |
|
|
653 { |
|
|
654 (*current_liboctave_error_handler) |
|
|
655 ("column dimension mismatch for stack"); |
|
|
656 return *this; |
|
|
657 } |
|
|
658 |
|
|
659 int nr_insert = nr; |
|
|
660 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
661 retval.insert (*this, 0, 0); |
|
|
662 retval.insert (a, nr_insert, 0); |
|
|
663 return retval; |
|
|
664 } |
|
|
665 |
|
|
666 ComplexMatrix |
|
|
667 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
668 { |
|
|
669 int nr = rows (); |
|
|
670 int nc = cols (); |
|
|
671 if (nc != a.cols ()) |
|
|
672 { |
|
|
673 (*current_liboctave_error_handler) |
|
|
674 ("column dimension mismatch for stack"); |
|
|
675 return *this; |
|
|
676 } |
|
|
677 |
|
|
678 int nr_insert = nr; |
|
|
679 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
680 retval.insert (*this, 0, 0); |
|
|
681 retval.insert (a, nr_insert, 0); |
|
|
682 return retval; |
|
|
683 } |
|
|
684 |
|
|
685 ComplexMatrix |
|
|
686 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
687 { |
|
|
688 int nr = rows (); |
|
|
689 int nc = cols (); |
|
|
690 if (nc != a.length ()) |
|
|
691 { |
|
|
692 (*current_liboctave_error_handler) |
|
|
693 ("column dimension mismatch for stack"); |
|
|
694 return *this; |
|
|
695 } |
|
|
696 |
|
|
697 int nr_insert = nr; |
|
|
698 ComplexMatrix retval (nr + 1, nc); |
|
|
699 retval.insert (*this, 0, 0); |
|
|
700 retval.insert (a, nr_insert, 0); |
|
|
701 return retval; |
|
|
702 } |
|
|
703 |
|
|
704 ComplexMatrix |
|
|
705 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
706 { |
|
|
707 int nr = rows (); |
|
|
708 int nc = cols (); |
|
|
709 if (nc != 1) |
|
|
710 { |
|
|
711 (*current_liboctave_error_handler) |
|
|
712 ("column dimension mismatch for stack"); |
|
|
713 return *this; |
|
|
714 } |
|
|
715 |
|
|
716 int nr_insert = nr; |
|
|
717 ComplexMatrix retval (nr + a.length (), nc); |
|
|
718 retval.insert (*this, 0, 0); |
|
|
719 retval.insert (a, nr_insert, 0); |
|
|
720 return retval; |
|
|
721 } |
|
|
722 |
|
|
723 ComplexMatrix |
|
|
724 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
725 { |
|
|
726 int nr = rows (); |
|
|
727 int nc = cols (); |
|
|
728 if (nc != a.cols ()) |
|
|
729 { |
|
|
730 (*current_liboctave_error_handler) |
|
|
731 ("column dimension mismatch for stack"); |
|
|
732 return *this; |
|
|
733 } |
|
|
734 |
|
|
735 int nr_insert = nr; |
|
|
736 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
737 retval.insert (*this, 0, 0); |
|
|
738 retval.insert (a, nr_insert, 0); |
|
|
739 return retval; |
|
|
740 } |
|
|
741 |
|
|
742 ComplexMatrix |
|
|
743 ComplexMatrix::hermitian (void) const |
|
|
744 { |
|
|
745 int nr = rows (); |
|
|
746 int nc = cols (); |
|
|
747 ComplexMatrix result; |
|
|
748 if (length () > 0) |
|
|
749 { |
|
|
750 result.resize (nc, nr); |
|
|
751 for (int j = 0; j < nc; j++) |
|
|
752 for (int i = 0; i < nr; i++) |
|
|
753 result.elem (j, i) = conj (elem (i, j)); |
|
|
754 } |
|
|
755 return result; |
|
|
756 } |
|
|
757 |
|
|
758 ComplexMatrix |
|
|
759 ComplexMatrix::transpose (void) const |
|
|
760 { |
|
|
761 int nr = rows (); |
|
|
762 int nc = cols (); |
|
|
763 ComplexMatrix result (nc, nr); |
|
|
764 if (length () > 0) |
|
|
765 { |
|
|
766 for (int j = 0; j < nc; j++) |
|
|
767 for (int i = 0; i < nr; i++) |
|
|
768 result.elem (j, i) = elem (i, j); |
|
|
769 } |
|
|
770 return result; |
|
|
771 } |
|
|
772 |
|
|
773 Matrix |
|
|
774 real (const ComplexMatrix& a) |
|
|
775 { |
|
|
776 int a_len = a.length (); |
|
|
777 Matrix retval; |
|
|
778 if (a_len > 0) |
|
|
779 retval = Matrix (real_dup (a.data (), a_len), a.rows (), a.cols ()); |
|
|
780 return retval; |
|
|
781 } |
|
|
782 |
|
|
783 Matrix |
|
|
784 imag (const ComplexMatrix& a) |
|
|
785 { |
|
|
786 int a_len = a.length (); |
|
|
787 Matrix retval; |
|
|
788 if (a_len > 0) |
|
|
789 retval = Matrix (imag_dup (a.data (), a_len), a.rows (), a.cols ()); |
|
|
790 return retval; |
|
|
791 } |
|
|
792 |
|
|
793 ComplexMatrix |
|
|
794 conj (const ComplexMatrix& a) |
|
|
795 { |
|
|
796 int a_len = a.length (); |
|
|
797 ComplexMatrix retval; |
|
|
798 if (a_len > 0) |
|
|
799 retval = ComplexMatrix (conj_dup (a.data (), a_len), a.rows (), |
|
|
800 a.cols ()); |
|
|
801 return retval; |
|
|
802 } |
|
|
803 |
|
|
804 // resize is the destructive equivalent for this one |
|
|
805 |
|
|
806 ComplexMatrix |
|
|
807 ComplexMatrix::extract (int r1, int c1, int r2, int c2) const |
|
|
808 { |
|
|
809 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
810 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
811 |
|
|
812 int new_r = r2 - r1 + 1; |
|
|
813 int new_c = c2 - c1 + 1; |
|
|
814 |
|
|
815 ComplexMatrix result (new_r, new_c); |
|
|
816 |
|
|
817 for (int j = 0; j < new_c; j++) |
|
|
818 for (int i = 0; i < new_r; i++) |
|
|
819 result.elem (i, j) = elem (r1+i, c1+j); |
|
|
820 |
|
|
821 return result; |
|
|
822 } |
|
|
823 |
|
|
824 // extract row or column i. |
|
|
825 |
|
|
826 ComplexRowVector |
|
|
827 ComplexMatrix::row (int i) const |
|
|
828 { |
|
|
829 int nc = cols (); |
|
|
830 if (i < 0 || i >= rows ()) |
|
|
831 { |
|
|
832 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
833 return ComplexRowVector (); |
|
|
834 } |
|
|
835 |
|
|
836 ComplexRowVector retval (nc); |
|
|
837 for (int j = 0; j < cols (); j++) |
|
|
838 retval.elem (j) = elem (i, j); |
|
|
839 |
|
|
840 return retval; |
|
|
841 } |
|
|
842 |
|
|
843 ComplexRowVector |
|
|
844 ComplexMatrix::row (char *s) const |
|
|
845 { |
|
533
|
846 if (! s) |
|
458
|
847 { |
|
|
848 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
849 return ComplexRowVector (); |
|
|
850 } |
|
|
851 |
|
|
852 char c = *s; |
|
|
853 if (c == 'f' || c == 'F') |
|
|
854 return row (0); |
|
|
855 else if (c == 'l' || c == 'L') |
|
|
856 return row (rows () - 1); |
|
|
857 else |
|
|
858 { |
|
|
859 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
860 return ComplexRowVector (); |
|
|
861 } |
|
|
862 } |
|
|
863 |
|
|
864 ComplexColumnVector |
|
|
865 ComplexMatrix::column (int i) const |
|
|
866 { |
|
|
867 int nr = rows (); |
|
|
868 if (i < 0 || i >= cols ()) |
|
|
869 { |
|
|
870 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
871 return ComplexColumnVector (); |
|
|
872 } |
|
|
873 |
|
|
874 ComplexColumnVector retval (nr); |
|
|
875 for (int j = 0; j < nr; j++) |
|
|
876 retval.elem (j) = elem (j, i); |
|
|
877 |
|
|
878 return retval; |
|
|
879 } |
|
|
880 |
|
|
881 ComplexColumnVector |
|
|
882 ComplexMatrix::column (char *s) const |
|
|
883 { |
|
533
|
884 if (! s) |
|
458
|
885 { |
|
|
886 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
887 return ComplexColumnVector (); |
|
|
888 } |
|
|
889 |
|
|
890 char c = *s; |
|
|
891 if (c == 'f' || c == 'F') |
|
|
892 return column (0); |
|
|
893 else if (c == 'l' || c == 'L') |
|
|
894 return column (cols () - 1); |
|
|
895 else |
|
|
896 { |
|
|
897 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
898 return ComplexColumnVector (); |
|
|
899 } |
|
|
900 } |
|
|
901 |
|
|
902 ComplexMatrix |
|
|
903 ComplexMatrix::inverse (void) const |
|
|
904 { |
|
|
905 int info; |
|
479
|
906 double rcond; |
|
|
907 return inverse (info, rcond); |
|
458
|
908 } |
|
|
909 |
|
|
910 ComplexMatrix |
|
|
911 ComplexMatrix::inverse (int& info) const |
|
|
912 { |
|
|
913 double rcond; |
|
|
914 return inverse (info, rcond); |
|
|
915 } |
|
|
916 |
|
|
917 ComplexMatrix |
|
532
|
918 ComplexMatrix::inverse (int& info, double& rcond) const |
|
458
|
919 { |
|
|
920 int nr = rows (); |
|
|
921 int nc = cols (); |
|
|
922 int len = length (); |
|
|
923 if (nr != nc) |
|
|
924 { |
|
|
925 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
926 return ComplexMatrix (); |
|
|
927 } |
|
|
928 |
|
|
929 info = 0; |
|
|
930 |
|
|
931 int *ipvt = new int [nr]; |
|
|
932 Complex *z = new Complex [nr]; |
|
|
933 Complex *tmp_data = dup (data (), len); |
|
|
934 |
|
|
935 F77_FCN (zgeco) (tmp_data, &nr, &nc, ipvt, &rcond, z); |
|
|
936 |
|
532
|
937 volatile double tmp_rcond = rcond; |
|
|
938 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
939 { |
|
|
940 info = -1; |
|
|
941 copy (tmp_data, data (), len); // Restore contents. |
|
|
942 } |
|
|
943 else |
|
|
944 { |
|
|
945 int job = 1; |
|
|
946 Complex dummy; |
|
|
947 |
|
|
948 F77_FCN (zgedi) (tmp_data, &nr, &nc, ipvt, &dummy, z, &job); |
|
|
949 } |
|
|
950 |
|
|
951 delete [] ipvt; |
|
|
952 delete [] z; |
|
|
953 |
|
|
954 return ComplexMatrix (tmp_data, nr, nc); |
|
|
955 } |
|
|
956 |
|
|
957 ComplexMatrix |
|
740
|
958 ComplexMatrix::pseudo_inverse (double tol) |
|
|
959 { |
|
|
960 ComplexSVD result (*this); |
|
|
961 |
|
|
962 DiagMatrix S = result.singular_values (); |
|
|
963 ComplexMatrix U = result.left_singular_matrix (); |
|
|
964 ComplexMatrix V = result.right_singular_matrix (); |
|
|
965 |
|
|
966 ColumnVector sigma = S.diag (); |
|
|
967 |
|
|
968 int r = sigma.length () - 1; |
|
|
969 int nr = rows (); |
|
|
970 int nc = cols (); |
|
|
971 |
|
|
972 if (tol <= 0.0) |
|
|
973 { |
|
|
974 if (nr > nc) |
|
|
975 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
976 else |
|
|
977 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
978 } |
|
|
979 |
|
|
980 while (r >= 0 && sigma.elem (r) < tol) |
|
|
981 r--; |
|
|
982 |
|
|
983 if (r < 0) |
|
|
984 return ComplexMatrix (nc, nr, 0.0); |
|
|
985 else |
|
|
986 { |
|
|
987 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
988 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
989 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
|
990 return Vr * D * Ur.hermitian (); |
|
|
991 } |
|
|
992 } |
|
|
993 |
|
|
994 ComplexMatrix |
|
458
|
995 ComplexMatrix::fourier (void) const |
|
|
996 { |
|
|
997 int nr = rows (); |
|
|
998 int nc = cols (); |
|
|
999 int npts, nsamples; |
|
|
1000 if (nr == 1 || nc == 1) |
|
|
1001 { |
|
|
1002 npts = nr > nc ? nr : nc; |
|
|
1003 nsamples = 1; |
|
|
1004 } |
|
|
1005 else |
|
|
1006 { |
|
|
1007 npts = nr; |
|
|
1008 nsamples = nc; |
|
|
1009 } |
|
|
1010 |
|
|
1011 int nn = 4*npts+15; |
|
|
1012 Complex *wsave = new Complex [nn]; |
|
|
1013 Complex *tmp_data = dup (data (), length ()); |
|
|
1014 |
|
|
1015 F77_FCN (cffti) (&npts, wsave); |
|
|
1016 |
|
|
1017 for (int j = 0; j < nsamples; j++) |
|
|
1018 F77_FCN (cfftf) (&npts, &tmp_data[npts*j], wsave); |
|
|
1019 |
|
|
1020 delete [] wsave; |
|
|
1021 |
|
|
1022 return ComplexMatrix (tmp_data, nr, nc); |
|
|
1023 } |
|
|
1024 |
|
|
1025 ComplexMatrix |
|
|
1026 ComplexMatrix::ifourier (void) const |
|
|
1027 { |
|
|
1028 int nr = rows (); |
|
|
1029 int nc = cols (); |
|
|
1030 int npts, nsamples; |
|
|
1031 if (nr == 1 || nc == 1) |
|
|
1032 { |
|
|
1033 npts = nr > nc ? nr : nc; |
|
|
1034 nsamples = 1; |
|
|
1035 } |
|
|
1036 else |
|
|
1037 { |
|
|
1038 npts = nr; |
|
|
1039 nsamples = nc; |
|
|
1040 } |
|
|
1041 |
|
|
1042 int nn = 4*npts+15; |
|
|
1043 Complex *wsave = new Complex [nn]; |
|
|
1044 Complex *tmp_data = dup (data (), length ()); |
|
|
1045 |
|
|
1046 F77_FCN (cffti) (&npts, wsave); |
|
|
1047 |
|
|
1048 for (int j = 0; j < nsamples; j++) |
|
|
1049 F77_FCN (cfftb) (&npts, &tmp_data[npts*j], wsave); |
|
|
1050 |
|
|
1051 for (j = 0; j < npts*nsamples; j++) |
|
|
1052 tmp_data[j] = tmp_data[j] / (double) npts; |
|
|
1053 |
|
|
1054 delete [] wsave; |
|
|
1055 |
|
|
1056 return ComplexMatrix (tmp_data, nr, nc); |
|
|
1057 } |
|
|
1058 |
|
677
|
1059 ComplexMatrix |
|
|
1060 ComplexMatrix::fourier2d (void) const |
|
|
1061 { |
|
|
1062 int nr = rows (); |
|
|
1063 int nc = cols (); |
|
|
1064 int npts, nsamples; |
|
|
1065 if (nr == 1 || nc == 1) |
|
|
1066 { |
|
|
1067 npts = nr > nc ? nr : nc; |
|
|
1068 nsamples = 1; |
|
|
1069 } |
|
|
1070 else |
|
|
1071 { |
|
|
1072 npts = nr; |
|
|
1073 nsamples = nc; |
|
|
1074 } |
|
|
1075 |
|
|
1076 int nn = 4*npts+15; |
|
|
1077 Complex *wsave = new Complex [nn]; |
|
|
1078 Complex *tmp_data = dup (data (), length ()); |
|
|
1079 |
|
|
1080 F77_FCN (cffti) (&npts, wsave); |
|
|
1081 |
|
|
1082 for (int j = 0; j < nsamples; j++) |
|
|
1083 F77_FCN (cfftf) (&npts, &tmp_data[npts*j], wsave); |
|
|
1084 |
|
|
1085 delete [] wsave; |
|
|
1086 |
|
|
1087 npts = nc; |
|
|
1088 nsamples = nr; |
|
|
1089 nn = 4*npts+15; |
|
|
1090 wsave = new Complex [nn]; |
|
|
1091 Complex *row = new Complex[npts]; |
|
|
1092 |
|
|
1093 F77_FCN (cffti) (&npts, wsave); |
|
|
1094 |
|
|
1095 for (j = 0; j < nsamples; j++) |
|
|
1096 { |
|
|
1097 for (int i = 0; i < npts; i++) |
|
|
1098 row[i] = tmp_data[i*nr + j]; |
|
|
1099 |
|
|
1100 F77_FCN (cfftf) (&npts, row, wsave); |
|
|
1101 |
|
|
1102 for (i = 0; i < npts; i++) |
|
|
1103 tmp_data[i*nr + j] = row[i]; |
|
|
1104 } |
|
|
1105 |
|
|
1106 delete [] wsave; |
|
|
1107 delete [] row; |
|
|
1108 |
|
|
1109 return ComplexMatrix (tmp_data, nr, nc); |
|
|
1110 } |
|
|
1111 |
|
|
1112 ComplexMatrix |
|
|
1113 ComplexMatrix::ifourier2d (void) const |
|
|
1114 { |
|
|
1115 int nr = rows (); |
|
|
1116 int nc = cols (); |
|
|
1117 int npts, nsamples; |
|
|
1118 if (nr == 1 || nc == 1) |
|
|
1119 { |
|
|
1120 npts = nr > nc ? nr : nc; |
|
|
1121 nsamples = 1; |
|
|
1122 } |
|
|
1123 else |
|
|
1124 { |
|
|
1125 npts = nr; |
|
|
1126 nsamples = nc; |
|
|
1127 } |
|
|
1128 |
|
|
1129 int nn = 4*npts+15; |
|
|
1130 Complex *wsave = new Complex [nn]; |
|
|
1131 Complex *tmp_data = dup (data (), length ()); |
|
|
1132 |
|
|
1133 F77_FCN (cffti) (&npts, wsave); |
|
|
1134 |
|
|
1135 for (int j = 0; j < nsamples; j++) |
|
|
1136 F77_FCN (cfftb) (&npts, &tmp_data[npts*j], wsave); |
|
|
1137 |
|
|
1138 delete [] wsave; |
|
|
1139 |
|
|
1140 for (j = 0; j < npts*nsamples; j++) |
|
|
1141 tmp_data[j] = tmp_data[j] / (double) npts; |
|
|
1142 |
|
|
1143 npts = nc; |
|
|
1144 nsamples = nr; |
|
|
1145 nn = 4*npts+15; |
|
|
1146 wsave = new Complex [nn]; |
|
|
1147 Complex *row = new Complex[npts]; |
|
|
1148 |
|
|
1149 F77_FCN (cffti) (&npts, wsave); |
|
|
1150 |
|
|
1151 for (j = 0; j < nsamples; j++) |
|
|
1152 { |
|
|
1153 for (int i = 0; i < npts; i++) |
|
|
1154 row[i] = tmp_data[i*nr + j]; |
|
|
1155 |
|
|
1156 F77_FCN (cfftb) (&npts, row, wsave); |
|
|
1157 |
|
|
1158 for (i = 0; i < npts; i++) |
|
|
1159 tmp_data[i*nr + j] = row[i] / (double) npts; |
|
|
1160 } |
|
|
1161 |
|
|
1162 delete [] wsave; |
|
|
1163 delete [] row; |
|
|
1164 |
|
|
1165 return ComplexMatrix (tmp_data, nr, nc); |
|
|
1166 } |
|
|
1167 |
|
458
|
1168 ComplexDET |
|
|
1169 ComplexMatrix::determinant (void) const |
|
|
1170 { |
|
|
1171 int info; |
|
|
1172 double rcond; |
|
|
1173 return determinant (info, rcond); |
|
|
1174 } |
|
|
1175 |
|
|
1176 ComplexDET |
|
|
1177 ComplexMatrix::determinant (int& info) const |
|
|
1178 { |
|
|
1179 double rcond; |
|
|
1180 return determinant (info, rcond); |
|
|
1181 } |
|
|
1182 |
|
|
1183 ComplexDET |
|
532
|
1184 ComplexMatrix::determinant (int& info, double& rcond) const |
|
458
|
1185 { |
|
|
1186 ComplexDET retval; |
|
|
1187 |
|
|
1188 int nr = rows (); |
|
|
1189 int nc = cols (); |
|
|
1190 |
|
|
1191 if (nr == 0 || nc == 0) |
|
|
1192 { |
|
|
1193 Complex d[2]; |
|
|
1194 d[0] = 1.0; |
|
|
1195 d[1] = 0.0; |
|
|
1196 retval = ComplexDET (d); |
|
|
1197 } |
|
|
1198 else |
|
|
1199 { |
|
|
1200 info = 0; |
|
|
1201 int *ipvt = new int [nr]; |
|
|
1202 |
|
|
1203 Complex *z = new Complex [nr]; |
|
|
1204 Complex *tmp_data = dup (data (), length ()); |
|
|
1205 |
|
|
1206 F77_FCN (zgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
1207 |
|
532
|
1208 volatile double tmp_rcond = rcond; |
|
|
1209 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
1210 { |
|
|
1211 info = -1; |
|
|
1212 retval = ComplexDET (); |
|
|
1213 } |
|
|
1214 else |
|
|
1215 { |
|
|
1216 int job = 10; |
|
|
1217 Complex d[2]; |
|
|
1218 F77_FCN (zgedi) (tmp_data, &nr, &nr, ipvt, d, z, &job); |
|
|
1219 retval = ComplexDET (d); |
|
|
1220 } |
|
|
1221 |
|
|
1222 delete [] tmp_data; |
|
|
1223 delete [] ipvt; |
|
|
1224 delete [] z; |
|
|
1225 } |
|
|
1226 |
|
|
1227 return retval; |
|
|
1228 } |
|
|
1229 |
|
|
1230 ComplexMatrix |
|
|
1231 ComplexMatrix::solve (const Matrix& b) const |
|
|
1232 { |
|
|
1233 int info; |
|
|
1234 double rcond; |
|
|
1235 return solve (b, info, rcond); |
|
|
1236 } |
|
|
1237 |
|
|
1238 ComplexMatrix |
|
|
1239 ComplexMatrix::solve (const Matrix& b, int& info) const |
|
|
1240 { |
|
|
1241 double rcond; |
|
|
1242 return solve (b, info, rcond); |
|
|
1243 } |
|
|
1244 |
|
|
1245 ComplexMatrix |
|
|
1246 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond) const |
|
|
1247 { |
|
|
1248 ComplexMatrix tmp (b); |
|
|
1249 return solve (tmp, info, rcond); |
|
|
1250 } |
|
|
1251 |
|
|
1252 ComplexMatrix |
|
|
1253 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1254 { |
|
|
1255 int info; |
|
|
1256 double rcond; |
|
|
1257 return solve (b, info, rcond); |
|
|
1258 } |
|
|
1259 |
|
|
1260 ComplexMatrix |
|
|
1261 ComplexMatrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1262 { |
|
|
1263 double rcond; |
|
|
1264 return solve (b, info, rcond); |
|
|
1265 } |
|
|
1266 ComplexMatrix |
|
532
|
1267 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
458
|
1268 { |
|
|
1269 ComplexMatrix retval; |
|
|
1270 |
|
|
1271 int nr = rows (); |
|
|
1272 int nc = cols (); |
|
|
1273 int b_nr = b.rows (); |
|
|
1274 int b_nc = b.cols (); |
|
|
1275 if (nr == 0 || nc == 0 || nr != nc || nr != b_nr) |
|
|
1276 { |
|
|
1277 (*current_liboctave_error_handler) |
|
|
1278 ("matrix dimension mismatch in solution of linear equations"); |
|
|
1279 return ComplexMatrix (); |
|
|
1280 } |
|
|
1281 |
|
|
1282 info = 0; |
|
|
1283 int *ipvt = new int [nr]; |
|
|
1284 |
|
|
1285 Complex *z = new Complex [nr]; |
|
|
1286 Complex *tmp_data = dup (data (), length ()); |
|
|
1287 |
|
|
1288 F77_FCN (zgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
1289 |
|
532
|
1290 volatile double tmp_rcond = rcond; |
|
|
1291 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
1292 { |
|
|
1293 info = -2; |
|
|
1294 } |
|
|
1295 else |
|
|
1296 { |
|
|
1297 int job = 0; |
|
|
1298 |
|
|
1299 Complex *result = dup (b.data (), b.length ()); |
|
|
1300 |
|
|
1301 for (int j = 0; j < b_nc; j++) |
|
|
1302 F77_FCN (zgesl) (tmp_data, &nr, &nr, ipvt, &result[nr*j], &job); |
|
|
1303 |
|
|
1304 retval = ComplexMatrix (result, b_nr, b_nc); |
|
|
1305 } |
|
|
1306 |
|
|
1307 delete [] tmp_data; |
|
|
1308 delete [] ipvt; |
|
|
1309 delete [] z; |
|
|
1310 |
|
|
1311 return retval; |
|
|
1312 } |
|
|
1313 |
|
|
1314 ComplexColumnVector |
|
|
1315 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1316 { |
|
|
1317 int info; |
|
|
1318 double rcond; |
|
|
1319 return solve (b, info, rcond); |
|
|
1320 } |
|
|
1321 |
|
|
1322 ComplexColumnVector |
|
|
1323 ComplexMatrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1324 { |
|
|
1325 double rcond; |
|
|
1326 return solve (b, info, rcond); |
|
|
1327 } |
|
|
1328 |
|
|
1329 ComplexColumnVector |
|
|
1330 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
532
|
1331 double& rcond) const |
|
458
|
1332 { |
|
|
1333 ComplexColumnVector retval; |
|
|
1334 |
|
|
1335 int nr = rows (); |
|
|
1336 int nc = cols (); |
|
|
1337 int b_len = b.length (); |
|
|
1338 if (nr == 0 || nc == 0 || nr != nc || nr != b_len) |
|
|
1339 { |
|
|
1340 (*current_liboctave_error_handler) |
|
|
1341 ("matrix dimension mismatch in solution of linear equations"); |
|
|
1342 return ComplexColumnVector (); |
|
|
1343 } |
|
|
1344 |
|
|
1345 info = 0; |
|
|
1346 int *ipvt = new int [nr]; |
|
|
1347 |
|
|
1348 Complex *z = new Complex [nr]; |
|
|
1349 Complex *tmp_data = dup (data (), length ()); |
|
|
1350 |
|
|
1351 F77_FCN (zgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
1352 |
|
532
|
1353 volatile double tmp_rcond = rcond; |
|
|
1354 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
1355 { |
|
|
1356 info = -2; |
|
|
1357 } |
|
|
1358 else |
|
|
1359 { |
|
|
1360 int job = 0; |
|
|
1361 |
|
|
1362 Complex *result = dup (b.data (), b_len); |
|
|
1363 |
|
|
1364 F77_FCN (zgesl) (tmp_data, &nr, &nr, ipvt, result, &job); |
|
|
1365 |
|
|
1366 retval = ComplexColumnVector (result, b_len); |
|
|
1367 } |
|
|
1368 |
|
|
1369 delete [] tmp_data; |
|
|
1370 delete [] ipvt; |
|
|
1371 delete [] z; |
|
|
1372 |
|
|
1373 return retval; |
|
|
1374 } |
|
|
1375 |
|
|
1376 ComplexMatrix |
|
|
1377 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1378 { |
|
|
1379 int info; |
|
|
1380 int rank; |
|
|
1381 return lssolve (b, info, rank); |
|
|
1382 } |
|
|
1383 |
|
|
1384 ComplexMatrix |
|
|
1385 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1386 { |
|
|
1387 int rank; |
|
|
1388 return lssolve (b, info, rank); |
|
|
1389 } |
|
|
1390 |
|
|
1391 ComplexMatrix |
|
|
1392 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1393 { |
|
|
1394 int nrhs = b.cols (); |
|
|
1395 |
|
|
1396 int m = rows (); |
|
|
1397 int n = cols (); |
|
|
1398 |
|
|
1399 if (m == 0 || n == 0 || m != b.rows ()) |
|
|
1400 { |
|
|
1401 (*current_liboctave_error_handler) |
|
|
1402 ("matrix dimension mismatch solution of linear equations"); |
|
|
1403 return Matrix (); |
|
|
1404 } |
|
|
1405 |
|
|
1406 Complex *tmp_data = dup (data (), length ()); |
|
|
1407 |
|
|
1408 int nrr = m > n ? m : n; |
|
|
1409 ComplexMatrix result (nrr, nrhs); |
|
|
1410 |
|
|
1411 int i, j; |
|
|
1412 for (j = 0; j < nrhs; j++) |
|
|
1413 for (i = 0; i < m; i++) |
|
|
1414 result.elem (i, j) = b.elem (i, j); |
|
|
1415 |
|
|
1416 Complex *presult = result.fortran_vec (); |
|
|
1417 |
|
|
1418 int len_s = m < n ? m : n; |
|
|
1419 double *s = new double [len_s]; |
|
|
1420 double rcond = -1.0; |
|
|
1421 int lwork; |
|
|
1422 if (m < n) |
|
|
1423 lwork = 2*m + (nrhs > n ? nrhs : n); |
|
|
1424 else |
|
|
1425 lwork = 2*n + (nrhs > m ? nrhs : m); |
|
|
1426 |
|
|
1427 Complex *work = new Complex [lwork]; |
|
|
1428 |
|
|
1429 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1430 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1431 double *rwork = new double [lrwork]; |
|
|
1432 |
|
|
1433 F77_FCN (zgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s, |
|
|
1434 &rcond, &rank, work, &lwork, rwork, &info); |
|
|
1435 |
|
|
1436 ComplexMatrix retval (n, nrhs); |
|
|
1437 for (j = 0; j < nrhs; j++) |
|
|
1438 for (i = 0; i < n; i++) |
|
|
1439 retval.elem (i, j) = result.elem (i, j); |
|
|
1440 |
|
|
1441 delete [] tmp_data; |
|
|
1442 delete [] s; |
|
|
1443 delete [] work; |
|
|
1444 delete [] rwork; |
|
|
1445 |
|
|
1446 return retval; |
|
|
1447 } |
|
|
1448 |
|
|
1449 ComplexColumnVector |
|
|
1450 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1451 { |
|
|
1452 int info; |
|
|
1453 int rank; |
|
|
1454 return lssolve (b, info, rank); |
|
|
1455 } |
|
|
1456 |
|
|
1457 ComplexColumnVector |
|
|
1458 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1459 { |
|
|
1460 int rank; |
|
|
1461 return lssolve (b, info, rank); |
|
|
1462 } |
|
|
1463 |
|
|
1464 ComplexColumnVector |
|
|
1465 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info, |
|
|
1466 int& rank) const |
|
|
1467 { |
|
|
1468 int nrhs = 1; |
|
|
1469 |
|
|
1470 int m = rows (); |
|
|
1471 int n = cols (); |
|
|
1472 |
|
|
1473 if (m == 0 || n == 0 || m != b.length ()) |
|
|
1474 { |
|
|
1475 (*current_liboctave_error_handler) |
|
|
1476 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1477 return ComplexColumnVector (); |
|
|
1478 } |
|
|
1479 |
|
|
1480 Complex *tmp_data = dup (data (), length ()); |
|
|
1481 |
|
|
1482 int nrr = m > n ? m : n; |
|
|
1483 ComplexColumnVector result (nrr); |
|
|
1484 |
|
|
1485 int i; |
|
|
1486 for (i = 0; i < m; i++) |
|
|
1487 result.elem (i) = b.elem (i); |
|
|
1488 |
|
|
1489 Complex *presult = result.fortran_vec (); |
|
|
1490 |
|
|
1491 int len_s = m < n ? m : n; |
|
|
1492 double *s = new double [len_s]; |
|
|
1493 double rcond = -1.0; |
|
|
1494 int lwork; |
|
|
1495 if (m < n) |
|
|
1496 lwork = 2*m + (nrhs > n ? nrhs : n); |
|
|
1497 else |
|
|
1498 lwork = 2*n + (nrhs > m ? nrhs : m); |
|
|
1499 |
|
|
1500 Complex *work = new Complex [lwork]; |
|
|
1501 |
|
|
1502 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1503 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1504 double *rwork = new double [lrwork]; |
|
|
1505 |
|
|
1506 F77_FCN (zgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s, |
|
|
1507 &rcond, &rank, work, &lwork, rwork, &info); |
|
|
1508 |
|
|
1509 ComplexColumnVector retval (n); |
|
|
1510 for (i = 0; i < n; i++) |
|
|
1511 retval.elem (i) = result.elem (i); |
|
|
1512 |
|
|
1513 delete [] tmp_data; |
|
|
1514 delete [] s; |
|
|
1515 delete [] work; |
|
|
1516 delete [] rwork; |
|
|
1517 |
|
|
1518 return retval; |
|
|
1519 } |
|
|
1520 |
|
|
1521 // matrix by diagonal matrix -> matrix operations |
|
|
1522 |
|
|
1523 ComplexMatrix& |
|
|
1524 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
1525 { |
|
|
1526 int nr = rows (); |
|
|
1527 int nc = cols (); |
|
|
1528 if (nr != a.rows () || nc != a.cols ()) |
|
|
1529 { |
|
|
1530 (*current_liboctave_error_handler) |
|
|
1531 ("nonconformant matrix += operation attempted"); |
|
889
|
1532 return *this; |
|
458
|
1533 } |
|
|
1534 |
|
|
1535 for (int i = 0; i < a.length (); i++) |
|
|
1536 elem (i, i) += a.elem (i, i); |
|
|
1537 |
|
|
1538 return *this; |
|
|
1539 } |
|
|
1540 |
|
|
1541 ComplexMatrix& |
|
|
1542 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
1543 { |
|
|
1544 int nr = rows (); |
|
|
1545 int nc = cols (); |
|
|
1546 if (nr != a.rows () || nc != a.cols ()) |
|
|
1547 { |
|
|
1548 (*current_liboctave_error_handler) |
|
|
1549 ("nonconformant matrix -= operation attempted"); |
|
889
|
1550 return *this; |
|
458
|
1551 } |
|
|
1552 |
|
|
1553 for (int i = 0; i < a.length (); i++) |
|
|
1554 elem (i, i) -= a.elem (i, i); |
|
|
1555 |
|
|
1556 return *this; |
|
|
1557 } |
|
|
1558 |
|
|
1559 ComplexMatrix& |
|
|
1560 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
1561 { |
|
|
1562 int nr = rows (); |
|
|
1563 int nc = cols (); |
|
|
1564 if (nr != a.rows () || nc != a.cols ()) |
|
|
1565 { |
|
|
1566 (*current_liboctave_error_handler) |
|
|
1567 ("nonconformant matrix += operation attempted"); |
|
889
|
1568 return *this; |
|
458
|
1569 } |
|
|
1570 |
|
|
1571 for (int i = 0; i < a.length (); i++) |
|
|
1572 elem (i, i) += a.elem (i, i); |
|
|
1573 |
|
|
1574 return *this; |
|
|
1575 } |
|
|
1576 |
|
|
1577 ComplexMatrix& |
|
|
1578 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
1579 { |
|
|
1580 int nr = rows (); |
|
|
1581 int nc = cols (); |
|
|
1582 if (nr != a.rows () || nc != a.cols ()) |
|
|
1583 { |
|
|
1584 (*current_liboctave_error_handler) |
|
|
1585 ("nonconformant matrix -= operation attempted"); |
|
889
|
1586 return *this; |
|
458
|
1587 } |
|
|
1588 |
|
|
1589 for (int i = 0; i < a.length (); i++) |
|
|
1590 elem (i, i) -= a.elem (i, i); |
|
|
1591 |
|
|
1592 return *this; |
|
|
1593 } |
|
|
1594 |
|
|
1595 // matrix by matrix -> matrix operations |
|
|
1596 |
|
|
1597 ComplexMatrix& |
|
|
1598 ComplexMatrix::operator += (const Matrix& a) |
|
|
1599 { |
|
|
1600 int nr = rows (); |
|
|
1601 int nc = cols (); |
|
|
1602 if (nr != a.rows () || nc != a.cols ()) |
|
|
1603 { |
|
|
1604 (*current_liboctave_error_handler) |
|
|
1605 ("nonconformant matrix += operation attempted"); |
|
|
1606 return *this; |
|
|
1607 } |
|
|
1608 |
|
|
1609 if (nr == 0 || nc == 0) |
|
|
1610 return *this; |
|
|
1611 |
|
|
1612 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1613 |
|
|
1614 add2 (d, a.data (), length ()); |
|
|
1615 return *this; |
|
|
1616 } |
|
|
1617 |
|
|
1618 ComplexMatrix& |
|
|
1619 ComplexMatrix::operator -= (const Matrix& a) |
|
|
1620 { |
|
|
1621 int nr = rows (); |
|
|
1622 int nc = cols (); |
|
|
1623 if (nr != a.rows () || nc != a.cols ()) |
|
|
1624 { |
|
|
1625 (*current_liboctave_error_handler) |
|
|
1626 ("nonconformant matrix -= operation attempted"); |
|
|
1627 return *this; |
|
|
1628 } |
|
|
1629 |
|
|
1630 if (nr == 0 || nc == 0) |
|
|
1631 return *this; |
|
|
1632 |
|
|
1633 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1634 |
|
|
1635 subtract2 (d, a.data (), length ()); |
|
|
1636 return *this; |
|
|
1637 } |
|
|
1638 |
|
|
1639 ComplexMatrix& |
|
|
1640 ComplexMatrix::operator += (const ComplexMatrix& a) |
|
|
1641 { |
|
|
1642 int nr = rows (); |
|
|
1643 int nc = cols (); |
|
|
1644 if (nr != a.rows () || nc != a.cols ()) |
|
|
1645 { |
|
|
1646 (*current_liboctave_error_handler) |
|
|
1647 ("nonconformant matrix += operation attempted"); |
|
|
1648 return *this; |
|
|
1649 } |
|
|
1650 |
|
|
1651 if (nr == 0 || nc == 0) |
|
|
1652 return *this; |
|
|
1653 |
|
|
1654 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1655 |
|
|
1656 add2 (d, a.data (), length ()); |
|
|
1657 return *this; |
|
|
1658 } |
|
|
1659 |
|
|
1660 ComplexMatrix& |
|
|
1661 ComplexMatrix::operator -= (const ComplexMatrix& a) |
|
|
1662 { |
|
|
1663 int nr = rows (); |
|
|
1664 int nc = cols (); |
|
|
1665 if (nr != a.rows () || nc != a.cols ()) |
|
|
1666 { |
|
|
1667 (*current_liboctave_error_handler) |
|
|
1668 ("nonconformant matrix -= operation attempted"); |
|
|
1669 return *this; |
|
|
1670 } |
|
|
1671 |
|
|
1672 if (nr == 0 || nc == 0) |
|
|
1673 return *this; |
|
|
1674 |
|
|
1675 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1676 |
|
|
1677 subtract2 (d, a.data (), length ()); |
|
|
1678 return *this; |
|
|
1679 } |
|
|
1680 |
|
|
1681 // unary operations |
|
|
1682 |
|
|
1683 Matrix |
|
|
1684 ComplexMatrix::operator ! (void) const |
|
|
1685 { |
|
|
1686 return Matrix (not (data (), length ()), rows (), cols ()); |
|
|
1687 } |
|
|
1688 |
|
|
1689 // matrix by scalar -> matrix operations |
|
|
1690 |
|
|
1691 ComplexMatrix |
|
|
1692 operator + (const ComplexMatrix& a, double s) |
|
|
1693 { |
|
|
1694 return ComplexMatrix (add (a.data (), a.length (), s), |
|
|
1695 a.rows (), a.cols ()); |
|
|
1696 } |
|
|
1697 |
|
|
1698 ComplexMatrix |
|
|
1699 operator - (const ComplexMatrix& a, double s) |
|
|
1700 { |
|
|
1701 return ComplexMatrix (subtract (a.data (), a.length (), s), |
|
|
1702 a.rows (), a.cols ()); |
|
|
1703 } |
|
|
1704 |
|
|
1705 ComplexMatrix |
|
|
1706 operator * (const ComplexMatrix& a, double s) |
|
|
1707 { |
|
|
1708 return ComplexMatrix (multiply (a.data (), a.length (), s), |
|
|
1709 a.rows (), a.cols ()); |
|
|
1710 } |
|
|
1711 |
|
|
1712 ComplexMatrix |
|
|
1713 operator / (const ComplexMatrix& a, double s) |
|
|
1714 { |
|
|
1715 return ComplexMatrix (divide (a.data (), a.length (), s), |
|
|
1716 a.rows (), a.cols ()); |
|
|
1717 } |
|
|
1718 |
|
|
1719 // scalar by matrix -> matrix operations |
|
|
1720 |
|
|
1721 ComplexMatrix |
|
|
1722 operator + (double s, const ComplexMatrix& a) |
|
|
1723 { |
|
|
1724 return ComplexMatrix (add (a.data (), a.length (), s), a.rows (), |
|
|
1725 a.cols ()); |
|
|
1726 } |
|
|
1727 |
|
|
1728 ComplexMatrix |
|
|
1729 operator - (double s, const ComplexMatrix& a) |
|
|
1730 { |
|
|
1731 return ComplexMatrix (subtract (s, a.data (), a.length ()), |
|
|
1732 a.rows (), a.cols ()); |
|
|
1733 } |
|
|
1734 |
|
|
1735 ComplexMatrix |
|
|
1736 operator * (double s, const ComplexMatrix& a) |
|
|
1737 { |
|
|
1738 return ComplexMatrix (multiply (a.data (), a.length (), s), |
|
|
1739 a.rows (), a.cols ()); |
|
|
1740 } |
|
|
1741 |
|
|
1742 ComplexMatrix |
|
|
1743 operator / (double s, const ComplexMatrix& a) |
|
|
1744 { |
|
|
1745 return ComplexMatrix (divide (s, a.data (), a.length ()), |
|
|
1746 a.rows (), a.cols ()); |
|
|
1747 } |
|
|
1748 |
|
|
1749 // matrix by column vector -> column vector operations |
|
|
1750 |
|
|
1751 ComplexColumnVector |
|
|
1752 operator * (const ComplexMatrix& m, const ColumnVector& a) |
|
|
1753 { |
|
|
1754 ComplexColumnVector tmp (a); |
|
|
1755 return m * tmp; |
|
|
1756 } |
|
|
1757 |
|
|
1758 ComplexColumnVector |
|
|
1759 operator * (const ComplexMatrix& m, const ComplexColumnVector& a) |
|
|
1760 { |
|
|
1761 int nr = m.rows (); |
|
|
1762 int nc = m.cols (); |
|
|
1763 if (nc != a.length ()) |
|
|
1764 { |
|
|
1765 (*current_liboctave_error_handler) |
|
|
1766 ("nonconformant matrix multiplication attempted"); |
|
|
1767 return ComplexColumnVector (); |
|
|
1768 } |
|
|
1769 |
|
|
1770 if (nc == 0 || nr == 0) |
|
|
1771 return ComplexColumnVector (0); |
|
|
1772 |
|
|
1773 char trans = 'N'; |
|
|
1774 int ld = nr; |
|
|
1775 Complex alpha (1.0); |
|
|
1776 Complex beta (0.0); |
|
|
1777 int i_one = 1; |
|
|
1778 |
|
|
1779 Complex *y = new Complex [nr]; |
|
|
1780 |
|
|
1781 F77_FCN (zgemv) (&trans, &nr, &nc, &alpha, m.data (), &ld, a.data (), |
|
|
1782 &i_one, &beta, y, &i_one, 1L); |
|
|
1783 |
|
|
1784 return ComplexColumnVector (y, nr); |
|
|
1785 } |
|
|
1786 |
|
|
1787 // matrix by diagonal matrix -> matrix operations |
|
|
1788 |
|
|
1789 ComplexMatrix |
|
|
1790 operator + (const ComplexMatrix& m, const DiagMatrix& a) |
|
|
1791 { |
|
|
1792 int nr = m.rows (); |
|
|
1793 int nc = m.cols (); |
|
|
1794 if (nr != a.rows () || nc != a.cols ()) |
|
|
1795 { |
|
|
1796 (*current_liboctave_error_handler) |
|
|
1797 ("nonconformant matrix addition attempted"); |
|
|
1798 return ComplexMatrix (); |
|
|
1799 } |
|
|
1800 |
|
|
1801 if (nr == 0 || nc == 0) |
|
|
1802 return ComplexMatrix (nr, nc); |
|
|
1803 |
|
|
1804 ComplexMatrix result (m); |
|
|
1805 for (int i = 0; i < a.length (); i++) |
|
|
1806 result.elem (i, i) += a.elem (i, i); |
|
|
1807 |
|
|
1808 return result; |
|
|
1809 } |
|
|
1810 |
|
|
1811 ComplexMatrix |
|
|
1812 operator - (const ComplexMatrix& m, const DiagMatrix& a) |
|
|
1813 { |
|
|
1814 int nr = m.rows (); |
|
|
1815 int nc = m.cols (); |
|
|
1816 if (nr != a.rows () || nc != a.cols ()) |
|
|
1817 { |
|
|
1818 (*current_liboctave_error_handler) |
|
|
1819 ("nonconformant matrix subtraction attempted"); |
|
|
1820 return ComplexMatrix (); |
|
|
1821 } |
|
|
1822 |
|
|
1823 if (nr == 0 || nc == 0) |
|
|
1824 return ComplexMatrix (nr, nc); |
|
|
1825 |
|
|
1826 ComplexMatrix result (m); |
|
|
1827 for (int i = 0; i < a.length (); i++) |
|
|
1828 result.elem (i, i) -= a.elem (i, i); |
|
|
1829 |
|
|
1830 return result; |
|
|
1831 } |
|
|
1832 |
|
|
1833 ComplexMatrix |
|
|
1834 operator * (const ComplexMatrix& m, const DiagMatrix& a) |
|
|
1835 { |
|
|
1836 int nr = m.rows (); |
|
|
1837 int nc = m.cols (); |
|
|
1838 int a_nc = a.cols (); |
|
|
1839 if (nc != a.rows ()) |
|
|
1840 { |
|
|
1841 (*current_liboctave_error_handler) |
|
|
1842 ("nonconformant matrix multiplication attempted"); |
|
|
1843 return ComplexMatrix (); |
|
|
1844 } |
|
|
1845 |
|
|
1846 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
1847 return ComplexMatrix (nr, nc, 0.0); |
|
|
1848 |
|
|
1849 Complex *c = new Complex [nr*a_nc]; |
|
533
|
1850 Complex *ctmp = 0; |
|
458
|
1851 |
|
|
1852 for (int j = 0; j < a.length (); j++) |
|
|
1853 { |
|
|
1854 int idx = j * nr; |
|
|
1855 ctmp = c + idx; |
|
|
1856 if (a.elem (j, j) == 1.0) |
|
|
1857 { |
|
|
1858 for (int i = 0; i < nr; i++) |
|
|
1859 ctmp[i] = m.elem (i, j); |
|
|
1860 } |
|
|
1861 else if (a.elem (j, j) == 0.0) |
|
|
1862 { |
|
|
1863 for (int i = 0; i < nr; i++) |
|
|
1864 ctmp[i] = 0.0; |
|
|
1865 } |
|
|
1866 else |
|
|
1867 { |
|
|
1868 for (int i = 0; i < nr; i++) |
|
|
1869 ctmp[i] = a.elem (j, j) * m.elem (i, j); |
|
|
1870 } |
|
|
1871 } |
|
|
1872 |
|
|
1873 if (a.rows () < a_nc) |
|
|
1874 { |
|
|
1875 for (int i = nr * nc; i < nr * a_nc; i++) |
|
|
1876 ctmp[i] = 0.0; |
|
|
1877 } |
|
|
1878 |
|
|
1879 return ComplexMatrix (c, nr, a_nc); |
|
|
1880 } |
|
|
1881 |
|
|
1882 ComplexMatrix |
|
|
1883 operator + (const ComplexMatrix& m, const ComplexDiagMatrix& a) |
|
|
1884 { |
|
|
1885 int nr = m.rows (); |
|
|
1886 int nc = m.cols (); |
|
|
1887 if (nr != a.rows () || nc != a.cols ()) |
|
|
1888 { |
|
|
1889 (*current_liboctave_error_handler) |
|
|
1890 ("nonconformant matrix addition attempted"); |
|
|
1891 return ComplexMatrix (); |
|
|
1892 } |
|
|
1893 |
|
|
1894 if (nr == 0 || nc == 0) |
|
|
1895 return ComplexMatrix (nr, nc); |
|
|
1896 |
|
|
1897 ComplexMatrix result (m); |
|
|
1898 for (int i = 0; i < a.length (); i++) |
|
|
1899 result.elem (i, i) += a.elem (i, i); |
|
|
1900 |
|
|
1901 return result; |
|
|
1902 } |
|
|
1903 |
|
|
1904 ComplexMatrix |
|
|
1905 operator - (const ComplexMatrix& m, const ComplexDiagMatrix& a) |
|
|
1906 { |
|
|
1907 int nr = m.rows (); |
|
|
1908 int nc = m.cols (); |
|
|
1909 if (nr != a.rows () || nc != a.cols ()) |
|
|
1910 { |
|
|
1911 (*current_liboctave_error_handler) |
|
|
1912 ("nonconformant matrix subtraction attempted"); |
|
|
1913 return ComplexMatrix (); |
|
|
1914 } |
|
|
1915 |
|
|
1916 if (nr == 0 || nc == 0) |
|
|
1917 return ComplexMatrix (nr, nc); |
|
|
1918 |
|
|
1919 ComplexMatrix result (m); |
|
|
1920 for (int i = 0; i < a.length (); i++) |
|
|
1921 result.elem (i, i) -= a.elem (i, i); |
|
|
1922 |
|
|
1923 return result; |
|
|
1924 } |
|
|
1925 |
|
|
1926 ComplexMatrix |
|
|
1927 operator * (const ComplexMatrix& m, const ComplexDiagMatrix& a) |
|
|
1928 { |
|
|
1929 int nr = m.rows (); |
|
|
1930 int nc = m.cols (); |
|
|
1931 int a_nc = a.cols (); |
|
|
1932 if (nc != a.rows ()) |
|
|
1933 { |
|
|
1934 (*current_liboctave_error_handler) |
|
|
1935 ("nonconformant matrix multiplication attempted"); |
|
|
1936 return ComplexMatrix (); |
|
|
1937 } |
|
|
1938 |
|
|
1939 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
1940 return ComplexMatrix (nr, nc, 0.0); |
|
|
1941 |
|
|
1942 Complex *c = new Complex [nr*a_nc]; |
|
533
|
1943 Complex *ctmp = 0; |
|
458
|
1944 |
|
|
1945 for (int j = 0; j < a.length (); j++) |
|
|
1946 { |
|
|
1947 int idx = j * nr; |
|
|
1948 ctmp = c + idx; |
|
|
1949 if (a.elem (j, j) == 1.0) |
|
|
1950 { |
|
|
1951 for (int i = 0; i < nr; i++) |
|
|
1952 ctmp[i] = m.elem (i, j); |
|
|
1953 } |
|
|
1954 else if (a.elem (j, j) == 0.0) |
|
|
1955 { |
|
|
1956 for (int i = 0; i < nr; i++) |
|
|
1957 ctmp[i] = 0.0; |
|
|
1958 } |
|
|
1959 else |
|
|
1960 { |
|
|
1961 for (int i = 0; i < nr; i++) |
|
|
1962 ctmp[i] = a.elem (j, j) * m.elem (i, j); |
|
|
1963 } |
|
|
1964 } |
|
|
1965 |
|
|
1966 if (a.rows () < a_nc) |
|
|
1967 { |
|
|
1968 for (int i = nr * nc; i < nr * a_nc; i++) |
|
|
1969 ctmp[i] = 0.0; |
|
|
1970 } |
|
|
1971 |
|
|
1972 return ComplexMatrix (c, nr, a_nc); |
|
|
1973 } |
|
|
1974 |
|
|
1975 // matrix by matrix -> matrix operations |
|
|
1976 |
|
|
1977 ComplexMatrix |
|
|
1978 operator + (const ComplexMatrix& m, const Matrix& a) |
|
|
1979 { |
|
|
1980 int nr = m.rows (); |
|
|
1981 int nc = m.cols (); |
|
|
1982 if (nr != a.rows () || nc != a.cols ()) |
|
|
1983 { |
|
|
1984 (*current_liboctave_error_handler) |
|
|
1985 ("nonconformant matrix addition attempted"); |
|
|
1986 return ComplexMatrix (); |
|
|
1987 } |
|
|
1988 |
|
|
1989 if (nr == 0 || nc == 0) |
|
|
1990 return ComplexMatrix (nr, nc); |
|
|
1991 |
|
|
1992 return ComplexMatrix (add (m.data (), a.data (), m.length ()), nr, nc); |
|
|
1993 } |
|
|
1994 |
|
|
1995 ComplexMatrix |
|
|
1996 operator - (const ComplexMatrix& m, const Matrix& a) |
|
|
1997 { |
|
|
1998 int nr = m.rows (); |
|
|
1999 int nc = m.cols (); |
|
|
2000 if (nr != a.rows () || nc != a.cols ()) |
|
|
2001 { |
|
|
2002 (*current_liboctave_error_handler) |
|
|
2003 ("nonconformant matrix subtraction attempted"); |
|
|
2004 return ComplexMatrix (); |
|
|
2005 } |
|
|
2006 |
|
|
2007 if (nr == 0 || nc == 0) |
|
|
2008 return ComplexMatrix (nr, nc); |
|
|
2009 |
|
|
2010 return ComplexMatrix (subtract (m.data (), a.data (), m.length ()), nr, nc); |
|
|
2011 } |
|
|
2012 |
|
|
2013 ComplexMatrix |
|
|
2014 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
2015 { |
|
|
2016 ComplexMatrix tmp (a); |
|
|
2017 return m * tmp; |
|
|
2018 } |
|
|
2019 |
|
|
2020 ComplexMatrix |
|
|
2021 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
2022 { |
|
|
2023 int nr = m.rows (); |
|
|
2024 int nc = m.cols (); |
|
|
2025 int a_nc = a.cols (); |
|
|
2026 if (nc != a.rows ()) |
|
|
2027 { |
|
|
2028 (*current_liboctave_error_handler) |
|
|
2029 ("nonconformant matrix multiplication attempted"); |
|
|
2030 return ComplexMatrix (); |
|
|
2031 } |
|
|
2032 |
|
|
2033 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2034 return ComplexMatrix (nr, nc, 0.0); |
|
|
2035 |
|
|
2036 char trans = 'N'; |
|
|
2037 char transa = 'N'; |
|
|
2038 |
|
|
2039 int ld = nr; |
|
|
2040 int lda = a.rows (); |
|
|
2041 |
|
|
2042 Complex alpha (1.0); |
|
|
2043 Complex beta (0.0); |
|
|
2044 |
|
|
2045 Complex *c = new Complex [nr*a_nc]; |
|
|
2046 |
|
|
2047 F77_FCN (zgemm) (&trans, &transa, &nr, &a_nc, &nc, &alpha, m.data (), |
|
|
2048 &ld, a.data (), &lda, &beta, c, &nr, 1L, 1L); |
|
|
2049 |
|
|
2050 return ComplexMatrix (c, nr, a_nc); |
|
|
2051 } |
|
|
2052 |
|
|
2053 ComplexMatrix |
|
|
2054 product (const ComplexMatrix& m, const Matrix& a) |
|
|
2055 { |
|
|
2056 int nr = m.rows (); |
|
|
2057 int nc = m.cols (); |
|
|
2058 if (nr != a.rows () || nc != a.cols ()) |
|
|
2059 { |
|
|
2060 (*current_liboctave_error_handler) |
|
|
2061 ("nonconformant matrix product attempted"); |
|
|
2062 return ComplexMatrix (); |
|
|
2063 } |
|
|
2064 |
|
|
2065 if (nr == 0 || nc == 0) |
|
|
2066 return ComplexMatrix (nr, nc); |
|
|
2067 |
|
|
2068 return ComplexMatrix (multiply (m.data (), a.data (), m.length ()), nr, nc); |
|
|
2069 } |
|
|
2070 |
|
|
2071 ComplexMatrix |
|
|
2072 quotient (const ComplexMatrix& m, const Matrix& a) |
|
|
2073 { |
|
|
2074 int nr = m.rows (); |
|
|
2075 int nc = m.cols (); |
|
|
2076 if (nr != a.rows () || nc != a.cols ()) |
|
|
2077 { |
|
|
2078 (*current_liboctave_error_handler) |
|
|
2079 ("nonconformant matrix quotient attempted"); |
|
|
2080 return ComplexMatrix (); |
|
|
2081 } |
|
|
2082 |
|
|
2083 if (nr == 0 || nc == 0) |
|
|
2084 return ComplexMatrix (nr, nc); |
|
|
2085 |
|
|
2086 return ComplexMatrix (divide (m.data (), a.data (), m.length ()), nr, nc); |
|
|
2087 } |
|
|
2088 |
|
|
2089 // other operations |
|
|
2090 |
|
|
2091 ComplexMatrix |
|
|
2092 map (c_c_Mapper f, const ComplexMatrix& a) |
|
|
2093 { |
|
|
2094 ComplexMatrix b (a); |
|
|
2095 b.map (f); |
|
|
2096 return b; |
|
|
2097 } |
|
|
2098 |
|
|
2099 Matrix |
|
|
2100 map (d_c_Mapper f, const ComplexMatrix& a) |
|
|
2101 { |
|
|
2102 int a_nc = a.cols (); |
|
|
2103 int a_nr = a.rows (); |
|
|
2104 Matrix b (a_nr, a_nc); |
|
|
2105 for (int j = 0; j < a_nc; j++) |
|
|
2106 for (int i = 0; i < a_nr; i++) |
|
|
2107 b.elem (i, j) = f (a.elem (i, j)); |
|
|
2108 return b; |
|
|
2109 } |
|
|
2110 |
|
|
2111 void |
|
|
2112 ComplexMatrix::map (c_c_Mapper f) |
|
|
2113 { |
|
|
2114 for (int j = 0; j < cols (); j++) |
|
|
2115 for (int i = 0; i < rows (); i++) |
|
|
2116 elem (i, j) = f (elem (i, j)); |
|
|
2117 } |
|
|
2118 |
|
|
2119 Matrix |
|
|
2120 ComplexMatrix::all (void) const |
|
|
2121 { |
|
|
2122 int nr = rows (); |
|
|
2123 int nc = cols (); |
|
|
2124 Matrix retval; |
|
|
2125 if (nr > 0 && nc > 0) |
|
|
2126 { |
|
|
2127 if (nr == 1) |
|
|
2128 { |
|
|
2129 retval.resize (1, 1); |
|
|
2130 retval.elem (0, 0) = 1.0; |
|
|
2131 for (int j = 0; j < nc; j++) |
|
|
2132 { |
|
|
2133 if (elem (0, j) == 0.0) |
|
|
2134 { |
|
|
2135 retval.elem (0, 0) = 0.0; |
|
|
2136 break; |
|
|
2137 } |
|
|
2138 } |
|
|
2139 } |
|
|
2140 else if (nc == 1) |
|
|
2141 { |
|
|
2142 retval.resize (1, 1); |
|
|
2143 retval.elem (0, 0) = 1.0; |
|
|
2144 for (int i = 0; i < nr; i++) |
|
|
2145 { |
|
|
2146 if (elem (i, 0) == 0.0) |
|
|
2147 { |
|
|
2148 retval.elem (0, 0) = 0.0; |
|
|
2149 break; |
|
|
2150 } |
|
|
2151 } |
|
|
2152 } |
|
|
2153 else |
|
|
2154 { |
|
|
2155 retval.resize (1, nc); |
|
|
2156 for (int j = 0; j < nc; j++) |
|
|
2157 { |
|
|
2158 retval.elem (0, j) = 1.0; |
|
|
2159 for (int i = 0; i < nr; i++) |
|
|
2160 { |
|
|
2161 if (elem (i, j) == 0.0) |
|
|
2162 { |
|
|
2163 retval.elem (0, j) = 0.0; |
|
|
2164 break; |
|
|
2165 } |
|
|
2166 } |
|
|
2167 } |
|
|
2168 } |
|
|
2169 } |
|
|
2170 return retval; |
|
|
2171 } |
|
|
2172 |
|
|
2173 Matrix |
|
|
2174 ComplexMatrix::any (void) const |
|
|
2175 { |
|
|
2176 int nr = rows (); |
|
|
2177 int nc = cols (); |
|
|
2178 Matrix retval; |
|
|
2179 if (nr > 0 && nc > 0) |
|
|
2180 { |
|
|
2181 if (nr == 1) |
|
|
2182 { |
|
|
2183 retval.resize (1, 1); |
|
|
2184 retval.elem (0, 0) = 0.0; |
|
|
2185 for (int j = 0; j < nc; j++) |
|
|
2186 { |
|
|
2187 if (elem (0, j) != 0.0) |
|
|
2188 { |
|
|
2189 retval.elem (0, 0) = 1.0; |
|
|
2190 break; |
|
|
2191 } |
|
|
2192 } |
|
|
2193 } |
|
|
2194 else if (nc == 1) |
|
|
2195 { |
|
|
2196 retval.resize (1, 1); |
|
|
2197 retval.elem (0, 0) = 0.0; |
|
|
2198 for (int i = 0; i < nr; i++) |
|
|
2199 { |
|
|
2200 if (elem (i, 0) != 0.0) |
|
|
2201 { |
|
|
2202 retval.elem (0, 0) = 1.0; |
|
|
2203 break; |
|
|
2204 } |
|
|
2205 } |
|
|
2206 } |
|
|
2207 else |
|
|
2208 { |
|
|
2209 retval.resize (1, nc); |
|
|
2210 for (int j = 0; j < nc; j++) |
|
|
2211 { |
|
|
2212 retval.elem (0, j) = 0.0; |
|
|
2213 for (int i = 0; i < nr; i++) |
|
|
2214 { |
|
|
2215 if (elem (i, j) != 0.0) |
|
|
2216 { |
|
|
2217 retval.elem (0, j) = 1.0; |
|
|
2218 break; |
|
|
2219 } |
|
|
2220 } |
|
|
2221 } |
|
|
2222 } |
|
|
2223 } |
|
|
2224 return retval; |
|
|
2225 } |
|
|
2226 |
|
|
2227 ComplexMatrix |
|
|
2228 ComplexMatrix::cumprod (void) const |
|
|
2229 { |
|
|
2230 int nr = rows (); |
|
|
2231 int nc = cols (); |
|
|
2232 ComplexMatrix retval; |
|
|
2233 if (nr > 0 && nc > 0) |
|
|
2234 { |
|
|
2235 if (nr == 1) |
|
|
2236 { |
|
|
2237 retval.resize (1, nc); |
|
|
2238 Complex prod = elem (0, 0); |
|
|
2239 for (int j = 0; j < nc; j++) |
|
|
2240 { |
|
|
2241 retval.elem (0, j) = prod; |
|
|
2242 if (j < nc - 1) |
|
|
2243 prod *= elem (0, j+1); |
|
|
2244 } |
|
|
2245 } |
|
|
2246 else if (nc == 1) |
|
|
2247 { |
|
|
2248 retval.resize (nr, 1); |
|
|
2249 Complex prod = elem (0, 0); |
|
|
2250 for (int i = 0; i < nr; i++) |
|
|
2251 { |
|
|
2252 retval.elem (i, 0) = prod; |
|
|
2253 if (i < nr - 1) |
|
|
2254 prod *= elem (i+1, 0); |
|
|
2255 } |
|
|
2256 } |
|
|
2257 else |
|
|
2258 { |
|
|
2259 retval.resize (nr, nc); |
|
|
2260 for (int j = 0; j < nc; j++) |
|
|
2261 { |
|
|
2262 Complex prod = elem (0, j); |
|
|
2263 for (int i = 0; i < nr; i++) |
|
|
2264 { |
|
|
2265 retval.elem (i, j) = prod; |
|
|
2266 if (i < nr - 1) |
|
|
2267 prod *= elem (i+1, j); |
|
|
2268 } |
|
|
2269 } |
|
|
2270 } |
|
|
2271 } |
|
|
2272 return retval; |
|
|
2273 } |
|
|
2274 |
|
|
2275 ComplexMatrix |
|
|
2276 ComplexMatrix::cumsum (void) const |
|
|
2277 { |
|
|
2278 int nr = rows (); |
|
|
2279 int nc = cols (); |
|
|
2280 ComplexMatrix retval; |
|
|
2281 if (nr > 0 && nc > 0) |
|
|
2282 { |
|
|
2283 if (nr == 1) |
|
|
2284 { |
|
|
2285 retval.resize (1, nc); |
|
|
2286 Complex sum = elem (0, 0); |
|
|
2287 for (int j = 0; j < nc; j++) |
|
|
2288 { |
|
|
2289 retval.elem (0, j) = sum; |
|
|
2290 if (j < nc - 1) |
|
|
2291 sum += elem (0, j+1); |
|
|
2292 } |
|
|
2293 } |
|
|
2294 else if (nc == 1) |
|
|
2295 { |
|
|
2296 retval.resize (nr, 1); |
|
|
2297 Complex sum = elem (0, 0); |
|
|
2298 for (int i = 0; i < nr; i++) |
|
|
2299 { |
|
|
2300 retval.elem (i, 0) = sum; |
|
|
2301 if (i < nr - 1) |
|
|
2302 sum += elem (i+1, 0); |
|
|
2303 } |
|
|
2304 } |
|
|
2305 else |
|
|
2306 { |
|
|
2307 retval.resize (nr, nc); |
|
|
2308 for (int j = 0; j < nc; j++) |
|
|
2309 { |
|
|
2310 Complex sum = elem (0, j); |
|
|
2311 for (int i = 0; i < nr; i++) |
|
|
2312 { |
|
|
2313 retval.elem (i, j) = sum; |
|
|
2314 if (i < nr - 1) |
|
|
2315 sum += elem (i+1, j); |
|
|
2316 } |
|
|
2317 } |
|
|
2318 } |
|
|
2319 } |
|
|
2320 return retval; |
|
|
2321 } |
|
|
2322 |
|
|
2323 ComplexMatrix |
|
|
2324 ComplexMatrix::prod (void) const |
|
|
2325 { |
|
|
2326 int nr = rows (); |
|
|
2327 int nc = cols (); |
|
|
2328 ComplexMatrix retval; |
|
|
2329 if (nr > 0 && nc > 0) |
|
|
2330 { |
|
|
2331 if (nr == 1) |
|
|
2332 { |
|
|
2333 retval.resize (1, 1); |
|
|
2334 retval.elem (0, 0) = 1.0; |
|
|
2335 for (int j = 0; j < nc; j++) |
|
|
2336 retval.elem (0, 0) *= elem (0, j); |
|
|
2337 } |
|
|
2338 else if (nc == 1) |
|
|
2339 { |
|
|
2340 retval.resize (1, 1); |
|
|
2341 retval.elem (0, 0) = 1.0; |
|
|
2342 for (int i = 0; i < nr; i++) |
|
|
2343 retval.elem (0, 0) *= elem (i, 0); |
|
|
2344 } |
|
|
2345 else |
|
|
2346 { |
|
|
2347 retval.resize (1, nc); |
|
|
2348 for (int j = 0; j < nc; j++) |
|
|
2349 { |
|
|
2350 retval.elem (0, j) = 1.0; |
|
|
2351 for (int i = 0; i < nr; i++) |
|
|
2352 retval.elem (0, j) *= elem (i, j); |
|
|
2353 } |
|
|
2354 } |
|
|
2355 } |
|
|
2356 return retval; |
|
|
2357 } |
|
|
2358 |
|
|
2359 ComplexMatrix |
|
|
2360 ComplexMatrix::sum (void) const |
|
|
2361 { |
|
|
2362 int nr = rows (); |
|
|
2363 int nc = cols (); |
|
|
2364 ComplexMatrix retval; |
|
|
2365 if (nr > 0 && nc > 0) |
|
|
2366 { |
|
|
2367 if (nr == 1) |
|
|
2368 { |
|
|
2369 retval.resize (1, 1); |
|
|
2370 retval.elem (0, 0) = 0.0; |
|
|
2371 for (int j = 0; j < nc; j++) |
|
|
2372 retval.elem (0, 0) += elem (0, j); |
|
|
2373 } |
|
|
2374 else if (nc == 1) |
|
|
2375 { |
|
|
2376 retval.resize (1, 1); |
|
|
2377 retval.elem (0, 0) = 0.0; |
|
|
2378 for (int i = 0; i < nr; i++) |
|
|
2379 retval.elem (0, 0) += elem (i, 0); |
|
|
2380 } |
|
|
2381 else |
|
|
2382 { |
|
|
2383 retval.resize (1, nc); |
|
|
2384 for (int j = 0; j < nc; j++) |
|
|
2385 { |
|
|
2386 retval.elem (0, j) = 0.0; |
|
|
2387 for (int i = 0; i < nr; i++) |
|
|
2388 retval.elem (0, j) += elem (i, j); |
|
|
2389 } |
|
|
2390 } |
|
|
2391 } |
|
|
2392 return retval; |
|
|
2393 } |
|
|
2394 |
|
|
2395 ComplexMatrix |
|
|
2396 ComplexMatrix::sumsq (void) const |
|
|
2397 { |
|
|
2398 int nr = rows (); |
|
|
2399 int nc = cols (); |
|
|
2400 ComplexMatrix retval; |
|
|
2401 if (nr > 0 && nc > 0) |
|
|
2402 { |
|
|
2403 if (nr == 1) |
|
|
2404 { |
|
|
2405 retval.resize (1, 1); |
|
|
2406 retval.elem (0, 0) = 0.0; |
|
|
2407 for (int j = 0; j < nc; j++) |
|
|
2408 { |
|
|
2409 Complex d = elem (0, j); |
|
|
2410 retval.elem (0, 0) += d * d; |
|
|
2411 } |
|
|
2412 } |
|
|
2413 else if (nc == 1) |
|
|
2414 { |
|
|
2415 retval.resize (1, 1); |
|
|
2416 retval.elem (0, 0) = 0.0; |
|
|
2417 for (int i = 0; i < nr; i++) |
|
|
2418 { |
|
|
2419 Complex d = elem (i, 0); |
|
|
2420 retval.elem (0, 0) += d * d; |
|
|
2421 } |
|
|
2422 } |
|
|
2423 else |
|
|
2424 { |
|
|
2425 retval.resize (1, nc); |
|
|
2426 for (int j = 0; j < nc; j++) |
|
|
2427 { |
|
|
2428 retval.elem (0, j) = 0.0; |
|
|
2429 for (int i = 0; i < nr; i++) |
|
|
2430 { |
|
|
2431 Complex d = elem (i, j); |
|
|
2432 retval.elem (0, j) += d * d; |
|
|
2433 } |
|
|
2434 } |
|
|
2435 } |
|
|
2436 } |
|
|
2437 return retval; |
|
|
2438 } |
|
|
2439 |
|
|
2440 ComplexColumnVector |
|
|
2441 ComplexMatrix::diag (void) const |
|
|
2442 { |
|
|
2443 return diag (0); |
|
|
2444 } |
|
|
2445 |
|
|
2446 ComplexColumnVector |
|
|
2447 ComplexMatrix::diag (int k) const |
|
|
2448 { |
|
|
2449 int nnr = rows (); |
|
|
2450 int nnc = cols (); |
|
|
2451 if (k > 0) |
|
|
2452 nnc -= k; |
|
|
2453 else if (k < 0) |
|
|
2454 nnr += k; |
|
|
2455 |
|
|
2456 ComplexColumnVector d; |
|
|
2457 |
|
|
2458 if (nnr > 0 && nnc > 0) |
|
|
2459 { |
|
|
2460 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2461 |
|
|
2462 d.resize (ndiag); |
|
|
2463 |
|
|
2464 if (k > 0) |
|
|
2465 { |
|
|
2466 for (int i = 0; i < ndiag; i++) |
|
|
2467 d.elem (i) = elem (i, i+k); |
|
|
2468 } |
|
|
2469 else if ( k < 0) |
|
|
2470 { |
|
|
2471 for (int i = 0; i < ndiag; i++) |
|
|
2472 d.elem (i) = elem (i-k, i); |
|
|
2473 } |
|
|
2474 else |
|
|
2475 { |
|
|
2476 for (int i = 0; i < ndiag; i++) |
|
|
2477 d.elem (i) = elem (i, i); |
|
|
2478 } |
|
|
2479 } |
|
|
2480 else |
|
|
2481 cerr << "diag: requested diagonal out of range\n"; |
|
|
2482 |
|
|
2483 return d; |
|
|
2484 } |
|
|
2485 |
|
891
|
2486 // XXX FIXME XXX -- it would be nice to share some code among all the |
|
|
2487 // min/max functions below. It would also be nice to combine the |
|
|
2488 // min/max and min_loc/max_loc functions. |
|
|
2489 |
|
458
|
2490 ComplexColumnVector |
|
|
2491 ComplexMatrix::row_min (void) const |
|
|
2492 { |
|
|
2493 ComplexColumnVector result; |
|
|
2494 |
|
|
2495 int nr = rows (); |
|
|
2496 int nc = cols (); |
|
|
2497 if (nr > 0 && nc > 0) |
|
|
2498 { |
|
|
2499 result.resize (nr); |
|
|
2500 |
|
|
2501 for (int i = 0; i < nr; i++) |
|
|
2502 { |
|
891
|
2503 int row_is_real_only = 1; |
|
|
2504 for (int j = 0; j < nc; j++) |
|
|
2505 if (imag (elem (i, j)) != 0.0) |
|
458
|
2506 { |
|
891
|
2507 row_is_real_only = 0; |
|
|
2508 break; |
|
458
|
2509 } |
|
891
|
2510 |
|
|
2511 if (row_is_real_only) |
|
|
2512 { |
|
|
2513 double res = real (elem (i, 0)); |
|
|
2514 for (int j = 1; j < nc; j++) |
|
|
2515 { |
|
|
2516 double tmp = real (elem (i, j)); |
|
|
2517 if (tmp < res) |
|
|
2518 res = tmp; |
|
|
2519 } |
|
|
2520 result.elem (i) = res; |
|
|
2521 } |
|
|
2522 else |
|
|
2523 { |
|
|
2524 Complex res = elem (i, 0); |
|
|
2525 double absres = abs (res); |
|
|
2526 for (int j = 1; j < nc; j++) |
|
|
2527 if (abs (elem (i, j)) < absres) |
|
|
2528 { |
|
|
2529 res = elem (i, j); |
|
|
2530 absres = abs (res); |
|
|
2531 } |
|
|
2532 result.elem (i) = res; |
|
|
2533 } |
|
458
|
2534 } |
|
|
2535 } |
|
|
2536 |
|
|
2537 return result; |
|
|
2538 } |
|
|
2539 |
|
|
2540 ComplexColumnVector |
|
|
2541 ComplexMatrix::row_min_loc (void) const |
|
|
2542 { |
|
|
2543 ComplexColumnVector result; |
|
|
2544 |
|
|
2545 int nr = rows (); |
|
|
2546 int nc = cols (); |
|
|
2547 |
|
|
2548 if (nr > 0 && nc > 0) |
|
|
2549 { |
|
|
2550 result.resize (nr); |
|
|
2551 |
|
|
2552 for (int i = 0; i < nr; i++) |
|
|
2553 { |
|
891
|
2554 int column_is_real_only = 1; |
|
|
2555 for (int j = 0; j < nc; j++) |
|
|
2556 if (imag (elem (i, j)) != 0.0) |
|
|
2557 { |
|
|
2558 column_is_real_only = 0; |
|
|
2559 break; |
|
|
2560 } |
|
|
2561 |
|
|
2562 if (column_is_real_only) |
|
|
2563 { |
|
|
2564 double res = 0; |
|
|
2565 double tmp = real (elem (i, 0)); |
|
|
2566 for (int j = 1; j < nc; j++) |
|
|
2567 if (real (elem (i, j)) < tmp) |
|
|
2568 res = j; |
|
|
2569 |
|
|
2570 result.elem (i) = res + 1; |
|
|
2571 } |
|
|
2572 else |
|
|
2573 { |
|
|
2574 Complex res = 0; |
|
|
2575 double absres = abs (elem (i, 0)); |
|
|
2576 for (int j = 1; j < nc; j++) |
|
|
2577 if (abs (elem (i, j)) < absres) |
|
|
2578 { |
|
|
2579 res = j; |
|
|
2580 absres = abs (elem (i, j)); |
|
|
2581 } |
|
|
2582 result.elem (i) = res + 1; |
|
|
2583 } |
|
458
|
2584 } |
|
|
2585 } |
|
|
2586 |
|
|
2587 return result; |
|
|
2588 } |
|
|
2589 |
|
|
2590 ComplexColumnVector |
|
|
2591 ComplexMatrix::row_max (void) const |
|
|
2592 { |
|
|
2593 ComplexColumnVector result; |
|
|
2594 |
|
|
2595 int nr = rows (); |
|
|
2596 int nc = cols (); |
|
|
2597 |
|
|
2598 if (nr > 0 && nc > 0) |
|
|
2599 { |
|
|
2600 result.resize (nr); |
|
|
2601 |
|
|
2602 for (int i = 0; i < nr; i++) |
|
|
2603 { |
|
891
|
2604 int row_is_real_only = 1; |
|
|
2605 for (int j = 0; j < nc; j++) |
|
|
2606 if (imag (elem (i, j)) != 0.0) |
|
458
|
2607 { |
|
891
|
2608 row_is_real_only = 0; |
|
|
2609 break; |
|
458
|
2610 } |
|
891
|
2611 |
|
|
2612 if (row_is_real_only) |
|
|
2613 { |
|
|
2614 double res = real (elem (i, 0)); |
|
|
2615 for (int j = 1; j < nc; j++) |
|
|
2616 { |
|
|
2617 double tmp = real (elem (i, j)); |
|
|
2618 if (tmp > res) |
|
|
2619 res = tmp; |
|
|
2620 } |
|
|
2621 result.elem (i) = res; |
|
|
2622 } |
|
|
2623 else |
|
|
2624 { |
|
|
2625 Complex res = elem (i, 0); |
|
|
2626 double absres = abs (res); |
|
|
2627 for (int j = 1; j < nc; j++) |
|
|
2628 if (abs (elem (i, j)) > absres) |
|
|
2629 { |
|
|
2630 res = elem (i, j); |
|
|
2631 absres = abs (res); |
|
|
2632 } |
|
|
2633 result.elem (i) = res; |
|
|
2634 } |
|
458
|
2635 } |
|
|
2636 } |
|
|
2637 |
|
|
2638 return result; |
|
|
2639 } |
|
|
2640 |
|
|
2641 ComplexColumnVector |
|
|
2642 ComplexMatrix::row_max_loc (void) const |
|
|
2643 { |
|
|
2644 ComplexColumnVector result; |
|
|
2645 |
|
|
2646 int nr = rows (); |
|
|
2647 int nc = cols (); |
|
|
2648 |
|
|
2649 if (nr > 0 && nc > 0) |
|
|
2650 { |
|
|
2651 result.resize (nr); |
|
|
2652 |
|
|
2653 for (int i = 0; i < nr; i++) |
|
|
2654 { |
|
891
|
2655 int column_is_real_only = 1; |
|
|
2656 for (int j = 0; j < nc; j++) |
|
|
2657 if (imag (elem (i, j)) != 0.0) |
|
|
2658 { |
|
|
2659 column_is_real_only = 0; |
|
|
2660 break; |
|
|
2661 } |
|
|
2662 |
|
|
2663 if (column_is_real_only) |
|
|
2664 { |
|
|
2665 double res = 0; |
|
|
2666 double tmp = real (elem (i, 0)); |
|
|
2667 for (int j = 1; j < nc; j++) |
|
|
2668 if (real (elem (i, j)) > tmp) |
|
|
2669 res = j; |
|
|
2670 |
|
|
2671 result.elem (i) = res + 1; |
|
|
2672 } |
|
|
2673 else |
|
|
2674 { |
|
|
2675 Complex res = 0; |
|
|
2676 double absres = abs (elem (i, 0)); |
|
|
2677 for (int j = 1; j < nc; j++) |
|
|
2678 if (abs (elem (i, j)) > absres) |
|
|
2679 { |
|
|
2680 res = j; |
|
|
2681 absres = abs (elem (i, j)); |
|
|
2682 } |
|
|
2683 result.elem (i) = res + 1; |
|
|
2684 } |
|
458
|
2685 } |
|
|
2686 } |
|
|
2687 |
|
|
2688 return result; |
|
|
2689 } |
|
|
2690 |
|
|
2691 ComplexRowVector |
|
|
2692 ComplexMatrix::column_min (void) const |
|
|
2693 { |
|
|
2694 ComplexRowVector result; |
|
|
2695 |
|
|
2696 int nr = rows (); |
|
|
2697 int nc = cols (); |
|
|
2698 |
|
|
2699 if (nr > 0 && nc > 0) |
|
|
2700 { |
|
|
2701 result.resize (nc); |
|
|
2702 |
|
|
2703 for (int j = 0; j < nc; j++) |
|
|
2704 { |
|
891
|
2705 int column_is_real_only = 1; |
|
|
2706 for (int i = 0; i < nr; i++) |
|
|
2707 if (imag (elem (i, j)) != 0.0) |
|
458
|
2708 { |
|
891
|
2709 column_is_real_only = 0; |
|
|
2710 break; |
|
458
|
2711 } |
|
891
|
2712 |
|
|
2713 if (column_is_real_only) |
|
|
2714 { |
|
|
2715 double res = real (elem (0, j)); |
|
|
2716 for (int i = 1; i < nr; i++) |
|
|
2717 { |
|
|
2718 double tmp = real (elem (i, j)); |
|
|
2719 if (tmp < res) |
|
|
2720 res = tmp; |
|
|
2721 } |
|
|
2722 result.elem (j) = res; |
|
|
2723 } |
|
|
2724 else |
|
|
2725 { |
|
|
2726 Complex res = elem (0, j); |
|
|
2727 double absres = abs (res); |
|
|
2728 for (int i = 1; i < nr; i++) |
|
|
2729 if (abs (elem (i, j)) < absres) |
|
|
2730 { |
|
|
2731 res = elem (i, j); |
|
|
2732 absres = abs (res); |
|
|
2733 } |
|
|
2734 result.elem (j) = res; |
|
|
2735 } |
|
458
|
2736 } |
|
|
2737 } |
|
|
2738 |
|
|
2739 return result; |
|
|
2740 } |
|
|
2741 |
|
|
2742 ComplexRowVector |
|
|
2743 ComplexMatrix::column_min_loc (void) const |
|
|
2744 { |
|
|
2745 ComplexRowVector result; |
|
|
2746 |
|
|
2747 int nr = rows (); |
|
|
2748 int nc = cols (); |
|
|
2749 |
|
|
2750 if (nr > 0 && nc > 0) |
|
|
2751 { |
|
|
2752 result.resize (nc); |
|
|
2753 |
|
|
2754 for (int j = 0; j < nc; j++) |
|
|
2755 { |
|
891
|
2756 int column_is_real_only = 1; |
|
|
2757 for (int i = 0; i < nr; i++) |
|
|
2758 if (imag (elem (i, j)) != 0.0) |
|
|
2759 { |
|
|
2760 column_is_real_only = 0; |
|
|
2761 break; |
|
|
2762 } |
|
|
2763 |
|
|
2764 if (column_is_real_only) |
|
|
2765 { |
|
|
2766 double res = 0; |
|
892
|
2767 double tmp = real (elem (0, j)); |
|
891
|
2768 for (int i = 1; i < nr; i++) |
|
|
2769 if (real (elem (i, j)) < tmp) |
|
|
2770 res = i; |
|
|
2771 |
|
|
2772 result.elem (j) = res + 1; |
|
|
2773 } |
|
|
2774 else |
|
|
2775 { |
|
|
2776 Complex res = 0; |
|
|
2777 double absres = abs (elem (0, j)); |
|
|
2778 for (int i = 1; i < nr; i++) |
|
|
2779 if (abs (elem (i, j)) < absres) |
|
|
2780 { |
|
|
2781 res = i; |
|
|
2782 absres = abs (elem (i, j)); |
|
|
2783 } |
|
|
2784 result.elem (j) = res + 1; |
|
|
2785 } |
|
458
|
2786 } |
|
|
2787 } |
|
|
2788 |
|
|
2789 return result; |
|
|
2790 } |
|
|
2791 |
|
|
2792 ComplexRowVector |
|
|
2793 ComplexMatrix::column_max (void) const |
|
|
2794 { |
|
|
2795 ComplexRowVector result; |
|
|
2796 |
|
|
2797 int nr = rows (); |
|
|
2798 int nc = cols (); |
|
|
2799 |
|
|
2800 if (nr > 0 && nc > 0) |
|
|
2801 { |
|
|
2802 result.resize (nc); |
|
|
2803 |
|
|
2804 for (int j = 0; j < nc; j++) |
|
|
2805 { |
|
891
|
2806 int column_is_real_only = 1; |
|
|
2807 for (int i = 0; i < nr; i++) |
|
|
2808 if (imag (elem (i, j)) != 0.0) |
|
458
|
2809 { |
|
891
|
2810 column_is_real_only = 0; |
|
|
2811 break; |
|
458
|
2812 } |
|
891
|
2813 |
|
|
2814 if (column_is_real_only) |
|
|
2815 { |
|
|
2816 double res = real (elem (0, j)); |
|
|
2817 for (int i = 1; i < nr; i++) |
|
|
2818 { |
|
|
2819 double tmp = real (elem (i, j)); |
|
|
2820 if (tmp > res) |
|
|
2821 res = tmp; |
|
|
2822 } |
|
|
2823 result.elem (j) = res; |
|
|
2824 } |
|
|
2825 else |
|
|
2826 { |
|
|
2827 Complex res = elem (0, j); |
|
|
2828 double absres = abs (res); |
|
|
2829 for (int i = 1; i < nr; i++) |
|
|
2830 if (abs (elem (i, j)) > absres) |
|
|
2831 { |
|
|
2832 res = elem (i, j); |
|
|
2833 absres = abs (res); |
|
|
2834 } |
|
|
2835 result.elem (j) = res; |
|
|
2836 } |
|
458
|
2837 } |
|
|
2838 } |
|
|
2839 |
|
|
2840 return result; |
|
|
2841 } |
|
|
2842 |
|
|
2843 ComplexRowVector |
|
|
2844 ComplexMatrix::column_max_loc (void) const |
|
|
2845 { |
|
|
2846 ComplexRowVector result; |
|
|
2847 |
|
|
2848 int nr = rows (); |
|
|
2849 int nc = cols (); |
|
|
2850 |
|
|
2851 if (nr > 0 && nc > 0) |
|
|
2852 { |
|
|
2853 result.resize (nc); |
|
|
2854 |
|
|
2855 for (int j = 0; j < nc; j++) |
|
|
2856 { |
|
891
|
2857 int column_is_real_only = 1; |
|
|
2858 for (int i = 0; i < nr; i++) |
|
|
2859 if (imag (elem (i, j)) != 0.0) |
|
|
2860 { |
|
|
2861 column_is_real_only = 0; |
|
|
2862 break; |
|
|
2863 } |
|
|
2864 |
|
|
2865 if (column_is_real_only) |
|
|
2866 { |
|
|
2867 double res = 0; |
|
892
|
2868 double tmp = real (elem (0, j)); |
|
891
|
2869 for (int i = 1; i < nr; i++) |
|
|
2870 if (real (elem (i, j)) > tmp) |
|
|
2871 res = i; |
|
|
2872 |
|
|
2873 result.elem (j) = res + 1; |
|
|
2874 } |
|
|
2875 else |
|
|
2876 { |
|
|
2877 Complex res = 0; |
|
|
2878 double absres = abs (elem (0, j)); |
|
|
2879 for (int i = 1; i < nr; i++) |
|
|
2880 if (abs (elem (i, j)) > absres) |
|
|
2881 { |
|
|
2882 res = i; |
|
|
2883 absres = abs (elem (i, j)); |
|
|
2884 } |
|
|
2885 result.elem (j) = res + 1; |
|
|
2886 } |
|
458
|
2887 } |
|
|
2888 } |
|
|
2889 |
|
|
2890 return result; |
|
|
2891 } |
|
|
2892 |
|
|
2893 // i/o |
|
|
2894 |
|
|
2895 ostream& |
|
|
2896 operator << (ostream& os, const ComplexMatrix& a) |
|
|
2897 { |
|
|
2898 // int field_width = os.precision () + 7; |
|
|
2899 for (int i = 0; i < a.rows (); i++) |
|
|
2900 { |
|
|
2901 for (int j = 0; j < a.cols (); j++) |
|
|
2902 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2903 os << "\n"; |
|
|
2904 } |
|
|
2905 return os; |
|
|
2906 } |
|
|
2907 |
|
|
2908 istream& |
|
|
2909 operator >> (istream& is, ComplexMatrix& a) |
|
|
2910 { |
|
|
2911 int nr = a.rows (); |
|
|
2912 int nc = a.cols (); |
|
|
2913 |
|
|
2914 if (nr < 1 || nc < 1) |
|
|
2915 is.clear (ios::badbit); |
|
|
2916 else |
|
|
2917 { |
|
|
2918 Complex tmp; |
|
|
2919 for (int i = 0; i < nr; i++) |
|
|
2920 for (int j = 0; j < nc; j++) |
|
|
2921 { |
|
|
2922 is >> tmp; |
|
|
2923 if (is) |
|
|
2924 a.elem (i, j) = tmp; |
|
|
2925 else |
|
|
2926 break; |
|
|
2927 } |
|
|
2928 } |
|
|
2929 |
|
|
2930 return is; |
|
|
2931 } |
|
|
2932 |
|
|
2933 /* |
|
|
2934 ;;; Local Variables: *** |
|
|
2935 ;;; mode: C++ *** |
|
|
2936 ;;; page-delimiter: "^/\\*" *** |
|
|
2937 ;;; End: *** |
|
|
2938 */ |
