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3
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1 // Extra Matrix manipulations. -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992 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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238
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24 #ifdef HAVE_CONFIG_H |
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25 #include "config.h" |
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3
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26 #endif |
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27 |
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238
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28 #include <iostream.h> |
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29 |
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3
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30 #include "Matrix.h" |
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31 #include "mx-inlines.cc" |
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227
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32 #include "lo-error.h" |
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233
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33 #include "f77-uscore.h" |
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34 |
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35 // Fortran functions we call. |
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36 |
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37 extern "C" |
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38 { |
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39 int F77_FCN (dgesv) (const int*, const int*, double*, const int*, |
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40 int*, double*, const int*, int*); |
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41 |
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42 int F77_FCN (dgeqrf) (const int*, const int*, double*, const int*, |
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43 double*, double*, const int*, int*); |
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44 |
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45 int F77_FCN (dorgqr) (const int*, const int*, const int*, double*, |
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46 const int*, double*, double*, const int*, int*); |
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47 |
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48 int F77_FCN (dgeev) (const char*, const char*, const int*, double*, |
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49 const int*, double*, double*, double*, |
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50 const int*, double*, const int*, double*, |
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51 const int*, int*, long, long); |
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52 |
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274
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53 int F77_FCN (dgeesx) (const char*, const char*, |
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54 int (*)(double*, double*), const char*, |
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233
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55 const int*, double*, const int*, int*, double*, |
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56 double*, double*, const int*, double*, double*, |
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57 double*, const int*, int*, const int*, int*, |
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58 int*, long, long); |
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59 |
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60 int F77_FCN (dgebal) (const char*, const int*, double*, |
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61 const int*, int*, int*, double*, |
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62 int*, long, long); |
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63 |
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64 int F77_FCN (dgebak) (const char*, const char*, const int*, const int*, |
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65 const int*, double*, const int*, double*, const int*, |
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66 int*, long, long); |
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67 |
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68 int F77_FCN (dgehrd) (const int*, const int*, const int*, |
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69 double*, const int*, double*, double*, |
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70 const int*, int*, long, long); |
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71 |
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72 int F77_FCN (dorghr) (const int*, const int*, const int*, |
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73 double*, const int*, double*, double*, |
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74 const int*, int*, long, long); |
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75 |
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76 int F77_FCN (dgesvd) (const char*, const char*, const int*, |
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77 const int*, double*, const int*, double*, |
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78 double*, const int*, double*, const int*, |
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79 double*, const int*, int*, long, long); |
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80 |
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81 int F77_FCN (dpotrf) (const char*, const int*, double*, const int*, |
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82 int*, long); |
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83 |
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84 // |
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85 // fortran functions for generalized eigenvalue problems |
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86 // |
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87 int F77_FCN (reduce) (const int*, const int*, double*, |
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88 const int*, double*, |
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89 int*, int*, double*, double*); |
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90 |
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91 int F77_FCN (scaleg) (const int*, const int*, double*, |
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92 const int*, double*, |
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93 const int*, const int*, double*, double*, double*); |
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94 |
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95 int F77_FCN (gradeq) (const int*, const int*, double*, |
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96 const int*, double*, |
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97 int*, int*, double*, double*); |
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98 |
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99 /* |
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100 * f2c translates complex*16 as |
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101 * |
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102 * typedef struct { doublereal re, im; } doublecomplex; |
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103 * |
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104 * and Complex.h from libg++ uses |
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105 * |
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106 * protected: |
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107 * double re; |
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108 * double im; |
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109 * |
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110 * as the only data members, so this should work (fingers crossed that |
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111 * things don't change). |
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112 */ |
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113 |
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114 int F77_FCN (zgesv) (const int*, const int*, Complex*, const int*, |
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115 int*, Complex*, const int*, int*); |
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116 |
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117 int F77_FCN (zgeqrf) (const int*, const int*, Complex*, const int*, |
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118 Complex*, Complex*, const int*, int*); |
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119 |
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274
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120 int F77_FCN (zgeesx) (const char*, const char*, int (*)(Complex*), |
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121 const char*, const int*, Complex*, const int*, |
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122 int*, Complex*, Complex*, const int*, double*, |
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123 double*, Complex*, const int*, double*, int*, |
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124 int*, long, long); |
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233
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125 |
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126 int F77_FCN (zgebal) (const char*, const int*, Complex*, const int*, |
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127 int*, int*, double*, int*, long, long); |
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128 |
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129 int F77_FCN (zgebak) (const char*, const char*, const int*, const int*, |
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130 const int*, double*, const int*, Complex*, |
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131 const int*, int*, long, long); |
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132 |
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133 int F77_FCN (zgehrd) (const int*, const int*, const int*, Complex*, |
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134 const int*, Complex*, Complex*, const int*, |
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135 int*, long, long); |
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136 |
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137 int F77_FCN (zunghr) (const int*, const int*, const int*, Complex*, |
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138 const int*, Complex*, Complex*, const int*, |
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139 int*, long, long); |
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140 |
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141 int F77_FCN (zungqr) (const int*, const int*, const int*, Complex*, |
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142 const int*, Complex*, Complex*, const int*, int*); |
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143 |
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144 int F77_FCN (zgeev) (const char*, const char*, const int*, Complex*, |
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145 const int*, Complex*, Complex*, const int*, |
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146 Complex*, const int*, Complex*, const int*, |
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147 double*, int*, long, long); |
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148 |
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149 int F77_FCN (zgesvd) (const char*, const char*, const int*, |
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150 const int*, Complex*, const int*, double*, |
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151 Complex*, const int*, Complex*, const int*, |
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152 Complex*, const int*, double*, int*, long, long); |
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153 |
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154 int F77_FCN (zpotrf) (const char*, const int*, Complex*, const int*, |
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155 int*, long); |
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156 } |
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157 |
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158 /* |
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22
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159 * AEPBALANCE operations |
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160 */ |
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161 |
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162 int |
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163 AEPBALANCE::init (const Matrix& a, const char *balance_job) |
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164 { |
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238
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165 int a_nc = a.cols (); |
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166 if (a.rows () != a_nc) |
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227
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167 { |
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168 (*current_liboctave_error_handler) ("AEPBALANCE requires square matrix"); |
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169 return -1; |
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170 } |
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171 |
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238
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172 int n = a_nc; |
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173 |
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174 // Parameters for balance call. |
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175 |
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176 int info; |
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177 int ilo; |
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178 int ihi; |
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179 double *scale = new double [n]; |
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180 |
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181 // Copy matrix into local structure. |
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182 |
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183 balanced_mat = a; |
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184 |
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185 F77_FCN (dgebal) (balance_job, &n, balanced_mat.fortran_vec (), |
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186 &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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187 |
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188 // Initialize balancing matrix to identity. |
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189 |
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190 balancing_mat = Matrix (n, n, 0.0); |
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191 for (int i = 0; i < n; i++) |
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192 balancing_mat.elem (i ,i) = 1.0; |
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193 |
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194 F77_FCN (dgebak) (balance_job, "R", &n, &ilo, &ihi, scale, &n, |
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195 balancing_mat.fortran_vec (), &n, &info, 1L, 1L); |
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196 |
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197 delete [] scale; |
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198 |
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199 return info; |
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200 } |
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201 |
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202 int |
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203 ComplexAEPBALANCE::init (const ComplexMatrix& a, const char *balance_job) |
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204 { |
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205 |
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238
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206 int n = a.cols (); |
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207 |
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208 // Parameters for balance call. |
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209 |
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210 int info; |
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211 int ilo; |
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212 int ihi; |
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213 double *scale = new double [n]; |
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214 |
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215 // Copy matrix into local structure. |
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216 |
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217 balanced_mat = a; |
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218 |
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219 F77_FCN (zgebal) (balance_job, &n, balanced_mat.fortran_vec (), |
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220 &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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221 |
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222 // Initialize balancing matrix to identity. |
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223 |
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224 balancing_mat = Matrix (n, n, 0.0); |
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225 for (int i = 0; i < n; i++) |
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226 balancing_mat (i, i) = 1.0; |
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227 |
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228 F77_FCN (zgebak) (balance_job, "R", &n, &ilo, &ihi, scale, &n, |
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238
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229 balancing_mat.fortran_vec (), &n, &info, 1L, 1L); |
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230 |
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231 delete [] scale; |
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232 |
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233 return info; |
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234 } |
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235 |
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236 /* |
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237 * GEPBALANCE operations |
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238 */ |
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239 |
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240 int |
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241 GEPBALANCE::init (const Matrix& a, const Matrix& b, const char *balance_job) |
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242 { |
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238
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243 int a_nr = a.rows (); |
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244 int a_nc = a.cols (); |
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245 int b_nr = b.rows (); |
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246 if (a_nr != a_nc || a_nr != b_nr || b_nr != b.cols ()) |
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227
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247 { |
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248 (*current_liboctave_error_handler) |
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249 ("GEPBALANCE requires square matrices of the same size"); |
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250 return -1; |
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251 } |
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252 |
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238
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253 int n = a_nc; |
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254 |
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255 // Parameters for balance call. |
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256 |
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257 int info; |
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258 int ilo; |
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259 int ihi; |
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260 double *cscale = new double [n]; |
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261 double *cperm = new double [n]; |
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262 Matrix wk (n, 6, 0.0); |
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263 |
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264 // Back out the permutations: |
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265 // |
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266 // cscale contains the exponents of the column scaling factors in its |
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267 // ilo through ihi locations and the reducing column permutations in |
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268 // its first ilo-1 and its ihi+1 through n locations. |
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269 // |
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270 // cperm contains the column permutations applied in grading the a and b |
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271 // submatrices in its ilo through ihi locations. |
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272 // |
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273 // wk contains the exponents of the row scaling factors in its ilo |
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274 // through ihi locations, the reducing row permutations in its first |
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275 // ilo-1 and its ihi+1 through n locations, and the row permutations |
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276 // applied in grading the a and b submatrices in its n+ilo through |
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277 // n+ihi locations. |
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278 |
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279 // Copy matrices into local structure. |
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280 |
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281 balanced_a_mat = a; |
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282 balanced_b_mat = b; |
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283 |
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284 // Initialize balancing matrices to identity. |
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285 |
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238
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286 left_balancing_mat = Matrix (n, n, 0.0); |
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287 for (int i = 0; i < n; i++) |
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288 left_balancing_mat (i, i) = 1.0; |
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289 |
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290 right_balancing_mat = left_balancing_mat; |
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291 |
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292 // Check for permutation option. |
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293 |
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294 if (*balance_job == 'P' || *balance_job == 'B') |
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295 { |
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233
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296 F77_FCN (reduce) (&n, &n, balanced_a_mat.fortran_vec (), |
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297 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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298 cscale, wk.fortran_vec ()); |
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22
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299 } |
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300 else |
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301 { |
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302 |
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303 // Set up for scaling later. |
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304 |
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305 ilo = 1; |
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306 ihi = n; |
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307 } |
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308 |
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309 // Check for scaling option. |
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310 |
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311 if ((*balance_job == 'S' || *balance_job == 'B') && ilo != ihi) |
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312 { |
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233
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313 F77_FCN (scaleg) (&n, &n, balanced_a_mat.fortran_vec (), |
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314 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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315 cscale, cperm, wk.fortran_vec ()); |
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316 } |
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317 else |
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318 { |
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319 |
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320 // Set scaling data to 0's. |
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321 |
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322 for (int tmp = ilo-1; tmp < ihi; tmp++) |
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323 { |
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324 cscale[tmp] = 0.0; |
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238
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325 wk.elem (tmp, 0) = 0.0; |
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326 } |
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327 } |
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328 |
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329 // Scaleg returns exponents, not values, so... |
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330 |
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331 for (int tmp = ilo-1; tmp < ihi; tmp++) |
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332 { |
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238
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333 cscale[tmp] = pow (2.0, cscale[tmp]); |
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334 wk.elem (tmp, 0) = pow (2.0, -wk.elem (tmp, 0)); |
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22
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335 } |
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336 |
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337 // Column permutations/scaling. |
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338 |
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339 F77_FCN (dgebak) (balance_job, "R", &n, &ilo, &ihi, cscale, &n, |
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340 right_balancing_mat.fortran_vec (), &n, &info, 1L, |
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341 1L); |
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342 |
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343 // Row permutations/scaling. |
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344 |
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345 F77_FCN (dgebak) (balance_job, "L", &n, &ilo, &ihi, &wk.elem (0, 0), &n, |
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346 left_balancing_mat.fortran_vec (), &n, &info, 1L, 1L); |
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347 |
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348 // XXX FIXME XXX --- these four lines need to be added and debugged. |
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349 // GEPBALANCE::init will work without them, though, so here they are. |
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350 |
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351 #if 0 |
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352 if ((*balance_job == 'P' || *balance_job == 'B') && ilo != ihi) |
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353 { |
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354 F77_FCN (gradeq) (&n, &n, balanced_a_mat.fortran_vec (), |
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355 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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356 cperm, &wk.elem (0, 1)); |
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357 } |
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358 #endif |
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359 |
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360 // Transpose for aa = cc*a*dd convention... |
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361 left_balancing_mat = left_balancing_mat.transpose (); |
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362 |
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363 delete [] cscale; |
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364 delete [] cperm; |
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365 |
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366 return info; |
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367 } |
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368 |
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369 /* |
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182
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370 * CHOL stuff |
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371 */ |
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372 |
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373 int |
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374 CHOL::init (const Matrix& a) |
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375 { |
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238
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376 int a_nr = a.rows (); |
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377 int a_nc = a.cols (); |
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378 if (a_nr != a_nc) |
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227
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379 { |
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380 (*current_liboctave_error_handler) ("CHOL requires square matrix"); |
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381 return -1; |
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382 } |
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182
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383 |
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384 char uplo = 'U'; |
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385 |
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238
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386 int n = a_nc; |
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182
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387 int info; |
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388 |
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238
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389 double *h = dup (a.data (), a.length ()); |
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182
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390 |
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391 F77_FCN (dpotrf) (&uplo, &n, h, &n, &info, 1L); |
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392 |
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393 chol_mat = Matrix (h, n, n); |
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394 |
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395 // If someone thinks of a more graceful way of doing this (or faster for |
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396 // that matter :-)), please let me know! |
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397 |
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398 if (n > 1) |
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238
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399 for (int j = 0; j < a_nc; j++) |
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400 for (int i = j+1; i < a_nr; i++) |
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182
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401 chol_mat.elem (i, j) = 0.0; |
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402 |
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403 return info; |
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404 } |
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405 |
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406 int |
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407 ComplexCHOL::init (const ComplexMatrix& a) |
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408 { |
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238
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409 int a_nr = a.rows (); |
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410 int a_nc = a.cols (); |
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411 if (a_nr != a_nc) |
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227
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412 { |
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413 (*current_liboctave_error_handler) |
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414 ("ComplexCHOL requires square matrix"); |
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415 return -1; |
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416 } |
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182
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417 |
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418 char uplo = 'U'; |
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419 |
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238
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420 int n = a_nc; |
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182
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421 int info; |
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422 |
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238
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423 Complex *h = dup (a.data (), a.length ()); |
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182
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424 |
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425 F77_FCN (zpotrf) (&uplo, &n, h, &n, &info, 1L); |
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426 |
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427 chol_mat = ComplexMatrix (h, n, n); |
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428 |
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429 // If someone thinks of a more graceful way of doing this (or faster for |
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430 // that matter :-)), please let me know! |
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431 |
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432 if (n > 1) |
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238
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433 for (int j = 0; j < a_nc; j++) |
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434 for (int i = j+1; i < a_nr; i++) |
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182
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435 chol_mat.elem (i, j) = 0.0; |
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436 |
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437 return info; |
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438 } |
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439 |
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440 /* |
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3
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441 * HESS stuff |
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442 */ |
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443 |
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444 int |
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445 HESS::init (const Matrix& a) |
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446 { |
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238
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447 int a_nr = a.rows (); |
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448 int a_nc = a.cols (); |
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449 if (a_nr != a_nc) |
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227
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450 { |
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451 (*current_liboctave_error_handler) ("HESS requires square matrix"); |
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452 return -1; |
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453 } |
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3
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454 |
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22
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455 char jobbal = 'N'; |
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3
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456 char side = 'R'; |
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457 |
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238
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458 int n = a_nc; |
|
3
|
459 int lwork = 32 * n; |
|
|
460 int info; |
|
|
461 int ilo; |
|
|
462 int ihi; |
|
|
463 |
|
238
|
464 double *h = dup (a.data (), a.length ()); |
|
3
|
465 |
|
|
466 double *tau = new double [n+1]; |
|
|
467 double *scale = new double [n]; |
|
|
468 double *z = new double [n*n]; |
|
|
469 double *work = new double [lwork]; |
|
|
470 |
|
|
471 F77_FCN (dgebal) (&jobbal, &n, h, &n, &ilo, &ihi, scale, &info, |
|
|
472 1L, 1L); |
|
|
473 |
|
|
474 F77_FCN (dgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, |
|
|
475 1L, 1L); |
|
|
476 |
|
238
|
477 copy (z, h, n*n); |
|
3
|
478 |
|
|
479 F77_FCN (dorghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, |
|
|
480 1L, 1L); |
|
|
481 |
|
|
482 F77_FCN (dgebak) (&jobbal, &side, &n, &ilo, &ihi, scale, &n, z, &n, |
|
|
483 &info, 1L, 1L); |
|
|
484 |
|
|
485 // We need to clear out all of the area below the sub-diagonal which was used |
|
|
486 // to store the unitary matrix. |
|
|
487 |
|
238
|
488 hess_mat = Matrix (h, n, n); |
|
|
489 unitary_hess_mat = Matrix (z, n, n); |
|
3
|
490 |
|
|
491 // If someone thinks of a more graceful way of doing this (or faster for |
|
|
492 // that matter :-)), please let me know! |
|
|
493 |
|
|
494 if (n > 2) |
|
238
|
495 for (int j = 0; j < a_nc; j++) |
|
|
496 for (int i = j+2; i < a_nr; i++) |
|
|
497 hess_mat.elem (i, j) = 0; |
|
3
|
498 |
|
|
499 delete [] tau; |
|
|
500 delete [] work; |
|
|
501 delete [] scale; |
|
|
502 |
|
|
503 return info; |
|
|
504 } |
|
|
505 |
|
|
506 int |
|
|
507 ComplexHESS::init (const ComplexMatrix& a) |
|
|
508 { |
|
238
|
509 int a_nr = a.rows (); |
|
|
510 int a_nc = a.cols (); |
|
|
511 if (a_nr != a_nc) |
|
227
|
512 { |
|
|
513 (*current_liboctave_error_handler) |
|
|
514 ("ComplexHESS requires square matrix"); |
|
|
515 return -1; |
|
|
516 } |
|
3
|
517 |
|
22
|
518 char job = 'N'; |
|
3
|
519 char side = 'R'; |
|
|
520 |
|
238
|
521 int n = a_nc; |
|
3
|
522 int lwork = 32 * n; |
|
|
523 int info; |
|
|
524 int ilo; |
|
|
525 int ihi; |
|
|
526 |
|
238
|
527 Complex *h = dup (a.data (), a.length ()); |
|
3
|
528 |
|
|
529 double *scale = new double [n]; |
|
|
530 Complex *tau = new Complex [n-1]; |
|
|
531 Complex *work = new Complex [lwork]; |
|
|
532 Complex *z = new Complex [n*n]; |
|
|
533 |
|
|
534 F77_FCN (zgebal) (&job, &n, h, &n, &ilo, &ihi, scale, &info, 1L, 1L); |
|
|
535 |
|
|
536 F77_FCN (zgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, 1L, |
|
233
|
537 1L); |
|
3
|
538 |
|
238
|
539 copy (z, h, n*n); |
|
3
|
540 |
|
|
541 F77_FCN (zunghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, 1L, |
|
233
|
542 1L); |
|
3
|
543 |
|
|
544 F77_FCN (zgebak) (&job, &side, &n, &ilo, &ihi, scale, &n, z, &n, &info, |
|
233
|
545 1L, 1L); |
|
3
|
546 |
|
|
547 hess_mat = ComplexMatrix (h,n,n); |
|
|
548 unitary_hess_mat = ComplexMatrix (z,n,n); |
|
|
549 |
|
|
550 // If someone thinks of a more graceful way of doing this (or faster for |
|
|
551 // that matter :-)), please let me know! |
|
|
552 |
|
|
553 if (n > 2) |
|
238
|
554 for (int j = 0; j < a_nc; j++) |
|
|
555 for (int i = j+2; i < a_nr; i++) |
|
|
556 hess_mat.elem (i, j) = 0; |
|
3
|
557 |
|
|
558 delete [] work; |
|
|
559 delete [] tau; |
|
|
560 delete [] scale; |
|
|
561 |
|
|
562 return info; |
|
|
563 } |
|
|
564 |
|
|
565 /* |
|
|
566 * SCHUR stuff |
|
|
567 */ |
|
|
568 |
|
|
569 static int |
|
|
570 select_ana (double *a, double *b) |
|
|
571 { |
|
|
572 return (*a < 0.0); |
|
|
573 } |
|
|
574 |
|
|
575 static int |
|
|
576 select_dig (double *a, double *b) |
|
|
577 { |
|
|
578 return (hypot (*a, *b) < 1.0); |
|
|
579 } |
|
|
580 |
|
|
581 int |
|
|
582 SCHUR::init (const Matrix& a, const char *ord) |
|
|
583 { |
|
238
|
584 int a_nr = a.rows (); |
|
|
585 int a_nc = a.cols (); |
|
|
586 if (a_nr != a_nc) |
|
227
|
587 { |
|
|
588 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
|
|
589 return -1; |
|
|
590 } |
|
3
|
591 |
|
|
592 char jobvs = 'V'; |
|
|
593 char sort; |
|
|
594 |
|
|
595 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
596 sort = 'S'; |
|
|
597 else |
|
|
598 sort = 'N'; |
|
|
599 |
|
|
600 char sense = 'N'; |
|
|
601 |
|
238
|
602 int n = a_nc; |
|
3
|
603 int lwork = 8 * n; |
|
|
604 int liwork = 1; |
|
|
605 int info; |
|
|
606 int sdim; |
|
|
607 double rconde; |
|
|
608 double rcondv; |
|
|
609 |
|
238
|
610 double *s = dup (a.data (), a.length ()); |
|
3
|
611 |
|
|
612 double *wr = new double [n]; |
|
|
613 double *wi = new double [n]; |
|
|
614 double *q = new double [n*n]; |
|
|
615 double *work = new double [lwork]; |
|
|
616 |
|
|
617 // These are not referenced for the non-ordered Schur routine. |
|
|
618 |
|
|
619 int *iwork = (int *) NULL; |
|
|
620 int *bwork = (int *) NULL; |
|
|
621 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
622 { |
|
|
623 iwork = new int [liwork]; |
|
|
624 bwork = new int [n]; |
|
|
625 } |
|
|
626 |
|
|
627 if (*ord == 'A' || *ord == 'a') |
|
|
628 { |
|
|
629 F77_FCN (dgeesx) (&jobvs, &sort, select_ana, &sense, &n, s, &n, |
|
|
630 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
|
|
631 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
|
|
632 } |
|
|
633 else if (*ord == 'D' || *ord == 'd') |
|
|
634 { |
|
|
635 F77_FCN (dgeesx) (&jobvs, &sort, select_dig, &sense, &n, s, &n, |
|
|
636 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
|
|
637 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
|
|
638 |
|
|
639 } |
|
|
640 else |
|
|
641 { |
|
274
|
642 F77_FCN (dgeesx) (&jobvs, &sort, (void *) 0, &sense, &n, s, |
|
3
|
643 &n, &sdim, wr, wi, q, &n, &rconde, &rcondv, |
|
|
644 work, &lwork, iwork, &liwork, bwork, &info, |
|
|
645 1L, 1L); |
|
|
646 } |
|
|
647 |
|
|
648 schur_mat = Matrix (s, n, n); |
|
|
649 unitary_mat = Matrix (q, n, n); |
|
|
650 |
|
|
651 delete [] wr; |
|
|
652 delete [] wi; |
|
|
653 delete [] work; |
|
|
654 delete [] iwork; |
|
|
655 delete [] bwork; |
|
|
656 |
|
|
657 return info; |
|
|
658 } |
|
|
659 |
|
|
660 static int |
|
|
661 complex_select_ana (Complex *a) |
|
|
662 { |
|
238
|
663 return a->real () < 0.0; |
|
3
|
664 } |
|
|
665 |
|
|
666 static int |
|
|
667 complex_select_dig (Complex *a) |
|
|
668 { |
|
|
669 return (abs (*a) < 1.0); |
|
|
670 } |
|
|
671 |
|
|
672 int |
|
|
673 ComplexSCHUR::init (const ComplexMatrix& a, const char *ord) |
|
|
674 { |
|
238
|
675 int a_nr = a.rows (); |
|
|
676 int a_nc = a.cols (); |
|
|
677 if (a_nr != a_nc) |
|
227
|
678 { |
|
|
679 (*current_liboctave_error_handler) |
|
|
680 ("ComplexSCHUR requires square matrix"); |
|
|
681 return -1; |
|
|
682 } |
|
3
|
683 |
|
|
684 char jobvs = 'V'; |
|
|
685 char sort; |
|
|
686 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
687 sort = 'S'; |
|
|
688 else |
|
|
689 sort = 'N'; |
|
|
690 |
|
|
691 char sense = 'N'; |
|
|
692 |
|
238
|
693 int n = a_nc; |
|
3
|
694 int lwork = 8 * n; |
|
|
695 int info; |
|
|
696 int sdim; |
|
|
697 double rconde; |
|
|
698 double rcondv; |
|
|
699 |
|
|
700 double *rwork = new double [n]; |
|
|
701 |
|
|
702 // bwork is not referenced for non-ordered Schur. |
|
|
703 |
|
|
704 int *bwork = (int *) NULL; |
|
|
705 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
706 bwork = new int [n]; |
|
|
707 |
|
238
|
708 Complex *s = dup (a.data (), a.length ()); |
|
3
|
709 |
|
|
710 Complex *work = new Complex [lwork]; |
|
|
711 Complex *q = new Complex [n*n]; |
|
|
712 Complex *w = new Complex [n]; |
|
|
713 |
|
|
714 if (*ord == 'A' || *ord == 'a') |
|
|
715 { |
|
|
716 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_ana, &sense, |
|
|
717 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
718 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
719 } |
|
|
720 else if (*ord == 'D' || *ord == 'd') |
|
|
721 { |
|
|
722 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_dig, &sense, |
|
|
723 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
724 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
725 } |
|
|
726 else |
|
|
727 { |
|
274
|
728 F77_FCN (zgeesx) (&jobvs, &sort, (void *) 0, &sense, &n, s, |
|
3
|
729 &n, &sdim, w, q, &n, &rconde, &rcondv, work, |
|
|
730 &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
731 } |
|
|
732 |
|
|
733 schur_mat = ComplexMatrix (s,n,n); |
|
|
734 unitary_mat = ComplexMatrix (q,n,n); |
|
|
735 |
|
|
736 delete [] w; |
|
|
737 delete [] work; |
|
|
738 delete [] rwork; |
|
|
739 delete [] bwork; |
|
|
740 |
|
|
741 return info; |
|
|
742 } |
|
|
743 |
|
|
744 ostream& |
|
|
745 operator << (ostream& os, const SCHUR& a) |
|
|
746 { |
|
|
747 os << a.schur_matrix () << "\n"; |
|
|
748 os << a.unitary_matrix () << "\n"; |
|
|
749 |
|
|
750 return os; |
|
|
751 } |
|
|
752 |
|
|
753 /* |
|
|
754 * SVD stuff |
|
|
755 */ |
|
|
756 |
|
|
757 int |
|
|
758 SVD::init (const Matrix& a) |
|
|
759 { |
|
|
760 int info; |
|
|
761 |
|
238
|
762 int m = a.rows (); |
|
|
763 int n = a.cols (); |
|
3
|
764 |
|
|
765 char jobu = 'A'; |
|
|
766 char jobv = 'A'; |
|
|
767 |
|
238
|
768 double *tmp_data = dup (a.data (), a.length ()); |
|
3
|
769 |
|
|
770 int min_mn = m < n ? m : n; |
|
|
771 int max_mn = m > n ? m : n; |
|
|
772 |
|
|
773 double *u = new double[m*m]; |
|
|
774 double *s_vec = new double[min_mn]; |
|
|
775 double *vt = new double[n*n]; |
|
|
776 |
|
|
777 int tmp1 = 3*min_mn + max_mn; |
|
|
778 int tmp2 = 5*min_mn - 4; |
|
|
779 int lwork = tmp1 > tmp2 ? tmp1 : tmp2; |
|
|
780 double *work = new double[lwork]; |
|
|
781 |
|
|
782 F77_FCN (dgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
783 vt, &n, work, &lwork, &info, 1L, 1L); |
|
|
784 |
|
|
785 left_sm = Matrix (u, m, m); |
|
|
786 sigma = DiagMatrix (s_vec, m, n); |
|
|
787 Matrix vt_m (vt, n, n); |
|
|
788 right_sm = Matrix (vt_m.transpose ()); |
|
|
789 |
|
|
790 delete [] tmp_data; |
|
|
791 delete [] work; |
|
|
792 |
|
|
793 return info; |
|
|
794 } |
|
|
795 |
|
|
796 ostream& |
|
|
797 operator << (ostream& os, const SVD& a) |
|
|
798 { |
|
|
799 os << a.left_singular_matrix () << "\n"; |
|
|
800 os << a.singular_values () << "\n"; |
|
|
801 os << a.right_singular_matrix () << "\n"; |
|
|
802 |
|
|
803 return os; |
|
|
804 } |
|
|
805 |
|
|
806 int |
|
|
807 ComplexSVD::init (const ComplexMatrix& a) |
|
|
808 { |
|
|
809 int info; |
|
|
810 |
|
238
|
811 int m = a.rows (); |
|
|
812 int n = a.cols (); |
|
3
|
813 |
|
|
814 char jobu = 'A'; |
|
|
815 char jobv = 'A'; |
|
|
816 |
|
238
|
817 Complex *tmp_data = dup (a.data (), a.length ()); |
|
3
|
818 |
|
|
819 int min_mn = m < n ? m : n; |
|
|
820 int max_mn = m > n ? m : n; |
|
|
821 |
|
|
822 Complex *u = new Complex[m*m]; |
|
|
823 double *s_vec = new double[min_mn]; |
|
|
824 Complex *vt = new Complex[n*n]; |
|
|
825 |
|
|
826 int lwork = 2*min_mn + max_mn; |
|
|
827 Complex *work = new Complex[lwork]; |
|
|
828 |
|
|
829 int lrwork = 5*max_mn; |
|
|
830 double *rwork = new double[lrwork]; |
|
|
831 |
|
|
832 F77_FCN (zgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
833 vt, &n, work, &lwork, rwork, &info, 1L, 1L); |
|
|
834 |
|
|
835 left_sm = ComplexMatrix (u, m, m); |
|
|
836 sigma = DiagMatrix (s_vec, m, n); |
|
|
837 ComplexMatrix vt_m (vt, n, n); |
|
|
838 right_sm = ComplexMatrix (vt_m.hermitian ()); |
|
|
839 |
|
|
840 delete [] tmp_data; |
|
|
841 delete [] work; |
|
|
842 |
|
|
843 return info; |
|
|
844 } |
|
|
845 |
|
|
846 /* |
|
238
|
847 * DET stuff. |
|
|
848 */ |
|
|
849 |
|
|
850 int |
|
|
851 DET::value_will_overflow (void) const |
|
|
852 { |
|
|
853 return det[2] + 1 > log10 (MAXDOUBLE) ? 1 : 0; |
|
|
854 } |
|
|
855 |
|
|
856 int |
|
|
857 DET::value_will_underflow (void) const |
|
|
858 { |
|
|
859 return det[2] - 1 < log10 (MINDOUBLE) ? 1 : 0; |
|
|
860 } |
|
|
861 |
|
|
862 double |
|
|
863 DET::coefficient (void) const |
|
|
864 { |
|
|
865 return det[0]; |
|
|
866 } |
|
|
867 |
|
|
868 int |
|
|
869 DET::exponent (void) const |
|
|
870 { |
|
|
871 return (int) det[1]; |
|
|
872 } |
|
|
873 |
|
|
874 double |
|
|
875 DET::value (void) const |
|
|
876 { |
|
|
877 return det[0] * pow (10.0, det[1]); |
|
|
878 } |
|
|
879 |
|
|
880 int |
|
|
881 ComplexDET::value_will_overflow (void) const |
|
|
882 { |
|
|
883 return det[2].real () + 1 > log10 (MAXDOUBLE) ? 1 : 0; |
|
|
884 } |
|
|
885 |
|
|
886 int |
|
|
887 ComplexDET::value_will_underflow (void) const |
|
|
888 { |
|
|
889 return det[2].real () - 1 < log10 (MINDOUBLE) ? 1 : 0; |
|
|
890 } |
|
|
891 |
|
|
892 Complex |
|
|
893 ComplexDET::coefficient (void) const |
|
|
894 { |
|
|
895 return det[0]; |
|
|
896 } |
|
|
897 |
|
|
898 int |
|
|
899 ComplexDET::exponent (void) const |
|
|
900 { |
|
|
901 return (int) (det[1].real ()); |
|
|
902 } |
|
|
903 |
|
|
904 Complex |
|
|
905 ComplexDET::value (void) const |
|
|
906 { |
|
|
907 return det[0] * pow (10.0, det[1].real ()); |
|
|
908 } |
|
|
909 |
|
|
910 /* |
|
3
|
911 * EIG stuff. |
|
|
912 */ |
|
|
913 |
|
|
914 int |
|
|
915 EIG::init (const Matrix& a) |
|
|
916 { |
|
238
|
917 int a_nr = a.rows (); |
|
|
918 if (a_nr != a.cols ()) |
|
227
|
919 { |
|
|
920 (*current_liboctave_error_handler) ("EIG requires square matrix"); |
|
|
921 return -1; |
|
|
922 } |
|
3
|
923 |
|
238
|
924 int n = a_nr; |
|
3
|
925 |
|
|
926 int info; |
|
|
927 |
|
|
928 char jobvl = 'N'; |
|
|
929 char jobvr = 'V'; |
|
|
930 |
|
238
|
931 double *tmp_data = dup (a.data (), a.length ()); |
|
3
|
932 double *wr = new double[n]; |
|
|
933 double *wi = new double[n]; |
|
|
934 Matrix vr (n, n); |
|
|
935 double *pvr = vr.fortran_vec (); |
|
|
936 int lwork = 8*n; |
|
|
937 double *work = new double[lwork]; |
|
|
938 |
|
|
939 double dummy; |
|
|
940 int idummy = 1; |
|
|
941 |
|
|
942 F77_FCN (dgeev) (&jobvl, &jobvr, &n, tmp_data, &n, wr, wi, &dummy, |
|
|
943 &idummy, pvr, &n, work, &lwork, &info, 1L, 1L); |
|
|
944 |
|
|
945 lambda.resize (n); |
|
|
946 v.resize (n, n); |
|
|
947 |
|
|
948 for (int j = 0; j < n; j++) |
|
|
949 { |
|
|
950 if (wi[j] == 0.0) |
|
|
951 { |
|
|
952 lambda.elem (j) = Complex (wr[j]); |
|
|
953 for (int i = 0; i < n; i++) |
|
|
954 v.elem (i, j) = vr.elem (i, j); |
|
|
955 } |
|
|
956 else |
|
|
957 { |
|
|
958 if (j+1 >= n) |
|
227
|
959 { |
|
|
960 (*current_liboctave_error_handler) ("EIG: internal error"); |
|
|
961 return -1; |
|
|
962 } |
|
3
|
963 |
|
|
964 for (int i = 0; i < n; i++) |
|
|
965 { |
|
|
966 lambda.elem (j) = Complex (wr[j], wi[j]); |
|
|
967 lambda.elem (j+1) = Complex (wr[j+1], wi[j+1]); |
|
|
968 double real_part = vr.elem (i, j); |
|
|
969 double imag_part = vr.elem (i, j+1); |
|
|
970 v.elem (i, j) = Complex (real_part, imag_part); |
|
|
971 v.elem (i, j+1) = Complex (real_part, -imag_part); |
|
|
972 } |
|
|
973 j++; |
|
|
974 } |
|
|
975 } |
|
|
976 |
|
|
977 delete [] tmp_data; |
|
|
978 delete [] wr; |
|
|
979 delete [] wi; |
|
|
980 delete [] work; |
|
|
981 |
|
|
982 return info; |
|
|
983 } |
|
|
984 |
|
|
985 int |
|
|
986 EIG::init (const ComplexMatrix& a) |
|
|
987 { |
|
238
|
988 int a_nr = a.rows (); |
|
|
989 if (a_nr != a.cols ()) |
|
227
|
990 { |
|
|
991 (*current_liboctave_error_handler) ("EIG requires square matrix"); |
|
|
992 return -1; |
|
|
993 } |
|
3
|
994 |
|
238
|
995 int n = a_nr; |
|
3
|
996 |
|
|
997 int info; |
|
|
998 |
|
|
999 char jobvl = 'N'; |
|
|
1000 char jobvr = 'V'; |
|
|
1001 |
|
|
1002 lambda.resize (n); |
|
|
1003 v.resize (n, n); |
|
|
1004 |
|
|
1005 Complex *pw = lambda.fortran_vec (); |
|
|
1006 Complex *pvr = v.fortran_vec (); |
|
|
1007 |
|
238
|
1008 Complex *tmp_data = dup (a.data (), a.length ()); |
|
3
|
1009 |
|
|
1010 int lwork = 8*n; |
|
|
1011 Complex *work = new Complex[lwork]; |
|
|
1012 double *rwork = new double[4*n]; |
|
|
1013 |
|
|
1014 Complex dummy; |
|
|
1015 int idummy = 1; |
|
|
1016 |
|
|
1017 F77_FCN (zgeev) (&jobvl, &jobvr, &n, tmp_data, &n, pw, &dummy, |
|
|
1018 &idummy, pvr, &n, work, &lwork, rwork, &info, 1L, |
|
|
1019 1L); |
|
|
1020 |
|
|
1021 delete [] tmp_data; |
|
|
1022 delete [] work; |
|
|
1023 delete [] rwork; |
|
|
1024 |
|
|
1025 return info; |
|
|
1026 } |
|
|
1027 |
|
|
1028 /* |
|
|
1029 * LU stuff. |
|
|
1030 */ |
|
|
1031 |
|
|
1032 LU::LU (const Matrix& a) |
|
|
1033 { |
|
238
|
1034 int a_nr = a.rows (); |
|
|
1035 int a_nc = a.cols (); |
|
|
1036 if (a_nr == 0 || a_nc == 0 || a_nr != a_nc) |
|
227
|
1037 { |
|
|
1038 (*current_liboctave_error_handler) ("LU requires square matrix"); |
|
|
1039 return; |
|
|
1040 } |
|
3
|
1041 |
|
238
|
1042 int n = a_nr; |
|
3
|
1043 |
|
|
1044 int *ipvt = new int [n]; |
|
|
1045 int *pvt = new int [n]; |
|
238
|
1046 double *tmp_data = dup (a.data (), a.length ()); |
|
3
|
1047 int info = 0; |
|
|
1048 int zero = 0; |
|
|
1049 double b; |
|
|
1050 |
|
|
1051 F77_FCN (dgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
1052 |
|
|
1053 Matrix A_fact (tmp_data, n, n); |
|
|
1054 |
|
|
1055 int i; |
|
|
1056 |
|
|
1057 for (i = 0; i < n; i++) |
|
|
1058 { |
|
|
1059 ipvt[i] -= 1; |
|
|
1060 pvt[i] = i; |
|
|
1061 } |
|
|
1062 |
|
|
1063 for (i = 0; i < n - 1; i++) |
|
|
1064 { |
|
|
1065 int k = ipvt[i]; |
|
|
1066 if (k != i) |
|
|
1067 { |
|
|
1068 int tmp = pvt[k]; |
|
|
1069 pvt[k] = pvt[i]; |
|
|
1070 pvt[i] = tmp; |
|
|
1071 } |
|
|
1072 } |
|
|
1073 |
|
|
1074 l.resize (n, n, 0.0); |
|
|
1075 u.resize (n, n, 0.0); |
|
|
1076 p.resize (n, n, 0.0); |
|
|
1077 |
|
|
1078 for (i = 0; i < n; i++) |
|
|
1079 { |
|
|
1080 p.elem (i, pvt[i]) = 1.0; |
|
|
1081 |
|
|
1082 int j; |
|
|
1083 |
|
|
1084 l.elem (i, i) = 1.0; |
|
|
1085 for (j = 0; j < i; j++) |
|
|
1086 l.elem (i, j) = A_fact.elem (i, j); |
|
|
1087 |
|
|
1088 for (j = i; j < n; j++) |
|
|
1089 u.elem (i, j) = A_fact.elem (i, j); |
|
|
1090 } |
|
|
1091 |
|
|
1092 delete [] ipvt; |
|
|
1093 delete [] pvt; |
|
|
1094 } |
|
|
1095 |
|
|
1096 ComplexLU::ComplexLU (const ComplexMatrix& a) |
|
|
1097 { |
|
238
|
1098 int a_nr = a.rows (); |
|
|
1099 int a_nc = a.cols (); |
|
|
1100 if (a_nr == 0 || a_nc == 0 || a_nr != a_nc) |
|
227
|
1101 { |
|
|
1102 (*current_liboctave_error_handler) ("ComplexLU requires square matrix"); |
|
|
1103 return; |
|
|
1104 } |
|
3
|
1105 |
|
238
|
1106 int n = a_nr; |
|
3
|
1107 |
|
|
1108 int *ipvt = new int [n]; |
|
|
1109 int *pvt = new int [n]; |
|
238
|
1110 Complex *tmp_data = dup (a.data (), a.length ()); |
|
3
|
1111 int info = 0; |
|
|
1112 int zero = 0; |
|
|
1113 Complex b; |
|
|
1114 |
|
|
1115 F77_FCN (zgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
1116 |
|
|
1117 ComplexMatrix A_fact (tmp_data, n, n); |
|
|
1118 |
|
|
1119 int i; |
|
|
1120 |
|
|
1121 for (i = 0; i < n; i++) |
|
|
1122 { |
|
|
1123 ipvt[i] -= 1; |
|
|
1124 pvt[i] = i; |
|
|
1125 } |
|
|
1126 |
|
|
1127 for (i = 0; i < n - 1; i++) |
|
|
1128 { |
|
|
1129 int k = ipvt[i]; |
|
|
1130 if (k != i) |
|
|
1131 { |
|
|
1132 int tmp = pvt[k]; |
|
|
1133 pvt[k] = pvt[i]; |
|
|
1134 pvt[i] = tmp; |
|
|
1135 } |
|
|
1136 } |
|
|
1137 |
|
|
1138 l.resize (n, n, 0.0); |
|
|
1139 u.resize (n, n, 0.0); |
|
|
1140 p.resize (n, n, 0.0); |
|
|
1141 |
|
|
1142 for (i = 0; i < n; i++) |
|
|
1143 { |
|
|
1144 p.elem (i, pvt[i]) = 1.0; |
|
|
1145 |
|
|
1146 int j; |
|
|
1147 |
|
|
1148 l.elem (i, i) = 1.0; |
|
|
1149 for (j = 0; j < i; j++) |
|
|
1150 l.elem (i, j) = A_fact.elem (i, j); |
|
|
1151 |
|
|
1152 for (j = i; j < n; j++) |
|
|
1153 u.elem (i, j) = A_fact.elem (i, j); |
|
|
1154 } |
|
|
1155 |
|
|
1156 delete [] ipvt; |
|
|
1157 delete [] pvt; |
|
|
1158 } |
|
|
1159 |
|
|
1160 /* |
|
|
1161 * QR stuff. |
|
|
1162 */ |
|
|
1163 |
|
|
1164 QR::QR (const Matrix& a) |
|
|
1165 { |
|
238
|
1166 int m = a.rows (); |
|
|
1167 int n = a.cols (); |
|
3
|
1168 |
|
|
1169 if (m == 0 || n == 0) |
|
227
|
1170 { |
|
|
1171 (*current_liboctave_error_handler) ("QR must have non-empty matrix"); |
|
|
1172 return; |
|
|
1173 } |
|
3
|
1174 |
|
|
1175 double *tmp_data; |
|
|
1176 int min_mn = m < n ? m : n; |
|
|
1177 double *tau = new double[min_mn]; |
|
|
1178 int lwork = 32*n; |
|
|
1179 double *work = new double[lwork]; |
|
|
1180 int info = 0; |
|
|
1181 |
|
|
1182 if (m > n) |
|
|
1183 { |
|
|
1184 tmp_data = new double [m*m]; |
|
238
|
1185 copy (tmp_data, a.data (), a.length ()); |
|
3
|
1186 } |
|
|
1187 else |
|
238
|
1188 tmp_data = dup (a.data (), a.length ()); |
|
3
|
1189 |
|
|
1190 F77_FCN (dgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1191 |
|
|
1192 delete [] work; |
|
|
1193 |
|
|
1194 r.resize (m, n, 0.0); |
|
|
1195 for (int j = 0; j < n; j++) |
|
|
1196 { |
|
|
1197 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
1198 for (int i = 0; i <= limit; i++) |
|
|
1199 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
1200 } |
|
|
1201 |
|
|
1202 lwork = 32*m; |
|
|
1203 work = new double[lwork]; |
|
|
1204 |
|
|
1205 F77_FCN (dorgqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1206 |
|
|
1207 q = Matrix (tmp_data, m, m); |
|
|
1208 |
|
|
1209 delete [] tau; |
|
|
1210 delete [] work; |
|
|
1211 } |
|
|
1212 |
|
|
1213 ComplexQR::ComplexQR (const ComplexMatrix& a) |
|
|
1214 { |
|
238
|
1215 int m = a.rows (); |
|
|
1216 int n = a.cols (); |
|
3
|
1217 |
|
|
1218 if (m == 0 || n == 0) |
|
227
|
1219 { |
|
|
1220 (*current_liboctave_error_handler) |
|
|
1221 ("ComplexQR must have non-empty matrix"); |
|
|
1222 return; |
|
|
1223 } |
|
3
|
1224 |
|
|
1225 Complex *tmp_data; |
|
|
1226 int min_mn = m < n ? m : n; |
|
|
1227 Complex *tau = new Complex[min_mn]; |
|
|
1228 int lwork = 32*n; |
|
|
1229 Complex *work = new Complex[lwork]; |
|
|
1230 int info = 0; |
|
|
1231 |
|
|
1232 if (m > n) |
|
|
1233 { |
|
|
1234 tmp_data = new Complex [m*m]; |
|
238
|
1235 copy (tmp_data, a.data (), a.length ()); |
|
3
|
1236 } |
|
|
1237 else |
|
238
|
1238 tmp_data = dup (a.data (), a.length ()); |
|
3
|
1239 |
|
|
1240 F77_FCN (zgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1241 |
|
|
1242 delete [] work; |
|
|
1243 |
|
|
1244 r.resize (m, n, 0.0); |
|
|
1245 for (int j = 0; j < n; j++) |
|
|
1246 { |
|
|
1247 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
1248 for (int i = 0; i <= limit; i++) |
|
|
1249 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
1250 } |
|
|
1251 |
|
|
1252 lwork = 32*m; |
|
|
1253 work = new Complex[lwork]; |
|
|
1254 |
|
|
1255 F77_FCN (zungqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1256 |
|
|
1257 q = ComplexMatrix (tmp_data, m, m); |
|
|
1258 |
|
|
1259 delete [] tau; |
|
|
1260 delete [] work; |
|
|
1261 } |
|
|
1262 |
|
|
1263 /* |
|
|
1264 ;;; Local Variables: *** |
|
|
1265 ;;; mode: C++ *** |
|
|
1266 ;;; page-delimiter: "^/\\*" *** |
|
|
1267 ;;; End: *** |
|
|
1268 */ |
