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1993
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1 // Matrix manipulations. |
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458
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2 /* |
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3 |
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2847
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4 Copyright (C) 1996, 1997 John W. Eaton |
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458
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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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1315
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20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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21 |
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22 */ |
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23 |
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1296
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24 #if defined (__GNUG__) |
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25 #pragma implementation |
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26 #endif |
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27 |
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458
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28 #ifdef HAVE_CONFIG_H |
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1192
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29 #include <config.h> |
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458
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30 #endif |
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31 |
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1367
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32 #include <cfloat> |
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33 |
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3503
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34 #include <iostream> |
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1367
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35 |
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2443
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36 // XXX FIXME XXX |
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37 #ifdef HAVE_SYS_TYPES_H |
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38 #include <sys/types.h> |
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39 #endif |
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458
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40 |
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2828
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41 #include "CMatrix.h" |
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1819
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42 #include "CmplxAEPBAL.h" |
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458
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43 #include "CmplxDET.h" |
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1819
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44 #include "CmplxSCHUR.h" |
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740
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45 #include "CmplxSVD.h" |
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1847
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46 #include "f77-fcn.h" |
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458
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47 #include "lo-error.h" |
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2354
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48 #include "lo-ieee.h" |
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49 #include "lo-mappers.h" |
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1968
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50 #include "lo-utils.h" |
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1367
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51 #include "mx-base.h" |
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2828
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52 #include "mx-cm-dm.h" |
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3176
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53 #include "mx-dm-cm.h" |
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2828
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54 #include "mx-cm-s.h" |
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1367
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55 #include "mx-inlines.cc" |
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1650
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56 #include "oct-cmplx.h" |
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458
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57 |
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58 // Fortran functions we call. |
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59 |
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60 extern "C" |
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61 { |
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3331
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62 int F77_FCN (zgebal, ZGEBAL) (const char*, const int&, Complex*, |
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63 const int&, int&, int&, double*, int&, |
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64 long, long); |
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65 |
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66 int F77_FCN (dgebak, DGEBAK) (const char*, const char*, const int&, |
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67 const int&, const int&, double*, |
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68 const int&, double*, const int&, |
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69 int&, long, long); |
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70 |
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1253
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71 int F77_FCN (zgemm, ZGEMM) (const char*, const char*, const int&, |
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72 const int&, const int&, const Complex&, |
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73 const Complex*, const int&, |
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74 const Complex*, const int&, |
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75 const Complex&, Complex*, const int&, |
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76 long, long); |
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77 |
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78 int F77_FCN (zgeco, ZGECO) (Complex*, const int&, const int&, int*, |
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79 double&, Complex*); |
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80 |
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81 int F77_FCN (zgedi, ZGEDI) (Complex*, const int&, const int&, int*, |
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82 Complex*, Complex*, const int&); |
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83 |
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84 int F77_FCN (zgesl, ZGESL) (Complex*, const int&, const int&, int*, |
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85 Complex*, const int&); |
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86 |
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87 int F77_FCN (zgelss, ZGELSS) (const int&, const int&, const int&, |
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88 Complex*, const int&, Complex*, |
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89 const int&, double*, double&, int&, |
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90 Complex*, const int&, double*, int&); |
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458
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91 |
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1360
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92 // Note that the original complex fft routines were not written for |
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93 // double complex arguments. They have been modified by adding an |
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94 // implicit double precision (a-h,o-z) statement at the beginning of |
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95 // each subroutine. |
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458
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96 |
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1253
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97 int F77_FCN (cffti, CFFTI) (const int&, Complex*); |
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98 |
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99 int F77_FCN (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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100 |
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101 int F77_FCN (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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1819
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102 |
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103 int F77_FCN (zlartg, ZLARTG) (const Complex&, const Complex&, |
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104 double&, Complex&, Complex&); |
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105 |
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106 int F77_FCN (ztrsyl, ZTRSYL) (const char*, const char*, const int&, |
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107 const int&, const int&, |
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108 const Complex*, const int&, |
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109 const Complex*, const int&, |
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110 const Complex*, const int&, double&, |
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111 int&, long, long); |
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112 |
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3130
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113 int F77_FCN (xzlange, XZLANGE) (const char*, const int&, |
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114 const int&, const Complex*, |
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115 const int&, double*, double&); |
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458
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116 } |
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117 |
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2354
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118 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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119 |
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1360
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120 // Complex Matrix class |
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458
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121 |
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122 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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1214
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123 : MArray2<Complex> (a.rows (), a.cols ()) |
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458
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124 { |
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125 for (int j = 0; j < cols (); j++) |
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126 for (int i = 0; i < rows (); i++) |
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127 elem (i, j) = a.elem (i, j); |
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128 } |
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129 |
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2349
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130 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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131 : MArray2<Complex> (1, rv.length (), 0.0) |
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132 { |
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133 for (int i = 0; i < rv.length (); i++) |
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134 elem (0, i) = rv.elem (i); |
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135 } |
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136 |
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137 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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138 : MArray2<Complex> (cv.length (), 1, 0.0) |
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139 { |
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140 for (int i = 0; i < cv.length (); i++) |
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141 elem (i, 0) = cv.elem (i); |
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142 } |
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143 |
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458
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144 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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1214
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145 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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146 { |
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147 for (int i = 0; i < a.length (); i++) |
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148 elem (i, i) = a.elem (i, i); |
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149 } |
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150 |
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2349
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151 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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152 : MArray2<Complex> (1, rv.length (), 0.0) |
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153 { |
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154 for (int i = 0; i < rv.length (); i++) |
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155 elem (0, i) = rv.elem (i); |
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156 } |
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157 |
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158 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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159 : MArray2<Complex> (cv.length (), 1, 0.0) |
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160 { |
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161 for (int i = 0; i < cv.length (); i++) |
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162 elem (i, 0) = cv.elem (i); |
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163 } |
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164 |
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458
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165 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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1214
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166 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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167 { |
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168 for (int i = 0; i < a.length (); i++) |
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169 elem (i, i) = a.elem (i, i); |
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170 } |
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171 |
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1574
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172 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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173 // here? |
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174 |
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2828
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175 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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3180
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176 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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2828
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177 { |
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178 for (int i = 0; i < a.cols (); i++) |
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179 for (int j = 0; j < a.rows (); j++) |
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180 elem (i, j) = a.elem (i, j); |
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181 } |
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182 |
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1574
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183 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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3180
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184 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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1574
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185 { |
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186 for (int i = 0; i < a.cols (); i++) |
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187 for (int j = 0; j < a.rows (); j++) |
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188 elem (i, j) = a.elem (i, j); |
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189 } |
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190 |
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2384
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191 bool |
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458
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192 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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193 { |
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194 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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195 return false; |
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458
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196 |
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197 return equal (data (), a.data (), length ()); |
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198 } |
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199 |
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2384
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200 bool |
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458
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201 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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202 { |
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203 return !(*this == a); |
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204 } |
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205 |
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2815
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206 bool |
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207 ComplexMatrix::is_hermitian (void) const |
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208 { |
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209 int nr = rows (); |
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210 int nc = cols (); |
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211 |
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212 if (is_square () && nr > 0) |
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213 { |
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214 for (int i = 0; i < nr; i++) |
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215 for (int j = i; j < nc; j++) |
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216 if (elem (i, j) != conj (elem (j, i))) |
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217 return false; |
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218 |
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219 return true; |
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220 } |
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221 |
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222 return false; |
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223 } |
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224 |
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458
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225 // destructive insert/delete/reorder operations |
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226 |
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227 ComplexMatrix& |
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228 ComplexMatrix::insert (const Matrix& a, int r, int c) |
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229 { |
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230 int a_nr = a.rows (); |
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231 int a_nc = a.cols (); |
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232 |
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233 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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234 { |
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235 (*current_liboctave_error_handler) ("range error for insert"); |
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236 return *this; |
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237 } |
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238 |
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239 for (int j = 0; j < a_nc; j++) |
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240 for (int i = 0; i < a_nr; i++) |
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241 elem (r+i, c+j) = a.elem (i, j); |
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242 |
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243 return *this; |
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244 } |
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245 |
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246 ComplexMatrix& |
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247 ComplexMatrix::insert (const RowVector& a, int r, int c) |
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248 { |
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249 int a_len = a.length (); |
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1699
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250 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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251 { |
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252 (*current_liboctave_error_handler) ("range error for insert"); |
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253 return *this; |
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254 } |
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255 |
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256 for (int i = 0; i < a_len; i++) |
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257 elem (r, c+i) = a.elem (i); |
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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 ColumnVector& a, int r, int c) |
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264 { |
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265 int a_len = a.length (); |
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1699
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266 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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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+i, c) = 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 DiagMatrix& a, int r, int c) |
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280 { |
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1699
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281 int a_nr = a.rows (); |
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282 int a_nc = a.cols (); |
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283 |
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284 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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285 { |
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286 (*current_liboctave_error_handler) ("range error for insert"); |
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287 return *this; |
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288 } |
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289 |
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290 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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291 |
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458
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292 for (int i = 0; i < a.length (); i++) |
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293 elem (r+i, c+i) = a.elem (i, i); |
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294 |
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295 return *this; |
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296 } |
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297 |
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298 ComplexMatrix& |
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299 ComplexMatrix::insert (const ComplexMatrix& a, int r, int c) |
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300 { |
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1561
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301 Array2<Complex>::insert (a, r, c); |
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458
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302 return *this; |
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303 } |
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304 |
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305 ComplexMatrix& |
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306 ComplexMatrix::insert (const ComplexRowVector& a, int r, int c) |
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307 { |
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308 int a_len = a.length (); |
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1699
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309 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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310 { |
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311 (*current_liboctave_error_handler) ("range error for insert"); |
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312 return *this; |
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313 } |
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314 |
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315 for (int i = 0; i < a_len; i++) |
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316 elem (r, c+i) = a.elem (i); |
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317 |
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318 return *this; |
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319 } |
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320 |
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321 ComplexMatrix& |
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322 ComplexMatrix::insert (const ComplexColumnVector& a, int r, int c) |
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323 { |
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324 int a_len = a.length (); |
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1699
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325 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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326 { |
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327 (*current_liboctave_error_handler) ("range error for insert"); |
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328 return *this; |
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329 } |
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330 |
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331 for (int i = 0; i < a_len; i++) |
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332 elem (r+i, c) = a.elem (i); |
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333 |
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334 return *this; |
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335 } |
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336 |
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337 ComplexMatrix& |
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338 ComplexMatrix::insert (const ComplexDiagMatrix& a, int r, int c) |
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339 { |
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1699
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340 int a_nr = a.rows (); |
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341 int a_nc = a.cols (); |
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342 |
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343 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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344 { |
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345 (*current_liboctave_error_handler) ("range error for insert"); |
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346 return *this; |
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347 } |
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348 |
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1699
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349 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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350 |
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458
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351 for (int i = 0; i < a.length (); i++) |
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352 elem (r+i, c+i) = a.elem (i, i); |
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353 |
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354 return *this; |
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355 } |
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356 |
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357 ComplexMatrix& |
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358 ComplexMatrix::fill (double val) |
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359 { |
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360 int nr = rows (); |
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361 int nc = cols (); |
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362 if (nr > 0 && nc > 0) |
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363 for (int j = 0; j < nc; j++) |
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364 for (int i = 0; i < nr; i++) |
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365 elem (i, j) = val; |
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366 |
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367 return *this; |
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368 } |
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369 |
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370 ComplexMatrix& |
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371 ComplexMatrix::fill (const Complex& val) |
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372 { |
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373 int nr = rows (); |
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374 int nc = cols (); |
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375 if (nr > 0 && nc > 0) |
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376 for (int j = 0; j < nc; j++) |
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377 for (int i = 0; i < nr; i++) |
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378 elem (i, j) = val; |
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379 |
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380 return *this; |
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381 } |
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382 |
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383 ComplexMatrix& |
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384 ComplexMatrix::fill (double val, int r1, int c1, int r2, int c2) |
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385 { |
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386 int nr = rows (); |
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387 int nc = cols (); |
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388 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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389 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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390 { |
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391 (*current_liboctave_error_handler) ("range error for fill"); |
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392 return *this; |
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393 } |
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394 |
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395 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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396 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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397 |
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398 for (int j = c1; j <= c2; j++) |
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399 for (int i = r1; i <= r2; i++) |
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400 elem (i, j) = val; |
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401 |
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402 return *this; |
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403 } |
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404 |
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405 ComplexMatrix& |
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406 ComplexMatrix::fill (const Complex& val, int r1, int c1, int r2, int c2) |
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407 { |
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408 int nr = rows (); |
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409 int nc = cols (); |
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410 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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411 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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412 { |
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413 (*current_liboctave_error_handler) ("range error for fill"); |
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414 return *this; |
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415 } |
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416 |
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417 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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418 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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419 |
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420 for (int j = c1; j <= c2; j++) |
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421 for (int i = r1; i <= r2; i++) |
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422 elem (i, j) = val; |
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423 |
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424 return *this; |
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425 } |
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426 |
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427 ComplexMatrix |
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428 ComplexMatrix::append (const Matrix& a) const |
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429 { |
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430 int nr = rows (); |
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431 int nc = cols (); |
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432 if (nr != a.rows ()) |
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433 { |
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434 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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435 return *this; |
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436 } |
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437 |
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438 int nc_insert = nc; |
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439 ComplexMatrix retval (nr, nc + a.cols ()); |
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440 retval.insert (*this, 0, 0); |
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441 retval.insert (a, 0, nc_insert); |
|
|
442 return retval; |
|
|
443 } |
|
|
444 |
|
|
445 ComplexMatrix |
|
|
446 ComplexMatrix::append (const RowVector& a) const |
|
|
447 { |
|
|
448 int nr = rows (); |
|
|
449 int nc = cols (); |
|
|
450 if (nr != 1) |
|
|
451 { |
|
|
452 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
453 return *this; |
|
|
454 } |
|
|
455 |
|
|
456 int nc_insert = nc; |
|
|
457 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
458 retval.insert (*this, 0, 0); |
|
|
459 retval.insert (a, 0, nc_insert); |
|
|
460 return retval; |
|
|
461 } |
|
|
462 |
|
|
463 ComplexMatrix |
|
|
464 ComplexMatrix::append (const ColumnVector& a) const |
|
|
465 { |
|
|
466 int nr = rows (); |
|
|
467 int nc = cols (); |
|
|
468 if (nr != a.length ()) |
|
|
469 { |
|
|
470 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
471 return *this; |
|
|
472 } |
|
|
473 |
|
|
474 int nc_insert = nc; |
|
|
475 ComplexMatrix retval (nr, nc + 1); |
|
|
476 retval.insert (*this, 0, 0); |
|
|
477 retval.insert (a, 0, nc_insert); |
|
|
478 return retval; |
|
|
479 } |
|
|
480 |
|
|
481 ComplexMatrix |
|
|
482 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
483 { |
|
|
484 int nr = rows (); |
|
|
485 int nc = cols (); |
|
|
486 if (nr != a.rows ()) |
|
|
487 { |
|
|
488 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
489 return *this; |
|
|
490 } |
|
|
491 |
|
|
492 int nc_insert = nc; |
|
|
493 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
494 retval.insert (*this, 0, 0); |
|
|
495 retval.insert (a, 0, nc_insert); |
|
|
496 return retval; |
|
|
497 } |
|
|
498 |
|
|
499 ComplexMatrix |
|
|
500 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
501 { |
|
|
502 int nr = rows (); |
|
|
503 int nc = cols (); |
|
|
504 if (nr != a.rows ()) |
|
|
505 { |
|
|
506 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
507 return *this; |
|
|
508 } |
|
|
509 |
|
|
510 int nc_insert = nc; |
|
|
511 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
512 retval.insert (*this, 0, 0); |
|
|
513 retval.insert (a, 0, nc_insert); |
|
|
514 return retval; |
|
|
515 } |
|
|
516 |
|
|
517 ComplexMatrix |
|
|
518 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
519 { |
|
|
520 int nr = rows (); |
|
|
521 int nc = cols (); |
|
|
522 if (nr != 1) |
|
|
523 { |
|
|
524 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
525 return *this; |
|
|
526 } |
|
|
527 |
|
|
528 int nc_insert = nc; |
|
|
529 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
530 retval.insert (*this, 0, 0); |
|
|
531 retval.insert (a, 0, nc_insert); |
|
|
532 return retval; |
|
|
533 } |
|
|
534 |
|
|
535 ComplexMatrix |
|
|
536 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
537 { |
|
|
538 int nr = rows (); |
|
|
539 int nc = cols (); |
|
|
540 if (nr != a.length ()) |
|
|
541 { |
|
|
542 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
543 return *this; |
|
|
544 } |
|
|
545 |
|
|
546 int nc_insert = nc; |
|
|
547 ComplexMatrix retval (nr, nc + 1); |
|
|
548 retval.insert (*this, 0, 0); |
|
|
549 retval.insert (a, 0, nc_insert); |
|
|
550 return retval; |
|
|
551 } |
|
|
552 |
|
|
553 ComplexMatrix |
|
|
554 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
555 { |
|
|
556 int nr = rows (); |
|
|
557 int nc = cols (); |
|
|
558 if (nr != a.rows ()) |
|
|
559 { |
|
|
560 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
561 return *this; |
|
|
562 } |
|
|
563 |
|
|
564 int nc_insert = nc; |
|
|
565 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
566 retval.insert (*this, 0, 0); |
|
|
567 retval.insert (a, 0, nc_insert); |
|
|
568 return retval; |
|
|
569 } |
|
|
570 |
|
|
571 ComplexMatrix |
|
|
572 ComplexMatrix::stack (const Matrix& a) const |
|
|
573 { |
|
|
574 int nr = rows (); |
|
|
575 int nc = cols (); |
|
|
576 if (nc != a.cols ()) |
|
|
577 { |
|
|
578 (*current_liboctave_error_handler) |
|
|
579 ("column dimension mismatch for stack"); |
|
|
580 return *this; |
|
|
581 } |
|
|
582 |
|
|
583 int nr_insert = nr; |
|
|
584 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
585 retval.insert (*this, 0, 0); |
|
|
586 retval.insert (a, nr_insert, 0); |
|
|
587 return retval; |
|
|
588 } |
|
|
589 |
|
|
590 ComplexMatrix |
|
|
591 ComplexMatrix::stack (const RowVector& a) const |
|
|
592 { |
|
|
593 int nr = rows (); |
|
|
594 int nc = cols (); |
|
|
595 if (nc != a.length ()) |
|
|
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 + 1, 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 ColumnVector& a) const |
|
|
611 { |
|
|
612 int nr = rows (); |
|
|
613 int nc = cols (); |
|
|
614 if (nc != 1) |
|
|
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 + a.length (), 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 DiagMatrix& a) const |
|
|
630 { |
|
|
631 int nr = rows (); |
|
|
632 int nc = cols (); |
|
|
633 if (nc != a.cols ()) |
|
|
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.rows (), 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 ComplexMatrix& 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 ComplexRowVector& a) const |
|
|
668 { |
|
|
669 int nr = rows (); |
|
|
670 int nc = cols (); |
|
|
671 if (nc != a.length ()) |
|
|
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 + 1, 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 ComplexColumnVector& a) const |
|
|
687 { |
|
|
688 int nr = rows (); |
|
|
689 int nc = cols (); |
|
|
690 if (nc != 1) |
|
|
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 + a.length (), 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 ComplexDiagMatrix& a) const |
|
|
706 { |
|
|
707 int nr = rows (); |
|
|
708 int nc = cols (); |
|
|
709 if (nc != a.cols ()) |
|
|
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.rows (), nc); |
|
|
718 retval.insert (*this, 0, 0); |
|
|
719 retval.insert (a, nr_insert, 0); |
|
|
720 return retval; |
|
|
721 } |
|
|
722 |
|
|
723 ComplexMatrix |
|
|
724 ComplexMatrix::hermitian (void) const |
|
|
725 { |
|
|
726 int nr = rows (); |
|
|
727 int nc = cols (); |
|
|
728 ComplexMatrix result; |
|
|
729 if (length () > 0) |
|
|
730 { |
|
|
731 result.resize (nc, nr); |
|
|
732 for (int j = 0; j < nc; j++) |
|
|
733 for (int i = 0; i < nr; i++) |
|
|
734 result.elem (j, i) = conj (elem (i, j)); |
|
|
735 } |
|
|
736 return result; |
|
|
737 } |
|
|
738 |
|
|
739 ComplexMatrix |
|
|
740 conj (const ComplexMatrix& a) |
|
|
741 { |
|
|
742 int a_len = a.length (); |
|
|
743 ComplexMatrix retval; |
|
|
744 if (a_len > 0) |
|
|
745 retval = ComplexMatrix (conj_dup (a.data (), a_len), a.rows (), |
|
|
746 a.cols ()); |
|
|
747 return retval; |
|
|
748 } |
|
|
749 |
|
|
750 // resize is the destructive equivalent for this one |
|
|
751 |
|
|
752 ComplexMatrix |
|
|
753 ComplexMatrix::extract (int r1, int c1, int r2, int c2) const |
|
|
754 { |
|
|
755 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
756 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
757 |
|
|
758 int new_r = r2 - r1 + 1; |
|
|
759 int new_c = c2 - c1 + 1; |
|
|
760 |
|
|
761 ComplexMatrix result (new_r, new_c); |
|
|
762 |
|
|
763 for (int j = 0; j < new_c; j++) |
|
|
764 for (int i = 0; i < new_r; i++) |
|
|
765 result.elem (i, j) = elem (r1+i, c1+j); |
|
|
766 |
|
|
767 return result; |
|
|
768 } |
|
|
769 |
|
|
770 // extract row or column i. |
|
|
771 |
|
|
772 ComplexRowVector |
|
|
773 ComplexMatrix::row (int i) const |
|
|
774 { |
|
|
775 int nc = cols (); |
|
|
776 if (i < 0 || i >= rows ()) |
|
|
777 { |
|
|
778 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
779 return ComplexRowVector (); |
|
|
780 } |
|
|
781 |
|
|
782 ComplexRowVector retval (nc); |
|
|
783 for (int j = 0; j < cols (); j++) |
|
|
784 retval.elem (j) = elem (i, j); |
|
|
785 |
|
|
786 return retval; |
|
|
787 } |
|
|
788 |
|
|
789 ComplexRowVector |
|
|
790 ComplexMatrix::row (char *s) const |
|
|
791 { |
|
533
|
792 if (! s) |
|
458
|
793 { |
|
|
794 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
795 return ComplexRowVector (); |
|
|
796 } |
|
|
797 |
|
|
798 char c = *s; |
|
|
799 if (c == 'f' || c == 'F') |
|
|
800 return row (0); |
|
|
801 else if (c == 'l' || c == 'L') |
|
|
802 return row (rows () - 1); |
|
|
803 else |
|
|
804 { |
|
|
805 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
806 return ComplexRowVector (); |
|
|
807 } |
|
|
808 } |
|
|
809 |
|
|
810 ComplexColumnVector |
|
|
811 ComplexMatrix::column (int i) const |
|
|
812 { |
|
|
813 int nr = rows (); |
|
|
814 if (i < 0 || i >= cols ()) |
|
|
815 { |
|
|
816 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
817 return ComplexColumnVector (); |
|
|
818 } |
|
|
819 |
|
|
820 ComplexColumnVector retval (nr); |
|
|
821 for (int j = 0; j < nr; j++) |
|
|
822 retval.elem (j) = elem (j, i); |
|
|
823 |
|
|
824 return retval; |
|
|
825 } |
|
|
826 |
|
|
827 ComplexColumnVector |
|
|
828 ComplexMatrix::column (char *s) const |
|
|
829 { |
|
533
|
830 if (! s) |
|
458
|
831 { |
|
|
832 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
833 return ComplexColumnVector (); |
|
|
834 } |
|
|
835 |
|
|
836 char c = *s; |
|
|
837 if (c == 'f' || c == 'F') |
|
|
838 return column (0); |
|
|
839 else if (c == 'l' || c == 'L') |
|
|
840 return column (cols () - 1); |
|
|
841 else |
|
|
842 { |
|
|
843 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
844 return ComplexColumnVector (); |
|
|
845 } |
|
|
846 } |
|
|
847 |
|
|
848 ComplexMatrix |
|
|
849 ComplexMatrix::inverse (void) const |
|
|
850 { |
|
|
851 int info; |
|
479
|
852 double rcond; |
|
|
853 return inverse (info, rcond); |
|
458
|
854 } |
|
|
855 |
|
|
856 ComplexMatrix |
|
|
857 ComplexMatrix::inverse (int& info) const |
|
|
858 { |
|
|
859 double rcond; |
|
|
860 return inverse (info, rcond); |
|
|
861 } |
|
|
862 |
|
|
863 ComplexMatrix |
|
1656
|
864 ComplexMatrix::inverse (int& info, double& rcond, int force) const |
|
458
|
865 { |
|
1948
|
866 ComplexMatrix retval; |
|
|
867 |
|
458
|
868 int nr = rows (); |
|
|
869 int nc = cols (); |
|
1948
|
870 |
|
458
|
871 if (nr != nc) |
|
1948
|
872 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
873 else |
|
|
874 { |
|
1948
|
875 info = 0; |
|
|
876 |
|
|
877 Array<int> ipvt (nr); |
|
|
878 int *pipvt = ipvt.fortran_vec (); |
|
|
879 |
|
|
880 Array<Complex> z (nr); |
|
|
881 Complex *pz = z.fortran_vec (); |
|
|
882 |
|
|
883 retval = *this; |
|
|
884 Complex *tmp_data = retval.fortran_vec (); |
|
|
885 |
|
|
886 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nc, pipvt, rcond, pz)); |
|
|
887 |
|
|
888 if (f77_exception_encountered) |
|
|
889 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
890 else |
|
|
891 { |
|
|
892 volatile double rcond_plus_one = rcond + 1.0; |
|
|
893 |
|
|
894 if (rcond_plus_one == 1.0) |
|
|
895 info = -1; |
|
|
896 |
|
|
897 if (info == -1 && ! force) |
|
|
898 retval = *this; // Restore contents. |
|
|
899 else |
|
|
900 { |
|
|
901 Complex *dummy = 0; |
|
|
902 |
|
|
903 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nc, pipvt, dummy, |
|
|
904 pz, 1)); |
|
|
905 |
|
|
906 if (f77_exception_encountered) |
|
|
907 (*current_liboctave_error_handler) |
|
|
908 ("unrecoverable error in zgedi"); |
|
|
909 } |
|
|
910 } |
|
458
|
911 } |
|
|
912 |
|
1948
|
913 return retval; |
|
458
|
914 } |
|
|
915 |
|
|
916 ComplexMatrix |
|
740
|
917 ComplexMatrix::pseudo_inverse (double tol) |
|
|
918 { |
|
1549
|
919 ComplexMatrix retval; |
|
|
920 |
|
3480
|
921 ComplexSVD result (*this, SVD::economy); |
|
740
|
922 |
|
|
923 DiagMatrix S = result.singular_values (); |
|
|
924 ComplexMatrix U = result.left_singular_matrix (); |
|
|
925 ComplexMatrix V = result.right_singular_matrix (); |
|
|
926 |
|
|
927 ColumnVector sigma = S.diag (); |
|
|
928 |
|
|
929 int r = sigma.length () - 1; |
|
|
930 int nr = rows (); |
|
|
931 int nc = cols (); |
|
|
932 |
|
|
933 if (tol <= 0.0) |
|
|
934 { |
|
|
935 if (nr > nc) |
|
|
936 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
937 else |
|
|
938 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
939 } |
|
|
940 |
|
|
941 while (r >= 0 && sigma.elem (r) < tol) |
|
|
942 r--; |
|
|
943 |
|
|
944 if (r < 0) |
|
1549
|
945 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
946 else |
|
|
947 { |
|
|
948 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
949 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
950 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
951 retval = Vr * D * Ur.hermitian (); |
|
740
|
952 } |
|
1549
|
953 |
|
|
954 return retval; |
|
740
|
955 } |
|
|
956 |
|
|
957 ComplexMatrix |
|
458
|
958 ComplexMatrix::fourier (void) const |
|
|
959 { |
|
1948
|
960 ComplexMatrix retval; |
|
|
961 |
|
458
|
962 int nr = rows (); |
|
|
963 int nc = cols (); |
|
1948
|
964 |
|
458
|
965 int npts, nsamples; |
|
1948
|
966 |
|
458
|
967 if (nr == 1 || nc == 1) |
|
|
968 { |
|
|
969 npts = nr > nc ? nr : nc; |
|
|
970 nsamples = 1; |
|
|
971 } |
|
|
972 else |
|
|
973 { |
|
|
974 npts = nr; |
|
|
975 nsamples = nc; |
|
|
976 } |
|
|
977 |
|
|
978 int nn = 4*npts+15; |
|
1948
|
979 |
|
|
980 Array<Complex> wsave (nn); |
|
|
981 Complex *pwsave = wsave.fortran_vec (); |
|
|
982 |
|
|
983 retval = *this; |
|
|
984 Complex *tmp_data = retval.fortran_vec (); |
|
|
985 |
|
|
986 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
987 |
|
|
988 for (int j = 0; j < nsamples; j++) |
|
1948
|
989 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
990 |
|
|
991 return retval; |
|
458
|
992 } |
|
|
993 |
|
|
994 ComplexMatrix |
|
|
995 ComplexMatrix::ifourier (void) const |
|
|
996 { |
|
1948
|
997 ComplexMatrix retval; |
|
|
998 |
|
458
|
999 int nr = rows (); |
|
|
1000 int nc = cols (); |
|
1948
|
1001 |
|
458
|
1002 int npts, nsamples; |
|
1948
|
1003 |
|
458
|
1004 if (nr == 1 || nc == 1) |
|
|
1005 { |
|
|
1006 npts = nr > nc ? nr : nc; |
|
|
1007 nsamples = 1; |
|
|
1008 } |
|
|
1009 else |
|
|
1010 { |
|
|
1011 npts = nr; |
|
|
1012 nsamples = nc; |
|
|
1013 } |
|
|
1014 |
|
|
1015 int nn = 4*npts+15; |
|
1948
|
1016 |
|
|
1017 Array<Complex> wsave (nn); |
|
|
1018 Complex *pwsave = wsave.fortran_vec (); |
|
|
1019 |
|
|
1020 retval = *this; |
|
|
1021 Complex *tmp_data = retval.fortran_vec (); |
|
|
1022 |
|
|
1023 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
1024 |
|
|
1025 for (int j = 0; j < nsamples; j++) |
|
1948
|
1026 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
458
|
1027 |
|
1321
|
1028 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1029 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1030 |
|
1948
|
1031 return retval; |
|
458
|
1032 } |
|
|
1033 |
|
677
|
1034 ComplexMatrix |
|
|
1035 ComplexMatrix::fourier2d (void) const |
|
|
1036 { |
|
1948
|
1037 ComplexMatrix retval; |
|
|
1038 |
|
677
|
1039 int nr = rows (); |
|
|
1040 int nc = cols (); |
|
1948
|
1041 |
|
677
|
1042 int npts, nsamples; |
|
1948
|
1043 |
|
677
|
1044 if (nr == 1 || nc == 1) |
|
|
1045 { |
|
|
1046 npts = nr > nc ? nr : nc; |
|
|
1047 nsamples = 1; |
|
|
1048 } |
|
|
1049 else |
|
|
1050 { |
|
|
1051 npts = nr; |
|
|
1052 nsamples = nc; |
|
|
1053 } |
|
|
1054 |
|
|
1055 int nn = 4*npts+15; |
|
1948
|
1056 |
|
|
1057 Array<Complex> wsave (nn); |
|
|
1058 Complex *pwsave = wsave.fortran_vec (); |
|
|
1059 |
|
|
1060 retval = *this; |
|
|
1061 Complex *tmp_data = retval.fortran_vec (); |
|
|
1062 |
|
|
1063 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1064 |
|
|
1065 for (int j = 0; j < nsamples; j++) |
|
1948
|
1066 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1067 |
|
|
1068 npts = nc; |
|
|
1069 nsamples = nr; |
|
|
1070 nn = 4*npts+15; |
|
1948
|
1071 |
|
|
1072 wsave.resize (nn); |
|
|
1073 pwsave = wsave.fortran_vec (); |
|
|
1074 |
|
|
1075 Array<Complex> row (npts); |
|
|
1076 Complex *prow = row.fortran_vec (); |
|
|
1077 |
|
|
1078 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1079 |
|
1321
|
1080 for (int j = 0; j < nsamples; j++) |
|
677
|
1081 { |
|
|
1082 for (int i = 0; i < npts; i++) |
|
1948
|
1083 prow[i] = tmp_data[i*nr + j]; |
|
|
1084 |
|
|
1085 F77_FCN (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1086 |
|
1321
|
1087 for (int i = 0; i < npts; i++) |
|
1948
|
1088 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1089 } |
|
|
1090 |
|
1948
|
1091 return retval; |
|
677
|
1092 } |
|
|
1093 |
|
|
1094 ComplexMatrix |
|
|
1095 ComplexMatrix::ifourier2d (void) const |
|
|
1096 { |
|
1948
|
1097 ComplexMatrix retval; |
|
|
1098 |
|
677
|
1099 int nr = rows (); |
|
|
1100 int nc = cols (); |
|
1948
|
1101 |
|
677
|
1102 int npts, nsamples; |
|
1948
|
1103 |
|
677
|
1104 if (nr == 1 || nc == 1) |
|
|
1105 { |
|
|
1106 npts = nr > nc ? nr : nc; |
|
|
1107 nsamples = 1; |
|
|
1108 } |
|
|
1109 else |
|
|
1110 { |
|
|
1111 npts = nr; |
|
|
1112 nsamples = nc; |
|
|
1113 } |
|
|
1114 |
|
|
1115 int nn = 4*npts+15; |
|
1948
|
1116 |
|
|
1117 Array<Complex> wsave (nn); |
|
|
1118 Complex *pwsave = wsave.fortran_vec (); |
|
|
1119 |
|
|
1120 retval = *this; |
|
|
1121 Complex *tmp_data = retval.fortran_vec (); |
|
|
1122 |
|
|
1123 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1124 |
|
|
1125 for (int j = 0; j < nsamples; j++) |
|
1948
|
1126 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1127 |
|
1321
|
1128 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1129 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1130 |
|
|
1131 npts = nc; |
|
|
1132 nsamples = nr; |
|
|
1133 nn = 4*npts+15; |
|
1948
|
1134 |
|
|
1135 wsave.resize (nn); |
|
|
1136 pwsave = wsave.fortran_vec (); |
|
|
1137 |
|
|
1138 Array<Complex> row (npts); |
|
|
1139 Complex *prow = row.fortran_vec (); |
|
|
1140 |
|
|
1141 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1142 |
|
1321
|
1143 for (int j = 0; j < nsamples; j++) |
|
677
|
1144 { |
|
|
1145 for (int i = 0; i < npts; i++) |
|
1948
|
1146 prow[i] = tmp_data[i*nr + j]; |
|
|
1147 |
|
|
1148 F77_FCN (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1149 |
|
1321
|
1150 for (int i = 0; i < npts; i++) |
|
3572
|
1151 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1152 } |
|
|
1153 |
|
1948
|
1154 return retval; |
|
677
|
1155 } |
|
|
1156 |
|
458
|
1157 ComplexDET |
|
|
1158 ComplexMatrix::determinant (void) const |
|
|
1159 { |
|
|
1160 int info; |
|
|
1161 double rcond; |
|
|
1162 return determinant (info, rcond); |
|
|
1163 } |
|
|
1164 |
|
|
1165 ComplexDET |
|
|
1166 ComplexMatrix::determinant (int& info) const |
|
|
1167 { |
|
|
1168 double rcond; |
|
|
1169 return determinant (info, rcond); |
|
|
1170 } |
|
|
1171 |
|
|
1172 ComplexDET |
|
532
|
1173 ComplexMatrix::determinant (int& info, double& rcond) const |
|
458
|
1174 { |
|
|
1175 ComplexDET retval; |
|
|
1176 |
|
|
1177 int nr = rows (); |
|
|
1178 int nc = cols (); |
|
|
1179 |
|
|
1180 if (nr == 0 || nc == 0) |
|
|
1181 { |
|
|
1182 Complex d[2]; |
|
|
1183 d[0] = 1.0; |
|
|
1184 d[1] = 0.0; |
|
|
1185 retval = ComplexDET (d); |
|
|
1186 } |
|
|
1187 else |
|
|
1188 { |
|
|
1189 info = 0; |
|
1948
|
1190 |
|
|
1191 Array<int> ipvt (nr); |
|
|
1192 int *pipvt = ipvt.fortran_vec (); |
|
|
1193 |
|
|
1194 Array<Complex> z (nr); |
|
|
1195 Complex *pz = z.fortran_vec (); |
|
|
1196 |
|
|
1197 ComplexMatrix atmp = *this; |
|
|
1198 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1199 |
|
|
1200 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1201 |
|
|
1202 if (f77_exception_encountered) |
|
|
1203 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
458
|
1204 else |
|
|
1205 { |
|
1948
|
1206 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1207 |
|
|
1208 if (rcond_plus_one == 1.0) |
|
|
1209 { |
|
|
1210 info = -1; |
|
|
1211 retval = ComplexDET (); |
|
|
1212 } |
|
|
1213 else |
|
|
1214 { |
|
|
1215 Complex d[2]; |
|
|
1216 |
|
|
1217 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nr, pipvt, d, pz, 10)); |
|
|
1218 |
|
|
1219 if (f77_exception_encountered) |
|
|
1220 (*current_liboctave_error_handler) |
|
|
1221 ("unrecoverable error in dgedi"); |
|
|
1222 else |
|
|
1223 retval = ComplexDET (d); |
|
|
1224 } |
|
458
|
1225 } |
|
|
1226 } |
|
|
1227 |
|
|
1228 return retval; |
|
|
1229 } |
|
|
1230 |
|
|
1231 ComplexMatrix |
|
|
1232 ComplexMatrix::solve (const Matrix& b) const |
|
|
1233 { |
|
|
1234 int info; |
|
|
1235 double rcond; |
|
3480
|
1236 return solve (b, info, rcond, 0); |
|
458
|
1237 } |
|
|
1238 |
|
|
1239 ComplexMatrix |
|
|
1240 ComplexMatrix::solve (const Matrix& b, int& info) const |
|
|
1241 { |
|
|
1242 double rcond; |
|
3480
|
1243 return solve (b, info, rcond, 0); |
|
458
|
1244 } |
|
|
1245 |
|
|
1246 ComplexMatrix |
|
|
1247 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond) const |
|
|
1248 { |
|
3480
|
1249 return solve (b, info, rcond, 0); |
|
|
1250 } |
|
|
1251 |
|
|
1252 ComplexMatrix |
|
|
1253 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond, |
|
|
1254 solve_singularity_handler sing_handler) const |
|
|
1255 { |
|
458
|
1256 ComplexMatrix tmp (b); |
|
3480
|
1257 return solve (tmp, info, rcond, sing_handler); |
|
458
|
1258 } |
|
|
1259 |
|
|
1260 ComplexMatrix |
|
|
1261 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1262 { |
|
|
1263 int info; |
|
|
1264 double rcond; |
|
3480
|
1265 return solve (b, info, rcond, 0); |
|
458
|
1266 } |
|
|
1267 |
|
|
1268 ComplexMatrix |
|
|
1269 ComplexMatrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1270 { |
|
|
1271 double rcond; |
|
3480
|
1272 return solve (b, info, rcond, 0); |
|
458
|
1273 } |
|
3480
|
1274 |
|
458
|
1275 ComplexMatrix |
|
532
|
1276 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
458
|
1277 { |
|
3480
|
1278 return solve (b, info, rcond, 0); |
|
|
1279 } |
|
|
1280 |
|
|
1281 ComplexMatrix |
|
|
1282 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond, |
|
|
1283 solve_singularity_handler sing_handler) const |
|
|
1284 { |
|
458
|
1285 ComplexMatrix retval; |
|
|
1286 |
|
|
1287 int nr = rows (); |
|
|
1288 int nc = cols (); |
|
1948
|
1289 |
|
|
1290 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1291 (*current_liboctave_error_handler) |
|
|
1292 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1293 else |
|
|
1294 { |
|
1948
|
1295 info = 0; |
|
|
1296 |
|
|
1297 Array<int> ipvt (nr); |
|
|
1298 int *pipvt = ipvt.fortran_vec (); |
|
|
1299 |
|
|
1300 Array<Complex> z (nr); |
|
|
1301 Complex *pz = z.fortran_vec (); |
|
|
1302 |
|
|
1303 ComplexMatrix atmp = *this; |
|
|
1304 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1305 |
|
|
1306 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1307 |
|
|
1308 if (f77_exception_encountered) |
|
|
1309 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
1310 else |
|
|
1311 { |
|
|
1312 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1313 |
|
|
1314 if (rcond_plus_one == 1.0) |
|
|
1315 { |
|
|
1316 info = -2; |
|
3480
|
1317 |
|
|
1318 if (sing_handler) |
|
|
1319 sing_handler (rcond); |
|
|
1320 else |
|
|
1321 (*current_liboctave_error_handler) |
|
|
1322 ("matrix singular to machine precision, rcond = %g", |
|
|
1323 rcond); |
|
1948
|
1324 } |
|
|
1325 else |
|
|
1326 { |
|
|
1327 retval = b; |
|
|
1328 Complex *result = retval.fortran_vec (); |
|
|
1329 |
|
|
1330 int b_nc = b.cols (); |
|
|
1331 |
|
|
1332 for (volatile int j = 0; j < b_nc; j++) |
|
|
1333 { |
|
|
1334 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, |
|
|
1335 &result[nr*j], 0)); |
|
|
1336 |
|
|
1337 if (f77_exception_encountered) |
|
|
1338 { |
|
|
1339 (*current_liboctave_error_handler) |
|
|
1340 ("unrecoverable error in dgesl"); |
|
|
1341 |
|
|
1342 break; |
|
|
1343 } |
|
|
1344 } |
|
|
1345 } |
|
|
1346 } |
|
458
|
1347 } |
|
|
1348 |
|
|
1349 return retval; |
|
|
1350 } |
|
|
1351 |
|
|
1352 ComplexColumnVector |
|
3585
|
1353 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
1354 { |
|
|
1355 int info; |
|
|
1356 double rcond; |
|
|
1357 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1358 } |
|
|
1359 |
|
|
1360 ComplexColumnVector |
|
|
1361 ComplexMatrix::solve (const ColumnVector& b, int& info) const |
|
|
1362 { |
|
|
1363 double rcond; |
|
|
1364 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1365 } |
|
|
1366 |
|
|
1367 ComplexColumnVector |
|
|
1368 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
|
1369 { |
|
|
1370 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1371 } |
|
|
1372 |
|
|
1373 ComplexColumnVector |
|
|
1374 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond, |
|
|
1375 solve_singularity_handler sing_handler) const |
|
|
1376 { |
|
|
1377 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
1378 } |
|
|
1379 |
|
|
1380 ComplexColumnVector |
|
458
|
1381 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1382 { |
|
|
1383 int info; |
|
|
1384 double rcond; |
|
3480
|
1385 return solve (b, info, rcond, 0); |
|
458
|
1386 } |
|
|
1387 |
|
|
1388 ComplexColumnVector |
|
|
1389 ComplexMatrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1390 { |
|
|
1391 double rcond; |
|
3480
|
1392 return solve (b, info, rcond, 0); |
|
458
|
1393 } |
|
|
1394 |
|
|
1395 ComplexColumnVector |
|
|
1396 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
532
|
1397 double& rcond) const |
|
458
|
1398 { |
|
3480
|
1399 return solve (b, info, rcond, 0); |
|
|
1400 } |
|
|
1401 |
|
|
1402 ComplexColumnVector |
|
|
1403 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
|
1404 double& rcond, |
|
|
1405 solve_singularity_handler sing_handler) const |
|
|
1406 { |
|
458
|
1407 ComplexColumnVector retval; |
|
|
1408 |
|
|
1409 int nr = rows (); |
|
|
1410 int nc = cols (); |
|
1948
|
1411 |
|
|
1412 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
1413 (*current_liboctave_error_handler) |
|
|
1414 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1415 else |
|
|
1416 { |
|
1948
|
1417 info = 0; |
|
|
1418 |
|
|
1419 Array<int> ipvt (nr); |
|
|
1420 int *pipvt = ipvt.fortran_vec (); |
|
|
1421 |
|
|
1422 Array<Complex> z (nr); |
|
|
1423 Complex *pz = z.fortran_vec (); |
|
|
1424 |
|
|
1425 ComplexMatrix atmp = *this; |
|
|
1426 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1427 |
|
|
1428 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1429 |
|
|
1430 if (f77_exception_encountered) |
|
|
1431 (*current_liboctave_error_handler) |
|
|
1432 ("unrecoverable error in dgeco"); |
|
|
1433 else |
|
|
1434 { |
|
|
1435 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1436 |
|
|
1437 if (rcond_plus_one == 1.0) |
|
|
1438 { |
|
|
1439 info = -2; |
|
3480
|
1440 |
|
|
1441 if (sing_handler) |
|
|
1442 sing_handler (rcond); |
|
|
1443 else |
|
|
1444 (*current_liboctave_error_handler) |
|
|
1445 ("matrix singular to machine precision, rcond = %g", |
|
|
1446 rcond); |
|
1948
|
1447 } |
|
|
1448 else |
|
|
1449 { |
|
|
1450 retval = b; |
|
|
1451 Complex *result = retval.fortran_vec (); |
|
|
1452 |
|
|
1453 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, result, 0)); |
|
|
1454 |
|
|
1455 if (f77_exception_encountered) |
|
|
1456 (*current_liboctave_error_handler) |
|
|
1457 ("unrecoverable error in dgesl"); |
|
|
1458 } |
|
|
1459 } |
|
458
|
1460 } |
|
|
1461 |
|
|
1462 return retval; |
|
|
1463 } |
|
|
1464 |
|
|
1465 ComplexMatrix |
|
3585
|
1466 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
1467 { |
|
|
1468 int info; |
|
|
1469 int rank; |
|
|
1470 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1471 } |
|
|
1472 |
|
|
1473 ComplexMatrix |
|
|
1474 ComplexMatrix::lssolve (const Matrix& b, int& info) const |
|
|
1475 { |
|
|
1476 int rank; |
|
|
1477 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1478 } |
|
|
1479 |
|
|
1480 ComplexMatrix |
|
|
1481 ComplexMatrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1482 { |
|
|
1483 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1484 } |
|
|
1485 |
|
|
1486 ComplexMatrix |
|
458
|
1487 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1488 { |
|
|
1489 int info; |
|
|
1490 int rank; |
|
|
1491 return lssolve (b, info, rank); |
|
|
1492 } |
|
|
1493 |
|
|
1494 ComplexMatrix |
|
|
1495 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1496 { |
|
|
1497 int rank; |
|
|
1498 return lssolve (b, info, rank); |
|
|
1499 } |
|
|
1500 |
|
|
1501 ComplexMatrix |
|
|
1502 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1503 { |
|
1948
|
1504 ComplexMatrix retval; |
|
|
1505 |
|
458
|
1506 int nrhs = b.cols (); |
|
|
1507 |
|
|
1508 int m = rows (); |
|
|
1509 int n = cols (); |
|
|
1510 |
|
|
1511 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1512 (*current_liboctave_error_handler) |
|
|
1513 ("matrix dimension mismatch solution of linear equations"); |
|
|
1514 else |
|
458
|
1515 { |
|
1948
|
1516 ComplexMatrix atmp = *this; |
|
|
1517 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1518 |
|
|
1519 int nrr = m > n ? m : n; |
|
|
1520 ComplexMatrix result (nrr, nrhs); |
|
|
1521 |
|
|
1522 for (int j = 0; j < nrhs; j++) |
|
|
1523 for (int i = 0; i < m; i++) |
|
|
1524 result.elem (i, j) = b.elem (i, j); |
|
|
1525 |
|
|
1526 Complex *presult = result.fortran_vec (); |
|
|
1527 |
|
|
1528 int len_s = m < n ? m : n; |
|
|
1529 Array<double> s (len_s); |
|
|
1530 double *ps = s.fortran_vec (); |
|
2563
|
1531 |
|
1948
|
1532 double rcond = -1.0; |
|
2563
|
1533 |
|
1948
|
1534 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1535 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1536 Array<double> rwork (lrwork); |
|
|
1537 double *prwork = rwork.fortran_vec (); |
|
|
1538 |
|
3752
|
1539 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1540 |
|
|
1541 int lwork = -1; |
|
|
1542 |
|
|
1543 Array<Complex> work (1); |
|
|
1544 |
|
1948
|
1545 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1546 nrr, ps, rcond, rank, |
|
|
1547 work.fortran_vec (), lwork, prwork, |
|
|
1548 info)); |
|
1948
|
1549 |
|
|
1550 if (f77_exception_encountered) |
|
|
1551 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1552 else |
|
|
1553 { |
|
3752
|
1554 lwork = static_cast<int> (real (work(0))); |
|
|
1555 work.resize (lwork); |
|
|
1556 |
|
|
1557 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1558 nrr, ps, rcond, rank, |
|
|
1559 work.fortran_vec (), lwork, |
|
|
1560 prwork, info)); |
|
|
1561 |
|
|
1562 if (f77_exception_encountered) |
|
|
1563 (*current_liboctave_error_handler) |
|
|
1564 ("unrecoverable error in zgelss"); |
|
|
1565 else |
|
|
1566 { |
|
|
1567 retval.resize (n, nrhs); |
|
|
1568 for (int j = 0; j < nrhs; j++) |
|
|
1569 for (int i = 0; i < n; i++) |
|
|
1570 retval.elem (i, j) = result.elem (i, j); |
|
|
1571 } |
|
1948
|
1572 } |
|
458
|
1573 } |
|
|
1574 |
|
|
1575 return retval; |
|
|
1576 } |
|
|
1577 |
|
|
1578 ComplexColumnVector |
|
3585
|
1579 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
1580 { |
|
|
1581 int info; |
|
|
1582 int rank; |
|
|
1583 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1584 } |
|
|
1585 |
|
|
1586 ComplexColumnVector |
|
|
1587 ComplexMatrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1588 { |
|
|
1589 int rank; |
|
|
1590 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1591 } |
|
|
1592 |
|
|
1593 ComplexColumnVector |
|
|
1594 ComplexMatrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1595 { |
|
|
1596 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1597 } |
|
|
1598 |
|
|
1599 ComplexColumnVector |
|
458
|
1600 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1601 { |
|
|
1602 int info; |
|
|
1603 int rank; |
|
|
1604 return lssolve (b, info, rank); |
|
|
1605 } |
|
|
1606 |
|
|
1607 ComplexColumnVector |
|
|
1608 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1609 { |
|
|
1610 int rank; |
|
|
1611 return lssolve (b, info, rank); |
|
|
1612 } |
|
|
1613 |
|
|
1614 ComplexColumnVector |
|
|
1615 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info, |
|
|
1616 int& rank) const |
|
|
1617 { |
|
1948
|
1618 ComplexColumnVector retval; |
|
|
1619 |
|
458
|
1620 int nrhs = 1; |
|
|
1621 |
|
|
1622 int m = rows (); |
|
|
1623 int n = cols (); |
|
|
1624 |
|
|
1625 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1626 (*current_liboctave_error_handler) |
|
|
1627 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1628 else |
|
458
|
1629 { |
|
1948
|
1630 ComplexMatrix atmp = *this; |
|
|
1631 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1632 |
|
|
1633 int nrr = m > n ? m : n; |
|
|
1634 ComplexColumnVector result (nrr); |
|
|
1635 |
|
|
1636 for (int i = 0; i < m; i++) |
|
|
1637 result.elem (i) = b.elem (i); |
|
|
1638 |
|
|
1639 Complex *presult = result.fortran_vec (); |
|
|
1640 |
|
|
1641 int len_s = m < n ? m : n; |
|
|
1642 Array<double> s (len_s); |
|
|
1643 double *ps = s.fortran_vec (); |
|
|
1644 |
|
|
1645 double rcond = -1.0; |
|
|
1646 |
|
|
1647 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1648 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1649 Array<double> rwork (lrwork); |
|
|
1650 double *prwork = rwork.fortran_vec (); |
|
|
1651 |
|
3752
|
1652 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1653 |
|
|
1654 int lwork = -1; |
|
|
1655 |
|
|
1656 Array<Complex> work (1); |
|
|
1657 |
|
1948
|
1658 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1659 nrr, ps, rcond, rank, |
|
|
1660 work.fortran_vec (), lwork, prwork, |
|
|
1661 info)); |
|
1948
|
1662 |
|
|
1663 if (f77_exception_encountered) |
|
|
1664 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1665 else |
|
|
1666 { |
|
3752
|
1667 lwork = static_cast<int> (real (work(0))); |
|
|
1668 work.resize (lwork); |
|
|
1669 |
|
|
1670 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1671 nrr, ps, rcond, rank, |
|
|
1672 work.fortran_vec (), lwork, |
|
|
1673 prwork, info)); |
|
|
1674 |
|
|
1675 if (f77_exception_encountered) |
|
|
1676 (*current_liboctave_error_handler) |
|
|
1677 ("unrecoverable error in zgelss"); |
|
|
1678 else |
|
|
1679 { |
|
|
1680 retval.resize (n); |
|
|
1681 for (int i = 0; i < n; i++) |
|
|
1682 retval.elem (i) = result.elem (i); |
|
|
1683 } |
|
1948
|
1684 } |
|
458
|
1685 } |
|
|
1686 |
|
|
1687 return retval; |
|
|
1688 } |
|
|
1689 |
|
1819
|
1690 // Constants for matrix exponential calculation. |
|
|
1691 |
|
|
1692 static double padec [] = |
|
|
1693 { |
|
|
1694 5.0000000000000000e-1, |
|
|
1695 1.1666666666666667e-1, |
|
|
1696 1.6666666666666667e-2, |
|
|
1697 1.6025641025641026e-3, |
|
|
1698 1.0683760683760684e-4, |
|
|
1699 4.8562548562548563e-6, |
|
|
1700 1.3875013875013875e-7, |
|
|
1701 1.9270852604185938e-9, |
|
|
1702 }; |
|
|
1703 |
|
|
1704 ComplexMatrix |
|
|
1705 ComplexMatrix::expm (void) const |
|
|
1706 { |
|
|
1707 ComplexMatrix retval; |
|
|
1708 |
|
|
1709 ComplexMatrix m = *this; |
|
|
1710 |
|
|
1711 int nc = columns (); |
|
|
1712 |
|
3130
|
1713 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1714 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1715 |
|
1819
|
1716 // trace shift value |
|
|
1717 Complex trshift = 0.0; |
|
|
1718 |
|
|
1719 for (int i = 0; i < nc; i++) |
|
|
1720 trshift += m.elem (i, i); |
|
|
1721 |
|
|
1722 trshift /= nc; |
|
|
1723 |
|
3130
|
1724 if (trshift.real () < 0.0) |
|
|
1725 trshift = trshift.imag (); |
|
|
1726 |
|
1819
|
1727 for (int i = 0; i < nc; i++) |
|
|
1728 m.elem (i, i) -= trshift; |
|
|
1729 |
|
|
1730 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
1731 // code follows development in AEPBAL |
|
|
1732 |
|
|
1733 Complex *mp = m.fortran_vec (); |
|
3467
|
1734 |
|
|
1735 int info, ilo, ihi,ilos,ihis; |
|
3468
|
1736 Array<double> dpermute (nc); |
|
|
1737 Array<double> dscale (nc); |
|
|
1738 |
|
|
1739 // XXX FIXME XXX -- should pass job as a parameter in expm |
|
|
1740 |
|
|
1741 // Permute first |
|
|
1742 char job = 'P'; |
|
3467
|
1743 F77_XFCN (zgebal, ZGEBAL, (&job, nc, mp, nc, ilo, ihi, |
|
3469
|
1744 dpermute.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1745 |
|
|
1746 if (f77_exception_encountered) |
|
|
1747 { |
|
|
1748 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
1749 return retval; |
|
|
1750 } |
|
|
1751 |
|
3468
|
1752 // then scale |
|
|
1753 job = 'S'; |
|
3467
|
1754 F77_XFCN (zgebal, ZGEBAL, (&job, nc, mp, nc, ilos, ihis, |
|
3469
|
1755 dscale.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1756 |
|
|
1757 if (f77_exception_encountered) |
|
|
1758 { |
|
3467
|
1759 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
1760 return retval; |
|
|
1761 } |
|
1819
|
1762 |
|
|
1763 // Preconditioning step 3: scaling. |
|
|
1764 |
|
|
1765 ColumnVector work (nc); |
|
3130
|
1766 double inf_norm; |
|
|
1767 |
|
3331
|
1768 F77_XFCN (xzlange, XZLANGE, ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1769 work.fortran_vec (), inf_norm)); |
|
|
1770 |
|
|
1771 if (f77_exception_encountered) |
|
|
1772 { |
|
|
1773 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
1774 return retval; |
|
|
1775 } |
|
1819
|
1776 |
|
2800
|
1777 int sqpow = (inf_norm > 0.0 |
|
|
1778 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
1779 |
|
|
1780 // Check whether we need to square at all. |
|
|
1781 |
|
|
1782 if (sqpow < 0) |
|
|
1783 sqpow = 0; |
|
|
1784 |
|
|
1785 if (sqpow > 0) |
|
|
1786 { |
|
|
1787 double scale_factor = 1.0; |
|
|
1788 for (int i = 0; i < sqpow; i++) |
|
|
1789 scale_factor *= 2.0; |
|
|
1790 |
|
|
1791 m = m / scale_factor; |
|
|
1792 } |
|
|
1793 |
|
|
1794 // npp, dpp: pade' approx polynomial matrices. |
|
|
1795 |
|
|
1796 ComplexMatrix npp (nc, nc, 0.0); |
|
|
1797 ComplexMatrix dpp = npp; |
|
|
1798 |
|
|
1799 // Now powers a^8 ... a^1. |
|
|
1800 |
|
|
1801 int minus_one_j = -1; |
|
|
1802 for (int j = 7; j >= 0; j--) |
|
|
1803 { |
|
|
1804 npp = m * npp + m * padec[j]; |
|
|
1805 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
1806 minus_one_j *= -1; |
|
|
1807 } |
|
|
1808 |
|
|
1809 // Zero power. |
|
|
1810 |
|
|
1811 dpp = -dpp; |
|
|
1812 for (int j = 0; j < nc; j++) |
|
|
1813 { |
|
|
1814 npp.elem (j, j) += 1.0; |
|
|
1815 dpp.elem (j, j) += 1.0; |
|
|
1816 } |
|
|
1817 |
|
|
1818 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1819 |
|
|
1820 retval = dpp.solve (npp); |
|
|
1821 |
|
|
1822 // Reverse preconditioning step 3: repeated squaring. |
|
|
1823 |
|
|
1824 while (sqpow) |
|
|
1825 { |
|
|
1826 retval = retval * retval; |
|
|
1827 sqpow--; |
|
|
1828 } |
|
|
1829 |
|
|
1830 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
1831 // Done in two steps: inverse scaling, then inverse permutation |
|
|
1832 |
|
|
1833 // inverse scaling (diagonal transformation) |
|
3468
|
1834 for (int i = 0; i < nc; i++) |
|
|
1835 for (int j = 0; j < nc; j++) |
|
|
1836 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
1837 |
|
|
1838 // construct balancing permutation vector |
|
3468
|
1839 Array<int> ipermute (nc); |
|
|
1840 for (int i = 0; i < nc; i++) |
|
|
1841 ipermute(i) = i; // initialize to identity permutation |
|
3467
|
1842 |
|
|
1843 // leading permutations in forward order |
|
3468
|
1844 for (int i = 0; i < (ilo-1); i++) |
|
|
1845 { |
|
|
1846 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1847 int tmp = ipermute(i); |
|
|
1848 ipermute(i) = ipermute(swapidx); |
|
|
1849 ipermute(swapidx) = tmp; |
|
|
1850 } |
|
3467
|
1851 |
|
|
1852 // trailing permutations must be done in reverse order |
|
3468
|
1853 for (int i = nc - 1; i >= ihi; i--) |
|
|
1854 { |
|
|
1855 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1856 int tmp = ipermute(i); |
|
|
1857 ipermute(i) = ipermute(swapidx); |
|
|
1858 ipermute(swapidx) = tmp; |
|
|
1859 } |
|
3467
|
1860 |
|
|
1861 // construct inverse balancing permutation vector |
|
3468
|
1862 Array<int> invpvec (nc); |
|
|
1863 for (int i = 0; i < nc; i++) |
|
|
1864 invpvec(ipermute(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
1865 |
|
|
1866 ComplexMatrix tmpMat = retval; |
|
3468
|
1867 for (int i = 0; i < nc; i++) |
|
|
1868 for (int j = 0; j < nc; j++) |
|
|
1869 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
1870 |
|
|
1871 // Reverse preconditioning step 1: fix trace normalization. |
|
|
1872 |
|
3130
|
1873 return exp (trshift) * retval; |
|
1819
|
1874 } |
|
|
1875 |
|
1205
|
1876 // column vector by row vector -> matrix operations |
|
|
1877 |
|
|
1878 ComplexMatrix |
|
|
1879 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
1880 { |
|
|
1881 ComplexColumnVector tmp (v); |
|
|
1882 return tmp * a; |
|
|
1883 } |
|
|
1884 |
|
|
1885 ComplexMatrix |
|
|
1886 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
1887 { |
|
|
1888 ComplexRowVector tmp (b); |
|
|
1889 return a * tmp; |
|
|
1890 } |
|
|
1891 |
|
|
1892 ComplexMatrix |
|
|
1893 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
1894 { |
|
1948
|
1895 ComplexMatrix retval; |
|
|
1896 |
|
1205
|
1897 int len = v.length (); |
|
3233
|
1898 |
|
|
1899 if (len != 0) |
|
1205
|
1900 { |
|
3233
|
1901 int a_len = a.length (); |
|
|
1902 |
|
|
1903 retval.resize (len, a_len); |
|
|
1904 Complex *c = retval.fortran_vec (); |
|
|
1905 |
|
|
1906 F77_XFCN (zgemm, ZGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
1907 v.data (), len, a.data (), 1, 0.0, |
|
|
1908 c, len, 1L, 1L)); |
|
|
1909 |
|
|
1910 if (f77_exception_encountered) |
|
|
1911 (*current_liboctave_error_handler) |
|
|
1912 ("unrecoverable error in zgemm"); |
|
1205
|
1913 } |
|
|
1914 |
|
1948
|
1915 return retval; |
|
1205
|
1916 } |
|
|
1917 |
|
458
|
1918 // matrix by diagonal matrix -> matrix operations |
|
|
1919 |
|
|
1920 ComplexMatrix& |
|
|
1921 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
1922 { |
|
|
1923 int nr = rows (); |
|
|
1924 int nc = cols (); |
|
2384
|
1925 |
|
|
1926 int a_nr = rows (); |
|
|
1927 int a_nc = cols (); |
|
|
1928 |
|
|
1929 if (nr != a_nr || nc != a_nc) |
|
458
|
1930 { |
|
2384
|
1931 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
1932 return *this; |
|
458
|
1933 } |
|
|
1934 |
|
|
1935 for (int i = 0; i < a.length (); i++) |
|
|
1936 elem (i, i) += a.elem (i, i); |
|
|
1937 |
|
|
1938 return *this; |
|
|
1939 } |
|
|
1940 |
|
|
1941 ComplexMatrix& |
|
|
1942 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
1943 { |
|
|
1944 int nr = rows (); |
|
|
1945 int nc = cols (); |
|
2384
|
1946 |
|
|
1947 int a_nr = rows (); |
|
|
1948 int a_nc = cols (); |
|
|
1949 |
|
|
1950 if (nr != a_nr || nc != a_nc) |
|
458
|
1951 { |
|
2384
|
1952 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
1953 return *this; |
|
458
|
1954 } |
|
|
1955 |
|
|
1956 for (int i = 0; i < a.length (); i++) |
|
|
1957 elem (i, i) -= a.elem (i, i); |
|
|
1958 |
|
|
1959 return *this; |
|
|
1960 } |
|
|
1961 |
|
|
1962 ComplexMatrix& |
|
|
1963 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
1964 { |
|
|
1965 int nr = rows (); |
|
|
1966 int nc = cols (); |
|
2384
|
1967 |
|
|
1968 int a_nr = rows (); |
|
|
1969 int a_nc = cols (); |
|
|
1970 |
|
|
1971 if (nr != a_nr || nc != a_nc) |
|
458
|
1972 { |
|
2384
|
1973 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
1974 return *this; |
|
458
|
1975 } |
|
|
1976 |
|
|
1977 for (int i = 0; i < a.length (); i++) |
|
|
1978 elem (i, i) += a.elem (i, i); |
|
|
1979 |
|
|
1980 return *this; |
|
|
1981 } |
|
|
1982 |
|
|
1983 ComplexMatrix& |
|
|
1984 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
1985 { |
|
|
1986 int nr = rows (); |
|
|
1987 int nc = cols (); |
|
2384
|
1988 |
|
|
1989 int a_nr = rows (); |
|
|
1990 int a_nc = cols (); |
|
|
1991 |
|
|
1992 if (nr != a_nr || nc != a_nc) |
|
458
|
1993 { |
|
2384
|
1994 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
1995 return *this; |
|
458
|
1996 } |
|
|
1997 |
|
|
1998 for (int i = 0; i < a.length (); i++) |
|
|
1999 elem (i, i) -= a.elem (i, i); |
|
|
2000 |
|
|
2001 return *this; |
|
|
2002 } |
|
|
2003 |
|
|
2004 // matrix by matrix -> matrix operations |
|
|
2005 |
|
|
2006 ComplexMatrix& |
|
|
2007 ComplexMatrix::operator += (const Matrix& a) |
|
|
2008 { |
|
|
2009 int nr = rows (); |
|
|
2010 int nc = cols (); |
|
2384
|
2011 |
|
|
2012 int a_nr = a.rows (); |
|
|
2013 int a_nc = a.cols (); |
|
|
2014 |
|
|
2015 if (nr != a_nr || nc != a_nc) |
|
458
|
2016 { |
|
2384
|
2017 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2018 return *this; |
|
|
2019 } |
|
|
2020 |
|
|
2021 if (nr == 0 || nc == 0) |
|
|
2022 return *this; |
|
|
2023 |
|
|
2024 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2025 |
|
|
2026 add2 (d, a.data (), length ()); |
|
|
2027 return *this; |
|
|
2028 } |
|
|
2029 |
|
|
2030 ComplexMatrix& |
|
|
2031 ComplexMatrix::operator -= (const Matrix& a) |
|
|
2032 { |
|
|
2033 int nr = rows (); |
|
|
2034 int nc = cols (); |
|
2384
|
2035 |
|
|
2036 int a_nr = a.rows (); |
|
|
2037 int a_nc = a.cols (); |
|
|
2038 |
|
|
2039 if (nr != a_nr || nc != a_nc) |
|
458
|
2040 { |
|
2384
|
2041 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2042 return *this; |
|
|
2043 } |
|
|
2044 |
|
|
2045 if (nr == 0 || nc == 0) |
|
|
2046 return *this; |
|
|
2047 |
|
|
2048 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2049 |
|
|
2050 subtract2 (d, a.data (), length ()); |
|
|
2051 return *this; |
|
|
2052 } |
|
|
2053 |
|
|
2054 // unary operations |
|
|
2055 |
|
2964
|
2056 boolMatrix |
|
458
|
2057 ComplexMatrix::operator ! (void) const |
|
|
2058 { |
|
2964
|
2059 int nr = rows (); |
|
|
2060 int nc = cols (); |
|
|
2061 |
|
|
2062 boolMatrix b (nr, nc); |
|
|
2063 |
|
|
2064 for (int j = 0; j < nc; j++) |
|
|
2065 for (int i = 0; i < nr; i++) |
|
|
2066 b.elem (i, j) = elem (i, j) != 0.0; |
|
|
2067 |
|
|
2068 return b; |
|
458
|
2069 } |
|
|
2070 |
|
|
2071 // other operations |
|
|
2072 |
|
|
2073 ComplexMatrix |
|
2676
|
2074 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
2075 { |
|
2676
|
2076 ComplexMatrix b (*this); |
|
|
2077 return b.apply (f); |
|
458
|
2078 } |
|
|
2079 |
|
2676
|
2080 Matrix |
|
|
2081 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
2082 { |
|
3248
|
2083 int nr = rows (); |
|
|
2084 int nc = cols (); |
|
|
2085 |
|
|
2086 Matrix retval (nr, nc); |
|
|
2087 |
|
|
2088 for (int j = 0; j < nc; j++) |
|
|
2089 for (int i = 0; i < nr; i++) |
|
|
2090 retval(i,j) = f (elem(i,j)); |
|
|
2091 |
|
|
2092 return retval; |
|
|
2093 } |
|
|
2094 |
|
|
2095 boolMatrix |
|
|
2096 ComplexMatrix::map (b_c_Mapper f) const |
|
|
2097 { |
|
|
2098 int nr = rows (); |
|
|
2099 int nc = cols (); |
|
|
2100 |
|
|
2101 boolMatrix retval (nr, nc); |
|
|
2102 |
|
|
2103 for (int j = 0; j < nc; j++) |
|
|
2104 for (int i = 0; i < nr; i++) |
|
|
2105 retval(i,j) = f (elem(i,j)); |
|
2676
|
2106 |
|
|
2107 return retval; |
|
|
2108 } |
|
|
2109 |
|
|
2110 ComplexMatrix& |
|
|
2111 ComplexMatrix::apply (c_c_Mapper f) |
|
|
2112 { |
|
|
2113 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2114 |
|
|
2115 for (int i = 0; i < length (); i++) |
|
|
2116 d[i] = f (d[i]); |
|
|
2117 |
|
|
2118 return *this; |
|
458
|
2119 } |
|
|
2120 |
|
2384
|
2121 bool |
|
|
2122 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
2123 { |
|
|
2124 int nr = rows (); |
|
|
2125 int nc = cols (); |
|
|
2126 |
|
|
2127 for (int j = 0; j < nc; j++) |
|
|
2128 for (int i = 0; i < nr; i++) |
|
|
2129 { |
|
|
2130 Complex val = elem (i, j); |
|
|
2131 if (xisinf (val) || xisnan (val)) |
|
|
2132 return true; |
|
|
2133 } |
|
|
2134 |
|
|
2135 return false; |
|
|
2136 } |
|
|
2137 |
|
2408
|
2138 // Return true if no elements have imaginary components. |
|
|
2139 |
|
|
2140 bool |
|
|
2141 ComplexMatrix::all_elements_are_real (void) const |
|
|
2142 { |
|
|
2143 int nr = rows (); |
|
|
2144 int nc = cols (); |
|
|
2145 |
|
|
2146 for (int j = 0; j < nc; j++) |
|
|
2147 for (int i = 0; i < nr; i++) |
|
|
2148 if (imag (elem (i, j)) != 0.0) |
|
|
2149 return false; |
|
|
2150 |
|
|
2151 return true; |
|
|
2152 } |
|
|
2153 |
|
1968
|
2154 // Return nonzero if any element of CM has a non-integer real or |
|
|
2155 // imaginary part. Also extract the largest and smallest (real or |
|
|
2156 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
2157 |
|
2384
|
2158 bool |
|
1968
|
2159 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
2160 { |
|
|
2161 int nr = rows (); |
|
2384
|
2162 int nc = cols (); |
|
1968
|
2163 |
|
|
2164 if (nr > 0 && nc > 0) |
|
|
2165 { |
|
|
2166 Complex val = elem (0, 0); |
|
|
2167 |
|
|
2168 double r_val = real (val); |
|
|
2169 double i_val = imag (val); |
|
|
2170 |
|
|
2171 max_val = r_val; |
|
|
2172 min_val = r_val; |
|
|
2173 |
|
|
2174 if (i_val > max_val) |
|
|
2175 max_val = i_val; |
|
|
2176 |
|
|
2177 if (i_val < max_val) |
|
|
2178 min_val = i_val; |
|
|
2179 } |
|
|
2180 else |
|
2384
|
2181 return false; |
|
1968
|
2182 |
|
|
2183 for (int j = 0; j < nc; j++) |
|
|
2184 for (int i = 0; i < nr; i++) |
|
|
2185 { |
|
|
2186 Complex val = elem (i, j); |
|
|
2187 |
|
|
2188 double r_val = real (val); |
|
|
2189 double i_val = imag (val); |
|
|
2190 |
|
|
2191 if (r_val > max_val) |
|
|
2192 max_val = r_val; |
|
|
2193 |
|
|
2194 if (i_val > max_val) |
|
|
2195 max_val = i_val; |
|
|
2196 |
|
|
2197 if (r_val < min_val) |
|
|
2198 min_val = r_val; |
|
|
2199 |
|
|
2200 if (i_val < min_val) |
|
|
2201 min_val = i_val; |
|
|
2202 |
|
|
2203 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
2204 return false; |
|
1968
|
2205 } |
|
2384
|
2206 |
|
|
2207 return true; |
|
1968
|
2208 } |
|
|
2209 |
|
2384
|
2210 bool |
|
1968
|
2211 ComplexMatrix::too_large_for_float (void) const |
|
|
2212 { |
|
|
2213 int nr = rows (); |
|
2384
|
2214 int nc = cols (); |
|
1968
|
2215 |
|
|
2216 for (int j = 0; j < nc; j++) |
|
|
2217 for (int i = 0; i < nr; i++) |
|
|
2218 { |
|
|
2219 Complex val = elem (i, j); |
|
|
2220 |
|
|
2221 double r_val = real (val); |
|
|
2222 double i_val = imag (val); |
|
|
2223 |
|
|
2224 if (r_val > FLT_MAX |
|
|
2225 || i_val > FLT_MAX |
|
|
2226 || r_val < FLT_MIN |
|
|
2227 || i_val < FLT_MIN) |
|
2384
|
2228 return true; |
|
1968
|
2229 } |
|
|
2230 |
|
2384
|
2231 return false; |
|
1968
|
2232 } |
|
|
2233 |
|
2832
|
2234 boolMatrix |
|
458
|
2235 ComplexMatrix::all (void) const |
|
|
2236 { |
|
|
2237 int nr = rows (); |
|
|
2238 int nc = cols (); |
|
2832
|
2239 boolMatrix retval; |
|
458
|
2240 if (nr > 0 && nc > 0) |
|
|
2241 { |
|
|
2242 if (nr == 1) |
|
|
2243 { |
|
|
2244 retval.resize (1, 1); |
|
2832
|
2245 retval.elem (0, 0) = true; |
|
458
|
2246 for (int j = 0; j < nc; j++) |
|
|
2247 { |
|
|
2248 if (elem (0, j) == 0.0) |
|
|
2249 { |
|
2832
|
2250 retval.elem (0, 0) = false; |
|
458
|
2251 break; |
|
|
2252 } |
|
|
2253 } |
|
|
2254 } |
|
|
2255 else if (nc == 1) |
|
|
2256 { |
|
|
2257 retval.resize (1, 1); |
|
2832
|
2258 retval.elem (0, 0) = true; |
|
458
|
2259 for (int i = 0; i < nr; i++) |
|
|
2260 { |
|
|
2261 if (elem (i, 0) == 0.0) |
|
|
2262 { |
|
2832
|
2263 retval.elem (0, 0) = false; |
|
458
|
2264 break; |
|
|
2265 } |
|
|
2266 } |
|
|
2267 } |
|
|
2268 else |
|
|
2269 { |
|
|
2270 retval.resize (1, nc); |
|
|
2271 for (int j = 0; j < nc; j++) |
|
|
2272 { |
|
2832
|
2273 retval.elem (0, j) = true; |
|
458
|
2274 for (int i = 0; i < nr; i++) |
|
|
2275 { |
|
|
2276 if (elem (i, j) == 0.0) |
|
|
2277 { |
|
2832
|
2278 retval.elem (0, j) = false; |
|
458
|
2279 break; |
|
|
2280 } |
|
|
2281 } |
|
|
2282 } |
|
|
2283 } |
|
|
2284 } |
|
|
2285 return retval; |
|
|
2286 } |
|
|
2287 |
|
2832
|
2288 boolMatrix |
|
458
|
2289 ComplexMatrix::any (void) const |
|
|
2290 { |
|
|
2291 int nr = rows (); |
|
|
2292 int nc = cols (); |
|
2832
|
2293 boolMatrix retval; |
|
458
|
2294 if (nr > 0 && nc > 0) |
|
|
2295 { |
|
|
2296 if (nr == 1) |
|
|
2297 { |
|
|
2298 retval.resize (1, 1); |
|
2832
|
2299 retval.elem (0, 0) = false; |
|
458
|
2300 for (int j = 0; j < nc; j++) |
|
|
2301 { |
|
|
2302 if (elem (0, j) != 0.0) |
|
|
2303 { |
|
2832
|
2304 retval.elem (0, 0) = true; |
|
458
|
2305 break; |
|
|
2306 } |
|
|
2307 } |
|
|
2308 } |
|
|
2309 else if (nc == 1) |
|
|
2310 { |
|
|
2311 retval.resize (1, 1); |
|
2832
|
2312 retval.elem (0, 0) = false; |
|
458
|
2313 for (int i = 0; i < nr; i++) |
|
|
2314 { |
|
|
2315 if (elem (i, 0) != 0.0) |
|
|
2316 { |
|
2832
|
2317 retval.elem (0, 0) = true; |
|
458
|
2318 break; |
|
|
2319 } |
|
|
2320 } |
|
|
2321 } |
|
|
2322 else |
|
|
2323 { |
|
|
2324 retval.resize (1, nc); |
|
|
2325 for (int j = 0; j < nc; j++) |
|
|
2326 { |
|
2832
|
2327 retval.elem (0, j) = false; |
|
458
|
2328 for (int i = 0; i < nr; i++) |
|
|
2329 { |
|
|
2330 if (elem (i, j) != 0.0) |
|
|
2331 { |
|
2832
|
2332 retval.elem (0, j) = true; |
|
458
|
2333 break; |
|
|
2334 } |
|
|
2335 } |
|
|
2336 } |
|
|
2337 } |
|
|
2338 } |
|
|
2339 return retval; |
|
|
2340 } |
|
|
2341 |
|
|
2342 ComplexMatrix |
|
3723
|
2343 ComplexMatrix::cumprod (int dim) const |
|
458
|
2344 { |
|
|
2345 int nr = rows (); |
|
|
2346 int nc = cols (); |
|
3723
|
2347 ComplexMatrix retval (nr, nc); |
|
458
|
2348 if (nr > 0 && nc > 0) |
|
|
2349 { |
|
3723
|
2350 if ((nr == 1 && dim == 0) || dim == 1) |
|
458
|
2351 { |
|
|
2352 for (int i = 0; i < nr; i++) |
|
|
2353 { |
|
3726
|
2354 Complex prod = elem (i, 0); |
|
3723
|
2355 for (int j = 0; j < nc; j++) |
|
|
2356 { |
|
3726
|
2357 retval.elem (i, j) = prod; |
|
3723
|
2358 if (j < nc - 1) |
|
|
2359 prod *= elem (i, j+1); |
|
|
2360 } |
|
458
|
2361 } |
|
|
2362 } |
|
|
2363 else |
|
|
2364 { |
|
|
2365 for (int j = 0; j < nc; j++) |
|
|
2366 { |
|
|
2367 Complex prod = elem (0, j); |
|
|
2368 for (int i = 0; i < nr; i++) |
|
|
2369 { |
|
|
2370 retval.elem (i, j) = prod; |
|
|
2371 if (i < nr - 1) |
|
|
2372 prod *= elem (i+1, j); |
|
|
2373 } |
|
|
2374 } |
|
|
2375 } |
|
|
2376 } |
|
|
2377 return retval; |
|
|
2378 } |
|
|
2379 |
|
|
2380 ComplexMatrix |
|
3723
|
2381 ComplexMatrix::cumsum (int dim) const |
|
458
|
2382 { |
|
|
2383 int nr = rows (); |
|
|
2384 int nc = cols (); |
|
3723
|
2385 ComplexMatrix retval (nr, nc); |
|
458
|
2386 if (nr > 0 && nc > 0) |
|
|
2387 { |
|
3723
|
2388 if ((nr == 1 && dim == 0) || dim == 1) |
|
458
|
2389 { |
|
|
2390 for (int i = 0; i < nr; i++) |
|
|
2391 { |
|
3726
|
2392 Complex sum = elem (i, 0); |
|
3723
|
2393 for (int j = 0; j < nc; j++) |
|
|
2394 { |
|
|
2395 retval.elem (i, j) = sum; |
|
|
2396 if (j < nc - 1) |
|
|
2397 sum += elem (i, j+1); |
|
|
2398 } |
|
458
|
2399 } |
|
|
2400 } |
|
|
2401 else |
|
|
2402 { |
|
|
2403 for (int j = 0; j < nc; j++) |
|
|
2404 { |
|
|
2405 Complex sum = elem (0, j); |
|
|
2406 for (int i = 0; i < nr; i++) |
|
|
2407 { |
|
|
2408 retval.elem (i, j) = sum; |
|
|
2409 if (i < nr - 1) |
|
|
2410 sum += elem (i+1, j); |
|
|
2411 } |
|
|
2412 } |
|
|
2413 } |
|
|
2414 } |
|
|
2415 return retval; |
|
|
2416 } |
|
|
2417 |
|
|
2418 ComplexMatrix |
|
3723
|
2419 ComplexMatrix::prod (int dim) const |
|
458
|
2420 { |
|
|
2421 int nr = rows (); |
|
|
2422 int nc = cols (); |
|
|
2423 ComplexMatrix retval; |
|
|
2424 if (nr > 0 && nc > 0) |
|
|
2425 { |
|
3723
|
2426 if ((nr == 1 && dim == 0) || dim == 1) |
|
458
|
2427 { |
|
3723
|
2428 retval.resize(nr, 1); |
|
458
|
2429 for (int i = 0; i < nr; i++) |
|
3723
|
2430 { |
|
|
2431 retval.elem (i, 0) = 1.0; |
|
|
2432 for (int j = 0; j < nc; j++) |
|
|
2433 retval.elem (i, 0) *= elem (i, j); |
|
|
2434 } |
|
458
|
2435 } |
|
|
2436 else |
|
|
2437 { |
|
|
2438 retval.resize (1, nc); |
|
|
2439 for (int j = 0; j < nc; j++) |
|
|
2440 { |
|
|
2441 retval.elem (0, j) = 1.0; |
|
|
2442 for (int i = 0; i < nr; i++) |
|
|
2443 retval.elem (0, j) *= elem (i, j); |
|
|
2444 } |
|
|
2445 } |
|
|
2446 } |
|
3723
|
2447 else |
|
|
2448 { |
|
|
2449 retval.resize (1,1); |
|
|
2450 retval.elem (0,0) = 1.0; |
|
|
2451 } |
|
458
|
2452 return retval; |
|
|
2453 } |
|
|
2454 |
|
|
2455 ComplexMatrix |
|
3723
|
2456 ComplexMatrix::sum (int dim) const |
|
458
|
2457 { |
|
|
2458 int nr = rows (); |
|
|
2459 int nc = cols (); |
|
|
2460 ComplexMatrix retval; |
|
|
2461 if (nr > 0 && nc > 0) |
|
|
2462 { |
|
3723
|
2463 if ((nr == 1 && dim == 0) || dim == 1) |
|
458
|
2464 { |
|
3723
|
2465 retval.resize (nr, 1); |
|
458
|
2466 for (int i = 0; i < nr; i++) |
|
3723
|
2467 { |
|
|
2468 retval.elem (i, 0) = 0.0; |
|
|
2469 for (int j = 0; j < nc; j++) |
|
|
2470 retval.elem (i, 0) += elem (i, j); |
|
|
2471 } |
|
458
|
2472 } |
|
|
2473 else |
|
|
2474 { |
|
|
2475 retval.resize (1, nc); |
|
|
2476 for (int j = 0; j < nc; j++) |
|
|
2477 { |
|
|
2478 retval.elem (0, j) = 0.0; |
|
|
2479 for (int i = 0; i < nr; i++) |
|
|
2480 retval.elem (0, j) += elem (i, j); |
|
|
2481 } |
|
|
2482 } |
|
|
2483 } |
|
3723
|
2484 else |
|
|
2485 { |
|
|
2486 retval.resize (1, 1); |
|
|
2487 retval.elem (0, 0) = 0.0; |
|
|
2488 } |
|
458
|
2489 return retval; |
|
|
2490 } |
|
|
2491 |
|
|
2492 ComplexMatrix |
|
3723
|
2493 ComplexMatrix::sumsq (int dim) const |
|
458
|
2494 { |
|
|
2495 int nr = rows (); |
|
|
2496 int nc = cols (); |
|
|
2497 ComplexMatrix retval; |
|
|
2498 if (nr > 0 && nc > 0) |
|
|
2499 { |
|
3723
|
2500 if ((nr == 1 && dim == 0) || dim == 1) |
|
458
|
2501 { |
|
3723
|
2502 retval.resize (nr, 1); |
|
458
|
2503 for (int i = 0; i < nr; i++) |
|
|
2504 { |
|
3723
|
2505 retval.elem (i, 0) = 0.0; |
|
|
2506 for (int j = 0; j < nc; j++) |
|
|
2507 { |
|
|
2508 Complex d = elem (i, j); |
|
|
2509 retval.elem (i, 0) += d * conj (d); |
|
|
2510 } |
|
458
|
2511 } |
|
|
2512 } |
|
|
2513 else |
|
|
2514 { |
|
|
2515 retval.resize (1, nc); |
|
|
2516 for (int j = 0; j < nc; j++) |
|
|
2517 { |
|
|
2518 retval.elem (0, j) = 0.0; |
|
|
2519 for (int i = 0; i < nr; i++) |
|
|
2520 { |
|
|
2521 Complex d = elem (i, j); |
|
3095
|
2522 retval.elem (0, j) += d * conj (d); |
|
458
|
2523 } |
|
|
2524 } |
|
|
2525 } |
|
|
2526 } |
|
3723
|
2527 else |
|
|
2528 { |
|
|
2529 retval.resize (1, 1); |
|
|
2530 retval.elem (0, 0) = 0.0; |
|
|
2531 } |
|
|
2532 |
|
458
|
2533 return retval; |
|
|
2534 } |
|
|
2535 |
|
|
2536 ComplexColumnVector |
|
|
2537 ComplexMatrix::diag (void) const |
|
|
2538 { |
|
|
2539 return diag (0); |
|
|
2540 } |
|
|
2541 |
|
|
2542 ComplexColumnVector |
|
|
2543 ComplexMatrix::diag (int k) const |
|
|
2544 { |
|
|
2545 int nnr = rows (); |
|
|
2546 int nnc = cols (); |
|
|
2547 if (k > 0) |
|
|
2548 nnc -= k; |
|
|
2549 else if (k < 0) |
|
|
2550 nnr += k; |
|
|
2551 |
|
|
2552 ComplexColumnVector d; |
|
|
2553 |
|
|
2554 if (nnr > 0 && nnc > 0) |
|
|
2555 { |
|
|
2556 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2557 |
|
|
2558 d.resize (ndiag); |
|
|
2559 |
|
|
2560 if (k > 0) |
|
|
2561 { |
|
|
2562 for (int i = 0; i < ndiag; i++) |
|
|
2563 d.elem (i) = elem (i, i+k); |
|
|
2564 } |
|
|
2565 else if ( k < 0) |
|
|
2566 { |
|
|
2567 for (int i = 0; i < ndiag; i++) |
|
|
2568 d.elem (i) = elem (i-k, i); |
|
|
2569 } |
|
|
2570 else |
|
|
2571 { |
|
|
2572 for (int i = 0; i < ndiag; i++) |
|
|
2573 d.elem (i) = elem (i, i); |
|
|
2574 } |
|
|
2575 } |
|
|
2576 else |
|
3504
|
2577 std::cerr << "diag: requested diagonal out of range\n"; |
|
458
|
2578 |
|
|
2579 return d; |
|
|
2580 } |
|
|
2581 |
|
2354
|
2582 bool |
|
|
2583 ComplexMatrix::row_is_real_only (int i) const |
|
|
2584 { |
|
|
2585 bool retval = true; |
|
|
2586 |
|
|
2587 int nc = columns (); |
|
|
2588 |
|
|
2589 for (int j = 0; j < nc; j++) |
|
|
2590 { |
|
|
2591 if (imag (elem (i, j)) != 0.0) |
|
|
2592 { |
|
|
2593 retval = false; |
|
|
2594 break; |
|
|
2595 } |
|
|
2596 } |
|
|
2597 |
|
|
2598 return retval; |
|
|
2599 } |
|
|
2600 |
|
|
2601 bool |
|
|
2602 ComplexMatrix::column_is_real_only (int j) const |
|
|
2603 { |
|
|
2604 bool retval = true; |
|
|
2605 |
|
|
2606 int nr = rows (); |
|
|
2607 |
|
|
2608 for (int i = 0; i < nr; i++) |
|
|
2609 { |
|
|
2610 if (imag (elem (i, j)) != 0.0) |
|
|
2611 { |
|
|
2612 retval = false; |
|
|
2613 break; |
|
|
2614 } |
|
|
2615 } |
|
|
2616 |
|
|
2617 return retval; |
|
|
2618 } |
|
891
|
2619 |
|
458
|
2620 ComplexColumnVector |
|
|
2621 ComplexMatrix::row_min (void) const |
|
|
2622 { |
|
2354
|
2623 Array<int> index; |
|
|
2624 return row_min (index); |
|
458
|
2625 } |
|
|
2626 |
|
|
2627 ComplexColumnVector |
|
2354
|
2628 ComplexMatrix::row_min (Array<int>& index) const |
|
458
|
2629 { |
|
|
2630 ComplexColumnVector result; |
|
|
2631 |
|
|
2632 int nr = rows (); |
|
|
2633 int nc = cols (); |
|
|
2634 |
|
|
2635 if (nr > 0 && nc > 0) |
|
|
2636 { |
|
|
2637 result.resize (nr); |
|
2354
|
2638 index.resize (nr); |
|
458
|
2639 |
|
|
2640 for (int i = 0; i < nr; i++) |
|
|
2641 { |
|
3504
|
2642 int idx_j = 0; |
|
|
2643 |
|
|
2644 Complex tmp_min = elem (i, idx_j); |
|
2354
|
2645 |
|
|
2646 bool real_only = row_is_real_only (i); |
|
|
2647 |
|
|
2648 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2649 |
|
|
2650 if (xisnan (tmp_min)) |
|
3504
|
2651 idx_j = -1; |
|
891
|
2652 else |
|
|
2653 { |
|
|
2654 for (int j = 1; j < nc; j++) |
|
2354
|
2655 { |
|
|
2656 Complex tmp = elem (i, j); |
|
|
2657 |
|
|
2658 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2659 |
|
|
2660 if (xisnan (tmp)) |
|
|
2661 { |
|
3504
|
2662 idx_j = -1; |
|
2354
|
2663 break; |
|
|
2664 } |
|
|
2665 else if (abs_tmp < abs_min) |
|
|
2666 { |
|
3504
|
2667 idx_j = j; |
|
2354
|
2668 tmp_min = tmp; |
|
|
2669 abs_min = abs_tmp; |
|
|
2670 } |
|
|
2671 } |
|
|
2672 |
|
3504
|
2673 result.elem (i) = (idx_j < 0) ? Complex_NaN_result : tmp_min; |
|
|
2674 index.elem (i) = idx_j; |
|
891
|
2675 } |
|
458
|
2676 } |
|
|
2677 } |
|
|
2678 |
|
|
2679 return result; |
|
|
2680 } |
|
|
2681 |
|
|
2682 ComplexColumnVector |
|
|
2683 ComplexMatrix::row_max (void) const |
|
|
2684 { |
|
2354
|
2685 Array<int> index; |
|
|
2686 return row_max (index); |
|
458
|
2687 } |
|
|
2688 |
|
|
2689 ComplexColumnVector |
|
2354
|
2690 ComplexMatrix::row_max (Array<int>& index) const |
|
458
|
2691 { |
|
|
2692 ComplexColumnVector result; |
|
|
2693 |
|
|
2694 int nr = rows (); |
|
|
2695 int nc = cols (); |
|
|
2696 |
|
|
2697 if (nr > 0 && nc > 0) |
|
|
2698 { |
|
|
2699 result.resize (nr); |
|
2354
|
2700 index.resize (nr); |
|
458
|
2701 |
|
|
2702 for (int i = 0; i < nr; i++) |
|
|
2703 { |
|
3504
|
2704 int idx_j = 0; |
|
|
2705 |
|
|
2706 Complex tmp_max = elem (i, idx_j); |
|
2354
|
2707 |
|
|
2708 bool real_only = row_is_real_only (i); |
|
|
2709 |
|
|
2710 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2711 |
|
|
2712 if (xisnan (tmp_max)) |
|
3504
|
2713 idx_j = -1; |
|
891
|
2714 else |
|
|
2715 { |
|
|
2716 for (int j = 1; j < nc; j++) |
|
2354
|
2717 { |
|
|
2718 Complex tmp = elem (i, j); |
|
|
2719 |
|
|
2720 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2721 |
|
|
2722 if (xisnan (tmp)) |
|
|
2723 { |
|
3504
|
2724 idx_j = -1; |
|
2354
|
2725 break; |
|
|
2726 } |
|
|
2727 else if (abs_tmp > abs_max) |
|
|
2728 { |
|
3504
|
2729 idx_j = j; |
|
2354
|
2730 tmp_max = tmp; |
|
|
2731 abs_max = abs_tmp; |
|
|
2732 } |
|
|
2733 } |
|
|
2734 |
|
3504
|
2735 result.elem (i) = (idx_j < 0) ? Complex_NaN_result : tmp_max; |
|
|
2736 index.elem (i) = idx_j; |
|
891
|
2737 } |
|
458
|
2738 } |
|
|
2739 } |
|
|
2740 |
|
|
2741 return result; |
|
|
2742 } |
|
|
2743 |
|
|
2744 ComplexRowVector |
|
|
2745 ComplexMatrix::column_min (void) const |
|
|
2746 { |
|
2354
|
2747 Array<int> index; |
|
|
2748 return column_min (index); |
|
458
|
2749 } |
|
|
2750 |
|
|
2751 ComplexRowVector |
|
2354
|
2752 ComplexMatrix::column_min (Array<int>& index) const |
|
458
|
2753 { |
|
|
2754 ComplexRowVector result; |
|
|
2755 |
|
|
2756 int nr = rows (); |
|
|
2757 int nc = cols (); |
|
|
2758 |
|
|
2759 if (nr > 0 && nc > 0) |
|
|
2760 { |
|
|
2761 result.resize (nc); |
|
2354
|
2762 index.resize (nc); |
|
458
|
2763 |
|
|
2764 for (int j = 0; j < nc; j++) |
|
|
2765 { |
|
3504
|
2766 int idx_i = 0; |
|
|
2767 |
|
|
2768 Complex tmp_min = elem (idx_i, j); |
|
2354
|
2769 |
|
|
2770 bool real_only = column_is_real_only (j); |
|
|
2771 |
|
|
2772 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2773 |
|
|
2774 if (xisnan (tmp_min)) |
|
3504
|
2775 idx_i = -1; |
|
891
|
2776 else |
|
|
2777 { |
|
|
2778 for (int i = 1; i < nr; i++) |
|
2354
|
2779 { |
|
|
2780 Complex tmp = elem (i, j); |
|
|
2781 |
|
|
2782 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2783 |
|
|
2784 if (xisnan (tmp)) |
|
|
2785 { |
|
3504
|
2786 idx_i = -1; |
|
2354
|
2787 break; |
|
|
2788 } |
|
|
2789 else if (abs_tmp < abs_min) |
|
|
2790 { |
|
3504
|
2791 idx_i = i; |
|
2354
|
2792 tmp_min = tmp; |
|
|
2793 abs_min = abs_tmp; |
|
|
2794 } |
|
|
2795 } |
|
|
2796 |
|
3504
|
2797 result.elem (j) = (idx_i < 0) ? Complex_NaN_result : tmp_min; |
|
|
2798 index.elem (j) = idx_i; |
|
891
|
2799 } |
|
458
|
2800 } |
|
|
2801 } |
|
|
2802 |
|
|
2803 return result; |
|
|
2804 } |
|
|
2805 |
|
|
2806 ComplexRowVector |
|
|
2807 ComplexMatrix::column_max (void) const |
|
|
2808 { |
|
2354
|
2809 Array<int> index; |
|
|
2810 return column_max (index); |
|
458
|
2811 } |
|
|
2812 |
|
|
2813 ComplexRowVector |
|
2354
|
2814 ComplexMatrix::column_max (Array<int>& index) const |
|
458
|
2815 { |
|
|
2816 ComplexRowVector result; |
|
|
2817 |
|
|
2818 int nr = rows (); |
|
|
2819 int nc = cols (); |
|
|
2820 |
|
|
2821 if (nr > 0 && nc > 0) |
|
|
2822 { |
|
|
2823 result.resize (nc); |
|
2354
|
2824 index.resize (nc); |
|
458
|
2825 |
|
|
2826 for (int j = 0; j < nc; j++) |
|
|
2827 { |
|
3504
|
2828 int idx_i = 0; |
|
|
2829 |
|
|
2830 Complex tmp_max = elem (idx_i, j); |
|
2354
|
2831 |
|
|
2832 bool real_only = column_is_real_only (j); |
|
|
2833 |
|
|
2834 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2835 |
|
|
2836 if (xisnan (tmp_max)) |
|
3504
|
2837 idx_i = -1; |
|
891
|
2838 else |
|
|
2839 { |
|
|
2840 for (int i = 1; i < nr; i++) |
|
2354
|
2841 { |
|
|
2842 Complex tmp = elem (i, j); |
|
|
2843 |
|
|
2844 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2845 |
|
|
2846 if (xisnan (tmp)) |
|
|
2847 { |
|
3504
|
2848 idx_i = -1; |
|
2354
|
2849 break; |
|
|
2850 } |
|
|
2851 else if (abs_tmp > abs_max) |
|
|
2852 { |
|
3504
|
2853 idx_i = i; |
|
2354
|
2854 tmp_max = tmp; |
|
|
2855 abs_max = abs_tmp; |
|
|
2856 } |
|
|
2857 } |
|
|
2858 |
|
3504
|
2859 result.elem (j) = (idx_i < 0) ? Complex_NaN_result : tmp_max; |
|
|
2860 index.elem (j) = idx_i; |
|
891
|
2861 } |
|
458
|
2862 } |
|
|
2863 } |
|
|
2864 |
|
|
2865 return result; |
|
|
2866 } |
|
|
2867 |
|
|
2868 // i/o |
|
|
2869 |
|
3504
|
2870 std::ostream& |
|
|
2871 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
2872 { |
|
|
2873 // int field_width = os.precision () + 7; |
|
|
2874 for (int i = 0; i < a.rows (); i++) |
|
|
2875 { |
|
|
2876 for (int j = 0; j < a.cols (); j++) |
|
|
2877 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2878 os << "\n"; |
|
|
2879 } |
|
|
2880 return os; |
|
|
2881 } |
|
|
2882 |
|
3504
|
2883 std::istream& |
|
|
2884 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
2885 { |
|
|
2886 int nr = a.rows (); |
|
|
2887 int nc = a.cols (); |
|
|
2888 |
|
|
2889 if (nr < 1 || nc < 1) |
|
3504
|
2890 is.clear (std::ios::badbit); |
|
458
|
2891 else |
|
|
2892 { |
|
|
2893 Complex tmp; |
|
|
2894 for (int i = 0; i < nr; i++) |
|
|
2895 for (int j = 0; j < nc; j++) |
|
|
2896 { |
|
|
2897 is >> tmp; |
|
|
2898 if (is) |
|
|
2899 a.elem (i, j) = tmp; |
|
|
2900 else |
|
2993
|
2901 goto done; |
|
458
|
2902 } |
|
|
2903 } |
|
|
2904 |
|
2993
|
2905 done: |
|
|
2906 |
|
458
|
2907 return is; |
|
|
2908 } |
|
|
2909 |
|
1819
|
2910 ComplexMatrix |
|
|
2911 Givens (const Complex& x, const Complex& y) |
|
|
2912 { |
|
|
2913 double cc; |
|
|
2914 Complex cs, temp_r; |
|
|
2915 |
|
|
2916 F77_FCN (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
|
2917 |
|
|
2918 ComplexMatrix g (2, 2); |
|
|
2919 |
|
|
2920 g.elem (0, 0) = cc; |
|
|
2921 g.elem (1, 1) = cc; |
|
|
2922 g.elem (0, 1) = cs; |
|
|
2923 g.elem (1, 0) = -conj (cs); |
|
|
2924 |
|
|
2925 return g; |
|
|
2926 } |
|
|
2927 |
|
|
2928 ComplexMatrix |
|
|
2929 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
2930 const ComplexMatrix& c) |
|
|
2931 { |
|
|
2932 ComplexMatrix retval; |
|
|
2933 |
|
|
2934 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2935 // size. |
|
|
2936 |
|
|
2937 // Compute Schur decompositions |
|
|
2938 |
|
|
2939 ComplexSCHUR as (a, "U"); |
|
|
2940 ComplexSCHUR bs (b, "U"); |
|
|
2941 |
|
|
2942 // Transform c to new coordinates. |
|
|
2943 |
|
|
2944 ComplexMatrix ua = as.unitary_matrix (); |
|
|
2945 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
2946 |
|
|
2947 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
2948 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
2949 |
|
|
2950 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
2951 |
|
|
2952 // Solve the sylvester equation, back-transform, and return the |
|
|
2953 // solution. |
|
|
2954 |
|
|
2955 int a_nr = a.rows (); |
|
|
2956 int b_nr = b.rows (); |
|
|
2957 |
|
|
2958 double scale; |
|
|
2959 int info; |
|
1950
|
2960 |
|
|
2961 Complex *pa = sch_a.fortran_vec (); |
|
|
2962 Complex *pb = sch_b.fortran_vec (); |
|
|
2963 Complex *px = cx.fortran_vec (); |
|
1819
|
2964 |
|
1950
|
2965 F77_XFCN (ztrsyl, ZTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2966 b_nr, px, a_nr, scale, |
|
|
2967 info, 1L, 1L)); |
|
|
2968 |
|
|
2969 if (f77_exception_encountered) |
|
|
2970 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
2971 else |
|
|
2972 { |
|
|
2973 // XXX FIXME XXX -- check info? |
|
|
2974 |
|
|
2975 retval = -ua * cx * ub.hermitian (); |
|
|
2976 } |
|
1819
|
2977 |
|
|
2978 return retval; |
|
|
2979 } |
|
|
2980 |
|
2828
|
2981 ComplexMatrix |
|
|
2982 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
2983 { |
|
|
2984 ComplexMatrix tmp (a); |
|
|
2985 return m * tmp; |
|
|
2986 } |
|
|
2987 |
|
|
2988 ComplexMatrix |
|
|
2989 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
2990 { |
|
|
2991 ComplexMatrix tmp (m); |
|
|
2992 return tmp * a; |
|
|
2993 } |
|
|
2994 |
|
|
2995 ComplexMatrix |
|
|
2996 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
2997 { |
|
|
2998 ComplexMatrix retval; |
|
|
2999 |
|
|
3000 int nr = m.rows (); |
|
|
3001 int nc = m.cols (); |
|
|
3002 |
|
|
3003 int a_nr = a.rows (); |
|
|
3004 int a_nc = a.cols (); |
|
|
3005 |
|
|
3006 if (nc != a_nr) |
|
|
3007 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3008 else |
|
|
3009 { |
|
|
3010 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
3011 retval.resize (nr, nc, 0.0); |
|
|
3012 else |
|
|
3013 { |
|
|
3014 int ld = nr; |
|
|
3015 int lda = a.rows (); |
|
|
3016 |
|
|
3017 retval.resize (nr, a_nc); |
|
|
3018 Complex *c = retval.fortran_vec (); |
|
|
3019 |
|
|
3020 F77_XFCN (zgemm, ZGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
3021 m.data (), ld, a.data (), lda, 0.0, |
|
|
3022 c, nr, 1L, 1L)); |
|
|
3023 |
|
|
3024 if (f77_exception_encountered) |
|
|
3025 (*current_liboctave_error_handler) |
|
|
3026 ("unrecoverable error in zgemm"); |
|
|
3027 } |
|
|
3028 } |
|
|
3029 |
|
|
3030 return retval; |
|
|
3031 } |
|
|
3032 |
|
2870
|
3033 MS_CMP_OPS(ComplexMatrix, real, Complex, real) |
|
3504
|
3034 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
3035 |
|
|
3036 SM_CMP_OPS(Complex, real, ComplexMatrix, real) |
|
3504
|
3037 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
3038 |
|
|
3039 MM_CMP_OPS(ComplexMatrix, real, ComplexMatrix, real) |
|
3504
|
3040 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
3041 |
|
458
|
3042 /* |
|
|
3043 ;;; Local Variables: *** |
|
|
3044 ;;; mode: C++ *** |
|
|
3045 ;;; End: *** |
|
|
3046 */ |
