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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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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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4192
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24 #if defined (__GNUG__) && defined (USE_PRAGMA_INTERFACE_IMPLEMENTATION) |
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1296
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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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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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4669
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41 #include "Array-util.h" |
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2828
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42 #include "CMatrix.h" |
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1819
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43 #include "CmplxAEPBAL.h" |
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458
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44 #include "CmplxDET.h" |
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1819
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45 #include "CmplxSCHUR.h" |
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740
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46 #include "CmplxSVD.h" |
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1847
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47 #include "f77-fcn.h" |
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458
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48 #include "lo-error.h" |
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2354
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49 #include "lo-ieee.h" |
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50 #include "lo-mappers.h" |
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1968
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51 #include "lo-utils.h" |
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1367
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52 #include "mx-base.h" |
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2828
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53 #include "mx-cm-dm.h" |
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3176
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54 #include "mx-dm-cm.h" |
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2828
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55 #include "mx-cm-s.h" |
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1367
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56 #include "mx-inlines.cc" |
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1650
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57 #include "oct-cmplx.h" |
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458
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58 |
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4773
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59 #if defined (HAVE_FFTW3) |
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3827
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60 #include "oct-fftw.h" |
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61 #endif |
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62 |
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458
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63 // Fortran functions we call. |
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64 |
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65 extern "C" |
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66 { |
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4552
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67 F77_RET_T |
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68 F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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69 const int&, Complex*, const int&, int&, |
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70 int&, double*, int& |
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71 F77_CHAR_ARG_LEN_DECL); |
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72 |
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73 F77_RET_T |
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74 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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75 F77_CONST_CHAR_ARG_DECL, |
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76 const int&, const int&, const int&, double*, |
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77 const int&, double*, const int&, int& |
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78 F77_CHAR_ARG_LEN_DECL |
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79 F77_CHAR_ARG_LEN_DECL); |
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80 |
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81 F77_RET_T |
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82 F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, |
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83 F77_CONST_CHAR_ARG_DECL, |
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84 const int&, const int&, const int&, |
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85 const Complex&, const Complex*, const int&, |
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86 const Complex*, const int&, const Complex&, |
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87 Complex*, const int& |
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88 F77_CHAR_ARG_LEN_DECL |
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89 F77_CHAR_ARG_LEN_DECL); |
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90 |
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91 F77_RET_T |
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92 F77_FUNC (zgetrf, ZGETRF) (const int&, const int&, Complex*, const int&, |
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93 int*, int&); |
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94 |
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95 F77_RET_T |
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96 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, |
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97 const int&, const int&, Complex*, const int&, |
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98 const int*, Complex*, const int&, int& |
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99 F77_CHAR_ARG_LEN_DECL); |
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100 |
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101 F77_RET_T |
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102 F77_FUNC (zgetri, ZGETRI) (const int&, Complex*, const int&, const int*, |
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103 Complex*, const int&, int&); |
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104 |
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105 F77_RET_T |
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106 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, |
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107 const int&, Complex*, |
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108 const int&, const double&, double&, |
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109 Complex*, double*, int& |
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110 F77_CHAR_ARG_LEN_DECL); |
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111 |
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112 F77_RET_T |
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113 F77_FUNC (zgelss, ZGELSS) (const int&, const int&, const int&, |
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114 Complex*, const int&, Complex*, |
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115 const int&, double*, double&, int&, |
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116 Complex*, const int&, double*, int&); |
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117 |
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1360
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118 // Note that the original complex fft routines were not written for |
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119 // double complex arguments. They have been modified by adding an |
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120 // implicit double precision (a-h,o-z) statement at the beginning of |
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121 // each subroutine. |
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122 |
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4552
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123 F77_RET_T |
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124 F77_FUNC (cffti, CFFTI) (const int&, Complex*); |
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125 |
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126 F77_RET_T |
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127 F77_FUNC (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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128 |
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129 F77_RET_T |
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130 F77_FUNC (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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131 |
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132 F77_RET_T |
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133 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, |
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134 double&, Complex&, Complex&); |
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135 |
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136 F77_RET_T |
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137 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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138 F77_CONST_CHAR_ARG_DECL, |
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139 const int&, const int&, const int&, |
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140 const Complex*, const int&, |
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141 const Complex*, const int&, |
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142 const Complex*, const int&, double&, int& |
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143 F77_CHAR_ARG_LEN_DECL |
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144 F77_CHAR_ARG_LEN_DECL); |
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145 |
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146 F77_RET_T |
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147 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, |
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148 const int&, const int&, const Complex*, |
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149 const int&, double*, double& |
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150 F77_CHAR_ARG_LEN_DECL); |
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458
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151 } |
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152 |
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2354
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153 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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154 |
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1360
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155 // Complex Matrix class |
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458
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156 |
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157 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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1214
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158 : MArray2<Complex> (a.rows (), a.cols ()) |
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458
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159 { |
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160 for (int j = 0; j < cols (); j++) |
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161 for (int i = 0; i < rows (); i++) |
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162 elem (i, j) = a.elem (i, j); |
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163 } |
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164 |
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2349
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165 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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166 : MArray2<Complex> (1, rv.length (), 0.0) |
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167 { |
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168 for (int i = 0; i < rv.length (); i++) |
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169 elem (0, i) = rv.elem (i); |
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170 } |
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171 |
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172 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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173 : MArray2<Complex> (cv.length (), 1, 0.0) |
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174 { |
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175 for (int i = 0; i < cv.length (); i++) |
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176 elem (i, 0) = cv.elem (i); |
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177 } |
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178 |
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458
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179 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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1214
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180 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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181 { |
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182 for (int i = 0; i < a.length (); i++) |
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183 elem (i, i) = a.elem (i, i); |
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184 } |
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185 |
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2349
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186 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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187 : MArray2<Complex> (1, rv.length (), 0.0) |
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188 { |
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189 for (int i = 0; i < rv.length (); i++) |
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190 elem (0, i) = rv.elem (i); |
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191 } |
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192 |
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193 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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194 : MArray2<Complex> (cv.length (), 1, 0.0) |
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195 { |
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196 for (int i = 0; i < cv.length (); i++) |
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197 elem (i, 0) = cv.elem (i); |
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198 } |
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199 |
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458
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200 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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201 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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202 { |
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203 for (int i = 0; i < a.length (); i++) |
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204 elem (i, i) = a.elem (i, i); |
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205 } |
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206 |
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1574
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207 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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208 // here? |
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209 |
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210 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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3180
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211 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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2828
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212 { |
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3998
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213 for (int i = 0; i < a.rows (); i++) |
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214 for (int j = 0; j < a.cols (); j++) |
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215 elem (i, j) = a.elem (i, j); |
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216 } |
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217 |
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218 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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219 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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220 { |
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3998
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221 for (int i = 0; i < a.rows (); i++) |
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222 for (int j = 0; j < a.cols (); j++) |
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1574
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223 elem (i, j) = a.elem (i, j); |
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224 } |
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225 |
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2384
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226 bool |
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458
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227 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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228 { |
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229 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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230 return false; |
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458
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231 |
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3769
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232 return mx_inline_equal (data (), a.data (), length ()); |
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458
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233 } |
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234 |
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2384
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235 bool |
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458
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236 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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237 { |
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238 return !(*this == a); |
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239 } |
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240 |
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2815
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241 bool |
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242 ComplexMatrix::is_hermitian (void) const |
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243 { |
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244 int nr = rows (); |
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245 int nc = cols (); |
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246 |
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247 if (is_square () && nr > 0) |
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248 { |
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249 for (int i = 0; i < nr; i++) |
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250 for (int j = i; j < nc; j++) |
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251 if (elem (i, j) != conj (elem (j, i))) |
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252 return false; |
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253 |
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254 return true; |
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255 } |
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256 |
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257 return false; |
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258 } |
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259 |
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458
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260 // destructive insert/delete/reorder operations |
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261 |
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262 ComplexMatrix& |
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263 ComplexMatrix::insert (const Matrix& a, int r, int c) |
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264 { |
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265 int a_nr = a.rows (); |
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266 int a_nc = a.cols (); |
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267 |
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268 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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269 { |
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270 (*current_liboctave_error_handler) ("range error for insert"); |
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271 return *this; |
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272 } |
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273 |
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4316
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274 if (a_nr >0 && a_nc > 0) |
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275 { |
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276 make_unique (); |
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277 |
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278 for (int j = 0; j < a_nc; j++) |
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279 for (int i = 0; i < a_nr; i++) |
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280 xelem (r+i, c+j) = a.elem (i, j); |
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281 } |
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458
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282 |
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283 return *this; |
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284 } |
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285 |
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286 ComplexMatrix& |
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287 ComplexMatrix::insert (const RowVector& a, int r, int c) |
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288 { |
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289 int a_len = a.length (); |
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4316
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290 |
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1699
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291 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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292 { |
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293 (*current_liboctave_error_handler) ("range error for insert"); |
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294 return *this; |
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295 } |
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296 |
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4316
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297 if (a_len > 0) |
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298 { |
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299 make_unique (); |
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300 |
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301 for (int i = 0; i < a_len; i++) |
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302 xelem (r, c+i) = a.elem (i); |
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303 } |
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458
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304 |
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305 return *this; |
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306 } |
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307 |
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308 ComplexMatrix& |
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309 ComplexMatrix::insert (const ColumnVector& a, int r, int c) |
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310 { |
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311 int a_len = a.length (); |
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4316
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312 |
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1699
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313 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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314 { |
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315 (*current_liboctave_error_handler) ("range error for insert"); |
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316 return *this; |
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317 } |
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318 |
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4316
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319 if (a_len > 0) |
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320 { |
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321 make_unique (); |
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322 |
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323 for (int i = 0; i < a_len; i++) |
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324 xelem (r+i, c) = a.elem (i); |
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325 } |
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458
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326 |
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327 return *this; |
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328 } |
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329 |
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330 ComplexMatrix& |
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331 ComplexMatrix::insert (const DiagMatrix& a, int r, int c) |
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332 { |
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1699
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333 int a_nr = a.rows (); |
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334 int a_nc = a.cols (); |
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335 |
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336 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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337 { |
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338 (*current_liboctave_error_handler) ("range error for insert"); |
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339 return *this; |
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340 } |
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341 |
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1699
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342 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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343 |
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4316
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344 int a_len = a.length (); |
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345 |
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346 if (a_len > 0) |
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347 { |
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348 make_unique (); |
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349 |
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350 for (int i = 0; i < a_len; i++) |
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351 xelem (r+i, c+i) = a.elem (i, i); |
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352 } |
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458
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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::insert (const ComplexMatrix& a, int r, int c) |
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359 { |
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1561
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360 Array2<Complex>::insert (a, r, c); |
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458
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361 return *this; |
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362 } |
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363 |
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364 ComplexMatrix& |
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365 ComplexMatrix::insert (const ComplexRowVector& a, int r, int c) |
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366 { |
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367 int a_len = a.length (); |
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1699
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368 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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369 { |
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370 (*current_liboctave_error_handler) ("range error for insert"); |
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371 return *this; |
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372 } |
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373 |
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374 for (int i = 0; i < a_len; i++) |
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375 elem (r, c+i) = a.elem (i); |
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376 |
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377 return *this; |
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378 } |
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379 |
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380 ComplexMatrix& |
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381 ComplexMatrix::insert (const ComplexColumnVector& a, int r, int c) |
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382 { |
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383 int a_len = a.length (); |
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4316
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384 |
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1699
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385 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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386 { |
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387 (*current_liboctave_error_handler) ("range error for insert"); |
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388 return *this; |
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389 } |
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390 |
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4316
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391 if (a_len > 0) |
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392 { |
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393 make_unique (); |
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394 |
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395 for (int i = 0; i < a_len; i++) |
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396 xelem (r+i, c) = a.elem (i); |
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397 } |
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458
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398 |
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399 return *this; |
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400 } |
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401 |
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402 ComplexMatrix& |
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403 ComplexMatrix::insert (const ComplexDiagMatrix& a, int r, int c) |
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404 { |
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1699
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405 int a_nr = a.rows (); |
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406 int a_nc = a.cols (); |
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407 |
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408 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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409 { |
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410 (*current_liboctave_error_handler) ("range error for insert"); |
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411 return *this; |
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412 } |
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413 |
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1699
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414 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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415 |
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4316
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416 int a_len = a.length (); |
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417 |
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418 if (a_len > 0) |
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419 { |
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420 make_unique (); |
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421 |
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422 for (int i = 0; i < a_len; i++) |
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423 xelem (r+i, c+i) = a.elem (i, i); |
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424 } |
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458
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425 |
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426 return *this; |
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427 } |
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428 |
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429 ComplexMatrix& |
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430 ComplexMatrix::fill (double val) |
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431 { |
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432 int nr = rows (); |
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433 int nc = cols (); |
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4316
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434 |
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458
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435 if (nr > 0 && nc > 0) |
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4316
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436 { |
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437 make_unique (); |
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438 |
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439 for (int j = 0; j < nc; j++) |
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440 for (int i = 0; i < nr; i++) |
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441 xelem (i, j) = val; |
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442 } |
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458
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443 |
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444 return *this; |
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445 } |
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446 |
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447 ComplexMatrix& |
|
|
448 ComplexMatrix::fill (const Complex& val) |
|
|
449 { |
|
|
450 int nr = rows (); |
|
|
451 int nc = cols (); |
|
4316
|
452 |
|
458
|
453 if (nr > 0 && nc > 0) |
|
4316
|
454 { |
|
|
455 make_unique (); |
|
|
456 |
|
|
457 for (int j = 0; j < nc; j++) |
|
|
458 for (int i = 0; i < nr; i++) |
|
|
459 xelem (i, j) = val; |
|
|
460 } |
|
458
|
461 |
|
|
462 return *this; |
|
|
463 } |
|
|
464 |
|
|
465 ComplexMatrix& |
|
|
466 ComplexMatrix::fill (double val, int r1, int c1, int r2, int c2) |
|
|
467 { |
|
|
468 int nr = rows (); |
|
|
469 int nc = cols (); |
|
4316
|
470 |
|
458
|
471 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
472 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
473 { |
|
|
474 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
475 return *this; |
|
|
476 } |
|
|
477 |
|
|
478 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
479 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
480 |
|
4316
|
481 if (r2 >= r1 && c2 >= c1) |
|
|
482 { |
|
|
483 make_unique (); |
|
|
484 |
|
|
485 for (int j = c1; j <= c2; j++) |
|
|
486 for (int i = r1; i <= r2; i++) |
|
|
487 xelem (i, j) = val; |
|
|
488 } |
|
458
|
489 |
|
|
490 return *this; |
|
|
491 } |
|
|
492 |
|
|
493 ComplexMatrix& |
|
|
494 ComplexMatrix::fill (const Complex& val, int r1, int c1, int r2, int c2) |
|
|
495 { |
|
|
496 int nr = rows (); |
|
|
497 int nc = cols (); |
|
4316
|
498 |
|
458
|
499 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
500 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
501 { |
|
|
502 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
503 return *this; |
|
|
504 } |
|
|
505 |
|
|
506 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
507 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
508 |
|
4316
|
509 if (r2 >= r1 && c2 >=c1) |
|
|
510 { |
|
|
511 make_unique (); |
|
|
512 |
|
|
513 for (int j = c1; j <= c2; j++) |
|
|
514 for (int i = r1; i <= r2; i++) |
|
|
515 xelem (i, j) = val; |
|
|
516 } |
|
458
|
517 |
|
|
518 return *this; |
|
|
519 } |
|
|
520 |
|
|
521 ComplexMatrix |
|
|
522 ComplexMatrix::append (const Matrix& a) const |
|
|
523 { |
|
|
524 int nr = rows (); |
|
|
525 int nc = cols (); |
|
|
526 if (nr != a.rows ()) |
|
|
527 { |
|
|
528 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
529 return *this; |
|
|
530 } |
|
|
531 |
|
|
532 int nc_insert = nc; |
|
|
533 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
534 retval.insert (*this, 0, 0); |
|
|
535 retval.insert (a, 0, nc_insert); |
|
|
536 return retval; |
|
|
537 } |
|
|
538 |
|
|
539 ComplexMatrix |
|
|
540 ComplexMatrix::append (const RowVector& a) const |
|
|
541 { |
|
|
542 int nr = rows (); |
|
|
543 int nc = cols (); |
|
|
544 if (nr != 1) |
|
|
545 { |
|
|
546 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
547 return *this; |
|
|
548 } |
|
|
549 |
|
|
550 int nc_insert = nc; |
|
|
551 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
552 retval.insert (*this, 0, 0); |
|
|
553 retval.insert (a, 0, nc_insert); |
|
|
554 return retval; |
|
|
555 } |
|
|
556 |
|
|
557 ComplexMatrix |
|
|
558 ComplexMatrix::append (const ColumnVector& a) const |
|
|
559 { |
|
|
560 int nr = rows (); |
|
|
561 int nc = cols (); |
|
|
562 if (nr != a.length ()) |
|
|
563 { |
|
|
564 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
565 return *this; |
|
|
566 } |
|
|
567 |
|
|
568 int nc_insert = nc; |
|
|
569 ComplexMatrix retval (nr, nc + 1); |
|
|
570 retval.insert (*this, 0, 0); |
|
|
571 retval.insert (a, 0, nc_insert); |
|
|
572 return retval; |
|
|
573 } |
|
|
574 |
|
|
575 ComplexMatrix |
|
|
576 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
577 { |
|
|
578 int nr = rows (); |
|
|
579 int nc = cols (); |
|
|
580 if (nr != a.rows ()) |
|
|
581 { |
|
|
582 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
583 return *this; |
|
|
584 } |
|
|
585 |
|
|
586 int nc_insert = nc; |
|
|
587 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
588 retval.insert (*this, 0, 0); |
|
|
589 retval.insert (a, 0, nc_insert); |
|
|
590 return retval; |
|
|
591 } |
|
|
592 |
|
|
593 ComplexMatrix |
|
|
594 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
595 { |
|
|
596 int nr = rows (); |
|
|
597 int nc = cols (); |
|
|
598 if (nr != a.rows ()) |
|
|
599 { |
|
|
600 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
601 return *this; |
|
|
602 } |
|
|
603 |
|
|
604 int nc_insert = nc; |
|
|
605 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
606 retval.insert (*this, 0, 0); |
|
|
607 retval.insert (a, 0, nc_insert); |
|
|
608 return retval; |
|
|
609 } |
|
|
610 |
|
|
611 ComplexMatrix |
|
|
612 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
613 { |
|
|
614 int nr = rows (); |
|
|
615 int nc = cols (); |
|
|
616 if (nr != 1) |
|
|
617 { |
|
|
618 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
619 return *this; |
|
|
620 } |
|
|
621 |
|
|
622 int nc_insert = nc; |
|
|
623 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
624 retval.insert (*this, 0, 0); |
|
|
625 retval.insert (a, 0, nc_insert); |
|
|
626 return retval; |
|
|
627 } |
|
|
628 |
|
|
629 ComplexMatrix |
|
|
630 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
631 { |
|
|
632 int nr = rows (); |
|
|
633 int nc = cols (); |
|
|
634 if (nr != a.length ()) |
|
|
635 { |
|
|
636 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
637 return *this; |
|
|
638 } |
|
|
639 |
|
|
640 int nc_insert = nc; |
|
|
641 ComplexMatrix retval (nr, nc + 1); |
|
|
642 retval.insert (*this, 0, 0); |
|
|
643 retval.insert (a, 0, nc_insert); |
|
|
644 return retval; |
|
|
645 } |
|
|
646 |
|
|
647 ComplexMatrix |
|
|
648 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
649 { |
|
|
650 int nr = rows (); |
|
|
651 int nc = cols (); |
|
|
652 if (nr != a.rows ()) |
|
|
653 { |
|
|
654 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
655 return *this; |
|
|
656 } |
|
|
657 |
|
|
658 int nc_insert = nc; |
|
|
659 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
660 retval.insert (*this, 0, 0); |
|
|
661 retval.insert (a, 0, nc_insert); |
|
|
662 return retval; |
|
|
663 } |
|
|
664 |
|
|
665 ComplexMatrix |
|
|
666 ComplexMatrix::stack (const Matrix& a) const |
|
|
667 { |
|
|
668 int nr = rows (); |
|
|
669 int nc = cols (); |
|
|
670 if (nc != a.cols ()) |
|
|
671 { |
|
|
672 (*current_liboctave_error_handler) |
|
|
673 ("column dimension mismatch for stack"); |
|
|
674 return *this; |
|
|
675 } |
|
|
676 |
|
|
677 int nr_insert = nr; |
|
|
678 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
679 retval.insert (*this, 0, 0); |
|
|
680 retval.insert (a, nr_insert, 0); |
|
|
681 return retval; |
|
|
682 } |
|
|
683 |
|
|
684 ComplexMatrix |
|
|
685 ComplexMatrix::stack (const RowVector& a) const |
|
|
686 { |
|
|
687 int nr = rows (); |
|
|
688 int nc = cols (); |
|
|
689 if (nc != a.length ()) |
|
|
690 { |
|
|
691 (*current_liboctave_error_handler) |
|
|
692 ("column dimension mismatch for stack"); |
|
|
693 return *this; |
|
|
694 } |
|
|
695 |
|
|
696 int nr_insert = nr; |
|
|
697 ComplexMatrix retval (nr + 1, nc); |
|
|
698 retval.insert (*this, 0, 0); |
|
|
699 retval.insert (a, nr_insert, 0); |
|
|
700 return retval; |
|
|
701 } |
|
|
702 |
|
|
703 ComplexMatrix |
|
|
704 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
705 { |
|
|
706 int nr = rows (); |
|
|
707 int nc = cols (); |
|
|
708 if (nc != 1) |
|
|
709 { |
|
|
710 (*current_liboctave_error_handler) |
|
|
711 ("column dimension mismatch for stack"); |
|
|
712 return *this; |
|
|
713 } |
|
|
714 |
|
|
715 int nr_insert = nr; |
|
|
716 ComplexMatrix retval (nr + a.length (), nc); |
|
|
717 retval.insert (*this, 0, 0); |
|
|
718 retval.insert (a, nr_insert, 0); |
|
|
719 return retval; |
|
|
720 } |
|
|
721 |
|
|
722 ComplexMatrix |
|
|
723 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
724 { |
|
|
725 int nr = rows (); |
|
|
726 int nc = cols (); |
|
|
727 if (nc != a.cols ()) |
|
|
728 { |
|
|
729 (*current_liboctave_error_handler) |
|
|
730 ("column dimension mismatch for stack"); |
|
|
731 return *this; |
|
|
732 } |
|
|
733 |
|
|
734 int nr_insert = nr; |
|
|
735 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
736 retval.insert (*this, 0, 0); |
|
|
737 retval.insert (a, nr_insert, 0); |
|
|
738 return retval; |
|
|
739 } |
|
|
740 |
|
|
741 ComplexMatrix |
|
|
742 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
743 { |
|
|
744 int nr = rows (); |
|
|
745 int nc = cols (); |
|
|
746 if (nc != a.cols ()) |
|
|
747 { |
|
|
748 (*current_liboctave_error_handler) |
|
|
749 ("column dimension mismatch for stack"); |
|
|
750 return *this; |
|
|
751 } |
|
|
752 |
|
|
753 int nr_insert = nr; |
|
|
754 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
755 retval.insert (*this, 0, 0); |
|
|
756 retval.insert (a, nr_insert, 0); |
|
|
757 return retval; |
|
|
758 } |
|
|
759 |
|
|
760 ComplexMatrix |
|
|
761 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
762 { |
|
|
763 int nr = rows (); |
|
|
764 int nc = cols (); |
|
|
765 if (nc != a.length ()) |
|
|
766 { |
|
|
767 (*current_liboctave_error_handler) |
|
|
768 ("column dimension mismatch for stack"); |
|
|
769 return *this; |
|
|
770 } |
|
|
771 |
|
|
772 int nr_insert = nr; |
|
|
773 ComplexMatrix retval (nr + 1, nc); |
|
|
774 retval.insert (*this, 0, 0); |
|
|
775 retval.insert (a, nr_insert, 0); |
|
|
776 return retval; |
|
|
777 } |
|
|
778 |
|
|
779 ComplexMatrix |
|
|
780 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
781 { |
|
|
782 int nr = rows (); |
|
|
783 int nc = cols (); |
|
|
784 if (nc != 1) |
|
|
785 { |
|
|
786 (*current_liboctave_error_handler) |
|
|
787 ("column dimension mismatch for stack"); |
|
|
788 return *this; |
|
|
789 } |
|
|
790 |
|
|
791 int nr_insert = nr; |
|
|
792 ComplexMatrix retval (nr + a.length (), nc); |
|
|
793 retval.insert (*this, 0, 0); |
|
|
794 retval.insert (a, nr_insert, 0); |
|
|
795 return retval; |
|
|
796 } |
|
|
797 |
|
|
798 ComplexMatrix |
|
|
799 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
800 { |
|
|
801 int nr = rows (); |
|
|
802 int nc = cols (); |
|
|
803 if (nc != a.cols ()) |
|
|
804 { |
|
|
805 (*current_liboctave_error_handler) |
|
|
806 ("column dimension mismatch for stack"); |
|
|
807 return *this; |
|
|
808 } |
|
|
809 |
|
|
810 int nr_insert = nr; |
|
|
811 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
812 retval.insert (*this, 0, 0); |
|
|
813 retval.insert (a, nr_insert, 0); |
|
|
814 return retval; |
|
|
815 } |
|
|
816 |
|
|
817 ComplexMatrix |
|
|
818 ComplexMatrix::hermitian (void) const |
|
|
819 { |
|
|
820 int nr = rows (); |
|
|
821 int nc = cols (); |
|
|
822 ComplexMatrix result; |
|
|
823 if (length () > 0) |
|
|
824 { |
|
|
825 result.resize (nc, nr); |
|
|
826 for (int j = 0; j < nc; j++) |
|
|
827 for (int i = 0; i < nr; i++) |
|
|
828 result.elem (j, i) = conj (elem (i, j)); |
|
|
829 } |
|
|
830 return result; |
|
|
831 } |
|
|
832 |
|
|
833 ComplexMatrix |
|
|
834 conj (const ComplexMatrix& a) |
|
|
835 { |
|
|
836 int a_len = a.length (); |
|
|
837 ComplexMatrix retval; |
|
|
838 if (a_len > 0) |
|
3769
|
839 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
|
|
840 a.rows (), a.cols ()); |
|
458
|
841 return retval; |
|
|
842 } |
|
|
843 |
|
|
844 // resize is the destructive equivalent for this one |
|
|
845 |
|
|
846 ComplexMatrix |
|
|
847 ComplexMatrix::extract (int r1, int c1, int r2, int c2) const |
|
|
848 { |
|
|
849 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
850 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
851 |
|
|
852 int new_r = r2 - r1 + 1; |
|
|
853 int new_c = c2 - c1 + 1; |
|
|
854 |
|
|
855 ComplexMatrix result (new_r, new_c); |
|
|
856 |
|
|
857 for (int j = 0; j < new_c; j++) |
|
|
858 for (int i = 0; i < new_r; i++) |
|
4316
|
859 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
860 |
|
|
861 return result; |
|
|
862 } |
|
|
863 |
|
|
864 ComplexMatrix |
|
|
865 ComplexMatrix::extract_n (int r1, int c1, int nr, int nc) const |
|
|
866 { |
|
|
867 ComplexMatrix result (nr, nc); |
|
|
868 |
|
|
869 for (int j = 0; j < nc; j++) |
|
|
870 for (int i = 0; i < nr; i++) |
|
|
871 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
872 |
|
|
873 return result; |
|
|
874 } |
|
|
875 |
|
|
876 // extract row or column i. |
|
|
877 |
|
|
878 ComplexRowVector |
|
|
879 ComplexMatrix::row (int i) const |
|
|
880 { |
|
|
881 int nc = cols (); |
|
|
882 if (i < 0 || i >= rows ()) |
|
|
883 { |
|
|
884 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
885 return ComplexRowVector (); |
|
|
886 } |
|
|
887 |
|
|
888 ComplexRowVector retval (nc); |
|
|
889 for (int j = 0; j < cols (); j++) |
|
4316
|
890 retval.xelem (j) = elem (i, j); |
|
458
|
891 |
|
|
892 return retval; |
|
|
893 } |
|
|
894 |
|
|
895 ComplexRowVector |
|
|
896 ComplexMatrix::row (char *s) const |
|
|
897 { |
|
533
|
898 if (! s) |
|
458
|
899 { |
|
|
900 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
901 return ComplexRowVector (); |
|
|
902 } |
|
|
903 |
|
|
904 char c = *s; |
|
|
905 if (c == 'f' || c == 'F') |
|
|
906 return row (0); |
|
|
907 else if (c == 'l' || c == 'L') |
|
|
908 return row (rows () - 1); |
|
|
909 else |
|
|
910 { |
|
|
911 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
912 return ComplexRowVector (); |
|
|
913 } |
|
|
914 } |
|
|
915 |
|
|
916 ComplexColumnVector |
|
|
917 ComplexMatrix::column (int i) const |
|
|
918 { |
|
|
919 int nr = rows (); |
|
|
920 if (i < 0 || i >= cols ()) |
|
|
921 { |
|
|
922 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
923 return ComplexColumnVector (); |
|
|
924 } |
|
|
925 |
|
|
926 ComplexColumnVector retval (nr); |
|
|
927 for (int j = 0; j < nr; j++) |
|
4316
|
928 retval.xelem (j) = elem (j, i); |
|
458
|
929 |
|
|
930 return retval; |
|
|
931 } |
|
|
932 |
|
|
933 ComplexColumnVector |
|
|
934 ComplexMatrix::column (char *s) const |
|
|
935 { |
|
533
|
936 if (! s) |
|
458
|
937 { |
|
|
938 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
939 return ComplexColumnVector (); |
|
|
940 } |
|
|
941 |
|
|
942 char c = *s; |
|
|
943 if (c == 'f' || c == 'F') |
|
|
944 return column (0); |
|
|
945 else if (c == 'l' || c == 'L') |
|
|
946 return column (cols () - 1); |
|
|
947 else |
|
|
948 { |
|
|
949 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
950 return ComplexColumnVector (); |
|
|
951 } |
|
|
952 } |
|
|
953 |
|
|
954 ComplexMatrix |
|
|
955 ComplexMatrix::inverse (void) const |
|
|
956 { |
|
|
957 int info; |
|
479
|
958 double rcond; |
|
4329
|
959 return inverse (info, rcond, 0, 0); |
|
458
|
960 } |
|
|
961 |
|
|
962 ComplexMatrix |
|
|
963 ComplexMatrix::inverse (int& info) const |
|
|
964 { |
|
|
965 double rcond; |
|
4329
|
966 return inverse (info, rcond, 0, 0); |
|
458
|
967 } |
|
|
968 |
|
|
969 ComplexMatrix |
|
4329
|
970 ComplexMatrix::inverse (int& info, double& rcond, int force, |
|
|
971 int calc_cond) const |
|
458
|
972 { |
|
1948
|
973 ComplexMatrix retval; |
|
|
974 |
|
458
|
975 int nr = rows (); |
|
|
976 int nc = cols (); |
|
1948
|
977 |
|
458
|
978 if (nr != nc) |
|
1948
|
979 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
980 else |
|
|
981 { |
|
1948
|
982 Array<int> ipvt (nr); |
|
|
983 int *pipvt = ipvt.fortran_vec (); |
|
|
984 |
|
|
985 retval = *this; |
|
|
986 Complex *tmp_data = retval.fortran_vec (); |
|
|
987 |
|
4329
|
988 Array<Complex> z(1); |
|
4330
|
989 int lwork = -1; |
|
|
990 |
|
|
991 // Query the optimum work array size. |
|
4329
|
992 |
|
|
993 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
|
994 z.fortran_vec (), lwork, info)); |
|
|
995 |
|
|
996 if (f77_exception_encountered) |
|
|
997 { |
|
|
998 (*current_liboctave_error_handler) |
|
|
999 ("unrecoverable error in zgetri"); |
|
|
1000 return retval; |
|
|
1001 } |
|
|
1002 |
|
|
1003 lwork = static_cast<int> (real(z(0))); |
|
|
1004 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
1005 z.resize (lwork); |
|
|
1006 Complex *pz = z.fortran_vec (); |
|
|
1007 |
|
|
1008 info = 0; |
|
|
1009 |
|
4330
|
1010 // Calculate the norm of the matrix, for later use. |
|
4329
|
1011 double anorm; |
|
|
1012 if (calc_cond) |
|
|
1013 anorm = retval.abs().sum().row(0).max(); |
|
|
1014 |
|
|
1015 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1016 |
|
|
1017 if (f77_exception_encountered) |
|
4329
|
1018 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1019 else |
|
|
1020 { |
|
4330
|
1021 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1022 rcond = 0.0; |
|
|
1023 if (info != 0) |
|
1948
|
1024 info = -1; |
|
4329
|
1025 else if (calc_cond) |
|
|
1026 { |
|
4330
|
1027 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1028 char job = '1'; |
|
|
1029 Array<double> rz (2 * nc); |
|
|
1030 double *prz = rz.fortran_vec (); |
|
4552
|
1031 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1032 nc, tmp_data, nr, anorm, |
|
|
1033 rcond, pz, prz, info |
|
|
1034 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1035 |
|
|
1036 if (f77_exception_encountered) |
|
|
1037 (*current_liboctave_error_handler) |
|
|
1038 ("unrecoverable error in zgecon"); |
|
|
1039 |
|
4509
|
1040 if (info != 0) |
|
4329
|
1041 info = -1; |
|
|
1042 } |
|
1948
|
1043 |
|
|
1044 if (info == -1 && ! force) |
|
|
1045 retval = *this; // Restore contents. |
|
|
1046 else |
|
|
1047 { |
|
4329
|
1048 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
4552
|
1049 pz, lwork, info)); |
|
1948
|
1050 |
|
|
1051 if (f77_exception_encountered) |
|
|
1052 (*current_liboctave_error_handler) |
|
4329
|
1053 ("unrecoverable error in zgetri"); |
|
|
1054 |
|
4509
|
1055 if (info != 0) |
|
4329
|
1056 info = -1; |
|
1948
|
1057 } |
|
|
1058 } |
|
458
|
1059 } |
|
4329
|
1060 |
|
1948
|
1061 return retval; |
|
458
|
1062 } |
|
|
1063 |
|
|
1064 ComplexMatrix |
|
4384
|
1065 ComplexMatrix::pseudo_inverse (double tol) const |
|
740
|
1066 { |
|
1549
|
1067 ComplexMatrix retval; |
|
|
1068 |
|
3480
|
1069 ComplexSVD result (*this, SVD::economy); |
|
740
|
1070 |
|
|
1071 DiagMatrix S = result.singular_values (); |
|
|
1072 ComplexMatrix U = result.left_singular_matrix (); |
|
|
1073 ComplexMatrix V = result.right_singular_matrix (); |
|
|
1074 |
|
|
1075 ColumnVector sigma = S.diag (); |
|
|
1076 |
|
|
1077 int r = sigma.length () - 1; |
|
|
1078 int nr = rows (); |
|
|
1079 int nc = cols (); |
|
|
1080 |
|
|
1081 if (tol <= 0.0) |
|
|
1082 { |
|
|
1083 if (nr > nc) |
|
|
1084 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
1085 else |
|
|
1086 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
1087 } |
|
|
1088 |
|
|
1089 while (r >= 0 && sigma.elem (r) < tol) |
|
|
1090 r--; |
|
|
1091 |
|
|
1092 if (r < 0) |
|
1549
|
1093 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
1094 else |
|
|
1095 { |
|
|
1096 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
1097 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
1098 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
1099 retval = Vr * D * Ur.hermitian (); |
|
740
|
1100 } |
|
1549
|
1101 |
|
|
1102 return retval; |
|
740
|
1103 } |
|
|
1104 |
|
4773
|
1105 #if defined (HAVE_FFTW3) |
|
3827
|
1106 |
|
|
1107 ComplexMatrix |
|
|
1108 ComplexMatrix::fourier (void) const |
|
|
1109 { |
|
|
1110 size_t nr = rows (); |
|
|
1111 size_t nc = cols (); |
|
|
1112 |
|
|
1113 ComplexMatrix retval (nr, nc); |
|
|
1114 |
|
|
1115 size_t npts, nsamples; |
|
|
1116 |
|
|
1117 if (nr == 1 || nc == 1) |
|
|
1118 { |
|
|
1119 npts = nr > nc ? nr : nc; |
|
|
1120 nsamples = 1; |
|
|
1121 } |
|
|
1122 else |
|
|
1123 { |
|
|
1124 npts = nr; |
|
|
1125 nsamples = nc; |
|
|
1126 } |
|
|
1127 |
|
|
1128 const Complex *in (data ()); |
|
|
1129 Complex *out (retval.fortran_vec ()); |
|
|
1130 |
|
4773
|
1131 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
1132 |
|
|
1133 return retval; |
|
|
1134 } |
|
|
1135 |
|
|
1136 ComplexMatrix |
|
|
1137 ComplexMatrix::ifourier (void) const |
|
|
1138 { |
|
|
1139 size_t nr = rows (); |
|
|
1140 size_t nc = cols (); |
|
|
1141 |
|
|
1142 ComplexMatrix retval (nr, nc); |
|
|
1143 |
|
|
1144 size_t npts, nsamples; |
|
|
1145 |
|
|
1146 if (nr == 1 || nc == 1) |
|
|
1147 { |
|
|
1148 npts = nr > nc ? nr : nc; |
|
|
1149 nsamples = 1; |
|
|
1150 } |
|
|
1151 else |
|
|
1152 { |
|
|
1153 npts = nr; |
|
|
1154 nsamples = nc; |
|
|
1155 } |
|
|
1156 |
|
|
1157 const Complex *in (data ()); |
|
|
1158 Complex *out (retval.fortran_vec ()); |
|
|
1159 |
|
4773
|
1160 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
1161 |
|
|
1162 return retval; |
|
|
1163 } |
|
|
1164 |
|
|
1165 ComplexMatrix |
|
|
1166 ComplexMatrix::fourier2d (void) const |
|
|
1167 { |
|
4773
|
1168 dim_vector dv(rows (), cols ()); |
|
|
1169 |
|
|
1170 ComplexMatrix retval (rows (), cols ()); |
|
|
1171 const Complex *in (data ()); |
|
|
1172 Complex *out (retval.fortran_vec ()); |
|
|
1173 |
|
|
1174 octave_fftw::fftNd (in, out, 2, dv); |
|
3827
|
1175 |
|
|
1176 return retval; |
|
|
1177 } |
|
|
1178 |
|
|
1179 ComplexMatrix |
|
|
1180 ComplexMatrix::ifourier2d (void) const |
|
|
1181 { |
|
4773
|
1182 dim_vector dv(rows (), cols ()); |
|
|
1183 |
|
|
1184 ComplexMatrix retval (rows (), cols ()); |
|
|
1185 const Complex *in (data ()); |
|
|
1186 Complex *out (retval.fortran_vec ()); |
|
|
1187 |
|
|
1188 octave_fftw::ifftNd (in, out, 2, dv); |
|
3827
|
1189 |
|
|
1190 return retval; |
|
|
1191 } |
|
|
1192 |
|
|
1193 #else |
|
|
1194 |
|
740
|
1195 ComplexMatrix |
|
458
|
1196 ComplexMatrix::fourier (void) const |
|
|
1197 { |
|
1948
|
1198 ComplexMatrix retval; |
|
|
1199 |
|
458
|
1200 int nr = rows (); |
|
|
1201 int nc = cols (); |
|
1948
|
1202 |
|
458
|
1203 int npts, nsamples; |
|
1948
|
1204 |
|
458
|
1205 if (nr == 1 || nc == 1) |
|
|
1206 { |
|
|
1207 npts = nr > nc ? nr : nc; |
|
|
1208 nsamples = 1; |
|
|
1209 } |
|
|
1210 else |
|
|
1211 { |
|
|
1212 npts = nr; |
|
|
1213 nsamples = nc; |
|
|
1214 } |
|
|
1215 |
|
|
1216 int nn = 4*npts+15; |
|
1948
|
1217 |
|
|
1218 Array<Complex> wsave (nn); |
|
|
1219 Complex *pwsave = wsave.fortran_vec (); |
|
|
1220 |
|
|
1221 retval = *this; |
|
|
1222 Complex *tmp_data = retval.fortran_vec (); |
|
|
1223 |
|
3887
|
1224 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1225 |
|
|
1226 for (int j = 0; j < nsamples; j++) |
|
4153
|
1227 { |
|
|
1228 OCTAVE_QUIT; |
|
|
1229 |
|
|
1230 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1231 } |
|
1948
|
1232 |
|
|
1233 return retval; |
|
458
|
1234 } |
|
|
1235 |
|
|
1236 ComplexMatrix |
|
|
1237 ComplexMatrix::ifourier (void) const |
|
|
1238 { |
|
1948
|
1239 ComplexMatrix retval; |
|
|
1240 |
|
458
|
1241 int nr = rows (); |
|
|
1242 int nc = cols (); |
|
1948
|
1243 |
|
458
|
1244 int npts, nsamples; |
|
1948
|
1245 |
|
458
|
1246 if (nr == 1 || nc == 1) |
|
|
1247 { |
|
|
1248 npts = nr > nc ? nr : nc; |
|
|
1249 nsamples = 1; |
|
|
1250 } |
|
|
1251 else |
|
|
1252 { |
|
|
1253 npts = nr; |
|
|
1254 nsamples = nc; |
|
|
1255 } |
|
|
1256 |
|
|
1257 int nn = 4*npts+15; |
|
1948
|
1258 |
|
|
1259 Array<Complex> wsave (nn); |
|
|
1260 Complex *pwsave = wsave.fortran_vec (); |
|
|
1261 |
|
|
1262 retval = *this; |
|
|
1263 Complex *tmp_data = retval.fortran_vec (); |
|
|
1264 |
|
3887
|
1265 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1266 |
|
|
1267 for (int j = 0; j < nsamples; j++) |
|
4153
|
1268 { |
|
|
1269 OCTAVE_QUIT; |
|
|
1270 |
|
|
1271 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1272 } |
|
458
|
1273 |
|
1321
|
1274 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1275 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1276 |
|
1948
|
1277 return retval; |
|
458
|
1278 } |
|
|
1279 |
|
677
|
1280 ComplexMatrix |
|
|
1281 ComplexMatrix::fourier2d (void) const |
|
|
1282 { |
|
1948
|
1283 ComplexMatrix retval; |
|
|
1284 |
|
677
|
1285 int nr = rows (); |
|
|
1286 int nc = cols (); |
|
1948
|
1287 |
|
677
|
1288 int npts, nsamples; |
|
1948
|
1289 |
|
677
|
1290 if (nr == 1 || nc == 1) |
|
|
1291 { |
|
|
1292 npts = nr > nc ? nr : nc; |
|
|
1293 nsamples = 1; |
|
|
1294 } |
|
|
1295 else |
|
|
1296 { |
|
|
1297 npts = nr; |
|
|
1298 nsamples = nc; |
|
|
1299 } |
|
|
1300 |
|
|
1301 int nn = 4*npts+15; |
|
1948
|
1302 |
|
|
1303 Array<Complex> wsave (nn); |
|
|
1304 Complex *pwsave = wsave.fortran_vec (); |
|
|
1305 |
|
|
1306 retval = *this; |
|
|
1307 Complex *tmp_data = retval.fortran_vec (); |
|
|
1308 |
|
3887
|
1309 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1310 |
|
|
1311 for (int j = 0; j < nsamples; j++) |
|
4153
|
1312 { |
|
|
1313 OCTAVE_QUIT; |
|
|
1314 |
|
|
1315 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1316 } |
|
677
|
1317 |
|
|
1318 npts = nc; |
|
|
1319 nsamples = nr; |
|
|
1320 nn = 4*npts+15; |
|
1948
|
1321 |
|
|
1322 wsave.resize (nn); |
|
|
1323 pwsave = wsave.fortran_vec (); |
|
|
1324 |
|
4773
|
1325 Array<Complex> tmp (npts); |
|
|
1326 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1327 |
|
3887
|
1328 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1329 |
|
1321
|
1330 for (int j = 0; j < nsamples; j++) |
|
677
|
1331 { |
|
4153
|
1332 OCTAVE_QUIT; |
|
|
1333 |
|
677
|
1334 for (int i = 0; i < npts; i++) |
|
1948
|
1335 prow[i] = tmp_data[i*nr + j]; |
|
|
1336 |
|
3887
|
1337 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1338 |
|
1321
|
1339 for (int i = 0; i < npts; i++) |
|
1948
|
1340 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1341 } |
|
|
1342 |
|
1948
|
1343 return retval; |
|
677
|
1344 } |
|
|
1345 |
|
|
1346 ComplexMatrix |
|
|
1347 ComplexMatrix::ifourier2d (void) const |
|
|
1348 { |
|
1948
|
1349 ComplexMatrix retval; |
|
|
1350 |
|
677
|
1351 int nr = rows (); |
|
|
1352 int nc = cols (); |
|
1948
|
1353 |
|
677
|
1354 int npts, nsamples; |
|
1948
|
1355 |
|
677
|
1356 if (nr == 1 || nc == 1) |
|
|
1357 { |
|
|
1358 npts = nr > nc ? nr : nc; |
|
|
1359 nsamples = 1; |
|
|
1360 } |
|
|
1361 else |
|
|
1362 { |
|
|
1363 npts = nr; |
|
|
1364 nsamples = nc; |
|
|
1365 } |
|
|
1366 |
|
|
1367 int nn = 4*npts+15; |
|
1948
|
1368 |
|
|
1369 Array<Complex> wsave (nn); |
|
|
1370 Complex *pwsave = wsave.fortran_vec (); |
|
|
1371 |
|
|
1372 retval = *this; |
|
|
1373 Complex *tmp_data = retval.fortran_vec (); |
|
|
1374 |
|
3887
|
1375 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1376 |
|
|
1377 for (int j = 0; j < nsamples; j++) |
|
4153
|
1378 { |
|
|
1379 OCTAVE_QUIT; |
|
|
1380 |
|
|
1381 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1382 } |
|
677
|
1383 |
|
1321
|
1384 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1385 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1386 |
|
|
1387 npts = nc; |
|
|
1388 nsamples = nr; |
|
|
1389 nn = 4*npts+15; |
|
1948
|
1390 |
|
|
1391 wsave.resize (nn); |
|
|
1392 pwsave = wsave.fortran_vec (); |
|
|
1393 |
|
4773
|
1394 Array<Complex> tmp (npts); |
|
|
1395 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1396 |
|
3887
|
1397 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1398 |
|
1321
|
1399 for (int j = 0; j < nsamples; j++) |
|
677
|
1400 { |
|
4153
|
1401 OCTAVE_QUIT; |
|
|
1402 |
|
677
|
1403 for (int i = 0; i < npts; i++) |
|
1948
|
1404 prow[i] = tmp_data[i*nr + j]; |
|
|
1405 |
|
3887
|
1406 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1407 |
|
1321
|
1408 for (int i = 0; i < npts; i++) |
|
3572
|
1409 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1410 } |
|
|
1411 |
|
1948
|
1412 return retval; |
|
677
|
1413 } |
|
|
1414 |
|
3827
|
1415 #endif |
|
|
1416 |
|
458
|
1417 ComplexDET |
|
|
1418 ComplexMatrix::determinant (void) const |
|
|
1419 { |
|
|
1420 int info; |
|
|
1421 double rcond; |
|
4329
|
1422 return determinant (info, rcond, 0); |
|
458
|
1423 } |
|
|
1424 |
|
|
1425 ComplexDET |
|
|
1426 ComplexMatrix::determinant (int& info) const |
|
|
1427 { |
|
|
1428 double rcond; |
|
4329
|
1429 return determinant (info, rcond, 0); |
|
458
|
1430 } |
|
|
1431 |
|
|
1432 ComplexDET |
|
4329
|
1433 ComplexMatrix::determinant (int& info, double& rcond, int calc_cond) const |
|
458
|
1434 { |
|
|
1435 ComplexDET retval; |
|
|
1436 |
|
|
1437 int nr = rows (); |
|
|
1438 int nc = cols (); |
|
|
1439 |
|
|
1440 if (nr == 0 || nc == 0) |
|
|
1441 { |
|
|
1442 Complex d[2]; |
|
|
1443 d[0] = 1.0; |
|
|
1444 d[1] = 0.0; |
|
|
1445 retval = ComplexDET (d); |
|
|
1446 } |
|
|
1447 else |
|
|
1448 { |
|
1948
|
1449 Array<int> ipvt (nr); |
|
|
1450 int *pipvt = ipvt.fortran_vec (); |
|
|
1451 |
|
|
1452 ComplexMatrix atmp = *this; |
|
|
1453 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1454 |
|
4329
|
1455 info = 0; |
|
|
1456 |
|
4330
|
1457 // Calculate the norm of the matrix, for later use. |
|
4329
|
1458 double anorm = 0; |
|
|
1459 if (calc_cond) |
|
|
1460 anorm = atmp.abs().sum().row(0).max(); |
|
|
1461 |
|
|
1462 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1463 |
|
|
1464 if (f77_exception_encountered) |
|
4329
|
1465 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
458
|
1466 else |
|
|
1467 { |
|
4330
|
1468 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1469 rcond = 0.0; |
|
|
1470 if (info != 0) |
|
1948
|
1471 { |
|
|
1472 info = -1; |
|
|
1473 retval = ComplexDET (); |
|
4329
|
1474 } |
|
|
1475 else |
|
1948
|
1476 { |
|
4329
|
1477 if (calc_cond) |
|
|
1478 { |
|
4330
|
1479 // Now calc the condition number for non-singular matrix. |
|
4329
|
1480 char job = '1'; |
|
|
1481 Array<Complex> z (2*nr); |
|
|
1482 Complex *pz = z.fortran_vec (); |
|
|
1483 Array<double> rz (2*nr); |
|
|
1484 double *prz = rz.fortran_vec (); |
|
|
1485 |
|
4552
|
1486 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1487 nc, tmp_data, nr, anorm, |
|
|
1488 rcond, pz, prz, info |
|
|
1489 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1490 |
|
|
1491 if (f77_exception_encountered) |
|
|
1492 (*current_liboctave_error_handler) |
|
|
1493 ("unrecoverable error in zgecon"); |
|
|
1494 } |
|
|
1495 |
|
4509
|
1496 if (info != 0) |
|
4329
|
1497 { |
|
|
1498 info = -1; |
|
|
1499 retval = ComplexDET (); |
|
|
1500 } |
|
|
1501 else |
|
|
1502 { |
|
|
1503 Complex d[2] = { 1., 0.}; |
|
|
1504 for (int i=0; i<nc; i++) |
|
|
1505 { |
|
|
1506 if (ipvt(i) != (i+1)) d[0] = -d[0]; |
|
|
1507 d[0] = d[0] * atmp(i,i); |
|
|
1508 if (d[0] == 0.) break; |
|
|
1509 while (::abs(d[0]) < 1.) |
|
|
1510 { |
|
|
1511 d[0] = 10. * d[0]; |
|
4509
|
1512 d[1] = d[1] - 1.0; |
|
4329
|
1513 } |
|
|
1514 while (::abs(d[0]) >= 10.) |
|
|
1515 { |
|
|
1516 d[0] = 0.1 * d[0]; |
|
4509
|
1517 d[1] = d[1] + 1.0; |
|
4329
|
1518 } |
|
|
1519 } |
|
|
1520 retval = ComplexDET (d); |
|
|
1521 } |
|
1948
|
1522 } |
|
458
|
1523 } |
|
|
1524 } |
|
4329
|
1525 |
|
458
|
1526 return retval; |
|
|
1527 } |
|
|
1528 |
|
|
1529 ComplexMatrix |
|
|
1530 ComplexMatrix::solve (const Matrix& b) const |
|
|
1531 { |
|
|
1532 int info; |
|
|
1533 double rcond; |
|
3480
|
1534 return solve (b, info, rcond, 0); |
|
458
|
1535 } |
|
|
1536 |
|
|
1537 ComplexMatrix |
|
|
1538 ComplexMatrix::solve (const Matrix& b, int& info) const |
|
|
1539 { |
|
|
1540 double rcond; |
|
3480
|
1541 return solve (b, info, rcond, 0); |
|
458
|
1542 } |
|
|
1543 |
|
|
1544 ComplexMatrix |
|
|
1545 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond) const |
|
|
1546 { |
|
3480
|
1547 return solve (b, info, rcond, 0); |
|
|
1548 } |
|
|
1549 |
|
|
1550 ComplexMatrix |
|
|
1551 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond, |
|
|
1552 solve_singularity_handler sing_handler) const |
|
|
1553 { |
|
458
|
1554 ComplexMatrix tmp (b); |
|
3480
|
1555 return solve (tmp, info, rcond, sing_handler); |
|
458
|
1556 } |
|
|
1557 |
|
|
1558 ComplexMatrix |
|
|
1559 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1560 { |
|
|
1561 int info; |
|
|
1562 double rcond; |
|
3480
|
1563 return solve (b, info, rcond, 0); |
|
458
|
1564 } |
|
|
1565 |
|
|
1566 ComplexMatrix |
|
|
1567 ComplexMatrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1568 { |
|
|
1569 double rcond; |
|
3480
|
1570 return solve (b, info, rcond, 0); |
|
458
|
1571 } |
|
3480
|
1572 |
|
458
|
1573 ComplexMatrix |
|
532
|
1574 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
458
|
1575 { |
|
3480
|
1576 return solve (b, info, rcond, 0); |
|
|
1577 } |
|
|
1578 |
|
|
1579 ComplexMatrix |
|
|
1580 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond, |
|
|
1581 solve_singularity_handler sing_handler) const |
|
|
1582 { |
|
458
|
1583 ComplexMatrix retval; |
|
|
1584 |
|
|
1585 int nr = rows (); |
|
|
1586 int nc = cols (); |
|
1948
|
1587 |
|
|
1588 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1589 (*current_liboctave_error_handler) |
|
|
1590 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1591 else |
|
|
1592 { |
|
1948
|
1593 info = 0; |
|
|
1594 |
|
|
1595 Array<int> ipvt (nr); |
|
|
1596 int *pipvt = ipvt.fortran_vec (); |
|
|
1597 |
|
|
1598 ComplexMatrix atmp = *this; |
|
|
1599 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1600 |
|
4329
|
1601 Array<Complex> z (2 * nc); |
|
|
1602 Complex *pz = z.fortran_vec (); |
|
|
1603 Array<double> rz (2 * nc); |
|
|
1604 double *prz = rz.fortran_vec (); |
|
|
1605 |
|
4330
|
1606 // Calculate the norm of the matrix, for later use. |
|
4329
|
1607 double anorm = atmp.abs().sum().row(0).max(); |
|
|
1608 |
|
|
1609 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1610 |
|
|
1611 if (f77_exception_encountered) |
|
4329
|
1612 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1613 else |
|
|
1614 { |
|
4330
|
1615 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1616 rcond = 0.0; |
|
|
1617 if (info != 0) |
|
4329
|
1618 { |
|
1948
|
1619 info = -2; |
|
3480
|
1620 |
|
|
1621 if (sing_handler) |
|
|
1622 sing_handler (rcond); |
|
|
1623 else |
|
|
1624 (*current_liboctave_error_handler) |
|
4329
|
1625 ("matrix singular to machine precision"); |
|
|
1626 |
|
|
1627 } |
|
|
1628 else |
|
1948
|
1629 { |
|
4330
|
1630 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1631 char job = '1'; |
|
4552
|
1632 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1633 nc, tmp_data, nr, anorm, |
|
|
1634 rcond, pz, prz, info |
|
|
1635 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1636 |
|
|
1637 if (f77_exception_encountered) |
|
|
1638 (*current_liboctave_error_handler) |
|
|
1639 ("unrecoverable error in zgecon"); |
|
|
1640 |
|
4509
|
1641 if (info != 0) |
|
4329
|
1642 info = -2; |
|
|
1643 |
|
|
1644 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1645 |
|
|
1646 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1647 { |
|
4329
|
1648 info = -2; |
|
|
1649 |
|
|
1650 if (sing_handler) |
|
|
1651 sing_handler (rcond); |
|
|
1652 else |
|
|
1653 (*current_liboctave_error_handler) |
|
|
1654 ("matrix singular to machine precision, rcond = %g", |
|
|
1655 rcond); |
|
|
1656 } |
|
|
1657 else |
|
|
1658 { |
|
|
1659 retval = b; |
|
|
1660 Complex *result = retval.fortran_vec (); |
|
|
1661 |
|
|
1662 int b_nc = b.cols (); |
|
|
1663 |
|
4587
|
1664 job = 'N'; |
|
4552
|
1665 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1666 nr, b_nc, tmp_data, nr, |
|
|
1667 pipvt, result, b.rows(), info |
|
|
1668 F77_CHAR_ARG_LEN (1))); |
|
1948
|
1669 |
|
|
1670 if (f77_exception_encountered) |
|
4329
|
1671 (*current_liboctave_error_handler) |
|
|
1672 ("unrecoverable error in zgetrs"); |
|
1948
|
1673 } |
|
|
1674 } |
|
|
1675 } |
|
458
|
1676 } |
|
4329
|
1677 |
|
458
|
1678 return retval; |
|
|
1679 } |
|
|
1680 |
|
|
1681 ComplexColumnVector |
|
3585
|
1682 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
1683 { |
|
|
1684 int info; |
|
|
1685 double rcond; |
|
|
1686 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1687 } |
|
|
1688 |
|
|
1689 ComplexColumnVector |
|
|
1690 ComplexMatrix::solve (const ColumnVector& b, int& info) const |
|
|
1691 { |
|
|
1692 double rcond; |
|
|
1693 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1694 } |
|
|
1695 |
|
|
1696 ComplexColumnVector |
|
|
1697 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
|
1698 { |
|
|
1699 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1700 } |
|
|
1701 |
|
|
1702 ComplexColumnVector |
|
|
1703 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond, |
|
|
1704 solve_singularity_handler sing_handler) const |
|
|
1705 { |
|
|
1706 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
1707 } |
|
|
1708 |
|
|
1709 ComplexColumnVector |
|
458
|
1710 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1711 { |
|
|
1712 int info; |
|
|
1713 double rcond; |
|
3480
|
1714 return solve (b, info, rcond, 0); |
|
458
|
1715 } |
|
|
1716 |
|
|
1717 ComplexColumnVector |
|
|
1718 ComplexMatrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1719 { |
|
|
1720 double rcond; |
|
3480
|
1721 return solve (b, info, rcond, 0); |
|
458
|
1722 } |
|
|
1723 |
|
|
1724 ComplexColumnVector |
|
|
1725 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
532
|
1726 double& rcond) const |
|
458
|
1727 { |
|
3480
|
1728 return solve (b, info, rcond, 0); |
|
|
1729 } |
|
|
1730 |
|
|
1731 ComplexColumnVector |
|
|
1732 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
|
1733 double& rcond, |
|
|
1734 solve_singularity_handler sing_handler) const |
|
|
1735 { |
|
458
|
1736 ComplexColumnVector retval; |
|
|
1737 |
|
|
1738 int nr = rows (); |
|
|
1739 int nc = cols (); |
|
1948
|
1740 |
|
|
1741 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
1742 (*current_liboctave_error_handler) |
|
|
1743 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1744 else |
|
|
1745 { |
|
1948
|
1746 info = 0; |
|
|
1747 |
|
|
1748 Array<int> ipvt (nr); |
|
|
1749 int *pipvt = ipvt.fortran_vec (); |
|
|
1750 |
|
|
1751 ComplexMatrix atmp = *this; |
|
|
1752 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1753 |
|
4329
|
1754 Array<Complex> z (2 * nc); |
|
|
1755 Complex *pz = z.fortran_vec (); |
|
|
1756 Array<double> rz (2 * nc); |
|
|
1757 double *prz = rz.fortran_vec (); |
|
|
1758 |
|
4330
|
1759 // Calculate the norm of the matrix, for later use. |
|
4329
|
1760 double anorm = atmp.abs().sum().row(0).max(); |
|
|
1761 |
|
|
1762 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1763 |
|
|
1764 if (f77_exception_encountered) |
|
4329
|
1765 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1766 else |
|
|
1767 { |
|
4330
|
1768 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1769 rcond = 0.0; |
|
|
1770 if (info != 0) |
|
4329
|
1771 { |
|
1948
|
1772 info = -2; |
|
3480
|
1773 |
|
|
1774 if (sing_handler) |
|
|
1775 sing_handler (rcond); |
|
|
1776 else |
|
|
1777 (*current_liboctave_error_handler) |
|
|
1778 ("matrix singular to machine precision, rcond = %g", |
|
|
1779 rcond); |
|
4329
|
1780 } |
|
|
1781 else |
|
1948
|
1782 { |
|
4330
|
1783 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1784 char job = '1'; |
|
4552
|
1785 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1786 nc, tmp_data, nr, anorm, |
|
|
1787 rcond, pz, prz, info |
|
|
1788 F77_CHAR_ARG_LEN (1))); |
|
1948
|
1789 |
|
|
1790 if (f77_exception_encountered) |
|
4329
|
1791 (*current_liboctave_error_handler) |
|
|
1792 ("unrecoverable error in zgecon"); |
|
|
1793 |
|
4509
|
1794 if (info != 0) |
|
4329
|
1795 info = -2; |
|
|
1796 |
|
|
1797 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1798 |
|
|
1799 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1800 { |
|
|
1801 info = -2; |
|
|
1802 |
|
|
1803 if (sing_handler) |
|
|
1804 sing_handler (rcond); |
|
|
1805 else |
|
|
1806 (*current_liboctave_error_handler) |
|
|
1807 ("matrix singular to machine precision, rcond = %g", |
|
|
1808 rcond); |
|
|
1809 } |
|
|
1810 else |
|
|
1811 { |
|
|
1812 retval = b; |
|
|
1813 Complex *result = retval.fortran_vec (); |
|
|
1814 |
|
4587
|
1815 job = 'N'; |
|
4552
|
1816 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1817 nr, 1, tmp_data, nr, pipvt, |
|
|
1818 result, b.length(), info |
|
|
1819 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1820 |
|
|
1821 if (f77_exception_encountered) |
|
|
1822 (*current_liboctave_error_handler) |
|
|
1823 ("unrecoverable error in zgetrs"); |
|
|
1824 |
|
|
1825 } |
|
1948
|
1826 } |
|
|
1827 } |
|
458
|
1828 } |
|
|
1829 return retval; |
|
|
1830 } |
|
|
1831 |
|
|
1832 ComplexMatrix |
|
3585
|
1833 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
1834 { |
|
|
1835 int info; |
|
|
1836 int rank; |
|
|
1837 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1838 } |
|
|
1839 |
|
|
1840 ComplexMatrix |
|
|
1841 ComplexMatrix::lssolve (const Matrix& b, int& info) const |
|
|
1842 { |
|
|
1843 int rank; |
|
|
1844 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1845 } |
|
|
1846 |
|
|
1847 ComplexMatrix |
|
|
1848 ComplexMatrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1849 { |
|
|
1850 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1851 } |
|
|
1852 |
|
|
1853 ComplexMatrix |
|
458
|
1854 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1855 { |
|
|
1856 int info; |
|
|
1857 int rank; |
|
|
1858 return lssolve (b, info, rank); |
|
|
1859 } |
|
|
1860 |
|
|
1861 ComplexMatrix |
|
|
1862 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1863 { |
|
|
1864 int rank; |
|
|
1865 return lssolve (b, info, rank); |
|
|
1866 } |
|
|
1867 |
|
|
1868 ComplexMatrix |
|
|
1869 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1870 { |
|
1948
|
1871 ComplexMatrix retval; |
|
|
1872 |
|
458
|
1873 int nrhs = b.cols (); |
|
|
1874 |
|
|
1875 int m = rows (); |
|
|
1876 int n = cols (); |
|
|
1877 |
|
|
1878 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1879 (*current_liboctave_error_handler) |
|
|
1880 ("matrix dimension mismatch solution of linear equations"); |
|
|
1881 else |
|
458
|
1882 { |
|
1948
|
1883 ComplexMatrix atmp = *this; |
|
|
1884 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1885 |
|
|
1886 int nrr = m > n ? m : n; |
|
|
1887 ComplexMatrix result (nrr, nrhs); |
|
|
1888 |
|
|
1889 for (int j = 0; j < nrhs; j++) |
|
|
1890 for (int i = 0; i < m; i++) |
|
|
1891 result.elem (i, j) = b.elem (i, j); |
|
|
1892 |
|
|
1893 Complex *presult = result.fortran_vec (); |
|
|
1894 |
|
|
1895 int len_s = m < n ? m : n; |
|
|
1896 Array<double> s (len_s); |
|
|
1897 double *ps = s.fortran_vec (); |
|
2563
|
1898 |
|
1948
|
1899 double rcond = -1.0; |
|
2563
|
1900 |
|
1948
|
1901 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1902 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1903 Array<double> rwork (lrwork); |
|
|
1904 double *prwork = rwork.fortran_vec (); |
|
|
1905 |
|
3752
|
1906 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1907 |
|
|
1908 int lwork = -1; |
|
|
1909 |
|
|
1910 Array<Complex> work (1); |
|
|
1911 |
|
1948
|
1912 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1913 nrr, ps, rcond, rank, |
|
|
1914 work.fortran_vec (), lwork, prwork, |
|
|
1915 info)); |
|
1948
|
1916 |
|
|
1917 if (f77_exception_encountered) |
|
|
1918 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1919 else |
|
|
1920 { |
|
3752
|
1921 lwork = static_cast<int> (real (work(0))); |
|
|
1922 work.resize (lwork); |
|
|
1923 |
|
|
1924 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1925 nrr, ps, rcond, rank, |
|
|
1926 work.fortran_vec (), lwork, |
|
|
1927 prwork, info)); |
|
|
1928 |
|
|
1929 if (f77_exception_encountered) |
|
|
1930 (*current_liboctave_error_handler) |
|
|
1931 ("unrecoverable error in zgelss"); |
|
|
1932 else |
|
|
1933 { |
|
|
1934 retval.resize (n, nrhs); |
|
|
1935 for (int j = 0; j < nrhs; j++) |
|
|
1936 for (int i = 0; i < n; i++) |
|
|
1937 retval.elem (i, j) = result.elem (i, j); |
|
|
1938 } |
|
1948
|
1939 } |
|
458
|
1940 } |
|
|
1941 |
|
|
1942 return retval; |
|
|
1943 } |
|
|
1944 |
|
|
1945 ComplexColumnVector |
|
3585
|
1946 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
1947 { |
|
|
1948 int info; |
|
|
1949 int rank; |
|
|
1950 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1951 } |
|
|
1952 |
|
|
1953 ComplexColumnVector |
|
|
1954 ComplexMatrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1955 { |
|
|
1956 int rank; |
|
|
1957 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1958 } |
|
|
1959 |
|
|
1960 ComplexColumnVector |
|
|
1961 ComplexMatrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1962 { |
|
|
1963 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1964 } |
|
|
1965 |
|
|
1966 ComplexColumnVector |
|
458
|
1967 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1968 { |
|
|
1969 int info; |
|
|
1970 int rank; |
|
|
1971 return lssolve (b, info, rank); |
|
|
1972 } |
|
|
1973 |
|
|
1974 ComplexColumnVector |
|
|
1975 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1976 { |
|
|
1977 int rank; |
|
|
1978 return lssolve (b, info, rank); |
|
|
1979 } |
|
|
1980 |
|
|
1981 ComplexColumnVector |
|
|
1982 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info, |
|
|
1983 int& rank) const |
|
|
1984 { |
|
1948
|
1985 ComplexColumnVector retval; |
|
|
1986 |
|
458
|
1987 int nrhs = 1; |
|
|
1988 |
|
|
1989 int m = rows (); |
|
|
1990 int n = cols (); |
|
|
1991 |
|
|
1992 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1993 (*current_liboctave_error_handler) |
|
|
1994 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1995 else |
|
458
|
1996 { |
|
1948
|
1997 ComplexMatrix atmp = *this; |
|
|
1998 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1999 |
|
|
2000 int nrr = m > n ? m : n; |
|
|
2001 ComplexColumnVector result (nrr); |
|
|
2002 |
|
|
2003 for (int i = 0; i < m; i++) |
|
|
2004 result.elem (i) = b.elem (i); |
|
|
2005 |
|
|
2006 Complex *presult = result.fortran_vec (); |
|
|
2007 |
|
|
2008 int len_s = m < n ? m : n; |
|
|
2009 Array<double> s (len_s); |
|
|
2010 double *ps = s.fortran_vec (); |
|
|
2011 |
|
|
2012 double rcond = -1.0; |
|
|
2013 |
|
|
2014 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
2015 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
2016 Array<double> rwork (lrwork); |
|
|
2017 double *prwork = rwork.fortran_vec (); |
|
|
2018 |
|
3752
|
2019 // Ask ZGELSS what the dimension of WORK should be. |
|
|
2020 |
|
|
2021 int lwork = -1; |
|
|
2022 |
|
|
2023 Array<Complex> work (1); |
|
|
2024 |
|
1948
|
2025 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
2026 nrr, ps, rcond, rank, |
|
|
2027 work.fortran_vec (), lwork, prwork, |
|
|
2028 info)); |
|
1948
|
2029 |
|
|
2030 if (f77_exception_encountered) |
|
|
2031 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
2032 else |
|
|
2033 { |
|
3752
|
2034 lwork = static_cast<int> (real (work(0))); |
|
|
2035 work.resize (lwork); |
|
|
2036 |
|
|
2037 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2038 nrr, ps, rcond, rank, |
|
|
2039 work.fortran_vec (), lwork, |
|
|
2040 prwork, info)); |
|
|
2041 |
|
|
2042 if (f77_exception_encountered) |
|
|
2043 (*current_liboctave_error_handler) |
|
|
2044 ("unrecoverable error in zgelss"); |
|
|
2045 else |
|
|
2046 { |
|
|
2047 retval.resize (n); |
|
|
2048 for (int i = 0; i < n; i++) |
|
|
2049 retval.elem (i) = result.elem (i); |
|
|
2050 } |
|
1948
|
2051 } |
|
458
|
2052 } |
|
|
2053 |
|
|
2054 return retval; |
|
|
2055 } |
|
|
2056 |
|
1819
|
2057 // Constants for matrix exponential calculation. |
|
|
2058 |
|
|
2059 static double padec [] = |
|
|
2060 { |
|
|
2061 5.0000000000000000e-1, |
|
|
2062 1.1666666666666667e-1, |
|
|
2063 1.6666666666666667e-2, |
|
|
2064 1.6025641025641026e-3, |
|
|
2065 1.0683760683760684e-4, |
|
|
2066 4.8562548562548563e-6, |
|
|
2067 1.3875013875013875e-7, |
|
|
2068 1.9270852604185938e-9, |
|
|
2069 }; |
|
|
2070 |
|
|
2071 ComplexMatrix |
|
|
2072 ComplexMatrix::expm (void) const |
|
|
2073 { |
|
|
2074 ComplexMatrix retval; |
|
|
2075 |
|
|
2076 ComplexMatrix m = *this; |
|
|
2077 |
|
|
2078 int nc = columns (); |
|
|
2079 |
|
3130
|
2080 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2081 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2082 |
|
1819
|
2083 // trace shift value |
|
|
2084 Complex trshift = 0.0; |
|
|
2085 |
|
|
2086 for (int i = 0; i < nc; i++) |
|
|
2087 trshift += m.elem (i, i); |
|
|
2088 |
|
|
2089 trshift /= nc; |
|
|
2090 |
|
3130
|
2091 if (trshift.real () < 0.0) |
|
|
2092 trshift = trshift.imag (); |
|
|
2093 |
|
1819
|
2094 for (int i = 0; i < nc; i++) |
|
|
2095 m.elem (i, i) -= trshift; |
|
|
2096 |
|
|
2097 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
2098 // code follows development in AEPBAL |
|
|
2099 |
|
|
2100 Complex *mp = m.fortran_vec (); |
|
3467
|
2101 |
|
|
2102 int info, ilo, ihi,ilos,ihis; |
|
3468
|
2103 Array<double> dpermute (nc); |
|
|
2104 Array<double> dscale (nc); |
|
|
2105 |
|
|
2106 // XXX FIXME XXX -- should pass job as a parameter in expm |
|
|
2107 |
|
|
2108 // Permute first |
|
|
2109 char job = 'P'; |
|
4552
|
2110 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2111 nc, mp, nc, ilo, ihi, |
|
|
2112 dpermute.fortran_vec (), info |
|
|
2113 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2114 |
|
|
2115 if (f77_exception_encountered) |
|
|
2116 { |
|
|
2117 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
2118 return retval; |
|
|
2119 } |
|
|
2120 |
|
3468
|
2121 // then scale |
|
|
2122 job = 'S'; |
|
4552
|
2123 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2124 nc, mp, nc, ilos, ihis, |
|
|
2125 dscale.fortran_vec (), info |
|
|
2126 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2127 |
|
|
2128 if (f77_exception_encountered) |
|
|
2129 { |
|
3467
|
2130 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
2131 return retval; |
|
|
2132 } |
|
1819
|
2133 |
|
|
2134 // Preconditioning step 3: scaling. |
|
|
2135 |
|
|
2136 ColumnVector work (nc); |
|
3130
|
2137 double inf_norm; |
|
|
2138 |
|
4552
|
2139 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2140 nc, nc, m.fortran_vec (), nc, |
|
|
2141 work.fortran_vec (), inf_norm |
|
|
2142 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2143 |
|
|
2144 if (f77_exception_encountered) |
|
|
2145 { |
|
|
2146 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
2147 return retval; |
|
|
2148 } |
|
1819
|
2149 |
|
2800
|
2150 int sqpow = (inf_norm > 0.0 |
|
|
2151 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
2152 |
|
|
2153 // Check whether we need to square at all. |
|
|
2154 |
|
|
2155 if (sqpow < 0) |
|
|
2156 sqpow = 0; |
|
|
2157 |
|
|
2158 if (sqpow > 0) |
|
|
2159 { |
|
|
2160 double scale_factor = 1.0; |
|
|
2161 for (int i = 0; i < sqpow; i++) |
|
|
2162 scale_factor *= 2.0; |
|
|
2163 |
|
|
2164 m = m / scale_factor; |
|
|
2165 } |
|
|
2166 |
|
|
2167 // npp, dpp: pade' approx polynomial matrices. |
|
|
2168 |
|
|
2169 ComplexMatrix npp (nc, nc, 0.0); |
|
|
2170 ComplexMatrix dpp = npp; |
|
|
2171 |
|
|
2172 // Now powers a^8 ... a^1. |
|
|
2173 |
|
|
2174 int minus_one_j = -1; |
|
|
2175 for (int j = 7; j >= 0; j--) |
|
|
2176 { |
|
|
2177 npp = m * npp + m * padec[j]; |
|
|
2178 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
2179 minus_one_j *= -1; |
|
|
2180 } |
|
|
2181 |
|
|
2182 // Zero power. |
|
|
2183 |
|
|
2184 dpp = -dpp; |
|
|
2185 for (int j = 0; j < nc; j++) |
|
|
2186 { |
|
|
2187 npp.elem (j, j) += 1.0; |
|
|
2188 dpp.elem (j, j) += 1.0; |
|
|
2189 } |
|
|
2190 |
|
|
2191 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2192 |
|
|
2193 retval = dpp.solve (npp); |
|
|
2194 |
|
|
2195 // Reverse preconditioning step 3: repeated squaring. |
|
|
2196 |
|
|
2197 while (sqpow) |
|
|
2198 { |
|
|
2199 retval = retval * retval; |
|
|
2200 sqpow--; |
|
|
2201 } |
|
|
2202 |
|
|
2203 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
2204 // Done in two steps: inverse scaling, then inverse permutation |
|
|
2205 |
|
|
2206 // inverse scaling (diagonal transformation) |
|
3468
|
2207 for (int i = 0; i < nc; i++) |
|
|
2208 for (int j = 0; j < nc; j++) |
|
|
2209 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
2210 |
|
4153
|
2211 OCTAVE_QUIT; |
|
|
2212 |
|
3467
|
2213 // construct balancing permutation vector |
|
4593
|
2214 Array<int> iperm (nc); |
|
3468
|
2215 for (int i = 0; i < nc; i++) |
|
4593
|
2216 iperm(i) = i; // initialize to identity permutation |
|
3467
|
2217 |
|
|
2218 // leading permutations in forward order |
|
3468
|
2219 for (int i = 0; i < (ilo-1); i++) |
|
|
2220 { |
|
|
2221 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
4593
|
2222 int tmp = iperm(i); |
|
|
2223 iperm(i) = iperm(swapidx); |
|
|
2224 iperm(swapidx) = tmp; |
|
3468
|
2225 } |
|
3467
|
2226 |
|
|
2227 // trailing permutations must be done in reverse order |
|
3468
|
2228 for (int i = nc - 1; i >= ihi; i--) |
|
|
2229 { |
|
|
2230 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
4593
|
2231 int tmp = iperm(i); |
|
|
2232 iperm(i) = iperm(swapidx); |
|
|
2233 iperm(swapidx) = tmp; |
|
3468
|
2234 } |
|
3467
|
2235 |
|
|
2236 // construct inverse balancing permutation vector |
|
3468
|
2237 Array<int> invpvec (nc); |
|
|
2238 for (int i = 0; i < nc; i++) |
|
4593
|
2239 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
2240 |
|
4153
|
2241 OCTAVE_QUIT; |
|
|
2242 |
|
3467
|
2243 ComplexMatrix tmpMat = retval; |
|
3468
|
2244 for (int i = 0; i < nc; i++) |
|
|
2245 for (int j = 0; j < nc; j++) |
|
|
2246 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
2247 |
|
|
2248 // Reverse preconditioning step 1: fix trace normalization. |
|
|
2249 |
|
3130
|
2250 return exp (trshift) * retval; |
|
1819
|
2251 } |
|
|
2252 |
|
1205
|
2253 // column vector by row vector -> matrix operations |
|
|
2254 |
|
|
2255 ComplexMatrix |
|
|
2256 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
2257 { |
|
|
2258 ComplexColumnVector tmp (v); |
|
|
2259 return tmp * a; |
|
|
2260 } |
|
|
2261 |
|
|
2262 ComplexMatrix |
|
|
2263 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
2264 { |
|
|
2265 ComplexRowVector tmp (b); |
|
|
2266 return a * tmp; |
|
|
2267 } |
|
|
2268 |
|
|
2269 ComplexMatrix |
|
|
2270 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
2271 { |
|
1948
|
2272 ComplexMatrix retval; |
|
|
2273 |
|
1205
|
2274 int len = v.length (); |
|
3233
|
2275 |
|
|
2276 if (len != 0) |
|
1205
|
2277 { |
|
3233
|
2278 int a_len = a.length (); |
|
|
2279 |
|
|
2280 retval.resize (len, a_len); |
|
|
2281 Complex *c = retval.fortran_vec (); |
|
|
2282 |
|
4552
|
2283 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2284 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2285 len, a_len, 1, 1.0, v.data (), len, |
|
|
2286 a.data (), 1, 0.0, c, len |
|
|
2287 F77_CHAR_ARG_LEN (1) |
|
|
2288 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2289 |
|
|
2290 if (f77_exception_encountered) |
|
|
2291 (*current_liboctave_error_handler) |
|
|
2292 ("unrecoverable error in zgemm"); |
|
1205
|
2293 } |
|
|
2294 |
|
1948
|
2295 return retval; |
|
1205
|
2296 } |
|
|
2297 |
|
458
|
2298 // matrix by diagonal matrix -> matrix operations |
|
|
2299 |
|
|
2300 ComplexMatrix& |
|
|
2301 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
2302 { |
|
|
2303 int nr = rows (); |
|
|
2304 int nc = cols (); |
|
2384
|
2305 |
|
|
2306 int a_nr = rows (); |
|
|
2307 int a_nc = cols (); |
|
|
2308 |
|
|
2309 if (nr != a_nr || nc != a_nc) |
|
458
|
2310 { |
|
2384
|
2311 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2312 return *this; |
|
458
|
2313 } |
|
|
2314 |
|
|
2315 for (int i = 0; i < a.length (); i++) |
|
|
2316 elem (i, i) += a.elem (i, i); |
|
|
2317 |
|
|
2318 return *this; |
|
|
2319 } |
|
|
2320 |
|
|
2321 ComplexMatrix& |
|
|
2322 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
2323 { |
|
|
2324 int nr = rows (); |
|
|
2325 int nc = cols (); |
|
2384
|
2326 |
|
|
2327 int a_nr = rows (); |
|
|
2328 int a_nc = cols (); |
|
|
2329 |
|
|
2330 if (nr != a_nr || nc != a_nc) |
|
458
|
2331 { |
|
2384
|
2332 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2333 return *this; |
|
458
|
2334 } |
|
|
2335 |
|
|
2336 for (int i = 0; i < a.length (); i++) |
|
|
2337 elem (i, i) -= a.elem (i, i); |
|
|
2338 |
|
|
2339 return *this; |
|
|
2340 } |
|
|
2341 |
|
|
2342 ComplexMatrix& |
|
|
2343 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
2344 { |
|
|
2345 int nr = rows (); |
|
|
2346 int nc = cols (); |
|
2384
|
2347 |
|
|
2348 int a_nr = rows (); |
|
|
2349 int a_nc = cols (); |
|
|
2350 |
|
|
2351 if (nr != a_nr || nc != a_nc) |
|
458
|
2352 { |
|
2384
|
2353 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2354 return *this; |
|
458
|
2355 } |
|
|
2356 |
|
|
2357 for (int i = 0; i < a.length (); i++) |
|
|
2358 elem (i, i) += a.elem (i, i); |
|
|
2359 |
|
|
2360 return *this; |
|
|
2361 } |
|
|
2362 |
|
|
2363 ComplexMatrix& |
|
|
2364 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
2365 { |
|
|
2366 int nr = rows (); |
|
|
2367 int nc = cols (); |
|
2384
|
2368 |
|
|
2369 int a_nr = rows (); |
|
|
2370 int a_nc = cols (); |
|
|
2371 |
|
|
2372 if (nr != a_nr || nc != a_nc) |
|
458
|
2373 { |
|
2384
|
2374 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2375 return *this; |
|
458
|
2376 } |
|
|
2377 |
|
|
2378 for (int i = 0; i < a.length (); i++) |
|
|
2379 elem (i, i) -= a.elem (i, i); |
|
|
2380 |
|
|
2381 return *this; |
|
|
2382 } |
|
|
2383 |
|
|
2384 // matrix by matrix -> matrix operations |
|
|
2385 |
|
|
2386 ComplexMatrix& |
|
|
2387 ComplexMatrix::operator += (const Matrix& a) |
|
|
2388 { |
|
|
2389 int nr = rows (); |
|
|
2390 int nc = cols (); |
|
2384
|
2391 |
|
|
2392 int a_nr = a.rows (); |
|
|
2393 int a_nc = a.cols (); |
|
|
2394 |
|
|
2395 if (nr != a_nr || nc != a_nc) |
|
458
|
2396 { |
|
2384
|
2397 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2398 return *this; |
|
|
2399 } |
|
|
2400 |
|
|
2401 if (nr == 0 || nc == 0) |
|
|
2402 return *this; |
|
|
2403 |
|
|
2404 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2405 |
|
3769
|
2406 mx_inline_add2 (d, a.data (), length ()); |
|
458
|
2407 return *this; |
|
|
2408 } |
|
|
2409 |
|
|
2410 ComplexMatrix& |
|
|
2411 ComplexMatrix::operator -= (const Matrix& a) |
|
|
2412 { |
|
|
2413 int nr = rows (); |
|
|
2414 int nc = cols (); |
|
2384
|
2415 |
|
|
2416 int a_nr = a.rows (); |
|
|
2417 int a_nc = a.cols (); |
|
|
2418 |
|
|
2419 if (nr != a_nr || nc != a_nc) |
|
458
|
2420 { |
|
2384
|
2421 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2422 return *this; |
|
|
2423 } |
|
|
2424 |
|
|
2425 if (nr == 0 || nc == 0) |
|
|
2426 return *this; |
|
|
2427 |
|
|
2428 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2429 |
|
3769
|
2430 mx_inline_subtract2 (d, a.data (), length ()); |
|
458
|
2431 return *this; |
|
|
2432 } |
|
|
2433 |
|
|
2434 // unary operations |
|
|
2435 |
|
2964
|
2436 boolMatrix |
|
458
|
2437 ComplexMatrix::operator ! (void) const |
|
|
2438 { |
|
2964
|
2439 int nr = rows (); |
|
|
2440 int nc = cols (); |
|
|
2441 |
|
|
2442 boolMatrix b (nr, nc); |
|
|
2443 |
|
|
2444 for (int j = 0; j < nc; j++) |
|
|
2445 for (int i = 0; i < nr; i++) |
|
|
2446 b.elem (i, j) = elem (i, j) != 0.0; |
|
|
2447 |
|
|
2448 return b; |
|
458
|
2449 } |
|
|
2450 |
|
|
2451 // other operations |
|
|
2452 |
|
|
2453 ComplexMatrix |
|
2676
|
2454 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
2455 { |
|
2676
|
2456 ComplexMatrix b (*this); |
|
|
2457 return b.apply (f); |
|
458
|
2458 } |
|
|
2459 |
|
2676
|
2460 Matrix |
|
|
2461 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
2462 { |
|
3248
|
2463 int nr = rows (); |
|
|
2464 int nc = cols (); |
|
|
2465 |
|
|
2466 Matrix retval (nr, nc); |
|
|
2467 |
|
|
2468 for (int j = 0; j < nc; j++) |
|
|
2469 for (int i = 0; i < nr; i++) |
|
|
2470 retval(i,j) = f (elem(i,j)); |
|
|
2471 |
|
|
2472 return retval; |
|
|
2473 } |
|
|
2474 |
|
|
2475 boolMatrix |
|
|
2476 ComplexMatrix::map (b_c_Mapper f) const |
|
|
2477 { |
|
|
2478 int nr = rows (); |
|
|
2479 int nc = cols (); |
|
|
2480 |
|
|
2481 boolMatrix retval (nr, nc); |
|
|
2482 |
|
|
2483 for (int j = 0; j < nc; j++) |
|
|
2484 for (int i = 0; i < nr; i++) |
|
|
2485 retval(i,j) = f (elem(i,j)); |
|
2676
|
2486 |
|
|
2487 return retval; |
|
|
2488 } |
|
|
2489 |
|
|
2490 ComplexMatrix& |
|
|
2491 ComplexMatrix::apply (c_c_Mapper f) |
|
|
2492 { |
|
|
2493 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2494 |
|
|
2495 for (int i = 0; i < length (); i++) |
|
|
2496 d[i] = f (d[i]); |
|
|
2497 |
|
|
2498 return *this; |
|
458
|
2499 } |
|
|
2500 |
|
2384
|
2501 bool |
|
|
2502 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
2503 { |
|
|
2504 int nr = rows (); |
|
|
2505 int nc = cols (); |
|
|
2506 |
|
|
2507 for (int j = 0; j < nc; j++) |
|
|
2508 for (int i = 0; i < nr; i++) |
|
|
2509 { |
|
|
2510 Complex val = elem (i, j); |
|
|
2511 if (xisinf (val) || xisnan (val)) |
|
|
2512 return true; |
|
|
2513 } |
|
|
2514 |
|
|
2515 return false; |
|
|
2516 } |
|
|
2517 |
|
2408
|
2518 // Return true if no elements have imaginary components. |
|
|
2519 |
|
|
2520 bool |
|
|
2521 ComplexMatrix::all_elements_are_real (void) const |
|
|
2522 { |
|
|
2523 int nr = rows (); |
|
|
2524 int nc = cols (); |
|
|
2525 |
|
|
2526 for (int j = 0; j < nc; j++) |
|
4349
|
2527 { |
|
|
2528 for (int i = 0; i < nr; i++) |
|
|
2529 { |
|
|
2530 double ip = imag (elem (i, j)); |
|
|
2531 |
|
|
2532 if (ip != 0.0 || lo_ieee_signbit (ip)) |
|
|
2533 return false; |
|
|
2534 } |
|
|
2535 } |
|
2408
|
2536 |
|
|
2537 return true; |
|
|
2538 } |
|
|
2539 |
|
1968
|
2540 // Return nonzero if any element of CM has a non-integer real or |
|
|
2541 // imaginary part. Also extract the largest and smallest (real or |
|
|
2542 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
2543 |
|
2384
|
2544 bool |
|
1968
|
2545 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
2546 { |
|
|
2547 int nr = rows (); |
|
2384
|
2548 int nc = cols (); |
|
1968
|
2549 |
|
|
2550 if (nr > 0 && nc > 0) |
|
|
2551 { |
|
|
2552 Complex val = elem (0, 0); |
|
|
2553 |
|
|
2554 double r_val = real (val); |
|
|
2555 double i_val = imag (val); |
|
|
2556 |
|
|
2557 max_val = r_val; |
|
|
2558 min_val = r_val; |
|
|
2559 |
|
|
2560 if (i_val > max_val) |
|
|
2561 max_val = i_val; |
|
|
2562 |
|
|
2563 if (i_val < max_val) |
|
|
2564 min_val = i_val; |
|
|
2565 } |
|
|
2566 else |
|
2384
|
2567 return false; |
|
1968
|
2568 |
|
|
2569 for (int j = 0; j < nc; j++) |
|
|
2570 for (int i = 0; i < nr; i++) |
|
|
2571 { |
|
|
2572 Complex val = elem (i, j); |
|
|
2573 |
|
|
2574 double r_val = real (val); |
|
|
2575 double i_val = imag (val); |
|
|
2576 |
|
|
2577 if (r_val > max_val) |
|
|
2578 max_val = r_val; |
|
|
2579 |
|
|
2580 if (i_val > max_val) |
|
|
2581 max_val = i_val; |
|
|
2582 |
|
|
2583 if (r_val < min_val) |
|
|
2584 min_val = r_val; |
|
|
2585 |
|
|
2586 if (i_val < min_val) |
|
|
2587 min_val = i_val; |
|
|
2588 |
|
|
2589 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
2590 return false; |
|
1968
|
2591 } |
|
2384
|
2592 |
|
|
2593 return true; |
|
1968
|
2594 } |
|
|
2595 |
|
2384
|
2596 bool |
|
1968
|
2597 ComplexMatrix::too_large_for_float (void) const |
|
|
2598 { |
|
|
2599 int nr = rows (); |
|
2384
|
2600 int nc = cols (); |
|
1968
|
2601 |
|
|
2602 for (int j = 0; j < nc; j++) |
|
|
2603 for (int i = 0; i < nr; i++) |
|
|
2604 { |
|
|
2605 Complex val = elem (i, j); |
|
|
2606 |
|
|
2607 double r_val = real (val); |
|
|
2608 double i_val = imag (val); |
|
|
2609 |
|
|
2610 if (r_val > FLT_MAX |
|
|
2611 || i_val > FLT_MAX |
|
|
2612 || r_val < FLT_MIN |
|
|
2613 || i_val < FLT_MIN) |
|
2384
|
2614 return true; |
|
1968
|
2615 } |
|
|
2616 |
|
2384
|
2617 return false; |
|
1968
|
2618 } |
|
|
2619 |
|
4015
|
2620 // XXX FIXME XXX Do these really belong here? Maybe they should be |
|
|
2621 // in a base class? |
|
|
2622 |
|
2832
|
2623 boolMatrix |
|
4015
|
2624 ComplexMatrix::all (int dim) const |
|
458
|
2625 { |
|
4015
|
2626 MX_ALL_OP (dim); |
|
458
|
2627 } |
|
|
2628 |
|
2832
|
2629 boolMatrix |
|
4015
|
2630 ComplexMatrix::any (int dim) const |
|
458
|
2631 { |
|
4015
|
2632 MX_ANY_OP (dim); |
|
458
|
2633 } |
|
|
2634 |
|
|
2635 ComplexMatrix |
|
3723
|
2636 ComplexMatrix::cumprod (int dim) const |
|
458
|
2637 { |
|
4015
|
2638 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
|
458
|
2639 } |
|
|
2640 |
|
|
2641 ComplexMatrix |
|
3723
|
2642 ComplexMatrix::cumsum (int dim) const |
|
458
|
2643 { |
|
4015
|
2644 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
|
458
|
2645 } |
|
|
2646 |
|
|
2647 ComplexMatrix |
|
3723
|
2648 ComplexMatrix::prod (int dim) const |
|
458
|
2649 { |
|
3864
|
2650 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
|
458
|
2651 } |
|
|
2652 |
|
|
2653 ComplexMatrix |
|
3723
|
2654 ComplexMatrix::sum (int dim) const |
|
458
|
2655 { |
|
3864
|
2656 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
|
458
|
2657 } |
|
|
2658 |
|
|
2659 ComplexMatrix |
|
3723
|
2660 ComplexMatrix::sumsq (int dim) const |
|
458
|
2661 { |
|
3864
|
2662 #define ROW_EXPR \ |
|
|
2663 Complex d = elem (i, j); \ |
|
|
2664 retval.elem (i, 0) += d * conj (d) |
|
|
2665 |
|
|
2666 #define COL_EXPR \ |
|
|
2667 Complex d = elem (i, j); \ |
|
|
2668 retval.elem (0, j) += d * conj (d) |
|
|
2669 |
|
|
2670 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2671 |
|
|
2672 #undef ROW_EXPR |
|
|
2673 #undef COL_EXPR |
|
458
|
2674 } |
|
|
2675 |
|
4329
|
2676 Matrix ComplexMatrix::abs (void) const |
|
|
2677 { |
|
|
2678 int nr = rows (); |
|
|
2679 int nc = cols (); |
|
|
2680 |
|
|
2681 Matrix retval (nr, nc); |
|
|
2682 |
|
|
2683 for (int j = 0; j < nc; j++) |
|
|
2684 for (int i = 0; i < nr; i++) |
|
|
2685 retval (i, j) = ::abs (elem (i, j)); |
|
|
2686 |
|
|
2687 return retval; |
|
|
2688 } |
|
|
2689 |
|
458
|
2690 ComplexColumnVector |
|
|
2691 ComplexMatrix::diag (void) const |
|
|
2692 { |
|
|
2693 return diag (0); |
|
|
2694 } |
|
|
2695 |
|
|
2696 ComplexColumnVector |
|
|
2697 ComplexMatrix::diag (int k) const |
|
|
2698 { |
|
|
2699 int nnr = rows (); |
|
|
2700 int nnc = cols (); |
|
|
2701 if (k > 0) |
|
|
2702 nnc -= k; |
|
|
2703 else if (k < 0) |
|
|
2704 nnr += k; |
|
|
2705 |
|
|
2706 ComplexColumnVector d; |
|
|
2707 |
|
|
2708 if (nnr > 0 && nnc > 0) |
|
|
2709 { |
|
|
2710 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2711 |
|
|
2712 d.resize (ndiag); |
|
|
2713 |
|
|
2714 if (k > 0) |
|
|
2715 { |
|
|
2716 for (int i = 0; i < ndiag; i++) |
|
|
2717 d.elem (i) = elem (i, i+k); |
|
|
2718 } |
|
4509
|
2719 else if (k < 0) |
|
458
|
2720 { |
|
|
2721 for (int i = 0; i < ndiag; i++) |
|
|
2722 d.elem (i) = elem (i-k, i); |
|
|
2723 } |
|
|
2724 else |
|
|
2725 { |
|
|
2726 for (int i = 0; i < ndiag; i++) |
|
|
2727 d.elem (i) = elem (i, i); |
|
|
2728 } |
|
|
2729 } |
|
|
2730 else |
|
4513
|
2731 (*current_liboctave_error_handler) |
|
|
2732 ("diag: requested diagonal out of range"); |
|
458
|
2733 |
|
|
2734 return d; |
|
|
2735 } |
|
|
2736 |
|
2354
|
2737 bool |
|
|
2738 ComplexMatrix::row_is_real_only (int i) const |
|
|
2739 { |
|
|
2740 bool retval = true; |
|
|
2741 |
|
|
2742 int nc = columns (); |
|
|
2743 |
|
|
2744 for (int j = 0; j < nc; j++) |
|
|
2745 { |
|
|
2746 if (imag (elem (i, j)) != 0.0) |
|
|
2747 { |
|
|
2748 retval = false; |
|
|
2749 break; |
|
|
2750 } |
|
|
2751 } |
|
|
2752 |
|
|
2753 return retval; |
|
|
2754 } |
|
|
2755 |
|
|
2756 bool |
|
|
2757 ComplexMatrix::column_is_real_only (int j) const |
|
|
2758 { |
|
|
2759 bool retval = true; |
|
|
2760 |
|
|
2761 int nr = rows (); |
|
|
2762 |
|
|
2763 for (int i = 0; i < nr; i++) |
|
|
2764 { |
|
|
2765 if (imag (elem (i, j)) != 0.0) |
|
|
2766 { |
|
|
2767 retval = false; |
|
|
2768 break; |
|
|
2769 } |
|
|
2770 } |
|
|
2771 |
|
|
2772 return retval; |
|
|
2773 } |
|
891
|
2774 |
|
458
|
2775 ComplexColumnVector |
|
|
2776 ComplexMatrix::row_min (void) const |
|
|
2777 { |
|
4587
|
2778 Array<int> dummy_idx; |
|
|
2779 return row_min (dummy_idx); |
|
458
|
2780 } |
|
|
2781 |
|
|
2782 ComplexColumnVector |
|
4587
|
2783 ComplexMatrix::row_min (Array<int>& idx_arg) const |
|
458
|
2784 { |
|
|
2785 ComplexColumnVector result; |
|
|
2786 |
|
|
2787 int nr = rows (); |
|
|
2788 int nc = cols (); |
|
|
2789 |
|
|
2790 if (nr > 0 && nc > 0) |
|
|
2791 { |
|
|
2792 result.resize (nr); |
|
4587
|
2793 idx_arg.resize (nr); |
|
458
|
2794 |
|
|
2795 for (int i = 0; i < nr; i++) |
|
|
2796 { |
|
2354
|
2797 bool real_only = row_is_real_only (i); |
|
|
2798 |
|
4469
|
2799 int idx_j; |
|
|
2800 |
|
|
2801 Complex tmp_min; |
|
|
2802 |
|
|
2803 double abs_min = octave_NaN; |
|
|
2804 |
|
|
2805 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
2806 { |
|
|
2807 tmp_min = elem (i, idx_j); |
|
|
2808 |
|
|
2809 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2810 { |
|
|
2811 abs_min = real_only ? real (tmp_min) : ::abs (tmp_min); |
|
|
2812 break; |
|
|
2813 } |
|
|
2814 } |
|
|
2815 |
|
|
2816 for (int j = idx_j+1; j < nc; j++) |
|
|
2817 { |
|
|
2818 Complex tmp = elem (i, j); |
|
|
2819 |
|
|
2820 if (octave_is_NaN_or_NA (tmp)) |
|
|
2821 continue; |
|
|
2822 |
|
|
2823 double abs_tmp = real_only ? real (tmp) : ::abs (tmp); |
|
|
2824 |
|
|
2825 if (abs_tmp < abs_min) |
|
|
2826 { |
|
|
2827 idx_j = j; |
|
|
2828 tmp_min = tmp; |
|
|
2829 abs_min = abs_tmp; |
|
|
2830 } |
|
|
2831 } |
|
|
2832 |
|
|
2833 if (octave_is_NaN_or_NA (tmp_min)) |
|
|
2834 { |
|
|
2835 result.elem (i) = Complex_NaN_result; |
|
4587
|
2836 idx_arg.elem (i) = 0; |
|
4469
|
2837 } |
|
891
|
2838 else |
|
|
2839 { |
|
4469
|
2840 result.elem (i) = tmp_min; |
|
4587
|
2841 idx_arg.elem (i) = idx_j; |
|
891
|
2842 } |
|
458
|
2843 } |
|
|
2844 } |
|
|
2845 |
|
|
2846 return result; |
|
|
2847 } |
|
|
2848 |
|
|
2849 ComplexColumnVector |
|
|
2850 ComplexMatrix::row_max (void) const |
|
|
2851 { |
|
4587
|
2852 Array<int> dummy_idx; |
|
|
2853 return row_max (dummy_idx); |
|
458
|
2854 } |
|
|
2855 |
|
|
2856 ComplexColumnVector |
|
4587
|
2857 ComplexMatrix::row_max (Array<int>& idx_arg) const |
|
458
|
2858 { |
|
|
2859 ComplexColumnVector result; |
|
|
2860 |
|
|
2861 int nr = rows (); |
|
|
2862 int nc = cols (); |
|
|
2863 |
|
|
2864 if (nr > 0 && nc > 0) |
|
|
2865 { |
|
|
2866 result.resize (nr); |
|
4587
|
2867 idx_arg.resize (nr); |
|
458
|
2868 |
|
|
2869 for (int i = 0; i < nr; i++) |
|
|
2870 { |
|
2354
|
2871 bool real_only = row_is_real_only (i); |
|
|
2872 |
|
4469
|
2873 int idx_j; |
|
|
2874 |
|
|
2875 Complex tmp_max; |
|
|
2876 |
|
|
2877 double abs_max = octave_NaN; |
|
|
2878 |
|
|
2879 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
2880 { |
|
|
2881 tmp_max = elem (i, idx_j); |
|
|
2882 |
|
|
2883 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
2884 { |
|
|
2885 abs_max = real_only ? real (tmp_max) : ::abs (tmp_max); |
|
|
2886 break; |
|
|
2887 } |
|
|
2888 } |
|
|
2889 |
|
|
2890 for (int j = idx_j+1; j < nc; j++) |
|
|
2891 { |
|
|
2892 Complex tmp = elem (i, j); |
|
|
2893 |
|
|
2894 if (octave_is_NaN_or_NA (tmp)) |
|
|
2895 continue; |
|
|
2896 |
|
|
2897 double abs_tmp = real_only ? real (tmp) : ::abs (tmp); |
|
|
2898 |
|
|
2899 if (abs_tmp > abs_max) |
|
|
2900 { |
|
|
2901 idx_j = j; |
|
|
2902 tmp_max = tmp; |
|
|
2903 abs_max = abs_tmp; |
|
|
2904 } |
|
|
2905 } |
|
|
2906 |
|
|
2907 if (octave_is_NaN_or_NA (tmp_max)) |
|
|
2908 { |
|
|
2909 result.elem (i) = Complex_NaN_result; |
|
4587
|
2910 idx_arg.elem (i) = 0; |
|
4469
|
2911 } |
|
891
|
2912 else |
|
|
2913 { |
|
4469
|
2914 result.elem (i) = tmp_max; |
|
4587
|
2915 idx_arg.elem (i) = idx_j; |
|
891
|
2916 } |
|
458
|
2917 } |
|
|
2918 } |
|
|
2919 |
|
|
2920 return result; |
|
|
2921 } |
|
|
2922 |
|
|
2923 ComplexRowVector |
|
|
2924 ComplexMatrix::column_min (void) const |
|
|
2925 { |
|
4587
|
2926 Array<int> dummy_idx; |
|
|
2927 return column_min (dummy_idx); |
|
458
|
2928 } |
|
|
2929 |
|
|
2930 ComplexRowVector |
|
4587
|
2931 ComplexMatrix::column_min (Array<int>& idx_arg) const |
|
458
|
2932 { |
|
|
2933 ComplexRowVector result; |
|
|
2934 |
|
|
2935 int nr = rows (); |
|
|
2936 int nc = cols (); |
|
|
2937 |
|
|
2938 if (nr > 0 && nc > 0) |
|
|
2939 { |
|
|
2940 result.resize (nc); |
|
4587
|
2941 idx_arg.resize (nc); |
|
458
|
2942 |
|
|
2943 for (int j = 0; j < nc; j++) |
|
|
2944 { |
|
2354
|
2945 bool real_only = column_is_real_only (j); |
|
|
2946 |
|
4469
|
2947 int idx_i; |
|
|
2948 |
|
|
2949 Complex tmp_min; |
|
|
2950 |
|
|
2951 double abs_min = octave_NaN; |
|
|
2952 |
|
|
2953 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
2954 { |
|
|
2955 tmp_min = elem (idx_i, j); |
|
|
2956 |
|
|
2957 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2958 { |
|
|
2959 abs_min = real_only ? real (tmp_min) : ::abs (tmp_min); |
|
|
2960 break; |
|
|
2961 } |
|
|
2962 } |
|
|
2963 |
|
|
2964 for (int i = idx_i+1; i < nr; i++) |
|
|
2965 { |
|
|
2966 Complex tmp = elem (i, j); |
|
|
2967 |
|
|
2968 if (octave_is_NaN_or_NA (tmp)) |
|
|
2969 continue; |
|
|
2970 |
|
|
2971 double abs_tmp = real_only ? real (tmp) : ::abs (tmp); |
|
|
2972 |
|
|
2973 if (abs_tmp < abs_min) |
|
|
2974 { |
|
|
2975 idx_i = i; |
|
|
2976 tmp_min = tmp; |
|
|
2977 abs_min = abs_tmp; |
|
|
2978 } |
|
|
2979 } |
|
|
2980 |
|
|
2981 if (octave_is_NaN_or_NA (tmp_min)) |
|
|
2982 { |
|
|
2983 result.elem (j) = Complex_NaN_result; |
|
4587
|
2984 idx_arg.elem (j) = 0; |
|
4469
|
2985 } |
|
891
|
2986 else |
|
|
2987 { |
|
4469
|
2988 result.elem (j) = tmp_min; |
|
4587
|
2989 idx_arg.elem (j) = idx_i; |
|
891
|
2990 } |
|
458
|
2991 } |
|
|
2992 } |
|
|
2993 |
|
|
2994 return result; |
|
|
2995 } |
|
|
2996 |
|
|
2997 ComplexRowVector |
|
|
2998 ComplexMatrix::column_max (void) const |
|
|
2999 { |
|
4587
|
3000 Array<int> dummy_idx; |
|
|
3001 return column_max (dummy_idx); |
|
458
|
3002 } |
|
|
3003 |
|
|
3004 ComplexRowVector |
|
4587
|
3005 ComplexMatrix::column_max (Array<int>& idx_arg) const |
|
458
|
3006 { |
|
|
3007 ComplexRowVector result; |
|
|
3008 |
|
|
3009 int nr = rows (); |
|
|
3010 int nc = cols (); |
|
|
3011 |
|
|
3012 if (nr > 0 && nc > 0) |
|
|
3013 { |
|
|
3014 result.resize (nc); |
|
4587
|
3015 idx_arg.resize (nc); |
|
458
|
3016 |
|
|
3017 for (int j = 0; j < nc; j++) |
|
|
3018 { |
|
2354
|
3019 bool real_only = column_is_real_only (j); |
|
|
3020 |
|
4469
|
3021 int idx_i; |
|
|
3022 |
|
|
3023 Complex tmp_max; |
|
|
3024 |
|
|
3025 double abs_max = octave_NaN; |
|
|
3026 |
|
|
3027 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3028 { |
|
|
3029 tmp_max = elem (idx_i, j); |
|
|
3030 |
|
|
3031 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
3032 { |
|
|
3033 abs_max = real_only ? real (tmp_max) : ::abs (tmp_max); |
|
|
3034 break; |
|
|
3035 } |
|
|
3036 } |
|
|
3037 |
|
|
3038 for (int i = idx_i+1; i < nr; i++) |
|
|
3039 { |
|
|
3040 Complex tmp = elem (i, j); |
|
|
3041 |
|
|
3042 if (octave_is_NaN_or_NA (tmp)) |
|
|
3043 continue; |
|
|
3044 |
|
|
3045 double abs_tmp = real_only ? real (tmp) : ::abs (tmp); |
|
|
3046 |
|
|
3047 if (abs_tmp > abs_max) |
|
|
3048 { |
|
|
3049 idx_i = i; |
|
|
3050 tmp_max = tmp; |
|
|
3051 abs_max = abs_tmp; |
|
|
3052 } |
|
|
3053 } |
|
|
3054 |
|
|
3055 if (octave_is_NaN_or_NA (tmp_max)) |
|
|
3056 { |
|
|
3057 result.elem (j) = Complex_NaN_result; |
|
4587
|
3058 idx_arg.elem (j) = 0; |
|
4469
|
3059 } |
|
891
|
3060 else |
|
|
3061 { |
|
4469
|
3062 result.elem (j) = tmp_max; |
|
4587
|
3063 idx_arg.elem (j) = idx_i; |
|
891
|
3064 } |
|
458
|
3065 } |
|
|
3066 } |
|
|
3067 |
|
|
3068 return result; |
|
|
3069 } |
|
|
3070 |
|
|
3071 // i/o |
|
|
3072 |
|
3504
|
3073 std::ostream& |
|
|
3074 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
3075 { |
|
|
3076 for (int i = 0; i < a.rows (); i++) |
|
|
3077 { |
|
|
3078 for (int j = 0; j < a.cols (); j++) |
|
4130
|
3079 { |
|
|
3080 os << " "; |
|
|
3081 octave_write_complex (os, a.elem (i, j)); |
|
|
3082 } |
|
458
|
3083 os << "\n"; |
|
|
3084 } |
|
|
3085 return os; |
|
|
3086 } |
|
|
3087 |
|
3504
|
3088 std::istream& |
|
|
3089 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
3090 { |
|
|
3091 int nr = a.rows (); |
|
|
3092 int nc = a.cols (); |
|
|
3093 |
|
|
3094 if (nr < 1 || nc < 1) |
|
3504
|
3095 is.clear (std::ios::badbit); |
|
458
|
3096 else |
|
|
3097 { |
|
|
3098 Complex tmp; |
|
|
3099 for (int i = 0; i < nr; i++) |
|
|
3100 for (int j = 0; j < nc; j++) |
|
|
3101 { |
|
4130
|
3102 tmp = octave_read_complex (is); |
|
458
|
3103 if (is) |
|
|
3104 a.elem (i, j) = tmp; |
|
|
3105 else |
|
2993
|
3106 goto done; |
|
458
|
3107 } |
|
|
3108 } |
|
|
3109 |
|
2993
|
3110 done: |
|
|
3111 |
|
458
|
3112 return is; |
|
|
3113 } |
|
|
3114 |
|
1819
|
3115 ComplexMatrix |
|
|
3116 Givens (const Complex& x, const Complex& y) |
|
|
3117 { |
|
|
3118 double cc; |
|
|
3119 Complex cs, temp_r; |
|
|
3120 |
|
3887
|
3121 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
1819
|
3122 |
|
|
3123 ComplexMatrix g (2, 2); |
|
|
3124 |
|
|
3125 g.elem (0, 0) = cc; |
|
|
3126 g.elem (1, 1) = cc; |
|
|
3127 g.elem (0, 1) = cs; |
|
|
3128 g.elem (1, 0) = -conj (cs); |
|
|
3129 |
|
|
3130 return g; |
|
|
3131 } |
|
|
3132 |
|
|
3133 ComplexMatrix |
|
|
3134 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
3135 const ComplexMatrix& c) |
|
|
3136 { |
|
|
3137 ComplexMatrix retval; |
|
|
3138 |
|
|
3139 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
3140 // size. |
|
|
3141 |
|
|
3142 // Compute Schur decompositions |
|
|
3143 |
|
|
3144 ComplexSCHUR as (a, "U"); |
|
|
3145 ComplexSCHUR bs (b, "U"); |
|
|
3146 |
|
|
3147 // Transform c to new coordinates. |
|
|
3148 |
|
|
3149 ComplexMatrix ua = as.unitary_matrix (); |
|
|
3150 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
3151 |
|
|
3152 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
3153 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
3154 |
|
|
3155 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
3156 |
|
|
3157 // Solve the sylvester equation, back-transform, and return the |
|
|
3158 // solution. |
|
|
3159 |
|
|
3160 int a_nr = a.rows (); |
|
|
3161 int b_nr = b.rows (); |
|
|
3162 |
|
|
3163 double scale; |
|
|
3164 int info; |
|
1950
|
3165 |
|
|
3166 Complex *pa = sch_a.fortran_vec (); |
|
|
3167 Complex *pb = sch_b.fortran_vec (); |
|
|
3168 Complex *px = cx.fortran_vec (); |
|
1819
|
3169 |
|
4552
|
3170 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3171 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3172 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3173 b_nr, px, a_nr, scale, info |
|
|
3174 F77_CHAR_ARG_LEN (1) |
|
|
3175 F77_CHAR_ARG_LEN (1))); |
|
1950
|
3176 |
|
|
3177 if (f77_exception_encountered) |
|
|
3178 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
3179 else |
|
|
3180 { |
|
|
3181 // XXX FIXME XXX -- check info? |
|
|
3182 |
|
|
3183 retval = -ua * cx * ub.hermitian (); |
|
|
3184 } |
|
1819
|
3185 |
|
|
3186 return retval; |
|
|
3187 } |
|
|
3188 |
|
2828
|
3189 ComplexMatrix |
|
|
3190 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
3191 { |
|
|
3192 ComplexMatrix tmp (a); |
|
|
3193 return m * tmp; |
|
|
3194 } |
|
|
3195 |
|
|
3196 ComplexMatrix |
|
|
3197 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
3198 { |
|
|
3199 ComplexMatrix tmp (m); |
|
|
3200 return tmp * a; |
|
|
3201 } |
|
|
3202 |
|
|
3203 ComplexMatrix |
|
|
3204 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
3205 { |
|
|
3206 ComplexMatrix retval; |
|
|
3207 |
|
|
3208 int nr = m.rows (); |
|
|
3209 int nc = m.cols (); |
|
|
3210 |
|
|
3211 int a_nr = a.rows (); |
|
|
3212 int a_nc = a.cols (); |
|
|
3213 |
|
|
3214 if (nc != a_nr) |
|
|
3215 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3216 else |
|
|
3217 { |
|
|
3218 if (nr == 0 || nc == 0 || a_nc == 0) |
|
3760
|
3219 retval.resize (nr, a_nc, 0.0); |
|
2828
|
3220 else |
|
|
3221 { |
|
|
3222 int ld = nr; |
|
|
3223 int lda = a.rows (); |
|
|
3224 |
|
|
3225 retval.resize (nr, a_nc); |
|
|
3226 Complex *c = retval.fortran_vec (); |
|
|
3227 |
|
4552
|
3228 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3229 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3230 nr, a_nc, nc, 1.0, m.data (), |
|
|
3231 ld, a.data (), lda, 0.0, c, nr |
|
|
3232 F77_CHAR_ARG_LEN (1) |
|
|
3233 F77_CHAR_ARG_LEN (1))); |
|
2828
|
3234 |
|
|
3235 if (f77_exception_encountered) |
|
|
3236 (*current_liboctave_error_handler) |
|
|
3237 ("unrecoverable error in zgemm"); |
|
|
3238 } |
|
|
3239 } |
|
|
3240 |
|
|
3241 return retval; |
|
|
3242 } |
|
|
3243 |
|
4309
|
3244 // XXX FIXME XXX -- it would be nice to share code among the min/max |
|
|
3245 // functions below. |
|
|
3246 |
|
|
3247 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3248 if (nr == 0 || nc == 0) \ |
|
|
3249 return T (nr, nc); |
|
|
3250 |
|
|
3251 ComplexMatrix |
|
|
3252 min (const Complex& c, const ComplexMatrix& m) |
|
|
3253 { |
|
|
3254 int nr = m.rows (); |
|
|
3255 int nc = m.columns (); |
|
|
3256 |
|
|
3257 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3258 |
|
|
3259 ComplexMatrix result (nr, nc); |
|
|
3260 |
|
|
3261 for (int j = 0; j < nc; j++) |
|
|
3262 for (int i = 0; i < nr; i++) |
|
|
3263 { |
|
|
3264 OCTAVE_QUIT; |
|
|
3265 result (i, j) = xmin (c, m (i, j)); |
|
|
3266 } |
|
|
3267 |
|
|
3268 return result; |
|
|
3269 } |
|
|
3270 |
|
|
3271 ComplexMatrix |
|
|
3272 min (const ComplexMatrix& m, const Complex& c) |
|
|
3273 { |
|
|
3274 int nr = m.rows (); |
|
|
3275 int nc = m.columns (); |
|
|
3276 |
|
|
3277 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3278 |
|
|
3279 ComplexMatrix result (nr, nc); |
|
|
3280 |
|
|
3281 for (int j = 0; j < nc; j++) |
|
|
3282 for (int i = 0; i < nr; i++) |
|
|
3283 { |
|
|
3284 OCTAVE_QUIT; |
|
|
3285 result (i, j) = xmin (m (i, j), c); |
|
|
3286 } |
|
|
3287 |
|
|
3288 return result; |
|
|
3289 } |
|
|
3290 |
|
|
3291 ComplexMatrix |
|
|
3292 min (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3293 { |
|
|
3294 int nr = a.rows (); |
|
|
3295 int nc = a.columns (); |
|
|
3296 |
|
|
3297 if (nr != b.rows () || nc != b.columns ()) |
|
|
3298 { |
|
|
3299 (*current_liboctave_error_handler) |
|
|
3300 ("two-arg min expecting args of same size"); |
|
|
3301 return ComplexMatrix (); |
|
|
3302 } |
|
|
3303 |
|
|
3304 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3305 |
|
|
3306 ComplexMatrix result (nr, nc); |
|
|
3307 |
|
|
3308 for (int j = 0; j < nc; j++) |
|
|
3309 { |
|
|
3310 int columns_are_real_only = 1; |
|
|
3311 for (int i = 0; i < nr; i++) |
|
|
3312 { |
|
|
3313 OCTAVE_QUIT; |
|
|
3314 if (imag (a (i, j)) != 0.0 || imag (b (i, j)) != 0.0) |
|
|
3315 { |
|
|
3316 columns_are_real_only = 0; |
|
|
3317 break; |
|
|
3318 } |
|
|
3319 } |
|
|
3320 |
|
|
3321 if (columns_are_real_only) |
|
|
3322 { |
|
|
3323 for (int i = 0; i < nr; i++) |
|
|
3324 result (i, j) = xmin (real (a (i, j)), real (b (i, j))); |
|
|
3325 } |
|
|
3326 else |
|
|
3327 { |
|
|
3328 for (int i = 0; i < nr; i++) |
|
|
3329 { |
|
|
3330 OCTAVE_QUIT; |
|
|
3331 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3332 } |
|
|
3333 } |
|
|
3334 } |
|
|
3335 |
|
|
3336 return result; |
|
|
3337 } |
|
|
3338 |
|
|
3339 ComplexMatrix |
|
|
3340 max (const Complex& c, const ComplexMatrix& m) |
|
|
3341 { |
|
|
3342 int nr = m.rows (); |
|
|
3343 int nc = m.columns (); |
|
|
3344 |
|
|
3345 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3346 |
|
|
3347 ComplexMatrix result (nr, nc); |
|
|
3348 |
|
|
3349 for (int j = 0; j < nc; j++) |
|
|
3350 for (int i = 0; i < nr; i++) |
|
|
3351 { |
|
|
3352 OCTAVE_QUIT; |
|
|
3353 result (i, j) = xmax (c, m (i, j)); |
|
|
3354 } |
|
|
3355 |
|
|
3356 return result; |
|
|
3357 } |
|
|
3358 |
|
|
3359 ComplexMatrix |
|
|
3360 max (const ComplexMatrix& m, const Complex& c) |
|
|
3361 { |
|
|
3362 int nr = m.rows (); |
|
|
3363 int nc = m.columns (); |
|
|
3364 |
|
|
3365 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3366 |
|
|
3367 ComplexMatrix result (nr, nc); |
|
|
3368 |
|
|
3369 for (int j = 0; j < nc; j++) |
|
|
3370 for (int i = 0; i < nr; i++) |
|
|
3371 { |
|
|
3372 OCTAVE_QUIT; |
|
|
3373 result (i, j) = xmax (m (i, j), c); |
|
|
3374 } |
|
|
3375 |
|
|
3376 return result; |
|
|
3377 } |
|
|
3378 |
|
|
3379 ComplexMatrix |
|
|
3380 max (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3381 { |
|
|
3382 int nr = a.rows (); |
|
|
3383 int nc = a.columns (); |
|
|
3384 |
|
|
3385 if (nr != b.rows () || nc != b.columns ()) |
|
|
3386 { |
|
|
3387 (*current_liboctave_error_handler) |
|
|
3388 ("two-arg max expecting args of same size"); |
|
|
3389 return ComplexMatrix (); |
|
|
3390 } |
|
|
3391 |
|
|
3392 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3393 |
|
|
3394 ComplexMatrix result (nr, nc); |
|
|
3395 |
|
|
3396 for (int j = 0; j < nc; j++) |
|
|
3397 { |
|
|
3398 int columns_are_real_only = 1; |
|
|
3399 for (int i = 0; i < nr; i++) |
|
|
3400 { |
|
|
3401 OCTAVE_QUIT; |
|
|
3402 if (imag (a (i, j)) != 0.0 || imag (b (i, j)) != 0.0) |
|
|
3403 { |
|
|
3404 columns_are_real_only = 0; |
|
|
3405 break; |
|
|
3406 } |
|
|
3407 } |
|
|
3408 |
|
|
3409 if (columns_are_real_only) |
|
|
3410 { |
|
|
3411 for (int i = 0; i < nr; i++) |
|
|
3412 { |
|
|
3413 OCTAVE_QUIT; |
|
|
3414 result (i, j) = xmax (real (a (i, j)), real (b (i, j))); |
|
|
3415 } |
|
|
3416 } |
|
|
3417 else |
|
|
3418 { |
|
|
3419 for (int i = 0; i < nr; i++) |
|
|
3420 { |
|
|
3421 OCTAVE_QUIT; |
|
|
3422 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3423 } |
|
|
3424 } |
|
|
3425 } |
|
|
3426 |
|
|
3427 return result; |
|
|
3428 } |
|
|
3429 |
|
2870
|
3430 MS_CMP_OPS(ComplexMatrix, real, Complex, real) |
|
3504
|
3431 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
3432 |
|
|
3433 SM_CMP_OPS(Complex, real, ComplexMatrix, real) |
|
3504
|
3434 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
3435 |
|
|
3436 MM_CMP_OPS(ComplexMatrix, real, ComplexMatrix, real) |
|
3504
|
3437 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
3438 |
|
458
|
3439 /* |
|
|
3440 ;;; Local Variables: *** |
|
|
3441 ;;; mode: C++ *** |
|
|
3442 ;;; End: *** |
|
|
3443 */ |
