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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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4 Copyright (C) 1996, 1997 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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21 02110-1301, USA. |
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22 |
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23 */ |
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24 |
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25 #ifdef HAVE_CONFIG_H |
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1192
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26 #include <config.h> |
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458
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27 #endif |
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28 |
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29 #include <cfloat> |
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30 |
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3503
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31 #include <iostream> |
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32 |
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33 // FIXME |
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2443
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34 #ifdef HAVE_SYS_TYPES_H |
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35 #include <sys/types.h> |
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36 #endif |
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37 |
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4669
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38 #include "Array-util.h" |
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2828
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39 #include "CMatrix.h" |
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1819
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40 #include "CmplxAEPBAL.h" |
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458
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41 #include "CmplxDET.h" |
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1819
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42 #include "CmplxSCHUR.h" |
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740
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43 #include "CmplxSVD.h" |
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44 #include "CmplxCHOL.h" |
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1847
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45 #include "f77-fcn.h" |
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458
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46 #include "lo-error.h" |
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2354
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47 #include "lo-ieee.h" |
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48 #include "lo-mappers.h" |
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1968
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49 #include "lo-utils.h" |
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1367
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50 #include "mx-base.h" |
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2828
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51 #include "mx-cm-dm.h" |
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3176
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52 #include "mx-dm-cm.h" |
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2828
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53 #include "mx-cm-s.h" |
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1367
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54 #include "mx-inlines.cc" |
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1650
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55 #include "oct-cmplx.h" |
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56 |
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4773
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57 #if defined (HAVE_FFTW3) |
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3827
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58 #include "oct-fftw.h" |
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59 #endif |
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60 |
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458
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61 // Fortran functions we call. |
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62 |
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63 extern "C" |
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64 { |
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65 F77_RET_T |
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66 F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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67 const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, |
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68 octave_idx_type&, double*, octave_idx_type& |
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69 F77_CHAR_ARG_LEN_DECL); |
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70 |
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71 F77_RET_T |
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72 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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73 F77_CONST_CHAR_ARG_DECL, |
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5275
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74 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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75 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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76 F77_CHAR_ARG_LEN_DECL |
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77 F77_CHAR_ARG_LEN_DECL); |
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78 |
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79 F77_RET_T |
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80 F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, |
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81 F77_CONST_CHAR_ARG_DECL, |
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82 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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83 const Complex&, const Complex*, const octave_idx_type&, |
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84 const Complex*, const octave_idx_type&, const Complex&, |
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85 Complex*, const octave_idx_type& |
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86 F77_CHAR_ARG_LEN_DECL |
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87 F77_CHAR_ARG_LEN_DECL); |
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88 |
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89 F77_RET_T |
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90 F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, |
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91 const octave_idx_type&, const octave_idx_type&, const Complex&, |
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92 const Complex*, const octave_idx_type&, const Complex*, |
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93 const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& |
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94 F77_CHAR_ARG_LEN_DECL); |
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95 |
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96 F77_RET_T |
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97 F77_FUNC (xzdotu, XZDOTU) (const octave_idx_type&, const Complex*, const octave_idx_type&, |
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98 const Complex*, const octave_idx_type&, Complex&); |
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99 |
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100 F77_RET_T |
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101 F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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102 octave_idx_type*, octave_idx_type&); |
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103 |
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104 F77_RET_T |
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105 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, |
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106 const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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107 const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& |
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108 F77_CHAR_ARG_LEN_DECL); |
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109 |
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110 F77_RET_T |
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111 F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, |
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112 Complex*, const octave_idx_type&, octave_idx_type&); |
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113 |
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114 F77_RET_T |
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115 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, |
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116 const octave_idx_type&, Complex*, |
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117 const octave_idx_type&, const double&, double&, |
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118 Complex*, double*, octave_idx_type& |
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119 F77_CHAR_ARG_LEN_DECL); |
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120 |
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121 F77_RET_T |
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122 F77_FUNC (zgelss, ZGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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123 Complex*, const octave_idx_type&, Complex*, |
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124 const octave_idx_type&, double*, double&, octave_idx_type&, |
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125 Complex*, const octave_idx_type&, double*, octave_idx_type&); |
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126 |
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127 F77_RET_T |
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128 F77_FUNC (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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129 Complex*, const octave_idx_type&, |
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130 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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131 |
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132 F77_RET_T |
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133 F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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134 Complex*, const octave_idx_type&, const double&, |
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135 double&, Complex*, double*, |
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136 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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137 |
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138 F77_RET_T |
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139 F77_FUNC (zpotrs, ZPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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140 const octave_idx_type&, const Complex*, |
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141 const octave_idx_type&, Complex*, |
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142 const octave_idx_type&, octave_idx_type& |
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143 F77_CHAR_ARG_LEN_DECL); |
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144 |
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145 F77_RET_T |
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146 F77_FUNC (ztrtri, ZTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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147 const octave_idx_type&, const Complex*, |
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148 const octave_idx_type&, octave_idx_type& |
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149 F77_CHAR_ARG_LEN_DECL |
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150 F77_CHAR_ARG_LEN_DECL); |
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151 |
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152 F77_RET_T |
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153 F77_FUNC (ztrcon, ZTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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154 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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155 const Complex*, const octave_idx_type&, double&, |
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156 Complex*, double*, octave_idx_type& |
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157 F77_CHAR_ARG_LEN_DECL |
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158 F77_CHAR_ARG_LEN_DECL |
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159 F77_CHAR_ARG_LEN_DECL); |
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160 |
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161 F77_RET_T |
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162 F77_FUNC (ztrtrs, ZTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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163 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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164 const octave_idx_type&, const Complex*, |
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165 const octave_idx_type&, Complex*, |
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166 const octave_idx_type&, octave_idx_type& |
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167 F77_CHAR_ARG_LEN_DECL |
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168 F77_CHAR_ARG_LEN_DECL |
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169 F77_CHAR_ARG_LEN_DECL); |
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170 |
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1360
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171 // Note that the original complex fft routines were not written for |
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172 // double complex arguments. They have been modified by adding an |
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173 // implicit double precision (a-h,o-z) statement at the beginning of |
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174 // each subroutine. |
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175 |
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176 F77_RET_T |
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177 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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178 |
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179 F77_RET_T |
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180 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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181 |
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182 F77_RET_T |
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183 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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184 |
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185 F77_RET_T |
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186 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, |
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187 double&, Complex&, Complex&); |
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188 |
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189 F77_RET_T |
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190 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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191 F77_CONST_CHAR_ARG_DECL, |
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192 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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193 const Complex*, const octave_idx_type&, |
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194 const Complex*, const octave_idx_type&, |
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195 const Complex*, const octave_idx_type&, double&, octave_idx_type& |
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196 F77_CHAR_ARG_LEN_DECL |
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197 F77_CHAR_ARG_LEN_DECL); |
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198 |
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199 F77_RET_T |
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200 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, |
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5275
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201 const octave_idx_type&, const octave_idx_type&, const Complex*, |
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202 const octave_idx_type&, double*, double& |
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203 F77_CHAR_ARG_LEN_DECL); |
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204 } |
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205 |
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206 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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207 |
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208 // Complex Matrix class |
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209 |
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210 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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211 : MArray2<Complex> (a.rows (), a.cols ()) |
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212 { |
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213 for (octave_idx_type j = 0; j < cols (); j++) |
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214 for (octave_idx_type i = 0; i < rows (); i++) |
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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 RowVector& rv) |
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219 : MArray2<Complex> (1, rv.length (), 0.0) |
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220 { |
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221 for (octave_idx_type i = 0; i < rv.length (); i++) |
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222 elem (0, i) = rv.elem (i); |
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223 } |
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224 |
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225 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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226 : MArray2<Complex> (cv.length (), 1, 0.0) |
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227 { |
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228 for (octave_idx_type i = 0; i < cv.length (); i++) |
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229 elem (i, 0) = cv.elem (i); |
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230 } |
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231 |
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232 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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233 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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234 { |
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235 for (octave_idx_type i = 0; i < a.length (); i++) |
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236 elem (i, i) = a.elem (i, i); |
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237 } |
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238 |
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239 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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240 : MArray2<Complex> (1, rv.length (), 0.0) |
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241 { |
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242 for (octave_idx_type i = 0; i < rv.length (); i++) |
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243 elem (0, i) = rv.elem (i); |
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244 } |
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245 |
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246 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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247 : MArray2<Complex> (cv.length (), 1, 0.0) |
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248 { |
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249 for (octave_idx_type i = 0; i < cv.length (); i++) |
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250 elem (i, 0) = cv.elem (i); |
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251 } |
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252 |
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458
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253 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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254 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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255 { |
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256 for (octave_idx_type i = 0; i < a.length (); i++) |
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257 elem (i, i) = a.elem (i, i); |
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258 } |
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259 |
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260 // FIXME -- could we use a templated mixed-type copy function |
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261 // here? |
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262 |
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263 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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3180
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264 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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265 { |
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266 for (octave_idx_type i = 0; i < a.rows (); i++) |
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267 for (octave_idx_type j = 0; j < a.cols (); j++) |
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268 elem (i, j) = a.elem (i, j); |
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269 } |
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270 |
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1574
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271 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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3180
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272 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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273 { |
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5275
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274 for (octave_idx_type i = 0; i < a.rows (); i++) |
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275 for (octave_idx_type j = 0; j < a.cols (); j++) |
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1574
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276 elem (i, j) = a.elem (i, j); |
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277 } |
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278 |
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2384
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279 bool |
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458
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280 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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281 { |
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282 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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283 return false; |
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458
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284 |
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3769
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285 return mx_inline_equal (data (), a.data (), length ()); |
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458
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286 } |
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287 |
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2384
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288 bool |
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458
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289 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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290 { |
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291 return !(*this == a); |
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292 } |
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293 |
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2815
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294 bool |
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295 ComplexMatrix::is_hermitian (void) const |
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296 { |
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5275
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297 octave_idx_type nr = rows (); |
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298 octave_idx_type nc = cols (); |
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299 |
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300 if (is_square () && nr > 0) |
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301 { |
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302 for (octave_idx_type i = 0; i < nr; i++) |
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303 for (octave_idx_type j = i; j < nc; j++) |
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2815
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304 if (elem (i, j) != conj (elem (j, i))) |
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305 return false; |
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306 |
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307 return true; |
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308 } |
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309 |
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310 return false; |
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311 } |
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312 |
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458
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313 // destructive insert/delete/reorder operations |
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314 |
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315 ComplexMatrix& |
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5275
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316 ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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317 { |
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5275
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318 octave_idx_type a_nr = a.rows (); |
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319 octave_idx_type a_nc = a.cols (); |
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320 |
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321 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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322 { |
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323 (*current_liboctave_error_handler) ("range error for insert"); |
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324 return *this; |
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325 } |
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326 |
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4316
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327 if (a_nr >0 && a_nc > 0) |
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328 { |
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329 make_unique (); |
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330 |
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5275
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331 for (octave_idx_type j = 0; j < a_nc; j++) |
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332 for (octave_idx_type i = 0; i < a_nr; i++) |
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333 xelem (r+i, c+j) = a.elem (i, j); |
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334 } |
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458
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335 |
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336 return *this; |
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337 } |
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338 |
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339 ComplexMatrix& |
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5275
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340 ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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341 { |
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5275
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342 octave_idx_type a_len = a.length (); |
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4316
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343 |
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1699
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344 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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345 { |
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346 (*current_liboctave_error_handler) ("range error for insert"); |
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347 return *this; |
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348 } |
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349 |
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4316
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350 if (a_len > 0) |
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351 { |
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352 make_unique (); |
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353 |
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5275
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354 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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355 xelem (r, c+i) = a.elem (i); |
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356 } |
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458
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357 |
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358 return *this; |
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359 } |
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360 |
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361 ComplexMatrix& |
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5275
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362 ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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363 { |
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5275
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364 octave_idx_type a_len = a.length (); |
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4316
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365 |
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1699
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366 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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367 { |
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368 (*current_liboctave_error_handler) ("range error for insert"); |
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369 return *this; |
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370 } |
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371 |
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4316
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372 if (a_len > 0) |
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373 { |
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374 make_unique (); |
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375 |
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5275
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376 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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377 xelem (r+i, c) = a.elem (i); |
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378 } |
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458
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379 |
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380 return *this; |
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381 } |
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382 |
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383 ComplexMatrix& |
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5275
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384 ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
385 { |
|
5275
|
386 octave_idx_type a_nr = a.rows (); |
|
|
387 octave_idx_type a_nc = a.cols (); |
|
1699
|
388 |
|
|
389 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
390 { |
|
|
391 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
392 return *this; |
|
|
393 } |
|
|
394 |
|
1699
|
395 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
396 |
|
5275
|
397 octave_idx_type a_len = a.length (); |
|
4316
|
398 |
|
|
399 if (a_len > 0) |
|
|
400 { |
|
|
401 make_unique (); |
|
|
402 |
|
5275
|
403 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
404 xelem (r+i, c+i) = a.elem (i, i); |
|
|
405 } |
|
458
|
406 |
|
|
407 return *this; |
|
|
408 } |
|
|
409 |
|
|
410 ComplexMatrix& |
|
5275
|
411 ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
412 { |
|
1561
|
413 Array2<Complex>::insert (a, r, c); |
|
458
|
414 return *this; |
|
|
415 } |
|
|
416 |
|
|
417 ComplexMatrix& |
|
5275
|
418 ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) |
|
458
|
419 { |
|
5275
|
420 octave_idx_type a_len = a.length (); |
|
1699
|
421 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
|
458
|
422 { |
|
|
423 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
424 return *this; |
|
|
425 } |
|
|
426 |
|
5275
|
427 for (octave_idx_type i = 0; i < a_len; i++) |
|
458
|
428 elem (r, c+i) = a.elem (i); |
|
|
429 |
|
|
430 return *this; |
|
|
431 } |
|
|
432 |
|
|
433 ComplexMatrix& |
|
5275
|
434 ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) |
|
458
|
435 { |
|
5275
|
436 octave_idx_type a_len = a.length (); |
|
4316
|
437 |
|
1699
|
438 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
|
458
|
439 { |
|
|
440 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
441 return *this; |
|
|
442 } |
|
|
443 |
|
4316
|
444 if (a_len > 0) |
|
|
445 { |
|
|
446 make_unique (); |
|
|
447 |
|
5275
|
448 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
449 xelem (r+i, c) = a.elem (i); |
|
|
450 } |
|
458
|
451 |
|
|
452 return *this; |
|
|
453 } |
|
|
454 |
|
|
455 ComplexMatrix& |
|
5275
|
456 ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
457 { |
|
5275
|
458 octave_idx_type a_nr = a.rows (); |
|
|
459 octave_idx_type a_nc = a.cols (); |
|
1699
|
460 |
|
|
461 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
462 { |
|
|
463 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
464 return *this; |
|
|
465 } |
|
|
466 |
|
1699
|
467 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
468 |
|
5275
|
469 octave_idx_type a_len = a.length (); |
|
4316
|
470 |
|
|
471 if (a_len > 0) |
|
|
472 { |
|
|
473 make_unique (); |
|
|
474 |
|
5275
|
475 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
476 xelem (r+i, c+i) = a.elem (i, i); |
|
|
477 } |
|
458
|
478 |
|
|
479 return *this; |
|
|
480 } |
|
|
481 |
|
|
482 ComplexMatrix& |
|
|
483 ComplexMatrix::fill (double val) |
|
|
484 { |
|
5275
|
485 octave_idx_type nr = rows (); |
|
|
486 octave_idx_type nc = cols (); |
|
4316
|
487 |
|
458
|
488 if (nr > 0 && nc > 0) |
|
4316
|
489 { |
|
|
490 make_unique (); |
|
|
491 |
|
5275
|
492 for (octave_idx_type j = 0; j < nc; j++) |
|
|
493 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
494 xelem (i, j) = val; |
|
|
495 } |
|
458
|
496 |
|
|
497 return *this; |
|
|
498 } |
|
|
499 |
|
|
500 ComplexMatrix& |
|
|
501 ComplexMatrix::fill (const Complex& val) |
|
|
502 { |
|
5275
|
503 octave_idx_type nr = rows (); |
|
|
504 octave_idx_type nc = cols (); |
|
4316
|
505 |
|
458
|
506 if (nr > 0 && nc > 0) |
|
4316
|
507 { |
|
|
508 make_unique (); |
|
|
509 |
|
5275
|
510 for (octave_idx_type j = 0; j < nc; j++) |
|
|
511 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
512 xelem (i, j) = val; |
|
|
513 } |
|
458
|
514 |
|
|
515 return *this; |
|
|
516 } |
|
|
517 |
|
|
518 ComplexMatrix& |
|
5275
|
519 ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
520 { |
|
5275
|
521 octave_idx_type nr = rows (); |
|
|
522 octave_idx_type nc = cols (); |
|
4316
|
523 |
|
458
|
524 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
525 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
526 { |
|
|
527 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
528 return *this; |
|
|
529 } |
|
|
530 |
|
5275
|
531 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
532 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
533 |
|
4316
|
534 if (r2 >= r1 && c2 >= c1) |
|
|
535 { |
|
|
536 make_unique (); |
|
|
537 |
|
5275
|
538 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
539 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
540 xelem (i, j) = val; |
|
|
541 } |
|
458
|
542 |
|
|
543 return *this; |
|
|
544 } |
|
|
545 |
|
|
546 ComplexMatrix& |
|
5275
|
547 ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
548 { |
|
5275
|
549 octave_idx_type nr = rows (); |
|
|
550 octave_idx_type nc = cols (); |
|
4316
|
551 |
|
458
|
552 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
553 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
554 { |
|
|
555 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
556 return *this; |
|
|
557 } |
|
|
558 |
|
5275
|
559 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
560 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
561 |
|
4316
|
562 if (r2 >= r1 && c2 >=c1) |
|
|
563 { |
|
|
564 make_unique (); |
|
|
565 |
|
5275
|
566 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
567 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
568 xelem (i, j) = val; |
|
|
569 } |
|
458
|
570 |
|
|
571 return *this; |
|
|
572 } |
|
|
573 |
|
|
574 ComplexMatrix |
|
|
575 ComplexMatrix::append (const Matrix& a) const |
|
|
576 { |
|
5275
|
577 octave_idx_type nr = rows (); |
|
|
578 octave_idx_type nc = cols (); |
|
458
|
579 if (nr != a.rows ()) |
|
|
580 { |
|
|
581 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
582 return *this; |
|
|
583 } |
|
|
584 |
|
5275
|
585 octave_idx_type nc_insert = nc; |
|
458
|
586 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
587 retval.insert (*this, 0, 0); |
|
|
588 retval.insert (a, 0, nc_insert); |
|
|
589 return retval; |
|
|
590 } |
|
|
591 |
|
|
592 ComplexMatrix |
|
|
593 ComplexMatrix::append (const RowVector& a) const |
|
|
594 { |
|
5275
|
595 octave_idx_type nr = rows (); |
|
|
596 octave_idx_type nc = cols (); |
|
458
|
597 if (nr != 1) |
|
|
598 { |
|
|
599 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
600 return *this; |
|
|
601 } |
|
|
602 |
|
5275
|
603 octave_idx_type nc_insert = nc; |
|
458
|
604 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
605 retval.insert (*this, 0, 0); |
|
|
606 retval.insert (a, 0, nc_insert); |
|
|
607 return retval; |
|
|
608 } |
|
|
609 |
|
|
610 ComplexMatrix |
|
|
611 ComplexMatrix::append (const ColumnVector& a) const |
|
|
612 { |
|
5275
|
613 octave_idx_type nr = rows (); |
|
|
614 octave_idx_type nc = cols (); |
|
458
|
615 if (nr != a.length ()) |
|
|
616 { |
|
|
617 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
618 return *this; |
|
|
619 } |
|
|
620 |
|
5275
|
621 octave_idx_type nc_insert = nc; |
|
458
|
622 ComplexMatrix retval (nr, nc + 1); |
|
|
623 retval.insert (*this, 0, 0); |
|
|
624 retval.insert (a, 0, nc_insert); |
|
|
625 return retval; |
|
|
626 } |
|
|
627 |
|
|
628 ComplexMatrix |
|
|
629 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
630 { |
|
5275
|
631 octave_idx_type nr = rows (); |
|
|
632 octave_idx_type nc = cols (); |
|
458
|
633 if (nr != a.rows ()) |
|
|
634 { |
|
|
635 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
636 return *this; |
|
|
637 } |
|
|
638 |
|
5275
|
639 octave_idx_type nc_insert = nc; |
|
458
|
640 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
641 retval.insert (*this, 0, 0); |
|
|
642 retval.insert (a, 0, nc_insert); |
|
|
643 return retval; |
|
|
644 } |
|
|
645 |
|
|
646 ComplexMatrix |
|
|
647 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
648 { |
|
5275
|
649 octave_idx_type nr = rows (); |
|
|
650 octave_idx_type nc = cols (); |
|
458
|
651 if (nr != a.rows ()) |
|
|
652 { |
|
|
653 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
654 return *this; |
|
|
655 } |
|
|
656 |
|
5275
|
657 octave_idx_type nc_insert = nc; |
|
458
|
658 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
659 retval.insert (*this, 0, 0); |
|
|
660 retval.insert (a, 0, nc_insert); |
|
|
661 return retval; |
|
|
662 } |
|
|
663 |
|
|
664 ComplexMatrix |
|
|
665 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
666 { |
|
5275
|
667 octave_idx_type nr = rows (); |
|
|
668 octave_idx_type nc = cols (); |
|
458
|
669 if (nr != 1) |
|
|
670 { |
|
|
671 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
672 return *this; |
|
|
673 } |
|
|
674 |
|
5275
|
675 octave_idx_type nc_insert = nc; |
|
458
|
676 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
677 retval.insert (*this, 0, 0); |
|
|
678 retval.insert (a, 0, nc_insert); |
|
|
679 return retval; |
|
|
680 } |
|
|
681 |
|
|
682 ComplexMatrix |
|
|
683 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
684 { |
|
5275
|
685 octave_idx_type nr = rows (); |
|
|
686 octave_idx_type nc = cols (); |
|
458
|
687 if (nr != a.length ()) |
|
|
688 { |
|
|
689 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
690 return *this; |
|
|
691 } |
|
|
692 |
|
5275
|
693 octave_idx_type nc_insert = nc; |
|
458
|
694 ComplexMatrix retval (nr, nc + 1); |
|
|
695 retval.insert (*this, 0, 0); |
|
|
696 retval.insert (a, 0, nc_insert); |
|
|
697 return retval; |
|
|
698 } |
|
|
699 |
|
|
700 ComplexMatrix |
|
|
701 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
702 { |
|
5275
|
703 octave_idx_type nr = rows (); |
|
|
704 octave_idx_type nc = cols (); |
|
458
|
705 if (nr != a.rows ()) |
|
|
706 { |
|
|
707 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
708 return *this; |
|
|
709 } |
|
|
710 |
|
5275
|
711 octave_idx_type nc_insert = nc; |
|
458
|
712 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
713 retval.insert (*this, 0, 0); |
|
|
714 retval.insert (a, 0, nc_insert); |
|
|
715 return retval; |
|
|
716 } |
|
|
717 |
|
|
718 ComplexMatrix |
|
|
719 ComplexMatrix::stack (const Matrix& a) const |
|
|
720 { |
|
5275
|
721 octave_idx_type nr = rows (); |
|
|
722 octave_idx_type nc = cols (); |
|
458
|
723 if (nc != a.cols ()) |
|
|
724 { |
|
|
725 (*current_liboctave_error_handler) |
|
|
726 ("column dimension mismatch for stack"); |
|
|
727 return *this; |
|
|
728 } |
|
|
729 |
|
5275
|
730 octave_idx_type nr_insert = nr; |
|
458
|
731 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
732 retval.insert (*this, 0, 0); |
|
|
733 retval.insert (a, nr_insert, 0); |
|
|
734 return retval; |
|
|
735 } |
|
|
736 |
|
|
737 ComplexMatrix |
|
|
738 ComplexMatrix::stack (const RowVector& a) const |
|
|
739 { |
|
5275
|
740 octave_idx_type nr = rows (); |
|
|
741 octave_idx_type nc = cols (); |
|
458
|
742 if (nc != a.length ()) |
|
|
743 { |
|
|
744 (*current_liboctave_error_handler) |
|
|
745 ("column dimension mismatch for stack"); |
|
|
746 return *this; |
|
|
747 } |
|
|
748 |
|
5275
|
749 octave_idx_type nr_insert = nr; |
|
458
|
750 ComplexMatrix retval (nr + 1, nc); |
|
|
751 retval.insert (*this, 0, 0); |
|
|
752 retval.insert (a, nr_insert, 0); |
|
|
753 return retval; |
|
|
754 } |
|
|
755 |
|
|
756 ComplexMatrix |
|
|
757 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
758 { |
|
5275
|
759 octave_idx_type nr = rows (); |
|
|
760 octave_idx_type nc = cols (); |
|
458
|
761 if (nc != 1) |
|
|
762 { |
|
|
763 (*current_liboctave_error_handler) |
|
|
764 ("column dimension mismatch for stack"); |
|
|
765 return *this; |
|
|
766 } |
|
|
767 |
|
5275
|
768 octave_idx_type nr_insert = nr; |
|
458
|
769 ComplexMatrix retval (nr + a.length (), nc); |
|
|
770 retval.insert (*this, 0, 0); |
|
|
771 retval.insert (a, nr_insert, 0); |
|
|
772 return retval; |
|
|
773 } |
|
|
774 |
|
|
775 ComplexMatrix |
|
|
776 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
777 { |
|
5275
|
778 octave_idx_type nr = rows (); |
|
|
779 octave_idx_type nc = cols (); |
|
458
|
780 if (nc != a.cols ()) |
|
|
781 { |
|
|
782 (*current_liboctave_error_handler) |
|
|
783 ("column dimension mismatch for stack"); |
|
|
784 return *this; |
|
|
785 } |
|
|
786 |
|
5275
|
787 octave_idx_type nr_insert = nr; |
|
458
|
788 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
789 retval.insert (*this, 0, 0); |
|
|
790 retval.insert (a, nr_insert, 0); |
|
|
791 return retval; |
|
|
792 } |
|
|
793 |
|
|
794 ComplexMatrix |
|
|
795 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
796 { |
|
5275
|
797 octave_idx_type nr = rows (); |
|
|
798 octave_idx_type nc = cols (); |
|
458
|
799 if (nc != a.cols ()) |
|
|
800 { |
|
|
801 (*current_liboctave_error_handler) |
|
|
802 ("column dimension mismatch for stack"); |
|
|
803 return *this; |
|
|
804 } |
|
|
805 |
|
5275
|
806 octave_idx_type nr_insert = nr; |
|
458
|
807 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
808 retval.insert (*this, 0, 0); |
|
|
809 retval.insert (a, nr_insert, 0); |
|
|
810 return retval; |
|
|
811 } |
|
|
812 |
|
|
813 ComplexMatrix |
|
|
814 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
815 { |
|
5275
|
816 octave_idx_type nr = rows (); |
|
|
817 octave_idx_type nc = cols (); |
|
458
|
818 if (nc != a.length ()) |
|
|
819 { |
|
|
820 (*current_liboctave_error_handler) |
|
|
821 ("column dimension mismatch for stack"); |
|
|
822 return *this; |
|
|
823 } |
|
|
824 |
|
5275
|
825 octave_idx_type nr_insert = nr; |
|
458
|
826 ComplexMatrix retval (nr + 1, nc); |
|
|
827 retval.insert (*this, 0, 0); |
|
|
828 retval.insert (a, nr_insert, 0); |
|
|
829 return retval; |
|
|
830 } |
|
|
831 |
|
|
832 ComplexMatrix |
|
|
833 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
834 { |
|
5275
|
835 octave_idx_type nr = rows (); |
|
|
836 octave_idx_type nc = cols (); |
|
458
|
837 if (nc != 1) |
|
|
838 { |
|
|
839 (*current_liboctave_error_handler) |
|
|
840 ("column dimension mismatch for stack"); |
|
|
841 return *this; |
|
|
842 } |
|
|
843 |
|
5275
|
844 octave_idx_type nr_insert = nr; |
|
458
|
845 ComplexMatrix retval (nr + a.length (), nc); |
|
|
846 retval.insert (*this, 0, 0); |
|
|
847 retval.insert (a, nr_insert, 0); |
|
|
848 return retval; |
|
|
849 } |
|
|
850 |
|
|
851 ComplexMatrix |
|
|
852 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
853 { |
|
5275
|
854 octave_idx_type nr = rows (); |
|
|
855 octave_idx_type nc = cols (); |
|
458
|
856 if (nc != a.cols ()) |
|
|
857 { |
|
|
858 (*current_liboctave_error_handler) |
|
|
859 ("column dimension mismatch for stack"); |
|
|
860 return *this; |
|
|
861 } |
|
|
862 |
|
5275
|
863 octave_idx_type nr_insert = nr; |
|
458
|
864 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
865 retval.insert (*this, 0, 0); |
|
|
866 retval.insert (a, nr_insert, 0); |
|
|
867 return retval; |
|
|
868 } |
|
|
869 |
|
|
870 ComplexMatrix |
|
|
871 ComplexMatrix::hermitian (void) const |
|
|
872 { |
|
5275
|
873 octave_idx_type nr = rows (); |
|
|
874 octave_idx_type nc = cols (); |
|
458
|
875 ComplexMatrix result; |
|
|
876 if (length () > 0) |
|
|
877 { |
|
|
878 result.resize (nc, nr); |
|
5275
|
879 for (octave_idx_type j = 0; j < nc; j++) |
|
|
880 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
881 result.elem (j, i) = conj (elem (i, j)); |
|
|
882 } |
|
|
883 return result; |
|
|
884 } |
|
|
885 |
|
|
886 ComplexMatrix |
|
|
887 conj (const ComplexMatrix& a) |
|
|
888 { |
|
5275
|
889 octave_idx_type a_len = a.length (); |
|
458
|
890 ComplexMatrix retval; |
|
|
891 if (a_len > 0) |
|
3769
|
892 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
|
|
893 a.rows (), a.cols ()); |
|
458
|
894 return retval; |
|
|
895 } |
|
|
896 |
|
|
897 // resize is the destructive equivalent for this one |
|
|
898 |
|
|
899 ComplexMatrix |
|
5275
|
900 ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
901 { |
|
5275
|
902 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
903 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
904 |
|
|
905 octave_idx_type new_r = r2 - r1 + 1; |
|
|
906 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
907 |
|
|
908 ComplexMatrix result (new_r, new_c); |
|
|
909 |
|
5275
|
910 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
911 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
912 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
913 |
|
|
914 return result; |
|
|
915 } |
|
|
916 |
|
|
917 ComplexMatrix |
|
5275
|
918 ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
919 { |
|
|
920 ComplexMatrix result (nr, nc); |
|
|
921 |
|
5275
|
922 for (octave_idx_type j = 0; j < nc; j++) |
|
|
923 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
924 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
925 |
|
|
926 return result; |
|
|
927 } |
|
|
928 |
|
|
929 // extract row or column i. |
|
|
930 |
|
|
931 ComplexRowVector |
|
5275
|
932 ComplexMatrix::row (octave_idx_type i) const |
|
458
|
933 { |
|
5275
|
934 octave_idx_type nc = cols (); |
|
458
|
935 if (i < 0 || i >= rows ()) |
|
|
936 { |
|
|
937 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
938 return ComplexRowVector (); |
|
|
939 } |
|
|
940 |
|
|
941 ComplexRowVector retval (nc); |
|
5275
|
942 for (octave_idx_type j = 0; j < cols (); j++) |
|
4316
|
943 retval.xelem (j) = elem (i, j); |
|
458
|
944 |
|
|
945 return retval; |
|
|
946 } |
|
|
947 |
|
|
948 ComplexColumnVector |
|
5275
|
949 ComplexMatrix::column (octave_idx_type i) const |
|
458
|
950 { |
|
5275
|
951 octave_idx_type nr = rows (); |
|
458
|
952 if (i < 0 || i >= cols ()) |
|
|
953 { |
|
|
954 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
955 return ComplexColumnVector (); |
|
|
956 } |
|
|
957 |
|
|
958 ComplexColumnVector retval (nr); |
|
5275
|
959 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
960 retval.xelem (j) = elem (j, i); |
|
458
|
961 |
|
|
962 return retval; |
|
|
963 } |
|
|
964 |
|
|
965 ComplexMatrix |
|
|
966 ComplexMatrix::inverse (void) const |
|
|
967 { |
|
5275
|
968 octave_idx_type info; |
|
479
|
969 double rcond; |
|
6207
|
970 MatrixType mattype (*this); |
|
|
971 return inverse (mattype, info, rcond, 0, 0); |
|
|
972 } |
|
|
973 |
|
|
974 ComplexMatrix |
|
|
975 ComplexMatrix::inverse (MatrixType &mattype) const |
|
|
976 { |
|
|
977 octave_idx_type info; |
|
|
978 double rcond; |
|
|
979 return inverse (mattype, info, rcond, 0, 0); |
|
|
980 } |
|
|
981 |
|
|
982 ComplexMatrix |
|
|
983 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const |
|
|
984 { |
|
|
985 double rcond; |
|
|
986 return inverse (mattype, info, rcond, 0, 0); |
|
458
|
987 } |
|
|
988 |
|
|
989 ComplexMatrix |
|
6207
|
990 ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, |
|
|
991 double& rcond, int force, int calc_cond) const |
|
458
|
992 { |
|
6207
|
993 ComplexMatrix retval; |
|
|
994 |
|
|
995 octave_idx_type nr = rows (); |
|
|
996 octave_idx_type nc = cols (); |
|
|
997 |
|
|
998 if (nr != nc || nr == 0 || nc == 0) |
|
|
999 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
1000 else |
|
|
1001 { |
|
|
1002 int typ = mattype.type (); |
|
|
1003 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); |
|
|
1004 char udiag = 'N'; |
|
|
1005 retval = *this; |
|
|
1006 Complex *tmp_data = retval.fortran_vec (); |
|
|
1007 |
|
|
1008 F77_XFCN (ztrtri, ZTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1009 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
1010 nr, tmp_data, nr, info |
|
|
1011 F77_CHAR_ARG_LEN (1) |
|
|
1012 F77_CHAR_ARG_LEN (1))); |
|
|
1013 |
|
|
1014 if (f77_exception_encountered) |
|
|
1015 (*current_liboctave_error_handler) ("unrecoverable error in ztrtri"); |
|
|
1016 else |
|
|
1017 { |
|
|
1018 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1019 rcond = 0.0; |
|
|
1020 if (info != 0) |
|
|
1021 info = -1; |
|
|
1022 else if (calc_cond) |
|
|
1023 { |
|
|
1024 octave_idx_type ztrcon_info = 0; |
|
|
1025 char job = '1'; |
|
|
1026 |
|
|
1027 OCTAVE_LOCAL_BUFFER (Complex, cwork, 2 * nr); |
|
|
1028 OCTAVE_LOCAL_BUFFER (double, rwork, nr); |
|
|
1029 |
|
|
1030 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1031 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1032 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
1033 nr, tmp_data, nr, rcond, |
|
|
1034 cwork, rwork, ztrcon_info |
|
|
1035 F77_CHAR_ARG_LEN (1) |
|
|
1036 F77_CHAR_ARG_LEN (1) |
|
|
1037 F77_CHAR_ARG_LEN (1))); |
|
|
1038 |
|
|
1039 if (f77_exception_encountered) |
|
|
1040 (*current_liboctave_error_handler) |
|
|
1041 ("unrecoverable error in ztrcon"); |
|
|
1042 |
|
|
1043 if (ztrcon_info != 0) |
|
|
1044 info = -1; |
|
|
1045 } |
|
|
1046 } |
|
|
1047 |
|
|
1048 if (info == -1 && ! force) |
|
|
1049 retval = *this; // Restore matrix contents. |
|
|
1050 } |
|
|
1051 |
|
|
1052 return retval; |
|
458
|
1053 } |
|
|
1054 |
|
|
1055 ComplexMatrix |
|
6207
|
1056 ComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, |
|
|
1057 double& rcond, int force, int calc_cond) const |
|
458
|
1058 { |
|
1948
|
1059 ComplexMatrix retval; |
|
|
1060 |
|
5275
|
1061 octave_idx_type nr = rows (); |
|
|
1062 octave_idx_type nc = cols (); |
|
1948
|
1063 |
|
458
|
1064 if (nr != nc) |
|
1948
|
1065 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
1066 else |
|
|
1067 { |
|
5275
|
1068 Array<octave_idx_type> ipvt (nr); |
|
|
1069 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1070 |
|
|
1071 retval = *this; |
|
|
1072 Complex *tmp_data = retval.fortran_vec (); |
|
|
1073 |
|
4329
|
1074 Array<Complex> z(1); |
|
5275
|
1075 octave_idx_type lwork = -1; |
|
4330
|
1076 |
|
|
1077 // Query the optimum work array size. |
|
4329
|
1078 |
|
|
1079 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
|
1080 z.fortran_vec (), lwork, info)); |
|
|
1081 |
|
|
1082 if (f77_exception_encountered) |
|
|
1083 { |
|
|
1084 (*current_liboctave_error_handler) |
|
|
1085 ("unrecoverable error in zgetri"); |
|
|
1086 return retval; |
|
|
1087 } |
|
|
1088 |
|
5315
|
1089 lwork = static_cast<octave_idx_type> (std::real(z(0))); |
|
4329
|
1090 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
1091 z.resize (lwork); |
|
|
1092 Complex *pz = z.fortran_vec (); |
|
|
1093 |
|
|
1094 info = 0; |
|
|
1095 |
|
4330
|
1096 // Calculate the norm of the matrix, for later use. |
|
4329
|
1097 double anorm; |
|
|
1098 if (calc_cond) |
|
5275
|
1099 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1100 |
|
|
1101 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1102 |
|
|
1103 if (f77_exception_encountered) |
|
4329
|
1104 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1105 else |
|
|
1106 { |
|
4330
|
1107 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1108 rcond = 0.0; |
|
|
1109 if (info != 0) |
|
1948
|
1110 info = -1; |
|
4329
|
1111 else if (calc_cond) |
|
|
1112 { |
|
4330
|
1113 // Now calculate the condition number for non-singular matrix. |
|
5275
|
1114 octave_idx_type zgecon_info = 0; |
|
4329
|
1115 char job = '1'; |
|
|
1116 Array<double> rz (2 * nc); |
|
|
1117 double *prz = rz.fortran_vec (); |
|
4552
|
1118 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1119 nc, tmp_data, nr, anorm, |
|
5061
|
1120 rcond, pz, prz, zgecon_info |
|
4552
|
1121 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1122 |
|
|
1123 if (f77_exception_encountered) |
|
|
1124 (*current_liboctave_error_handler) |
|
|
1125 ("unrecoverable error in zgecon"); |
|
|
1126 |
|
5061
|
1127 if (zgecon_info != 0) |
|
4329
|
1128 info = -1; |
|
|
1129 } |
|
1948
|
1130 |
|
|
1131 if (info == -1 && ! force) |
|
|
1132 retval = *this; // Restore contents. |
|
|
1133 else |
|
|
1134 { |
|
5275
|
1135 octave_idx_type zgetri_info = 0; |
|
5061
|
1136 |
|
4329
|
1137 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
1138 pz, lwork, zgetri_info)); |
|
1948
|
1139 |
|
|
1140 if (f77_exception_encountered) |
|
|
1141 (*current_liboctave_error_handler) |
|
4329
|
1142 ("unrecoverable error in zgetri"); |
|
|
1143 |
|
5061
|
1144 if (zgetri_info != 0) |
|
4329
|
1145 info = -1; |
|
1948
|
1146 } |
|
|
1147 } |
|
6207
|
1148 |
|
|
1149 if (info != 0) |
|
|
1150 mattype.mark_as_rectangular(); |
|
458
|
1151 } |
|
4329
|
1152 |
|
1948
|
1153 return retval; |
|
458
|
1154 } |
|
|
1155 |
|
|
1156 ComplexMatrix |
|
6207
|
1157 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, |
|
|
1158 double& rcond, int force, int calc_cond) const |
|
|
1159 { |
|
|
1160 int typ = mattype.type (false); |
|
|
1161 ComplexMatrix ret; |
|
|
1162 |
|
|
1163 if (typ == MatrixType::Unknown) |
|
|
1164 typ = mattype.type (*this); |
|
|
1165 |
|
|
1166 if (typ == MatrixType::Upper || typ == MatrixType::Lower) |
|
|
1167 ret = tinverse (mattype, info, rcond, force, calc_cond); |
|
|
1168 else if (typ != MatrixType::Rectangular) |
|
|
1169 { |
|
|
1170 if (mattype.is_hermitian ()) |
|
|
1171 { |
|
|
1172 ComplexCHOL chol (*this, info); |
|
|
1173 if (info == 0) |
|
|
1174 ret = chol.inverse (); |
|
|
1175 else |
|
|
1176 mattype.mark_as_unsymmetric (); |
|
|
1177 } |
|
|
1178 |
|
|
1179 if (!mattype.is_hermitian ()) |
|
|
1180 ret = finverse(mattype, info, rcond, force, calc_cond); |
|
|
1181 } |
|
|
1182 |
|
|
1183 return ret; |
|
|
1184 } |
|
|
1185 |
|
|
1186 ComplexMatrix |
|
4384
|
1187 ComplexMatrix::pseudo_inverse (double tol) const |
|
740
|
1188 { |
|
1549
|
1189 ComplexMatrix retval; |
|
|
1190 |
|
3480
|
1191 ComplexSVD result (*this, SVD::economy); |
|
740
|
1192 |
|
|
1193 DiagMatrix S = result.singular_values (); |
|
|
1194 ComplexMatrix U = result.left_singular_matrix (); |
|
|
1195 ComplexMatrix V = result.right_singular_matrix (); |
|
|
1196 |
|
|
1197 ColumnVector sigma = S.diag (); |
|
|
1198 |
|
5275
|
1199 octave_idx_type r = sigma.length () - 1; |
|
|
1200 octave_idx_type nr = rows (); |
|
|
1201 octave_idx_type nc = cols (); |
|
740
|
1202 |
|
|
1203 if (tol <= 0.0) |
|
|
1204 { |
|
|
1205 if (nr > nc) |
|
|
1206 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
1207 else |
|
|
1208 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
1209 } |
|
|
1210 |
|
|
1211 while (r >= 0 && sigma.elem (r) < tol) |
|
|
1212 r--; |
|
|
1213 |
|
|
1214 if (r < 0) |
|
1549
|
1215 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
1216 else |
|
|
1217 { |
|
|
1218 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
1219 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
1220 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
1221 retval = Vr * D * Ur.hermitian (); |
|
740
|
1222 } |
|
1549
|
1223 |
|
|
1224 return retval; |
|
740
|
1225 } |
|
|
1226 |
|
4773
|
1227 #if defined (HAVE_FFTW3) |
|
3827
|
1228 |
|
|
1229 ComplexMatrix |
|
|
1230 ComplexMatrix::fourier (void) const |
|
|
1231 { |
|
|
1232 size_t nr = rows (); |
|
|
1233 size_t nc = cols (); |
|
|
1234 |
|
|
1235 ComplexMatrix retval (nr, nc); |
|
|
1236 |
|
|
1237 size_t npts, nsamples; |
|
|
1238 |
|
|
1239 if (nr == 1 || nc == 1) |
|
|
1240 { |
|
|
1241 npts = nr > nc ? nr : nc; |
|
|
1242 nsamples = 1; |
|
|
1243 } |
|
|
1244 else |
|
|
1245 { |
|
|
1246 npts = nr; |
|
|
1247 nsamples = nc; |
|
|
1248 } |
|
|
1249 |
|
|
1250 const Complex *in (data ()); |
|
|
1251 Complex *out (retval.fortran_vec ()); |
|
|
1252 |
|
4773
|
1253 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
1254 |
|
|
1255 return retval; |
|
|
1256 } |
|
|
1257 |
|
|
1258 ComplexMatrix |
|
|
1259 ComplexMatrix::ifourier (void) const |
|
|
1260 { |
|
|
1261 size_t nr = rows (); |
|
|
1262 size_t nc = cols (); |
|
|
1263 |
|
|
1264 ComplexMatrix retval (nr, nc); |
|
|
1265 |
|
|
1266 size_t npts, nsamples; |
|
|
1267 |
|
|
1268 if (nr == 1 || nc == 1) |
|
|
1269 { |
|
|
1270 npts = nr > nc ? nr : nc; |
|
|
1271 nsamples = 1; |
|
|
1272 } |
|
|
1273 else |
|
|
1274 { |
|
|
1275 npts = nr; |
|
|
1276 nsamples = nc; |
|
|
1277 } |
|
|
1278 |
|
|
1279 const Complex *in (data ()); |
|
|
1280 Complex *out (retval.fortran_vec ()); |
|
|
1281 |
|
4773
|
1282 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
1283 |
|
|
1284 return retval; |
|
|
1285 } |
|
|
1286 |
|
|
1287 ComplexMatrix |
|
|
1288 ComplexMatrix::fourier2d (void) const |
|
|
1289 { |
|
4773
|
1290 dim_vector dv(rows (), cols ()); |
|
|
1291 |
|
|
1292 ComplexMatrix retval (rows (), cols ()); |
|
|
1293 const Complex *in (data ()); |
|
|
1294 Complex *out (retval.fortran_vec ()); |
|
|
1295 |
|
|
1296 octave_fftw::fftNd (in, out, 2, dv); |
|
3827
|
1297 |
|
|
1298 return retval; |
|
|
1299 } |
|
|
1300 |
|
|
1301 ComplexMatrix |
|
|
1302 ComplexMatrix::ifourier2d (void) const |
|
|
1303 { |
|
4773
|
1304 dim_vector dv(rows (), cols ()); |
|
|
1305 |
|
|
1306 ComplexMatrix retval (rows (), cols ()); |
|
|
1307 const Complex *in (data ()); |
|
|
1308 Complex *out (retval.fortran_vec ()); |
|
|
1309 |
|
|
1310 octave_fftw::ifftNd (in, out, 2, dv); |
|
3827
|
1311 |
|
|
1312 return retval; |
|
|
1313 } |
|
|
1314 |
|
|
1315 #else |
|
|
1316 |
|
740
|
1317 ComplexMatrix |
|
458
|
1318 ComplexMatrix::fourier (void) const |
|
|
1319 { |
|
1948
|
1320 ComplexMatrix retval; |
|
|
1321 |
|
5275
|
1322 octave_idx_type nr = rows (); |
|
|
1323 octave_idx_type nc = cols (); |
|
|
1324 |
|
|
1325 octave_idx_type npts, nsamples; |
|
1948
|
1326 |
|
458
|
1327 if (nr == 1 || nc == 1) |
|
|
1328 { |
|
|
1329 npts = nr > nc ? nr : nc; |
|
|
1330 nsamples = 1; |
|
|
1331 } |
|
|
1332 else |
|
|
1333 { |
|
|
1334 npts = nr; |
|
|
1335 nsamples = nc; |
|
|
1336 } |
|
|
1337 |
|
5275
|
1338 octave_idx_type nn = 4*npts+15; |
|
1948
|
1339 |
|
|
1340 Array<Complex> wsave (nn); |
|
|
1341 Complex *pwsave = wsave.fortran_vec (); |
|
|
1342 |
|
|
1343 retval = *this; |
|
|
1344 Complex *tmp_data = retval.fortran_vec (); |
|
|
1345 |
|
3887
|
1346 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1347 |
|
5275
|
1348 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1349 { |
|
|
1350 OCTAVE_QUIT; |
|
|
1351 |
|
|
1352 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1353 } |
|
1948
|
1354 |
|
|
1355 return retval; |
|
458
|
1356 } |
|
|
1357 |
|
|
1358 ComplexMatrix |
|
|
1359 ComplexMatrix::ifourier (void) const |
|
|
1360 { |
|
1948
|
1361 ComplexMatrix retval; |
|
|
1362 |
|
5275
|
1363 octave_idx_type nr = rows (); |
|
|
1364 octave_idx_type nc = cols (); |
|
|
1365 |
|
|
1366 octave_idx_type npts, nsamples; |
|
1948
|
1367 |
|
458
|
1368 if (nr == 1 || nc == 1) |
|
|
1369 { |
|
|
1370 npts = nr > nc ? nr : nc; |
|
|
1371 nsamples = 1; |
|
|
1372 } |
|
|
1373 else |
|
|
1374 { |
|
|
1375 npts = nr; |
|
|
1376 nsamples = nc; |
|
|
1377 } |
|
|
1378 |
|
5275
|
1379 octave_idx_type nn = 4*npts+15; |
|
1948
|
1380 |
|
|
1381 Array<Complex> wsave (nn); |
|
|
1382 Complex *pwsave = wsave.fortran_vec (); |
|
|
1383 |
|
|
1384 retval = *this; |
|
|
1385 Complex *tmp_data = retval.fortran_vec (); |
|
|
1386 |
|
3887
|
1387 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1388 |
|
5275
|
1389 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1390 { |
|
|
1391 OCTAVE_QUIT; |
|
|
1392 |
|
|
1393 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1394 } |
|
458
|
1395 |
|
5275
|
1396 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1397 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1398 |
|
1948
|
1399 return retval; |
|
458
|
1400 } |
|
|
1401 |
|
677
|
1402 ComplexMatrix |
|
|
1403 ComplexMatrix::fourier2d (void) const |
|
|
1404 { |
|
1948
|
1405 ComplexMatrix retval; |
|
|
1406 |
|
5275
|
1407 octave_idx_type nr = rows (); |
|
|
1408 octave_idx_type nc = cols (); |
|
|
1409 |
|
|
1410 octave_idx_type npts, nsamples; |
|
1948
|
1411 |
|
677
|
1412 if (nr == 1 || nc == 1) |
|
|
1413 { |
|
|
1414 npts = nr > nc ? nr : nc; |
|
|
1415 nsamples = 1; |
|
|
1416 } |
|
|
1417 else |
|
|
1418 { |
|
|
1419 npts = nr; |
|
|
1420 nsamples = nc; |
|
|
1421 } |
|
|
1422 |
|
5275
|
1423 octave_idx_type nn = 4*npts+15; |
|
1948
|
1424 |
|
|
1425 Array<Complex> wsave (nn); |
|
|
1426 Complex *pwsave = wsave.fortran_vec (); |
|
|
1427 |
|
|
1428 retval = *this; |
|
|
1429 Complex *tmp_data = retval.fortran_vec (); |
|
|
1430 |
|
3887
|
1431 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1432 |
|
5275
|
1433 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1434 { |
|
|
1435 OCTAVE_QUIT; |
|
|
1436 |
|
|
1437 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1438 } |
|
677
|
1439 |
|
|
1440 npts = nc; |
|
|
1441 nsamples = nr; |
|
|
1442 nn = 4*npts+15; |
|
1948
|
1443 |
|
|
1444 wsave.resize (nn); |
|
|
1445 pwsave = wsave.fortran_vec (); |
|
|
1446 |
|
4773
|
1447 Array<Complex> tmp (npts); |
|
|
1448 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1449 |
|
3887
|
1450 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1451 |
|
5275
|
1452 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1453 { |
|
4153
|
1454 OCTAVE_QUIT; |
|
|
1455 |
|
5275
|
1456 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1457 prow[i] = tmp_data[i*nr + j]; |
|
|
1458 |
|
3887
|
1459 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1460 |
|
5275
|
1461 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1462 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1463 } |
|
|
1464 |
|
1948
|
1465 return retval; |
|
677
|
1466 } |
|
|
1467 |
|
|
1468 ComplexMatrix |
|
|
1469 ComplexMatrix::ifourier2d (void) const |
|
|
1470 { |
|
1948
|
1471 ComplexMatrix retval; |
|
|
1472 |
|
5275
|
1473 octave_idx_type nr = rows (); |
|
|
1474 octave_idx_type nc = cols (); |
|
|
1475 |
|
|
1476 octave_idx_type npts, nsamples; |
|
1948
|
1477 |
|
677
|
1478 if (nr == 1 || nc == 1) |
|
|
1479 { |
|
|
1480 npts = nr > nc ? nr : nc; |
|
|
1481 nsamples = 1; |
|
|
1482 } |
|
|
1483 else |
|
|
1484 { |
|
|
1485 npts = nr; |
|
|
1486 nsamples = nc; |
|
|
1487 } |
|
|
1488 |
|
5275
|
1489 octave_idx_type nn = 4*npts+15; |
|
1948
|
1490 |
|
|
1491 Array<Complex> wsave (nn); |
|
|
1492 Complex *pwsave = wsave.fortran_vec (); |
|
|
1493 |
|
|
1494 retval = *this; |
|
|
1495 Complex *tmp_data = retval.fortran_vec (); |
|
|
1496 |
|
3887
|
1497 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1498 |
|
5275
|
1499 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1500 { |
|
|
1501 OCTAVE_QUIT; |
|
|
1502 |
|
|
1503 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1504 } |
|
677
|
1505 |
|
5275
|
1506 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1507 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1508 |
|
|
1509 npts = nc; |
|
|
1510 nsamples = nr; |
|
|
1511 nn = 4*npts+15; |
|
1948
|
1512 |
|
|
1513 wsave.resize (nn); |
|
|
1514 pwsave = wsave.fortran_vec (); |
|
|
1515 |
|
4773
|
1516 Array<Complex> tmp (npts); |
|
|
1517 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1518 |
|
3887
|
1519 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1520 |
|
5275
|
1521 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1522 { |
|
4153
|
1523 OCTAVE_QUIT; |
|
|
1524 |
|
5275
|
1525 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1526 prow[i] = tmp_data[i*nr + j]; |
|
|
1527 |
|
3887
|
1528 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1529 |
|
5275
|
1530 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1531 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1532 } |
|
|
1533 |
|
1948
|
1534 return retval; |
|
677
|
1535 } |
|
|
1536 |
|
3827
|
1537 #endif |
|
|
1538 |
|
458
|
1539 ComplexDET |
|
|
1540 ComplexMatrix::determinant (void) const |
|
|
1541 { |
|
5275
|
1542 octave_idx_type info; |
|
458
|
1543 double rcond; |
|
4329
|
1544 return determinant (info, rcond, 0); |
|
458
|
1545 } |
|
|
1546 |
|
|
1547 ComplexDET |
|
5275
|
1548 ComplexMatrix::determinant (octave_idx_type& info) const |
|
458
|
1549 { |
|
|
1550 double rcond; |
|
4329
|
1551 return determinant (info, rcond, 0); |
|
458
|
1552 } |
|
|
1553 |
|
|
1554 ComplexDET |
|
5275
|
1555 ComplexMatrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1556 { |
|
|
1557 ComplexDET retval; |
|
|
1558 |
|
5275
|
1559 octave_idx_type nr = rows (); |
|
|
1560 octave_idx_type nc = cols (); |
|
458
|
1561 |
|
|
1562 if (nr == 0 || nc == 0) |
|
|
1563 { |
|
5634
|
1564 retval = ComplexDET (1.0, 0); |
|
458
|
1565 } |
|
|
1566 else |
|
|
1567 { |
|
5275
|
1568 Array<octave_idx_type> ipvt (nr); |
|
|
1569 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1570 |
|
|
1571 ComplexMatrix atmp = *this; |
|
|
1572 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1573 |
|
4329
|
1574 info = 0; |
|
|
1575 |
|
4330
|
1576 // Calculate the norm of the matrix, for later use. |
|
4329
|
1577 double anorm = 0; |
|
|
1578 if (calc_cond) |
|
5275
|
1579 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1580 |
|
|
1581 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1582 |
|
|
1583 if (f77_exception_encountered) |
|
4329
|
1584 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
458
|
1585 else |
|
|
1586 { |
|
4330
|
1587 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1588 rcond = 0.0; |
|
|
1589 if (info != 0) |
|
1948
|
1590 { |
|
|
1591 info = -1; |
|
|
1592 retval = ComplexDET (); |
|
4329
|
1593 } |
|
|
1594 else |
|
1948
|
1595 { |
|
4329
|
1596 if (calc_cond) |
|
|
1597 { |
|
4330
|
1598 // Now calc the condition number for non-singular matrix. |
|
4329
|
1599 char job = '1'; |
|
|
1600 Array<Complex> z (2*nr); |
|
|
1601 Complex *pz = z.fortran_vec (); |
|
|
1602 Array<double> rz (2*nr); |
|
|
1603 double *prz = rz.fortran_vec (); |
|
|
1604 |
|
4552
|
1605 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1606 nc, tmp_data, nr, anorm, |
|
|
1607 rcond, pz, prz, info |
|
|
1608 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1609 |
|
|
1610 if (f77_exception_encountered) |
|
|
1611 (*current_liboctave_error_handler) |
|
|
1612 ("unrecoverable error in zgecon"); |
|
|
1613 } |
|
|
1614 |
|
4509
|
1615 if (info != 0) |
|
4329
|
1616 { |
|
|
1617 info = -1; |
|
|
1618 retval = ComplexDET (); |
|
|
1619 } |
|
|
1620 else |
|
|
1621 { |
|
5634
|
1622 Complex c = 1.0; |
|
|
1623 int e = 0; |
|
|
1624 |
|
|
1625 for (octave_idx_type i = 0; i < nc; i++) |
|
4329
|
1626 { |
|
5634
|
1627 if (ipvt(i) != (i+1)) |
|
|
1628 c = -c; |
|
|
1629 |
|
|
1630 c *= atmp(i,i); |
|
|
1631 |
|
|
1632 if (c == 0.0) |
|
|
1633 break; |
|
|
1634 |
|
|
1635 while (std::abs(c) < 0.5) |
|
4329
|
1636 { |
|
5634
|
1637 c *= 2.0; |
|
|
1638 e--; |
|
4329
|
1639 } |
|
5634
|
1640 |
|
|
1641 while (std::abs(c) >= 2.0) |
|
4329
|
1642 { |
|
5634
|
1643 c /= 2.0; |
|
|
1644 e++; |
|
4329
|
1645 } |
|
|
1646 } |
|
5634
|
1647 |
|
|
1648 retval = ComplexDET (c, e); |
|
4329
|
1649 } |
|
1948
|
1650 } |
|
458
|
1651 } |
|
|
1652 } |
|
4329
|
1653 |
|
458
|
1654 return retval; |
|
|
1655 } |
|
|
1656 |
|
|
1657 ComplexMatrix |
|
5785
|
1658 ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1659 octave_idx_type& info, double& rcond, |
|
|
1660 solve_singularity_handler sing_handler, |
|
|
1661 bool calc_cond) const |
|
|
1662 { |
|
|
1663 ComplexMatrix retval; |
|
|
1664 |
|
|
1665 octave_idx_type nr = rows (); |
|
|
1666 octave_idx_type nc = cols (); |
|
|
1667 |
|
|
1668 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1669 (*current_liboctave_error_handler) |
|
|
1670 ("matrix dimension mismatch solution of linear equations"); |
|
|
1671 else |
|
|
1672 { |
|
|
1673 volatile int typ = mattype.type (); |
|
|
1674 |
|
|
1675 if (typ == MatrixType::Permuted_Upper || |
|
|
1676 typ == MatrixType::Upper) |
|
|
1677 { |
|
|
1678 octave_idx_type b_nc = b.cols (); |
|
|
1679 rcond = 1.; |
|
|
1680 info = 0; |
|
|
1681 |
|
|
1682 if (typ == MatrixType::Permuted_Upper) |
|
|
1683 { |
|
|
1684 (*current_liboctave_error_handler) |
|
|
1685 ("Permuted triangular matrix not implemented"); |
|
|
1686 } |
|
|
1687 else |
|
|
1688 { |
|
|
1689 const Complex *tmp_data = fortran_vec (); |
|
|
1690 |
|
|
1691 if (calc_cond) |
|
|
1692 { |
|
|
1693 char norm = '1'; |
|
|
1694 char uplo = 'U'; |
|
|
1695 char dia = 'N'; |
|
|
1696 |
|
|
1697 Array<Complex> z (2 * nc); |
|
|
1698 Complex *pz = z.fortran_vec (); |
|
|
1699 Array<double> rz (nc); |
|
|
1700 double *prz = rz.fortran_vec (); |
|
|
1701 |
|
|
1702 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1703 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1704 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1705 nr, tmp_data, nr, rcond, |
|
|
1706 pz, prz, info |
|
|
1707 F77_CHAR_ARG_LEN (1) |
|
|
1708 F77_CHAR_ARG_LEN (1) |
|
|
1709 F77_CHAR_ARG_LEN (1))); |
|
|
1710 |
|
|
1711 if (f77_exception_encountered) |
|
|
1712 (*current_liboctave_error_handler) |
|
|
1713 ("unrecoverable error in ztrcon"); |
|
|
1714 |
|
|
1715 if (info != 0) |
|
|
1716 info = -2; |
|
|
1717 |
|
|
1718 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1719 |
|
|
1720 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1721 { |
|
|
1722 info = -2; |
|
|
1723 |
|
|
1724 if (sing_handler) |
|
|
1725 sing_handler (rcond); |
|
|
1726 else |
|
|
1727 (*current_liboctave_error_handler) |
|
|
1728 ("matrix singular to machine precision, rcond = %g", |
|
|
1729 rcond); |
|
|
1730 } |
|
|
1731 } |
|
|
1732 |
|
|
1733 if (info == 0) |
|
|
1734 { |
|
|
1735 retval = b; |
|
|
1736 Complex *result = retval.fortran_vec (); |
|
|
1737 |
|
|
1738 char uplo = 'U'; |
|
|
1739 char trans = 'N'; |
|
|
1740 char dia = 'N'; |
|
|
1741 |
|
|
1742 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1743 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1744 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1745 nr, b_nc, tmp_data, nr, |
|
|
1746 result, nr, info |
|
|
1747 F77_CHAR_ARG_LEN (1) |
|
|
1748 F77_CHAR_ARG_LEN (1) |
|
|
1749 F77_CHAR_ARG_LEN (1))); |
|
|
1750 |
|
|
1751 if (f77_exception_encountered) |
|
|
1752 (*current_liboctave_error_handler) |
|
|
1753 ("unrecoverable error in dtrtrs"); |
|
|
1754 } |
|
|
1755 } |
|
|
1756 } |
|
|
1757 else |
|
|
1758 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1759 } |
|
|
1760 |
|
|
1761 return retval; |
|
|
1762 } |
|
|
1763 |
|
|
1764 ComplexMatrix |
|
|
1765 ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1766 octave_idx_type& info, double& rcond, |
|
|
1767 solve_singularity_handler sing_handler, |
|
|
1768 bool calc_cond) const |
|
|
1769 { |
|
|
1770 ComplexMatrix retval; |
|
|
1771 |
|
|
1772 octave_idx_type nr = rows (); |
|
|
1773 octave_idx_type nc = cols (); |
|
|
1774 |
|
|
1775 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1776 (*current_liboctave_error_handler) |
|
|
1777 ("matrix dimension mismatch solution of linear equations"); |
|
|
1778 else |
|
|
1779 { |
|
|
1780 volatile int typ = mattype.type (); |
|
|
1781 |
|
|
1782 if (typ == MatrixType::Permuted_Lower || |
|
|
1783 typ == MatrixType::Lower) |
|
|
1784 { |
|
|
1785 octave_idx_type b_nc = b.cols (); |
|
|
1786 rcond = 1.; |
|
|
1787 info = 0; |
|
|
1788 |
|
|
1789 if (typ == MatrixType::Permuted_Lower) |
|
|
1790 { |
|
|
1791 (*current_liboctave_error_handler) |
|
|
1792 ("Permuted triangular matrix not implemented"); |
|
|
1793 } |
|
|
1794 else |
|
|
1795 { |
|
|
1796 const Complex *tmp_data = fortran_vec (); |
|
|
1797 |
|
|
1798 if (calc_cond) |
|
|
1799 { |
|
|
1800 char norm = '1'; |
|
|
1801 char uplo = 'L'; |
|
|
1802 char dia = 'N'; |
|
|
1803 |
|
|
1804 Array<Complex> z (2 * nc); |
|
|
1805 Complex *pz = z.fortran_vec (); |
|
|
1806 Array<double> rz (nc); |
|
|
1807 double *prz = rz.fortran_vec (); |
|
|
1808 |
|
|
1809 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1810 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1811 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1812 nr, tmp_data, nr, rcond, |
|
|
1813 pz, prz, info |
|
|
1814 F77_CHAR_ARG_LEN (1) |
|
|
1815 F77_CHAR_ARG_LEN (1) |
|
|
1816 F77_CHAR_ARG_LEN (1))); |
|
|
1817 |
|
|
1818 if (f77_exception_encountered) |
|
|
1819 (*current_liboctave_error_handler) |
|
|
1820 ("unrecoverable error in ztrcon"); |
|
|
1821 |
|
|
1822 if (info != 0) |
|
|
1823 info = -2; |
|
|
1824 |
|
|
1825 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1826 |
|
|
1827 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1828 { |
|
|
1829 info = -2; |
|
|
1830 |
|
|
1831 if (sing_handler) |
|
|
1832 sing_handler (rcond); |
|
|
1833 else |
|
|
1834 (*current_liboctave_error_handler) |
|
|
1835 ("matrix singular to machine precision, rcond = %g", |
|
|
1836 rcond); |
|
|
1837 } |
|
|
1838 } |
|
|
1839 |
|
|
1840 if (info == 0) |
|
|
1841 { |
|
|
1842 retval = b; |
|
|
1843 Complex *result = retval.fortran_vec (); |
|
|
1844 |
|
|
1845 char uplo = 'L'; |
|
|
1846 char trans = 'N'; |
|
|
1847 char dia = 'N'; |
|
|
1848 |
|
|
1849 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1850 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1851 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1852 nr, b_nc, tmp_data, nr, |
|
|
1853 result, nr, info |
|
|
1854 F77_CHAR_ARG_LEN (1) |
|
|
1855 F77_CHAR_ARG_LEN (1) |
|
|
1856 F77_CHAR_ARG_LEN (1))); |
|
|
1857 |
|
|
1858 if (f77_exception_encountered) |
|
|
1859 (*current_liboctave_error_handler) |
|
|
1860 ("unrecoverable error in dtrtrs"); |
|
|
1861 } |
|
|
1862 } |
|
|
1863 } |
|
|
1864 else |
|
|
1865 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1866 } |
|
|
1867 |
|
|
1868 return retval; |
|
|
1869 } |
|
|
1870 |
|
|
1871 ComplexMatrix |
|
|
1872 ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1873 octave_idx_type& info, double& rcond, |
|
|
1874 solve_singularity_handler sing_handler, |
|
|
1875 bool calc_cond) const |
|
|
1876 { |
|
|
1877 ComplexMatrix retval; |
|
|
1878 |
|
|
1879 octave_idx_type nr = rows (); |
|
|
1880 octave_idx_type nc = cols (); |
|
|
1881 |
|
|
1882 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1883 (*current_liboctave_error_handler) |
|
|
1884 ("matrix dimension mismatch in solution of linear equations"); |
|
|
1885 else |
|
|
1886 { |
|
|
1887 volatile int typ = mattype.type (); |
|
|
1888 |
|
|
1889 // Calculate the norm of the matrix, for later use. |
|
|
1890 double anorm = -1.; |
|
|
1891 |
|
|
1892 if (typ == MatrixType::Hermitian) |
|
|
1893 { |
|
|
1894 info = 0; |
|
|
1895 char job = 'L'; |
|
|
1896 ComplexMatrix atmp = *this; |
|
|
1897 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1898 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1899 |
|
|
1900 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
|
1901 tmp_data, nr, info |
|
|
1902 F77_CHAR_ARG_LEN (1))); |
|
|
1903 |
|
|
1904 if (f77_exception_encountered) |
|
|
1905 (*current_liboctave_error_handler) |
|
|
1906 ("unrecoverable error in zpotrf"); |
|
|
1907 else |
|
|
1908 { |
|
|
1909 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1910 rcond = 0.0; |
|
|
1911 if (info != 0) |
|
|
1912 { |
|
|
1913 info = -2; |
|
|
1914 |
|
|
1915 mattype.mark_as_unsymmetric (); |
|
|
1916 typ = MatrixType::Full; |
|
|
1917 } |
|
|
1918 else |
|
|
1919 { |
|
|
1920 if (calc_cond) |
|
|
1921 { |
|
|
1922 Array<Complex> z (2 * nc); |
|
|
1923 Complex *pz = z.fortran_vec (); |
|
|
1924 Array<double> rz (nc); |
|
|
1925 double *prz = rz.fortran_vec (); |
|
|
1926 |
|
|
1927 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1928 nr, tmp_data, nr, anorm, |
|
|
1929 rcond, pz, prz, info |
|
|
1930 F77_CHAR_ARG_LEN (1))); |
|
|
1931 |
|
|
1932 if (f77_exception_encountered) |
|
|
1933 (*current_liboctave_error_handler) |
|
|
1934 ("unrecoverable error in zpocon"); |
|
|
1935 |
|
|
1936 if (info != 0) |
|
|
1937 info = -2; |
|
|
1938 |
|
|
1939 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1940 |
|
|
1941 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1942 { |
|
|
1943 info = -2; |
|
|
1944 |
|
|
1945 if (sing_handler) |
|
|
1946 sing_handler (rcond); |
|
|
1947 else |
|
|
1948 (*current_liboctave_error_handler) |
|
|
1949 ("matrix singular to machine precision, rcond = %g", |
|
|
1950 rcond); |
|
|
1951 } |
|
|
1952 } |
|
|
1953 |
|
|
1954 if (info == 0) |
|
|
1955 { |
|
|
1956 retval = b; |
|
|
1957 Complex *result = retval.fortran_vec (); |
|
|
1958 |
|
|
1959 octave_idx_type b_nc = b.cols (); |
|
|
1960 |
|
|
1961 F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1962 nr, b_nc, tmp_data, nr, |
|
|
1963 result, b.rows(), info |
|
|
1964 F77_CHAR_ARG_LEN (1))); |
|
|
1965 |
|
|
1966 if (f77_exception_encountered) |
|
|
1967 (*current_liboctave_error_handler) |
|
|
1968 ("unrecoverable error in zpotrs"); |
|
|
1969 } |
|
|
1970 else |
|
|
1971 { |
|
|
1972 mattype.mark_as_unsymmetric (); |
|
|
1973 typ = MatrixType::Full; |
|
|
1974 } |
|
|
1975 } |
|
|
1976 } |
|
|
1977 } |
|
|
1978 |
|
|
1979 if (typ == MatrixType::Full) |
|
|
1980 { |
|
|
1981 info = 0; |
|
|
1982 |
|
|
1983 Array<octave_idx_type> ipvt (nr); |
|
|
1984 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
|
1985 |
|
|
1986 ComplexMatrix atmp = *this; |
|
|
1987 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1988 |
|
|
1989 Array<Complex> z (2 * nc); |
|
|
1990 Complex *pz = z.fortran_vec (); |
|
|
1991 Array<double> rz (2 * nc); |
|
|
1992 double *prz = rz.fortran_vec (); |
|
|
1993 |
|
|
1994 // Calculate the norm of the matrix, for later use. |
|
|
1995 if (anorm < 0.) |
|
|
1996 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1997 |
|
|
1998 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
|
1999 |
|
|
2000 if (f77_exception_encountered) |
|
|
2001 (*current_liboctave_error_handler) |
|
|
2002 ("unrecoverable error in zgetrf"); |
|
|
2003 else |
|
|
2004 { |
|
|
2005 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
2006 rcond = 0.0; |
|
|
2007 if (info != 0) |
|
|
2008 { |
|
|
2009 info = -2; |
|
|
2010 |
|
|
2011 if (sing_handler) |
|
|
2012 sing_handler (rcond); |
|
|
2013 else |
|
|
2014 (*current_liboctave_error_handler) |
|
|
2015 ("matrix singular to machine precision"); |
|
|
2016 |
|
|
2017 mattype.mark_as_rectangular (); |
|
|
2018 } |
|
|
2019 else |
|
|
2020 { |
|
|
2021 if (calc_cond) |
|
|
2022 { |
|
|
2023 // Now calculate the condition number for |
|
|
2024 // non-singular matrix. |
|
|
2025 char job = '1'; |
|
|
2026 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2027 nc, tmp_data, nr, anorm, |
|
|
2028 rcond, pz, prz, info |
|
|
2029 F77_CHAR_ARG_LEN (1))); |
|
|
2030 |
|
|
2031 if (f77_exception_encountered) |
|
|
2032 (*current_liboctave_error_handler) |
|
|
2033 ("unrecoverable error in zgecon"); |
|
|
2034 |
|
|
2035 if (info != 0) |
|
|
2036 info = -2; |
|
|
2037 |
|
|
2038 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2039 |
|
|
2040 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2041 { |
|
|
2042 info = -2; |
|
|
2043 |
|
|
2044 if (sing_handler) |
|
|
2045 sing_handler (rcond); |
|
|
2046 else |
|
|
2047 (*current_liboctave_error_handler) |
|
|
2048 ("matrix singular to machine precision, rcond = %g", |
|
|
2049 rcond); |
|
|
2050 } |
|
|
2051 } |
|
|
2052 |
|
|
2053 if (info == 0) |
|
|
2054 { |
|
|
2055 retval = b; |
|
|
2056 Complex *result = retval.fortran_vec (); |
|
|
2057 |
|
|
2058 octave_idx_type b_nc = b.cols (); |
|
|
2059 |
|
|
2060 char job = 'N'; |
|
|
2061 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2062 nr, b_nc, tmp_data, nr, |
|
|
2063 pipvt, result, b.rows(), info |
|
|
2064 F77_CHAR_ARG_LEN (1))); |
|
|
2065 |
|
|
2066 if (f77_exception_encountered) |
|
|
2067 (*current_liboctave_error_handler) |
|
|
2068 ("unrecoverable error in zgetrs"); |
|
|
2069 } |
|
|
2070 else |
|
|
2071 mattype.mark_as_rectangular (); |
|
|
2072 } |
|
|
2073 } |
|
|
2074 } |
|
|
2075 } |
|
|
2076 |
|
|
2077 return retval; |
|
|
2078 } |
|
|
2079 |
|
|
2080 ComplexMatrix |
|
|
2081 ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const |
|
|
2082 { |
|
|
2083 octave_idx_type info; |
|
|
2084 double rcond; |
|
|
2085 return solve (typ, b, info, rcond, 0); |
|
|
2086 } |
|
|
2087 |
|
|
2088 ComplexMatrix |
|
|
2089 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, |
|
|
2090 octave_idx_type& info) const |
|
|
2091 { |
|
|
2092 double rcond; |
|
|
2093 return solve (typ, b, info, rcond, 0); |
|
|
2094 } |
|
|
2095 |
|
|
2096 ComplexMatrix |
|
|
2097 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
2098 double& rcond) const |
|
|
2099 { |
|
|
2100 return solve (typ, b, info, rcond, 0); |
|
|
2101 } |
|
|
2102 |
|
|
2103 ComplexMatrix |
|
|
2104 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
2105 double& rcond, solve_singularity_handler sing_handler, |
|
|
2106 bool singular_fallback) const |
|
|
2107 { |
|
|
2108 ComplexMatrix tmp (b); |
|
|
2109 return solve (typ, tmp, info, rcond, sing_handler, singular_fallback); |
|
|
2110 } |
|
|
2111 |
|
|
2112 ComplexMatrix |
|
|
2113 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const |
|
|
2114 { |
|
|
2115 octave_idx_type info; |
|
|
2116 double rcond; |
|
|
2117 return solve (typ, b, info, rcond, 0); |
|
|
2118 } |
|
|
2119 |
|
|
2120 ComplexMatrix |
|
|
2121 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
2122 octave_idx_type& info) const |
|
|
2123 { |
|
|
2124 double rcond; |
|
|
2125 return solve (typ, b, info, rcond, 0); |
|
|
2126 } |
|
|
2127 |
|
|
2128 ComplexMatrix |
|
|
2129 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
2130 octave_idx_type& info, double& rcond) const |
|
|
2131 { |
|
|
2132 return solve (typ, b, info, rcond, 0); |
|
|
2133 } |
|
|
2134 |
|
|
2135 ComplexMatrix |
|
|
2136 ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
2137 octave_idx_type& info, double& rcond, |
|
|
2138 solve_singularity_handler sing_handler, |
|
|
2139 bool singular_fallback) const |
|
|
2140 { |
|
|
2141 ComplexMatrix retval; |
|
|
2142 int typ = mattype.type (); |
|
|
2143 |
|
|
2144 if (typ == MatrixType::Unknown) |
|
|
2145 typ = mattype.type (*this); |
|
|
2146 |
|
|
2147 // Only calculate the condition number for LU/Cholesky |
|
|
2148 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
|
2149 retval = utsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
2150 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
|
2151 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
2152 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
|
2153 retval = fsolve (mattype, b, info, rcond, sing_handler, true); |
|
|
2154 else if (typ != MatrixType::Rectangular) |
|
|
2155 { |
|
|
2156 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
|
2157 return ComplexMatrix (); |
|
|
2158 } |
|
|
2159 |
|
|
2160 // Rectangular or one of the above solvers flags a singular matrix |
|
|
2161 if (singular_fallback && mattype.type () == MatrixType::Rectangular) |
|
|
2162 { |
|
|
2163 octave_idx_type rank; |
|
|
2164 retval = lssolve (b, info, rank); |
|
|
2165 } |
|
|
2166 |
|
|
2167 return retval; |
|
|
2168 } |
|
|
2169 |
|
|
2170 ComplexColumnVector |
|
|
2171 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const |
|
|
2172 { |
|
|
2173 octave_idx_type info; |
|
|
2174 double rcond; |
|
|
2175 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2176 } |
|
|
2177 |
|
|
2178 ComplexColumnVector |
|
|
2179 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2180 octave_idx_type& info) const |
|
|
2181 { |
|
|
2182 double rcond; |
|
|
2183 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2184 } |
|
|
2185 |
|
|
2186 ComplexColumnVector |
|
|
2187 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2188 octave_idx_type& info, double& rcond) const |
|
|
2189 { |
|
|
2190 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2191 } |
|
|
2192 |
|
|
2193 ComplexColumnVector |
|
|
2194 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2195 octave_idx_type& info, double& rcond, |
|
|
2196 solve_singularity_handler sing_handler) const |
|
|
2197 { |
|
|
2198 return solve (typ, ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
2199 } |
|
|
2200 |
|
|
2201 ComplexColumnVector |
|
|
2202 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const |
|
|
2203 { |
|
|
2204 octave_idx_type info; |
|
|
2205 double rcond; |
|
|
2206 return solve (typ, b, info, rcond, 0); |
|
|
2207 } |
|
|
2208 |
|
|
2209 ComplexColumnVector |
|
|
2210 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2211 octave_idx_type& info) const |
|
|
2212 { |
|
|
2213 double rcond; |
|
|
2214 return solve (typ, b, info, rcond, 0); |
|
|
2215 } |
|
|
2216 |
|
|
2217 ComplexColumnVector |
|
|
2218 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2219 octave_idx_type& info, double& rcond) const |
|
|
2220 { |
|
|
2221 return solve (typ, b, info, rcond, 0); |
|
|
2222 } |
|
|
2223 |
|
|
2224 ComplexColumnVector |
|
|
2225 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2226 octave_idx_type& info, double& rcond, |
|
|
2227 solve_singularity_handler sing_handler) const |
|
|
2228 { |
|
|
2229 |
|
|
2230 ComplexMatrix tmp (b); |
|
|
2231 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); |
|
|
2232 } |
|
|
2233 |
|
|
2234 ComplexMatrix |
|
458
|
2235 ComplexMatrix::solve (const Matrix& b) const |
|
|
2236 { |
|
5275
|
2237 octave_idx_type info; |
|
458
|
2238 double rcond; |
|
3480
|
2239 return solve (b, info, rcond, 0); |
|
458
|
2240 } |
|
|
2241 |
|
|
2242 ComplexMatrix |
|
5275
|
2243 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
2244 { |
|
|
2245 double rcond; |
|
3480
|
2246 return solve (b, info, rcond, 0); |
|
458
|
2247 } |
|
|
2248 |
|
|
2249 ComplexMatrix |
|
5275
|
2250 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
2251 { |
|
3480
|
2252 return solve (b, info, rcond, 0); |
|
|
2253 } |
|
|
2254 |
|
|
2255 ComplexMatrix |
|
5275
|
2256 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
2257 solve_singularity_handler sing_handler) const |
|
|
2258 { |
|
458
|
2259 ComplexMatrix tmp (b); |
|
3480
|
2260 return solve (tmp, info, rcond, sing_handler); |
|
458
|
2261 } |
|
|
2262 |
|
|
2263 ComplexMatrix |
|
|
2264 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
2265 { |
|
5275
|
2266 octave_idx_type info; |
|
458
|
2267 double rcond; |
|
3480
|
2268 return solve (b, info, rcond, 0); |
|
458
|
2269 } |
|
|
2270 |
|
|
2271 ComplexMatrix |
|
5275
|
2272 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
2273 { |
|
|
2274 double rcond; |
|
3480
|
2275 return solve (b, info, rcond, 0); |
|
458
|
2276 } |
|
3480
|
2277 |
|
458
|
2278 ComplexMatrix |
|
5275
|
2279 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
2280 { |
|
3480
|
2281 return solve (b, info, rcond, 0); |
|
|
2282 } |
|
|
2283 |
|
|
2284 ComplexMatrix |
|
5275
|
2285 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
2286 solve_singularity_handler sing_handler) const |
|
|
2287 { |
|
5785
|
2288 MatrixType mattype (*this); |
|
6060
|
2289 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
2290 } |
|
|
2291 |
|
|
2292 ComplexColumnVector |
|
3585
|
2293 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
2294 { |
|
5275
|
2295 octave_idx_type info; |
|
3585
|
2296 double rcond; |
|
|
2297 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2298 } |
|
|
2299 |
|
|
2300 ComplexColumnVector |
|
5275
|
2301 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
2302 { |
|
|
2303 double rcond; |
|
|
2304 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2305 } |
|
|
2306 |
|
|
2307 ComplexColumnVector |
|
5785
|
2308 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
|
|
2309 double& rcond) const |
|
3585
|
2310 { |
|
|
2311 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2312 } |
|
|
2313 |
|
|
2314 ComplexColumnVector |
|
5785
|
2315 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
|
|
2316 double& rcond, |
|
3585
|
2317 solve_singularity_handler sing_handler) const |
|
|
2318 { |
|
|
2319 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
2320 } |
|
|
2321 |
|
|
2322 ComplexColumnVector |
|
458
|
2323 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
2324 { |
|
5275
|
2325 octave_idx_type info; |
|
458
|
2326 double rcond; |
|
3480
|
2327 return solve (b, info, rcond, 0); |
|
458
|
2328 } |
|
|
2329 |
|
|
2330 ComplexColumnVector |
|
5275
|
2331 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2332 { |
|
|
2333 double rcond; |
|
3480
|
2334 return solve (b, info, rcond, 0); |
|
458
|
2335 } |
|
|
2336 |
|
|
2337 ComplexColumnVector |
|
5275
|
2338 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
532
|
2339 double& rcond) const |
|
458
|
2340 { |
|
3480
|
2341 return solve (b, info, rcond, 0); |
|
|
2342 } |
|
|
2343 |
|
|
2344 ComplexColumnVector |
|
5275
|
2345 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
3480
|
2346 double& rcond, |
|
|
2347 solve_singularity_handler sing_handler) const |
|
|
2348 { |
|
5785
|
2349 MatrixType mattype (*this); |
|
|
2350 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
2351 } |
|
|
2352 |
|
|
2353 ComplexMatrix |
|
3585
|
2354 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
2355 { |
|
5275
|
2356 octave_idx_type info; |
|
|
2357 octave_idx_type rank; |
|
3585
|
2358 return lssolve (ComplexMatrix (b), info, rank); |
|
|
2359 } |
|
|
2360 |
|
|
2361 ComplexMatrix |
|
5275
|
2362 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
3585
|
2363 { |
|
5275
|
2364 octave_idx_type rank; |
|
3585
|
2365 return lssolve (ComplexMatrix (b), info, rank); |
|
|
2366 } |
|
|
2367 |
|
|
2368 ComplexMatrix |
|
5275
|
2369 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
3585
|
2370 { |
|
|
2371 return lssolve (ComplexMatrix (b), info, rank); |
|
|
2372 } |
|
|
2373 |
|
|
2374 ComplexMatrix |
|
458
|
2375 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
2376 { |
|
5275
|
2377 octave_idx_type info; |
|
|
2378 octave_idx_type rank; |
|
458
|
2379 return lssolve (b, info, rank); |
|
|
2380 } |
|
|
2381 |
|
|
2382 ComplexMatrix |
|
5275
|
2383 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
2384 { |
|
5275
|
2385 octave_idx_type rank; |
|
458
|
2386 return lssolve (b, info, rank); |
|
|
2387 } |
|
|
2388 |
|
|
2389 ComplexMatrix |
|
5275
|
2390 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2391 { |
|
1948
|
2392 ComplexMatrix retval; |
|
|
2393 |
|
5275
|
2394 octave_idx_type nrhs = b.cols (); |
|
|
2395 |
|
|
2396 octave_idx_type m = rows (); |
|
|
2397 octave_idx_type n = cols (); |
|
458
|
2398 |
|
|
2399 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
2400 (*current_liboctave_error_handler) |
|
|
2401 ("matrix dimension mismatch solution of linear equations"); |
|
|
2402 else |
|
458
|
2403 { |
|
1948
|
2404 ComplexMatrix atmp = *this; |
|
|
2405 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2406 |
|
5275
|
2407 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2408 ComplexMatrix result (nrr, nrhs); |
|
|
2409 |
|
5275
|
2410 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
2411 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2412 result.elem (i, j) = b.elem (i, j); |
|
|
2413 |
|
|
2414 Complex *presult = result.fortran_vec (); |
|
|
2415 |
|
5275
|
2416 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2417 Array<double> s (len_s); |
|
|
2418 double *ps = s.fortran_vec (); |
|
2563
|
2419 |
|
1948
|
2420 double rcond = -1.0; |
|
2563
|
2421 |
|
5275
|
2422 octave_idx_type lrwork = (5 * (m < n ? m : n)) - 4; |
|
1948
|
2423 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
2424 Array<double> rwork (lrwork); |
|
|
2425 double *prwork = rwork.fortran_vec (); |
|
|
2426 |
|
3752
|
2427 // Ask ZGELSS what the dimension of WORK should be. |
|
|
2428 |
|
5275
|
2429 octave_idx_type lwork = -1; |
|
3752
|
2430 |
|
|
2431 Array<Complex> work (1); |
|
|
2432 |
|
1948
|
2433 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
2434 nrr, ps, rcond, rank, |
|
|
2435 work.fortran_vec (), lwork, prwork, |
|
|
2436 info)); |
|
1948
|
2437 |
|
|
2438 if (f77_exception_encountered) |
|
|
2439 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
2440 else |
|
|
2441 { |
|
5315
|
2442 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
|
3752
|
2443 work.resize (lwork); |
|
|
2444 |
|
|
2445 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2446 nrr, ps, rcond, rank, |
|
|
2447 work.fortran_vec (), lwork, |
|
|
2448 prwork, info)); |
|
|
2449 |
|
|
2450 if (f77_exception_encountered) |
|
|
2451 (*current_liboctave_error_handler) |
|
|
2452 ("unrecoverable error in zgelss"); |
|
|
2453 else |
|
|
2454 { |
|
|
2455 retval.resize (n, nrhs); |
|
5275
|
2456 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
2457 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2458 retval.elem (i, j) = result.elem (i, j); |
|
|
2459 } |
|
1948
|
2460 } |
|
458
|
2461 } |
|
|
2462 |
|
|
2463 return retval; |
|
|
2464 } |
|
|
2465 |
|
|
2466 ComplexColumnVector |
|
3585
|
2467 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
2468 { |
|
5275
|
2469 octave_idx_type info; |
|
|
2470 octave_idx_type rank; |
|
3585
|
2471 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
2472 } |
|
|
2473 |
|
|
2474 ComplexColumnVector |
|
5275
|
2475 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
2476 { |
|
5275
|
2477 octave_idx_type rank; |
|
3585
|
2478 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
2479 } |
|
|
2480 |
|
|
2481 ComplexColumnVector |
|
5275
|
2482 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
3585
|
2483 { |
|
|
2484 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
2485 } |
|
|
2486 |
|
|
2487 ComplexColumnVector |
|
458
|
2488 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
2489 { |
|
5275
|
2490 octave_idx_type info; |
|
|
2491 octave_idx_type rank; |
|
458
|
2492 return lssolve (b, info, rank); |
|
|
2493 } |
|
|
2494 |
|
|
2495 ComplexColumnVector |
|
5275
|
2496 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2497 { |
|
5275
|
2498 octave_idx_type rank; |
|
458
|
2499 return lssolve (b, info, rank); |
|
|
2500 } |
|
|
2501 |
|
|
2502 ComplexColumnVector |
|
5275
|
2503 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
|
|
2504 octave_idx_type& rank) const |
|
458
|
2505 { |
|
1948
|
2506 ComplexColumnVector retval; |
|
|
2507 |
|
5275
|
2508 octave_idx_type nrhs = 1; |
|
|
2509 |
|
|
2510 octave_idx_type m = rows (); |
|
|
2511 octave_idx_type n = cols (); |
|
458
|
2512 |
|
|
2513 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
2514 (*current_liboctave_error_handler) |
|
|
2515 ("matrix dimension mismatch solution of least squares problem"); |
|
|
2516 else |
|
458
|
2517 { |
|
1948
|
2518 ComplexMatrix atmp = *this; |
|
|
2519 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2520 |
|
5275
|
2521 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2522 ComplexColumnVector result (nrr); |
|
|
2523 |
|
5275
|
2524 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2525 result.elem (i) = b.elem (i); |
|
|
2526 |
|
|
2527 Complex *presult = result.fortran_vec (); |
|
|
2528 |
|
5275
|
2529 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2530 Array<double> s (len_s); |
|
|
2531 double *ps = s.fortran_vec (); |
|
|
2532 |
|
|
2533 double rcond = -1.0; |
|
|
2534 |
|
5275
|
2535 octave_idx_type lrwork = (5 * (m < n ? m : n)) - 4; |
|
1948
|
2536 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
2537 Array<double> rwork (lrwork); |
|
|
2538 double *prwork = rwork.fortran_vec (); |
|
|
2539 |
|
3752
|
2540 // Ask ZGELSS what the dimension of WORK should be. |
|
|
2541 |
|
5275
|
2542 octave_idx_type lwork = -1; |
|
3752
|
2543 |
|
|
2544 Array<Complex> work (1); |
|
|
2545 |
|
1948
|
2546 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
2547 nrr, ps, rcond, rank, |
|
|
2548 work.fortran_vec (), lwork, prwork, |
|
|
2549 info)); |
|
1948
|
2550 |
|
|
2551 if (f77_exception_encountered) |
|
|
2552 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
2553 else |
|
|
2554 { |
|
5315
|
2555 lwork = static_cast<int> (std::real (work(0))); |
|
3752
|
2556 work.resize (lwork); |
|
|
2557 |
|
|
2558 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2559 nrr, ps, rcond, rank, |
|
|
2560 work.fortran_vec (), lwork, |
|
|
2561 prwork, info)); |
|
|
2562 |
|
|
2563 if (f77_exception_encountered) |
|
|
2564 (*current_liboctave_error_handler) |
|
|
2565 ("unrecoverable error in zgelss"); |
|
|
2566 else |
|
|
2567 { |
|
|
2568 retval.resize (n); |
|
5275
|
2569 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2570 retval.elem (i) = result.elem (i); |
|
|
2571 } |
|
1948
|
2572 } |
|
458
|
2573 } |
|
|
2574 |
|
|
2575 return retval; |
|
|
2576 } |
|
|
2577 |
|
1819
|
2578 // Constants for matrix exponential calculation. |
|
|
2579 |
|
|
2580 static double padec [] = |
|
|
2581 { |
|
|
2582 5.0000000000000000e-1, |
|
|
2583 1.1666666666666667e-1, |
|
|
2584 1.6666666666666667e-2, |
|
|
2585 1.6025641025641026e-3, |
|
|
2586 1.0683760683760684e-4, |
|
|
2587 4.8562548562548563e-6, |
|
|
2588 1.3875013875013875e-7, |
|
|
2589 1.9270852604185938e-9, |
|
|
2590 }; |
|
|
2591 |
|
|
2592 ComplexMatrix |
|
|
2593 ComplexMatrix::expm (void) const |
|
|
2594 { |
|
|
2595 ComplexMatrix retval; |
|
|
2596 |
|
|
2597 ComplexMatrix m = *this; |
|
|
2598 |
|
5275
|
2599 octave_idx_type nc = columns (); |
|
1819
|
2600 |
|
3130
|
2601 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2602 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2603 |
|
1819
|
2604 // trace shift value |
|
|
2605 Complex trshift = 0.0; |
|
|
2606 |
|
5275
|
2607 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2608 trshift += m.elem (i, i); |
|
|
2609 |
|
|
2610 trshift /= nc; |
|
|
2611 |
|
3130
|
2612 if (trshift.real () < 0.0) |
|
|
2613 trshift = trshift.imag (); |
|
|
2614 |
|
5275
|
2615 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2616 m.elem (i, i) -= trshift; |
|
|
2617 |
|
|
2618 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
2619 // code follows development in AEPBAL |
|
|
2620 |
|
|
2621 Complex *mp = m.fortran_vec (); |
|
3467
|
2622 |
|
5275
|
2623 octave_idx_type info, ilo, ihi,ilos,ihis; |
|
3468
|
2624 Array<double> dpermute (nc); |
|
|
2625 Array<double> dscale (nc); |
|
|
2626 |
|
5775
|
2627 // FIXME -- should pass job as a parameter in expm |
|
3468
|
2628 |
|
|
2629 // Permute first |
|
|
2630 char job = 'P'; |
|
4552
|
2631 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2632 nc, mp, nc, ilo, ihi, |
|
|
2633 dpermute.fortran_vec (), info |
|
|
2634 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2635 |
|
|
2636 if (f77_exception_encountered) |
|
|
2637 { |
|
|
2638 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
2639 return retval; |
|
|
2640 } |
|
|
2641 |
|
3468
|
2642 // then scale |
|
|
2643 job = 'S'; |
|
4552
|
2644 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2645 nc, mp, nc, ilos, ihis, |
|
|
2646 dscale.fortran_vec (), info |
|
|
2647 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2648 |
|
|
2649 if (f77_exception_encountered) |
|
|
2650 { |
|
3467
|
2651 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
2652 return retval; |
|
|
2653 } |
|
1819
|
2654 |
|
|
2655 // Preconditioning step 3: scaling. |
|
|
2656 |
|
|
2657 ColumnVector work (nc); |
|
3130
|
2658 double inf_norm; |
|
|
2659 |
|
4552
|
2660 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2661 nc, nc, m.fortran_vec (), nc, |
|
|
2662 work.fortran_vec (), inf_norm |
|
|
2663 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2664 |
|
|
2665 if (f77_exception_encountered) |
|
|
2666 { |
|
|
2667 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
2668 return retval; |
|
|
2669 } |
|
1819
|
2670 |
|
2800
|
2671 int sqpow = (inf_norm > 0.0 |
|
|
2672 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
2673 |
|
|
2674 // Check whether we need to square at all. |
|
|
2675 |
|
|
2676 if (sqpow < 0) |
|
|
2677 sqpow = 0; |
|
|
2678 |
|
|
2679 if (sqpow > 0) |
|
|
2680 { |
|
|
2681 double scale_factor = 1.0; |
|
5275
|
2682 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2683 scale_factor *= 2.0; |
|
|
2684 |
|
|
2685 m = m / scale_factor; |
|
|
2686 } |
|
|
2687 |
|
|
2688 // npp, dpp: pade' approx polynomial matrices. |
|
|
2689 |
|
|
2690 ComplexMatrix npp (nc, nc, 0.0); |
|
|
2691 ComplexMatrix dpp = npp; |
|
|
2692 |
|
|
2693 // Now powers a^8 ... a^1. |
|
|
2694 |
|
|
2695 int minus_one_j = -1; |
|
5275
|
2696 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2697 { |
|
|
2698 npp = m * npp + m * padec[j]; |
|
|
2699 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
2700 minus_one_j *= -1; |
|
|
2701 } |
|
|
2702 |
|
|
2703 // Zero power. |
|
|
2704 |
|
|
2705 dpp = -dpp; |
|
5275
|
2706 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2707 { |
|
|
2708 npp.elem (j, j) += 1.0; |
|
|
2709 dpp.elem (j, j) += 1.0; |
|
|
2710 } |
|
|
2711 |
|
|
2712 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2713 |
|
|
2714 retval = dpp.solve (npp); |
|
|
2715 |
|
|
2716 // Reverse preconditioning step 3: repeated squaring. |
|
|
2717 |
|
|
2718 while (sqpow) |
|
|
2719 { |
|
|
2720 retval = retval * retval; |
|
|
2721 sqpow--; |
|
|
2722 } |
|
|
2723 |
|
|
2724 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
2725 // Done in two steps: inverse scaling, then inverse permutation |
|
|
2726 |
|
|
2727 // inverse scaling (diagonal transformation) |
|
5275
|
2728 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2729 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2730 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
2731 |
|
4153
|
2732 OCTAVE_QUIT; |
|
|
2733 |
|
3467
|
2734 // construct balancing permutation vector |
|
4593
|
2735 Array<int> iperm (nc); |
|
5275
|
2736 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2737 iperm(i) = i; // initialize to identity permutation |
|
3467
|
2738 |
|
|
2739 // leading permutations in forward order |
|
5275
|
2740 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2741 { |
|
5275
|
2742 octave_idx_type swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
2743 octave_idx_type tmp = iperm(i); |
|
4593
|
2744 iperm(i) = iperm(swapidx); |
|
|
2745 iperm(swapidx) = tmp; |
|
3468
|
2746 } |
|
3467
|
2747 |
|
|
2748 // trailing permutations must be done in reverse order |
|
5275
|
2749 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2750 { |
|
5275
|
2751 octave_idx_type swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
2752 octave_idx_type tmp = iperm(i); |
|
4593
|
2753 iperm(i) = iperm(swapidx); |
|
|
2754 iperm(swapidx) = tmp; |
|
3468
|
2755 } |
|
3467
|
2756 |
|
|
2757 // construct inverse balancing permutation vector |
|
3468
|
2758 Array<int> invpvec (nc); |
|
5275
|
2759 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2760 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
2761 |
|
4153
|
2762 OCTAVE_QUIT; |
|
|
2763 |
|
3467
|
2764 ComplexMatrix tmpMat = retval; |
|
5275
|
2765 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2766 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2767 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
2768 |
|
|
2769 // Reverse preconditioning step 1: fix trace normalization. |
|
|
2770 |
|
3130
|
2771 return exp (trshift) * retval; |
|
1819
|
2772 } |
|
|
2773 |
|
1205
|
2774 // column vector by row vector -> matrix operations |
|
|
2775 |
|
|
2776 ComplexMatrix |
|
|
2777 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
2778 { |
|
|
2779 ComplexColumnVector tmp (v); |
|
|
2780 return tmp * a; |
|
|
2781 } |
|
|
2782 |
|
|
2783 ComplexMatrix |
|
|
2784 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
2785 { |
|
|
2786 ComplexRowVector tmp (b); |
|
|
2787 return a * tmp; |
|
|
2788 } |
|
|
2789 |
|
|
2790 ComplexMatrix |
|
|
2791 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
2792 { |
|
1948
|
2793 ComplexMatrix retval; |
|
|
2794 |
|
5275
|
2795 octave_idx_type len = v.length (); |
|
3233
|
2796 |
|
|
2797 if (len != 0) |
|
1205
|
2798 { |
|
5275
|
2799 octave_idx_type a_len = a.length (); |
|
3233
|
2800 |
|
|
2801 retval.resize (len, a_len); |
|
|
2802 Complex *c = retval.fortran_vec (); |
|
|
2803 |
|
4552
|
2804 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2805 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2806 len, a_len, 1, 1.0, v.data (), len, |
|
|
2807 a.data (), 1, 0.0, c, len |
|
|
2808 F77_CHAR_ARG_LEN (1) |
|
|
2809 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2810 |
|
|
2811 if (f77_exception_encountered) |
|
|
2812 (*current_liboctave_error_handler) |
|
|
2813 ("unrecoverable error in zgemm"); |
|
1205
|
2814 } |
|
|
2815 |
|
1948
|
2816 return retval; |
|
1205
|
2817 } |
|
|
2818 |
|
458
|
2819 // matrix by diagonal matrix -> matrix operations |
|
|
2820 |
|
|
2821 ComplexMatrix& |
|
|
2822 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
2823 { |
|
5275
|
2824 octave_idx_type nr = rows (); |
|
|
2825 octave_idx_type nc = cols (); |
|
|
2826 |
|
|
2827 octave_idx_type a_nr = rows (); |
|
|
2828 octave_idx_type a_nc = cols (); |
|
2384
|
2829 |
|
|
2830 if (nr != a_nr || nc != a_nc) |
|
458
|
2831 { |
|
2384
|
2832 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2833 return *this; |
|
458
|
2834 } |
|
|
2835 |
|
5275
|
2836 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2837 elem (i, i) += a.elem (i, i); |
|
|
2838 |
|
|
2839 return *this; |
|
|
2840 } |
|
|
2841 |
|
|
2842 ComplexMatrix& |
|
|
2843 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
2844 { |
|
5275
|
2845 octave_idx_type nr = rows (); |
|
|
2846 octave_idx_type nc = cols (); |
|
|
2847 |
|
|
2848 octave_idx_type a_nr = rows (); |
|
|
2849 octave_idx_type a_nc = cols (); |
|
2384
|
2850 |
|
|
2851 if (nr != a_nr || nc != a_nc) |
|
458
|
2852 { |
|
2384
|
2853 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2854 return *this; |
|
458
|
2855 } |
|
|
2856 |
|
5275
|
2857 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2858 elem (i, i) -= a.elem (i, i); |
|
|
2859 |
|
|
2860 return *this; |
|
|
2861 } |
|
|
2862 |
|
|
2863 ComplexMatrix& |
|
|
2864 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
2865 { |
|
5275
|
2866 octave_idx_type nr = rows (); |
|
|
2867 octave_idx_type nc = cols (); |
|
|
2868 |
|
|
2869 octave_idx_type a_nr = rows (); |
|
|
2870 octave_idx_type a_nc = cols (); |
|
2384
|
2871 |
|
|
2872 if (nr != a_nr || nc != a_nc) |
|
458
|
2873 { |
|
2384
|
2874 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2875 return *this; |
|
458
|
2876 } |
|
|
2877 |
|
5275
|
2878 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2879 elem (i, i) += a.elem (i, i); |
|
|
2880 |
|
|
2881 return *this; |
|
|
2882 } |
|
|
2883 |
|
|
2884 ComplexMatrix& |
|
|
2885 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
2886 { |
|
5275
|
2887 octave_idx_type nr = rows (); |
|
|
2888 octave_idx_type nc = cols (); |
|
|
2889 |
|
|
2890 octave_idx_type a_nr = rows (); |
|
|
2891 octave_idx_type a_nc = cols (); |
|
2384
|
2892 |
|
|
2893 if (nr != a_nr || nc != a_nc) |
|
458
|
2894 { |
|
2384
|
2895 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2896 return *this; |
|
458
|
2897 } |
|
|
2898 |
|
5275
|
2899 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2900 elem (i, i) -= a.elem (i, i); |
|
|
2901 |
|
|
2902 return *this; |
|
|
2903 } |
|
|
2904 |
|
|
2905 // matrix by matrix -> matrix operations |
|
|
2906 |
|
|
2907 ComplexMatrix& |
|
|
2908 ComplexMatrix::operator += (const Matrix& a) |
|
|
2909 { |
|
5275
|
2910 octave_idx_type nr = rows (); |
|
|
2911 octave_idx_type nc = cols (); |
|
|
2912 |
|
|
2913 octave_idx_type a_nr = a.rows (); |
|
|
2914 octave_idx_type a_nc = a.cols (); |
|
2384
|
2915 |
|
|
2916 if (nr != a_nr || nc != a_nc) |
|
458
|
2917 { |
|
2384
|
2918 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2919 return *this; |
|
|
2920 } |
|
|
2921 |
|
|
2922 if (nr == 0 || nc == 0) |
|
|
2923 return *this; |
|
|
2924 |
|
|
2925 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2926 |
|
3769
|
2927 mx_inline_add2 (d, a.data (), length ()); |
|
458
|
2928 return *this; |
|
|
2929 } |
|
|
2930 |
|
|
2931 ComplexMatrix& |
|
|
2932 ComplexMatrix::operator -= (const Matrix& a) |
|
|
2933 { |
|
5275
|
2934 octave_idx_type nr = rows (); |
|
|
2935 octave_idx_type nc = cols (); |
|
|
2936 |
|
|
2937 octave_idx_type a_nr = a.rows (); |
|
|
2938 octave_idx_type a_nc = a.cols (); |
|
2384
|
2939 |
|
|
2940 if (nr != a_nr || nc != a_nc) |
|
458
|
2941 { |
|
2384
|
2942 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2943 return *this; |
|
|
2944 } |
|
|
2945 |
|
|
2946 if (nr == 0 || nc == 0) |
|
|
2947 return *this; |
|
|
2948 |
|
|
2949 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2950 |
|
3769
|
2951 mx_inline_subtract2 (d, a.data (), length ()); |
|
458
|
2952 return *this; |
|
|
2953 } |
|
|
2954 |
|
|
2955 // unary operations |
|
|
2956 |
|
2964
|
2957 boolMatrix |
|
458
|
2958 ComplexMatrix::operator ! (void) const |
|
|
2959 { |
|
5275
|
2960 octave_idx_type nr = rows (); |
|
|
2961 octave_idx_type nc = cols (); |
|
2964
|
2962 |
|
|
2963 boolMatrix b (nr, nc); |
|
|
2964 |
|
5275
|
2965 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2966 for (octave_idx_type i = 0; i < nr; i++) |
|
5139
|
2967 b.elem (i, j) = elem (i, j) == 0.0; |
|
2964
|
2968 |
|
|
2969 return b; |
|
458
|
2970 } |
|
|
2971 |
|
|
2972 // other operations |
|
|
2973 |
|
|
2974 ComplexMatrix |
|
2676
|
2975 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
2976 { |
|
2676
|
2977 ComplexMatrix b (*this); |
|
|
2978 return b.apply (f); |
|
458
|
2979 } |
|
|
2980 |
|
2676
|
2981 Matrix |
|
|
2982 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
2983 { |
|
5275
|
2984 octave_idx_type nr = rows (); |
|
|
2985 octave_idx_type nc = cols (); |
|
3248
|
2986 |
|
|
2987 Matrix retval (nr, nc); |
|
|
2988 |
|
5275
|
2989 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2990 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2991 retval(i,j) = f (elem(i,j)); |
|
|
2992 |
|
|
2993 return retval; |
|
|
2994 } |
|
|
2995 |
|
|
2996 boolMatrix |
|
|
2997 ComplexMatrix::map (b_c_Mapper f) const |
|
|
2998 { |
|
5275
|
2999 octave_idx_type nr = rows (); |
|
|
3000 octave_idx_type nc = cols (); |
|
3248
|
3001 |
|
|
3002 boolMatrix retval (nr, nc); |
|
|
3003 |
|
5275
|
3004 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3005 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
3006 retval(i,j) = f (elem(i,j)); |
|
2676
|
3007 |
|
|
3008 return retval; |
|
|
3009 } |
|
|
3010 |
|
|
3011 ComplexMatrix& |
|
|
3012 ComplexMatrix::apply (c_c_Mapper f) |
|
|
3013 { |
|
|
3014 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
3015 |
|
5275
|
3016 for (octave_idx_type i = 0; i < length (); i++) |
|
2676
|
3017 d[i] = f (d[i]); |
|
|
3018 |
|
|
3019 return *this; |
|
458
|
3020 } |
|
|
3021 |
|
2384
|
3022 bool |
|
|
3023 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
3024 { |
|
5275
|
3025 octave_idx_type nr = rows (); |
|
|
3026 octave_idx_type nc = cols (); |
|
|
3027 |
|
|
3028 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3029 for (octave_idx_type i = 0; i < nr; i++) |
|
2384
|
3030 { |
|
|
3031 Complex val = elem (i, j); |
|
|
3032 if (xisinf (val) || xisnan (val)) |
|
|
3033 return true; |
|
|
3034 } |
|
|
3035 |
|
|
3036 return false; |
|
|
3037 } |
|
|
3038 |
|
2408
|
3039 // Return true if no elements have imaginary components. |
|
|
3040 |
|
|
3041 bool |
|
|
3042 ComplexMatrix::all_elements_are_real (void) const |
|
|
3043 { |
|
5275
|
3044 octave_idx_type nr = rows (); |
|
|
3045 octave_idx_type nc = cols (); |
|
|
3046 |
|
|
3047 for (octave_idx_type j = 0; j < nc; j++) |
|
4349
|
3048 { |
|
5275
|
3049 for (octave_idx_type i = 0; i < nr; i++) |
|
4349
|
3050 { |
|
5315
|
3051 double ip = std::imag (elem (i, j)); |
|
4349
|
3052 |
|
|
3053 if (ip != 0.0 || lo_ieee_signbit (ip)) |
|
|
3054 return false; |
|
|
3055 } |
|
|
3056 } |
|
2408
|
3057 |
|
|
3058 return true; |
|
|
3059 } |
|
|
3060 |
|
1968
|
3061 // Return nonzero if any element of CM has a non-integer real or |
|
|
3062 // imaginary part. Also extract the largest and smallest (real or |
|
|
3063 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
3064 |
|
2384
|
3065 bool |
|
1968
|
3066 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
3067 { |
|
5275
|
3068 octave_idx_type nr = rows (); |
|
|
3069 octave_idx_type nc = cols (); |
|
1968
|
3070 |
|
|
3071 if (nr > 0 && nc > 0) |
|
|
3072 { |
|
|
3073 Complex val = elem (0, 0); |
|
|
3074 |
|
5315
|
3075 double r_val = std::real (val); |
|
|
3076 double i_val = std::imag (val); |
|
1968
|
3077 |
|
|
3078 max_val = r_val; |
|
|
3079 min_val = r_val; |
|
|
3080 |
|
|
3081 if (i_val > max_val) |
|
|
3082 max_val = i_val; |
|
|
3083 |
|
|
3084 if (i_val < max_val) |
|
|
3085 min_val = i_val; |
|
|
3086 } |
|
|
3087 else |
|
2384
|
3088 return false; |
|
1968
|
3089 |
|
5275
|
3090 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3091 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
3092 { |
|
|
3093 Complex val = elem (i, j); |
|
|
3094 |
|
5315
|
3095 double r_val = std::real (val); |
|
|
3096 double i_val = std::imag (val); |
|
1968
|
3097 |
|
|
3098 if (r_val > max_val) |
|
|
3099 max_val = r_val; |
|
|
3100 |
|
|
3101 if (i_val > max_val) |
|
|
3102 max_val = i_val; |
|
|
3103 |
|
|
3104 if (r_val < min_val) |
|
|
3105 min_val = r_val; |
|
|
3106 |
|
|
3107 if (i_val < min_val) |
|
|
3108 min_val = i_val; |
|
|
3109 |
|
|
3110 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
3111 return false; |
|
1968
|
3112 } |
|
2384
|
3113 |
|
|
3114 return true; |
|
1968
|
3115 } |
|
|
3116 |
|
2384
|
3117 bool |
|
1968
|
3118 ComplexMatrix::too_large_for_float (void) const |
|
|
3119 { |
|
5275
|
3120 octave_idx_type nr = rows (); |
|
|
3121 octave_idx_type nc = cols (); |
|
|
3122 |
|
|
3123 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3124 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
3125 { |
|
|
3126 Complex val = elem (i, j); |
|
|
3127 |
|
5315
|
3128 double r_val = std::real (val); |
|
|
3129 double i_val = std::imag (val); |
|
1968
|
3130 |
|
5389
|
3131 if ((! (xisnan (r_val) || xisinf (r_val)) |
|
5387
|
3132 && fabs (r_val) > FLT_MAX) |
|
5389
|
3133 || (! (xisnan (i_val) || xisinf (i_val)) |
|
5387
|
3134 && fabs (i_val) > FLT_MAX)) |
|
2384
|
3135 return true; |
|
1968
|
3136 } |
|
|
3137 |
|
2384
|
3138 return false; |
|
1968
|
3139 } |
|
|
3140 |
|
5775
|
3141 // FIXME Do these really belong here? Maybe they should be |
|
4015
|
3142 // in a base class? |
|
|
3143 |
|
2832
|
3144 boolMatrix |
|
4015
|
3145 ComplexMatrix::all (int dim) const |
|
458
|
3146 { |
|
4015
|
3147 MX_ALL_OP (dim); |
|
458
|
3148 } |
|
|
3149 |
|
2832
|
3150 boolMatrix |
|
4015
|
3151 ComplexMatrix::any (int dim) const |
|
458
|
3152 { |
|
4015
|
3153 MX_ANY_OP (dim); |
|
458
|
3154 } |
|
|
3155 |
|
|
3156 ComplexMatrix |
|
3723
|
3157 ComplexMatrix::cumprod (int dim) const |
|
458
|
3158 { |
|
4015
|
3159 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
|
458
|
3160 } |
|
|
3161 |
|
|
3162 ComplexMatrix |
|
3723
|
3163 ComplexMatrix::cumsum (int dim) const |
|
458
|
3164 { |
|
4015
|
3165 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
|
458
|
3166 } |
|
|
3167 |
|
|
3168 ComplexMatrix |
|
3723
|
3169 ComplexMatrix::prod (int dim) const |
|
458
|
3170 { |
|
3864
|
3171 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
|
458
|
3172 } |
|
|
3173 |
|
|
3174 ComplexMatrix |
|
3723
|
3175 ComplexMatrix::sum (int dim) const |
|
458
|
3176 { |
|
3864
|
3177 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
|
458
|
3178 } |
|
|
3179 |
|
|
3180 ComplexMatrix |
|
3723
|
3181 ComplexMatrix::sumsq (int dim) const |
|
458
|
3182 { |
|
3864
|
3183 #define ROW_EXPR \ |
|
|
3184 Complex d = elem (i, j); \ |
|
|
3185 retval.elem (i, 0) += d * conj (d) |
|
|
3186 |
|
|
3187 #define COL_EXPR \ |
|
|
3188 Complex d = elem (i, j); \ |
|
|
3189 retval.elem (0, j) += d * conj (d) |
|
|
3190 |
|
|
3191 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
3192 |
|
|
3193 #undef ROW_EXPR |
|
|
3194 #undef COL_EXPR |
|
458
|
3195 } |
|
|
3196 |
|
4329
|
3197 Matrix ComplexMatrix::abs (void) const |
|
|
3198 { |
|
5275
|
3199 octave_idx_type nr = rows (); |
|
|
3200 octave_idx_type nc = cols (); |
|
4329
|
3201 |
|
|
3202 Matrix retval (nr, nc); |
|
|
3203 |
|
5275
|
3204 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3205 for (octave_idx_type i = 0; i < nr; i++) |
|
5315
|
3206 retval (i, j) = std::abs (elem (i, j)); |
|
4329
|
3207 |
|
|
3208 return retval; |
|
|
3209 } |
|
|
3210 |
|
458
|
3211 ComplexColumnVector |
|
|
3212 ComplexMatrix::diag (void) const |
|
|
3213 { |
|
|
3214 return diag (0); |
|
|
3215 } |
|
|
3216 |
|
|
3217 ComplexColumnVector |
|
5275
|
3218 ComplexMatrix::diag (octave_idx_type k) const |
|
458
|
3219 { |
|
5275
|
3220 octave_idx_type nnr = rows (); |
|
|
3221 octave_idx_type nnc = cols (); |
|
458
|
3222 if (k > 0) |
|
|
3223 nnc -= k; |
|
|
3224 else if (k < 0) |
|
|
3225 nnr += k; |
|
|
3226 |
|
|
3227 ComplexColumnVector d; |
|
|
3228 |
|
|
3229 if (nnr > 0 && nnc > 0) |
|
|
3230 { |
|
5275
|
3231 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
3232 |
|
|
3233 d.resize (ndiag); |
|
|
3234 |
|
|
3235 if (k > 0) |
|
|
3236 { |
|
5275
|
3237 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3238 d.elem (i) = elem (i, i+k); |
|
|
3239 } |
|
4509
|
3240 else if (k < 0) |
|
458
|
3241 { |
|
5275
|
3242 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3243 d.elem (i) = elem (i-k, i); |
|
|
3244 } |
|
|
3245 else |
|
|
3246 { |
|
5275
|
3247 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3248 d.elem (i) = elem (i, i); |
|
|
3249 } |
|
|
3250 } |
|
|
3251 else |
|
4513
|
3252 (*current_liboctave_error_handler) |
|
|
3253 ("diag: requested diagonal out of range"); |
|
458
|
3254 |
|
|
3255 return d; |
|
|
3256 } |
|
|
3257 |
|
2354
|
3258 bool |
|
5275
|
3259 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
|
2354
|
3260 { |
|
|
3261 bool retval = true; |
|
|
3262 |
|
5275
|
3263 octave_idx_type nc = columns (); |
|
|
3264 |
|
|
3265 for (octave_idx_type j = 0; j < nc; j++) |
|
2354
|
3266 { |
|
5315
|
3267 if (std::imag (elem (i, j)) != 0.0) |
|
2354
|
3268 { |
|
|
3269 retval = false; |
|
|
3270 break; |
|
|
3271 } |
|
|
3272 } |
|
|
3273 |
|
|
3274 return retval; |
|
|
3275 } |
|
|
3276 |
|
|
3277 bool |
|
5275
|
3278 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
|
2354
|
3279 { |
|
|
3280 bool retval = true; |
|
|
3281 |
|
5275
|
3282 octave_idx_type nr = rows (); |
|
|
3283 |
|
|
3284 for (octave_idx_type i = 0; i < nr; i++) |
|
2354
|
3285 { |
|
5315
|
3286 if (std::imag (elem (i, j)) != 0.0) |
|
2354
|
3287 { |
|
|
3288 retval = false; |
|
|
3289 break; |
|
|
3290 } |
|
|
3291 } |
|
|
3292 |
|
|
3293 return retval; |
|
|
3294 } |
|
891
|
3295 |
|
458
|
3296 ComplexColumnVector |
|
|
3297 ComplexMatrix::row_min (void) const |
|
|
3298 { |
|
5275
|
3299 Array<octave_idx_type> dummy_idx; |
|
4587
|
3300 return row_min (dummy_idx); |
|
458
|
3301 } |
|
|
3302 |
|
|
3303 ComplexColumnVector |
|
5275
|
3304 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
3305 { |
|
|
3306 ComplexColumnVector result; |
|
|
3307 |
|
5275
|
3308 octave_idx_type nr = rows (); |
|
|
3309 octave_idx_type nc = cols (); |
|
458
|
3310 |
|
|
3311 if (nr > 0 && nc > 0) |
|
|
3312 { |
|
|
3313 result.resize (nr); |
|
4587
|
3314 idx_arg.resize (nr); |
|
458
|
3315 |
|
5275
|
3316 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
3317 { |
|
2354
|
3318 bool real_only = row_is_real_only (i); |
|
|
3319 |
|
5275
|
3320 octave_idx_type idx_j; |
|
4469
|
3321 |
|
|
3322 Complex tmp_min; |
|
|
3323 |
|
|
3324 double abs_min = octave_NaN; |
|
|
3325 |
|
|
3326 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
3327 { |
|
|
3328 tmp_min = elem (i, idx_j); |
|
|
3329 |
|
5389
|
3330 if (! xisnan (tmp_min)) |
|
4469
|
3331 { |
|
5315
|
3332 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
|
4469
|
3333 break; |
|
|
3334 } |
|
|
3335 } |
|
|
3336 |
|
5275
|
3337 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
3338 { |
|
|
3339 Complex tmp = elem (i, j); |
|
|
3340 |
|
5389
|
3341 if (xisnan (tmp)) |
|
4469
|
3342 continue; |
|
|
3343 |
|
5315
|
3344 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3345 |
|
|
3346 if (abs_tmp < abs_min) |
|
|
3347 { |
|
|
3348 idx_j = j; |
|
|
3349 tmp_min = tmp; |
|
|
3350 abs_min = abs_tmp; |
|
|
3351 } |
|
|
3352 } |
|
|
3353 |
|
5389
|
3354 if (xisnan (tmp_min)) |
|
4469
|
3355 { |
|
|
3356 result.elem (i) = Complex_NaN_result; |
|
4587
|
3357 idx_arg.elem (i) = 0; |
|
4469
|
3358 } |
|
891
|
3359 else |
|
|
3360 { |
|
4469
|
3361 result.elem (i) = tmp_min; |
|
4587
|
3362 idx_arg.elem (i) = idx_j; |
|
891
|
3363 } |
|
458
|
3364 } |
|
|
3365 } |
|
|
3366 |
|
|
3367 return result; |
|
|
3368 } |
|
|
3369 |
|
|
3370 ComplexColumnVector |
|
|
3371 ComplexMatrix::row_max (void) const |
|
|
3372 { |
|
5275
|
3373 Array<octave_idx_type> dummy_idx; |
|
4587
|
3374 return row_max (dummy_idx); |
|
458
|
3375 } |
|
|
3376 |
|
|
3377 ComplexColumnVector |
|
5275
|
3378 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
3379 { |
|
|
3380 ComplexColumnVector result; |
|
|
3381 |
|
5275
|
3382 octave_idx_type nr = rows (); |
|
|
3383 octave_idx_type nc = cols (); |
|
458
|
3384 |
|
|
3385 if (nr > 0 && nc > 0) |
|
|
3386 { |
|
|
3387 result.resize (nr); |
|
4587
|
3388 idx_arg.resize (nr); |
|
458
|
3389 |
|
5275
|
3390 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
3391 { |
|
2354
|
3392 bool real_only = row_is_real_only (i); |
|
|
3393 |
|
5275
|
3394 octave_idx_type idx_j; |
|
4469
|
3395 |
|
|
3396 Complex tmp_max; |
|
|
3397 |
|
|
3398 double abs_max = octave_NaN; |
|
|
3399 |
|
|
3400 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
3401 { |
|
|
3402 tmp_max = elem (i, idx_j); |
|
|
3403 |
|
5389
|
3404 if (! xisnan (tmp_max)) |
|
4469
|
3405 { |
|
5315
|
3406 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
|
4469
|
3407 break; |
|
|
3408 } |
|
|
3409 } |
|
|
3410 |
|
5275
|
3411 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
3412 { |
|
|
3413 Complex tmp = elem (i, j); |
|
|
3414 |
|
5389
|
3415 if (xisnan (tmp)) |
|
4469
|
3416 continue; |
|
|
3417 |
|
5315
|
3418 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3419 |
|
|
3420 if (abs_tmp > abs_max) |
|
|
3421 { |
|
|
3422 idx_j = j; |
|
|
3423 tmp_max = tmp; |
|
|
3424 abs_max = abs_tmp; |
|
|
3425 } |
|
|
3426 } |
|
|
3427 |
|
5389
|
3428 if (xisnan (tmp_max)) |
|
4469
|
3429 { |
|
|
3430 result.elem (i) = Complex_NaN_result; |
|
4587
|
3431 idx_arg.elem (i) = 0; |
|
4469
|
3432 } |
|
891
|
3433 else |
|
|
3434 { |
|
4469
|
3435 result.elem (i) = tmp_max; |
|
4587
|
3436 idx_arg.elem (i) = idx_j; |
|
891
|
3437 } |
|
458
|
3438 } |
|
|
3439 } |
|
|
3440 |
|
|
3441 return result; |
|
|
3442 } |
|
|
3443 |
|
|
3444 ComplexRowVector |
|
|
3445 ComplexMatrix::column_min (void) const |
|
|
3446 { |
|
5275
|
3447 Array<octave_idx_type> dummy_idx; |
|
4587
|
3448 return column_min (dummy_idx); |
|
458
|
3449 } |
|
|
3450 |
|
|
3451 ComplexRowVector |
|
5275
|
3452 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
3453 { |
|
|
3454 ComplexRowVector result; |
|
|
3455 |
|
5275
|
3456 octave_idx_type nr = rows (); |
|
|
3457 octave_idx_type nc = cols (); |
|
458
|
3458 |
|
|
3459 if (nr > 0 && nc > 0) |
|
|
3460 { |
|
|
3461 result.resize (nc); |
|
4587
|
3462 idx_arg.resize (nc); |
|
458
|
3463 |
|
5275
|
3464 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3465 { |
|
2354
|
3466 bool real_only = column_is_real_only (j); |
|
|
3467 |
|
5275
|
3468 octave_idx_type idx_i; |
|
4469
|
3469 |
|
|
3470 Complex tmp_min; |
|
|
3471 |
|
|
3472 double abs_min = octave_NaN; |
|
|
3473 |
|
|
3474 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3475 { |
|
|
3476 tmp_min = elem (idx_i, j); |
|
|
3477 |
|
5389
|
3478 if (! xisnan (tmp_min)) |
|
4469
|
3479 { |
|
5315
|
3480 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
|
4469
|
3481 break; |
|
|
3482 } |
|
|
3483 } |
|
|
3484 |
|
5275
|
3485 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
3486 { |
|
|
3487 Complex tmp = elem (i, j); |
|
|
3488 |
|
5389
|
3489 if (xisnan (tmp)) |
|
4469
|
3490 continue; |
|
|
3491 |
|
5315
|
3492 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3493 |
|
|
3494 if (abs_tmp < abs_min) |
|
|
3495 { |
|
|
3496 idx_i = i; |
|
|
3497 tmp_min = tmp; |
|
|
3498 abs_min = abs_tmp; |
|
|
3499 } |
|
|
3500 } |
|
|
3501 |
|
5389
|
3502 if (xisnan (tmp_min)) |
|
4469
|
3503 { |
|
|
3504 result.elem (j) = Complex_NaN_result; |
|
4587
|
3505 idx_arg.elem (j) = 0; |
|
4469
|
3506 } |
|
891
|
3507 else |
|
|
3508 { |
|
4469
|
3509 result.elem (j) = tmp_min; |
|
4587
|
3510 idx_arg.elem (j) = idx_i; |
|
891
|
3511 } |
|
458
|
3512 } |
|
|
3513 } |
|
|
3514 |
|
|
3515 return result; |
|
|
3516 } |
|
|
3517 |
|
|
3518 ComplexRowVector |
|
|
3519 ComplexMatrix::column_max (void) const |
|
|
3520 { |
|
5275
|
3521 Array<octave_idx_type> dummy_idx; |
|
4587
|
3522 return column_max (dummy_idx); |
|
458
|
3523 } |
|
|
3524 |
|
|
3525 ComplexRowVector |
|
5275
|
3526 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
3527 { |
|
|
3528 ComplexRowVector result; |
|
|
3529 |
|
5275
|
3530 octave_idx_type nr = rows (); |
|
|
3531 octave_idx_type nc = cols (); |
|
458
|
3532 |
|
|
3533 if (nr > 0 && nc > 0) |
|
|
3534 { |
|
|
3535 result.resize (nc); |
|
4587
|
3536 idx_arg.resize (nc); |
|
458
|
3537 |
|
5275
|
3538 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3539 { |
|
2354
|
3540 bool real_only = column_is_real_only (j); |
|
|
3541 |
|
5275
|
3542 octave_idx_type idx_i; |
|
4469
|
3543 |
|
|
3544 Complex tmp_max; |
|
|
3545 |
|
|
3546 double abs_max = octave_NaN; |
|
|
3547 |
|
|
3548 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3549 { |
|
|
3550 tmp_max = elem (idx_i, j); |
|
|
3551 |
|
5389
|
3552 if (! xisnan (tmp_max)) |
|
4469
|
3553 { |
|
5315
|
3554 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
|
4469
|
3555 break; |
|
|
3556 } |
|
|
3557 } |
|
|
3558 |
|
5275
|
3559 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
3560 { |
|
|
3561 Complex tmp = elem (i, j); |
|
|
3562 |
|
5389
|
3563 if (xisnan (tmp)) |
|
4469
|
3564 continue; |
|
|
3565 |
|
5315
|
3566 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3567 |
|
|
3568 if (abs_tmp > abs_max) |
|
|
3569 { |
|
|
3570 idx_i = i; |
|
|
3571 tmp_max = tmp; |
|
|
3572 abs_max = abs_tmp; |
|
|
3573 } |
|
|
3574 } |
|
|
3575 |
|
5389
|
3576 if (xisnan (tmp_max)) |
|
4469
|
3577 { |
|
|
3578 result.elem (j) = Complex_NaN_result; |
|
4587
|
3579 idx_arg.elem (j) = 0; |
|
4469
|
3580 } |
|
891
|
3581 else |
|
|
3582 { |
|
4469
|
3583 result.elem (j) = tmp_max; |
|
4587
|
3584 idx_arg.elem (j) = idx_i; |
|
891
|
3585 } |
|
458
|
3586 } |
|
|
3587 } |
|
|
3588 |
|
|
3589 return result; |
|
|
3590 } |
|
|
3591 |
|
|
3592 // i/o |
|
|
3593 |
|
3504
|
3594 std::ostream& |
|
|
3595 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
3596 { |
|
5275
|
3597 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
3598 { |
|
5275
|
3599 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
3600 { |
|
|
3601 os << " "; |
|
|
3602 octave_write_complex (os, a.elem (i, j)); |
|
|
3603 } |
|
458
|
3604 os << "\n"; |
|
|
3605 } |
|
|
3606 return os; |
|
|
3607 } |
|
|
3608 |
|
3504
|
3609 std::istream& |
|
|
3610 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
3611 { |
|
5275
|
3612 octave_idx_type nr = a.rows (); |
|
|
3613 octave_idx_type nc = a.cols (); |
|
458
|
3614 |
|
|
3615 if (nr < 1 || nc < 1) |
|
3504
|
3616 is.clear (std::ios::badbit); |
|
458
|
3617 else |
|
|
3618 { |
|
|
3619 Complex tmp; |
|
5275
|
3620 for (octave_idx_type i = 0; i < nr; i++) |
|
|
3621 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3622 { |
|
4130
|
3623 tmp = octave_read_complex (is); |
|
458
|
3624 if (is) |
|
|
3625 a.elem (i, j) = tmp; |
|
|
3626 else |
|
2993
|
3627 goto done; |
|
458
|
3628 } |
|
|
3629 } |
|
|
3630 |
|
2993
|
3631 done: |
|
|
3632 |
|
458
|
3633 return is; |
|
|
3634 } |
|
|
3635 |
|
1819
|
3636 ComplexMatrix |
|
|
3637 Givens (const Complex& x, const Complex& y) |
|
|
3638 { |
|
|
3639 double cc; |
|
|
3640 Complex cs, temp_r; |
|
|
3641 |
|
3887
|
3642 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
1819
|
3643 |
|
|
3644 ComplexMatrix g (2, 2); |
|
|
3645 |
|
|
3646 g.elem (0, 0) = cc; |
|
|
3647 g.elem (1, 1) = cc; |
|
|
3648 g.elem (0, 1) = cs; |
|
|
3649 g.elem (1, 0) = -conj (cs); |
|
|
3650 |
|
|
3651 return g; |
|
|
3652 } |
|
|
3653 |
|
|
3654 ComplexMatrix |
|
|
3655 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
3656 const ComplexMatrix& c) |
|
|
3657 { |
|
|
3658 ComplexMatrix retval; |
|
|
3659 |
|
5775
|
3660 // FIXME -- need to check that a, b, and c are all the same |
|
1819
|
3661 // size. |
|
|
3662 |
|
|
3663 // Compute Schur decompositions |
|
|
3664 |
|
|
3665 ComplexSCHUR as (a, "U"); |
|
|
3666 ComplexSCHUR bs (b, "U"); |
|
|
3667 |
|
|
3668 // Transform c to new coordinates. |
|
|
3669 |
|
|
3670 ComplexMatrix ua = as.unitary_matrix (); |
|
|
3671 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
3672 |
|
|
3673 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
3674 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
3675 |
|
|
3676 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
3677 |
|
|
3678 // Solve the sylvester equation, back-transform, and return the |
|
|
3679 // solution. |
|
|
3680 |
|
5275
|
3681 octave_idx_type a_nr = a.rows (); |
|
|
3682 octave_idx_type b_nr = b.rows (); |
|
1819
|
3683 |
|
|
3684 double scale; |
|
5275
|
3685 octave_idx_type info; |
|
1950
|
3686 |
|
|
3687 Complex *pa = sch_a.fortran_vec (); |
|
|
3688 Complex *pb = sch_b.fortran_vec (); |
|
|
3689 Complex *px = cx.fortran_vec (); |
|
1819
|
3690 |
|
4552
|
3691 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3692 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3693 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3694 b_nr, px, a_nr, scale, info |
|
|
3695 F77_CHAR_ARG_LEN (1) |
|
|
3696 F77_CHAR_ARG_LEN (1))); |
|
1950
|
3697 |
|
|
3698 if (f77_exception_encountered) |
|
|
3699 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
3700 else |
|
|
3701 { |
|
5775
|
3702 // FIXME -- check info? |
|
1950
|
3703 |
|
|
3704 retval = -ua * cx * ub.hermitian (); |
|
|
3705 } |
|
1819
|
3706 |
|
|
3707 return retval; |
|
|
3708 } |
|
|
3709 |
|
2828
|
3710 ComplexMatrix |
|
|
3711 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
3712 { |
|
|
3713 ComplexMatrix tmp (a); |
|
|
3714 return m * tmp; |
|
|
3715 } |
|
|
3716 |
|
|
3717 ComplexMatrix |
|
|
3718 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
3719 { |
|
|
3720 ComplexMatrix tmp (m); |
|
|
3721 return tmp * a; |
|
|
3722 } |
|
|
3723 |
|
6162
|
3724 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
|
|
3725 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) |
|
|
3726 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) |
|
|
3727 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i 6+i ; 7+i 8+i], [17 + 15i 20 + 17i; 41 + 19i 48 + 21i], 1e-14) |
|
|
3728 */ |
|
|
3729 |
|
|
3730 /* Test some simple identities |
|
|
3731 %!shared M, cv, rv |
|
|
3732 %! M = randn(10,10)+i*rand(10,10); |
|
|
3733 %! cv = randn(10,1)+i*rand(10,1); |
|
|
3734 %! rv = randn(1,10)+i*rand(1,10); |
|
|
3735 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) |
|
|
3736 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) |
|
|
3737 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) |
|
|
3738 */ |
|
|
3739 |
|
2828
|
3740 ComplexMatrix |
|
|
3741 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
3742 { |
|
|
3743 ComplexMatrix retval; |
|
|
3744 |
|
5275
|
3745 octave_idx_type nr = m.rows (); |
|
|
3746 octave_idx_type nc = m.cols (); |
|
|
3747 |
|
|
3748 octave_idx_type a_nr = a.rows (); |
|
|
3749 octave_idx_type a_nc = a.cols (); |
|
2828
|
3750 |
|
|
3751 if (nc != a_nr) |
|
|
3752 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3753 else |
|
|
3754 { |
|
|
3755 if (nr == 0 || nc == 0 || a_nc == 0) |
|
3760
|
3756 retval.resize (nr, a_nc, 0.0); |
|
2828
|
3757 else |
|
|
3758 { |
|
5275
|
3759 octave_idx_type ld = nr; |
|
|
3760 octave_idx_type lda = a.rows (); |
|
2828
|
3761 |
|
|
3762 retval.resize (nr, a_nc); |
|
|
3763 Complex *c = retval.fortran_vec (); |
|
|
3764 |
|
5983
|
3765 if (a_nc == 1) |
|
|
3766 { |
|
|
3767 if (nr == 1) |
|
|
3768 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); |
|
|
3769 else |
|
|
3770 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3771 nr, nc, 1.0, m.data (), ld, |
|
|
3772 a.data (), 1, 0.0, c, 1 |
|
|
3773 F77_CHAR_ARG_LEN (1))); |
|
|
3774 } |
|
|
3775 else |
|
|
3776 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3777 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3778 nr, a_nc, nc, 1.0, m.data (), |
|
|
3779 ld, a.data (), lda, 0.0, c, nr |
|
|
3780 F77_CHAR_ARG_LEN (1) |
|
|
3781 F77_CHAR_ARG_LEN (1))); |
|
2828
|
3782 |
|
|
3783 if (f77_exception_encountered) |
|
|
3784 (*current_liboctave_error_handler) |
|
|
3785 ("unrecoverable error in zgemm"); |
|
|
3786 } |
|
|
3787 } |
|
|
3788 |
|
|
3789 return retval; |
|
|
3790 } |
|
|
3791 |
|
5775
|
3792 // FIXME -- it would be nice to share code among the min/max |
|
4309
|
3793 // functions below. |
|
|
3794 |
|
|
3795 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3796 if (nr == 0 || nc == 0) \ |
|
|
3797 return T (nr, nc); |
|
|
3798 |
|
|
3799 ComplexMatrix |
|
|
3800 min (const Complex& c, const ComplexMatrix& m) |
|
|
3801 { |
|
5275
|
3802 octave_idx_type nr = m.rows (); |
|
|
3803 octave_idx_type nc = m.columns (); |
|
4309
|
3804 |
|
|
3805 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3806 |
|
|
3807 ComplexMatrix result (nr, nc); |
|
|
3808 |
|
5275
|
3809 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3810 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3811 { |
|
|
3812 OCTAVE_QUIT; |
|
|
3813 result (i, j) = xmin (c, m (i, j)); |
|
|
3814 } |
|
|
3815 |
|
|
3816 return result; |
|
|
3817 } |
|
|
3818 |
|
|
3819 ComplexMatrix |
|
|
3820 min (const ComplexMatrix& m, const Complex& c) |
|
|
3821 { |
|
5275
|
3822 octave_idx_type nr = m.rows (); |
|
|
3823 octave_idx_type nc = m.columns (); |
|
4309
|
3824 |
|
|
3825 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3826 |
|
|
3827 ComplexMatrix result (nr, nc); |
|
|
3828 |
|
5275
|
3829 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3830 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3831 { |
|
|
3832 OCTAVE_QUIT; |
|
|
3833 result (i, j) = xmin (m (i, j), c); |
|
|
3834 } |
|
|
3835 |
|
|
3836 return result; |
|
|
3837 } |
|
|
3838 |
|
|
3839 ComplexMatrix |
|
|
3840 min (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3841 { |
|
5275
|
3842 octave_idx_type nr = a.rows (); |
|
|
3843 octave_idx_type nc = a.columns (); |
|
4309
|
3844 |
|
|
3845 if (nr != b.rows () || nc != b.columns ()) |
|
|
3846 { |
|
|
3847 (*current_liboctave_error_handler) |
|
|
3848 ("two-arg min expecting args of same size"); |
|
|
3849 return ComplexMatrix (); |
|
|
3850 } |
|
|
3851 |
|
|
3852 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3853 |
|
|
3854 ComplexMatrix result (nr, nc); |
|
|
3855 |
|
5275
|
3856 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
3857 { |
|
|
3858 int columns_are_real_only = 1; |
|
5275
|
3859 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3860 { |
|
|
3861 OCTAVE_QUIT; |
|
5315
|
3862 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
|
4309
|
3863 { |
|
|
3864 columns_are_real_only = 0; |
|
|
3865 break; |
|
|
3866 } |
|
|
3867 } |
|
|
3868 |
|
|
3869 if (columns_are_real_only) |
|
|
3870 { |
|
5275
|
3871 for (octave_idx_type i = 0; i < nr; i++) |
|
5315
|
3872 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
|
4309
|
3873 } |
|
|
3874 else |
|
|
3875 { |
|
5275
|
3876 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3877 { |
|
|
3878 OCTAVE_QUIT; |
|
|
3879 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3880 } |
|
|
3881 } |
|
|
3882 } |
|
|
3883 |
|
|
3884 return result; |
|
|
3885 } |
|
|
3886 |
|
|
3887 ComplexMatrix |
|
|
3888 max (const Complex& c, const ComplexMatrix& m) |
|
|
3889 { |
|
5275
|
3890 octave_idx_type nr = m.rows (); |
|
|
3891 octave_idx_type nc = m.columns (); |
|
4309
|
3892 |
|
|
3893 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3894 |
|
|
3895 ComplexMatrix result (nr, nc); |
|
|
3896 |
|
5275
|
3897 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3898 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3899 { |
|
|
3900 OCTAVE_QUIT; |
|
|
3901 result (i, j) = xmax (c, m (i, j)); |
|
|
3902 } |
|
|
3903 |
|
|
3904 return result; |
|
|
3905 } |
|
|
3906 |
|
|
3907 ComplexMatrix |
|
|
3908 max (const ComplexMatrix& m, const Complex& c) |
|
|
3909 { |
|
5275
|
3910 octave_idx_type nr = m.rows (); |
|
|
3911 octave_idx_type nc = m.columns (); |
|
4309
|
3912 |
|
|
3913 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3914 |
|
|
3915 ComplexMatrix result (nr, nc); |
|
|
3916 |
|
5275
|
3917 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3918 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3919 { |
|
|
3920 OCTAVE_QUIT; |
|
|
3921 result (i, j) = xmax (m (i, j), c); |
|
|
3922 } |
|
|
3923 |
|
|
3924 return result; |
|
|
3925 } |
|
|
3926 |
|
|
3927 ComplexMatrix |
|
|
3928 max (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3929 { |
|
5275
|
3930 octave_idx_type nr = a.rows (); |
|
|
3931 octave_idx_type nc = a.columns (); |
|
4309
|
3932 |
|
|
3933 if (nr != b.rows () || nc != b.columns ()) |
|
|
3934 { |
|
|
3935 (*current_liboctave_error_handler) |
|
|
3936 ("two-arg max expecting args of same size"); |
|
|
3937 return ComplexMatrix (); |
|
|
3938 } |
|
|
3939 |
|
|
3940 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3941 |
|
|
3942 ComplexMatrix result (nr, nc); |
|
|
3943 |
|
5275
|
3944 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
3945 { |
|
|
3946 int columns_are_real_only = 1; |
|
5275
|
3947 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3948 { |
|
|
3949 OCTAVE_QUIT; |
|
5315
|
3950 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
|
4309
|
3951 { |
|
|
3952 columns_are_real_only = 0; |
|
|
3953 break; |
|
|
3954 } |
|
|
3955 } |
|
|
3956 |
|
|
3957 if (columns_are_real_only) |
|
|
3958 { |
|
5275
|
3959 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3960 { |
|
|
3961 OCTAVE_QUIT; |
|
5315
|
3962 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
|
4309
|
3963 } |
|
|
3964 } |
|
|
3965 else |
|
|
3966 { |
|
5275
|
3967 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3968 { |
|
|
3969 OCTAVE_QUIT; |
|
|
3970 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3971 } |
|
|
3972 } |
|
|
3973 } |
|
|
3974 |
|
|
3975 return result; |
|
|
3976 } |
|
|
3977 |
|
5315
|
3978 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
|
3504
|
3979 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
3980 |
|
5315
|
3981 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
|
3504
|
3982 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
3983 |
|
5315
|
3984 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
|
3504
|
3985 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
3986 |
|
458
|
3987 /* |
|
|
3988 ;;; Local Variables: *** |
|
|
3989 ;;; mode: C++ *** |
|
|
3990 ;;; End: *** |
|
|
3991 */ |
