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1993
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1 // Matrix manipulations. |
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2 /* |
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3 |
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4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
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5 2003, 2004, 2005, 2006, 2007 John W. Eaton |
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6 |
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7 This file is part of Octave. |
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8 |
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9 Octave is free software; you can redistribute it and/or modify it |
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10 under the terms of the GNU General Public License as published by the |
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11 Free Software Foundation; either version 3 of the License, or (at your |
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12 option) any later version. |
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13 |
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14 Octave is distributed in the hope that it will be useful, but WITHOUT |
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15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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17 for more details. |
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18 |
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19 You should have received a copy of the GNU General Public License |
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20 along with Octave; see the file COPYING. If not, see |
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21 <http://www.gnu.org/licenses/>. |
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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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27 #endif |
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28 |
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29 #include <cfloat> |
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30 |
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31 #include <iostream> |
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32 #include <vector> |
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33 |
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34 // FIXME |
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35 #ifdef HAVE_SYS_TYPES_H |
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36 #include <sys/types.h> |
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37 #endif |
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38 |
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39 #include "Array-util.h" |
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40 #include "CMatrix.h" |
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1819
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41 #include "CmplxAEPBAL.h" |
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42 #include "CmplxDET.h" |
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1819
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43 #include "CmplxSCHUR.h" |
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740
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44 #include "CmplxSVD.h" |
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45 #include "CmplxCHOL.h" |
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1847
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46 #include "f77-fcn.h" |
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458
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47 #include "lo-error.h" |
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2354
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48 #include "lo-ieee.h" |
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49 #include "lo-mappers.h" |
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50 #include "lo-utils.h" |
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1367
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51 #include "mx-base.h" |
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2828
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52 #include "mx-cm-dm.h" |
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3176
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53 #include "mx-dm-cm.h" |
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2828
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54 #include "mx-cm-s.h" |
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1367
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55 #include "mx-inlines.cc" |
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1650
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56 #include "oct-cmplx.h" |
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57 |
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4773
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58 #if defined (HAVE_FFTW3) |
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3827
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59 #include "oct-fftw.h" |
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60 #endif |
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61 |
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62 // Fortran functions we call. |
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63 |
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64 extern "C" |
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65 { |
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66 F77_RET_T |
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67 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
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68 F77_CONST_CHAR_ARG_DECL, |
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69 const octave_idx_type&, const octave_idx_type&, |
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70 const octave_idx_type&, const octave_idx_type&, |
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71 octave_idx_type& |
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72 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); |
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73 |
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74 F77_RET_T |
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75 F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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76 const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, |
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77 octave_idx_type&, double*, octave_idx_type& |
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78 F77_CHAR_ARG_LEN_DECL); |
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79 |
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80 F77_RET_T |
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81 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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82 F77_CONST_CHAR_ARG_DECL, |
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83 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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84 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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85 F77_CHAR_ARG_LEN_DECL |
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86 F77_CHAR_ARG_LEN_DECL); |
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87 |
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88 F77_RET_T |
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89 F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, |
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90 F77_CONST_CHAR_ARG_DECL, |
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91 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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92 const Complex&, const Complex*, const octave_idx_type&, |
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93 const Complex*, const octave_idx_type&, const Complex&, |
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94 Complex*, const octave_idx_type& |
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95 F77_CHAR_ARG_LEN_DECL |
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96 F77_CHAR_ARG_LEN_DECL); |
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97 |
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98 F77_RET_T |
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99 F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, |
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100 const octave_idx_type&, const octave_idx_type&, const Complex&, |
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101 const Complex*, const octave_idx_type&, const Complex*, |
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102 const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& |
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103 F77_CHAR_ARG_LEN_DECL); |
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104 |
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105 F77_RET_T |
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106 F77_FUNC (xzdotu, XZDOTU) (const octave_idx_type&, const Complex*, const octave_idx_type&, |
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107 const Complex*, const octave_idx_type&, Complex&); |
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108 |
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109 F77_RET_T |
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110 F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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111 octave_idx_type*, octave_idx_type&); |
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112 |
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113 F77_RET_T |
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114 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, |
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115 const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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116 const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& |
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117 F77_CHAR_ARG_LEN_DECL); |
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118 |
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119 F77_RET_T |
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120 F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, |
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121 Complex*, const octave_idx_type&, octave_idx_type&); |
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122 |
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123 F77_RET_T |
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124 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, |
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125 const octave_idx_type&, Complex*, |
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126 const octave_idx_type&, const double&, double&, |
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127 Complex*, double*, octave_idx_type& |
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128 F77_CHAR_ARG_LEN_DECL); |
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129 |
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130 F77_RET_T |
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131 F77_FUNC (zgelsy, ZGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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132 Complex*, const octave_idx_type&, Complex*, |
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133 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, |
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134 Complex*, const octave_idx_type&, double*, octave_idx_type&); |
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135 |
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136 F77_RET_T |
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137 F77_FUNC (zgelsd, ZGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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138 Complex*, const octave_idx_type&, Complex*, |
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139 const octave_idx_type&, double*, double&, octave_idx_type&, |
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140 Complex*, const octave_idx_type&, double*, |
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141 octave_idx_type*, octave_idx_type&); |
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142 |
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143 F77_RET_T |
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144 F77_FUNC (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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145 Complex*, const octave_idx_type&, |
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146 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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147 |
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148 F77_RET_T |
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149 F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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150 Complex*, const octave_idx_type&, const double&, |
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151 double&, Complex*, double*, |
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152 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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153 |
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154 F77_RET_T |
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155 F77_FUNC (zpotrs, ZPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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156 const octave_idx_type&, const Complex*, |
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157 const octave_idx_type&, Complex*, |
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158 const octave_idx_type&, octave_idx_type& |
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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 (ztrtri, ZTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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163 const octave_idx_type&, const Complex*, |
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164 const octave_idx_type&, octave_idx_type& |
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165 F77_CHAR_ARG_LEN_DECL |
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166 F77_CHAR_ARG_LEN_DECL); |
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167 |
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168 F77_RET_T |
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169 F77_FUNC (ztrcon, ZTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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170 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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171 const Complex*, const octave_idx_type&, double&, |
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172 Complex*, double*, octave_idx_type& |
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173 F77_CHAR_ARG_LEN_DECL |
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174 F77_CHAR_ARG_LEN_DECL |
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175 F77_CHAR_ARG_LEN_DECL); |
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176 |
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177 F77_RET_T |
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178 F77_FUNC (ztrtrs, ZTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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179 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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180 const octave_idx_type&, const Complex*, |
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181 const octave_idx_type&, Complex*, |
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182 const octave_idx_type&, octave_idx_type& |
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183 F77_CHAR_ARG_LEN_DECL |
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184 F77_CHAR_ARG_LEN_DECL |
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185 F77_CHAR_ARG_LEN_DECL); |
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186 |
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1360
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187 // Note that the original complex fft routines were not written for |
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188 // double complex arguments. They have been modified by adding an |
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189 // implicit double precision (a-h,o-z) statement at the beginning of |
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190 // each subroutine. |
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191 |
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192 F77_RET_T |
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193 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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194 |
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195 F77_RET_T |
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196 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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197 |
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198 F77_RET_T |
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199 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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200 |
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201 F77_RET_T |
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202 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, |
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203 double&, Complex&, Complex&); |
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204 |
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205 F77_RET_T |
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206 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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207 F77_CONST_CHAR_ARG_DECL, |
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208 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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209 const Complex*, const octave_idx_type&, |
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210 const Complex*, const octave_idx_type&, |
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211 const Complex*, const octave_idx_type&, double&, octave_idx_type& |
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212 F77_CHAR_ARG_LEN_DECL |
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213 F77_CHAR_ARG_LEN_DECL); |
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214 |
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215 F77_RET_T |
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216 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, |
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5275
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217 const octave_idx_type&, const octave_idx_type&, const Complex*, |
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218 const octave_idx_type&, double*, double& |
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219 F77_CHAR_ARG_LEN_DECL); |
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220 } |
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221 |
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222 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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223 |
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224 // Complex Matrix class |
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225 |
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226 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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227 : MArray2<Complex> (a.rows (), a.cols ()) |
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228 { |
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229 for (octave_idx_type j = 0; j < cols (); j++) |
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230 for (octave_idx_type i = 0; i < rows (); i++) |
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231 elem (i, j) = a.elem (i, j); |
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232 } |
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233 |
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2349
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234 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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235 : MArray2<Complex> (1, rv.length (), 0.0) |
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236 { |
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237 for (octave_idx_type i = 0; i < rv.length (); i++) |
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238 elem (0, i) = rv.elem (i); |
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239 } |
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240 |
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241 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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242 : MArray2<Complex> (cv.length (), 1, 0.0) |
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243 { |
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244 for (octave_idx_type i = 0; i < cv.length (); i++) |
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245 elem (i, 0) = cv.elem (i); |
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246 } |
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247 |
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248 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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249 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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250 { |
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251 for (octave_idx_type i = 0; i < a.length (); i++) |
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252 elem (i, i) = a.elem (i, i); |
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253 } |
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254 |
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255 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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256 : MArray2<Complex> (1, rv.length (), 0.0) |
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257 { |
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258 for (octave_idx_type i = 0; i < rv.length (); i++) |
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259 elem (0, i) = rv.elem (i); |
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260 } |
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261 |
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262 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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263 : MArray2<Complex> (cv.length (), 1, 0.0) |
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264 { |
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265 for (octave_idx_type i = 0; i < cv.length (); i++) |
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266 elem (i, 0) = cv.elem (i); |
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267 } |
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268 |
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458
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269 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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270 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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271 { |
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272 for (octave_idx_type i = 0; i < a.length (); i++) |
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273 elem (i, i) = a.elem (i, i); |
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274 } |
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275 |
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276 // FIXME -- could we use a templated mixed-type copy function |
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277 // here? |
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278 |
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279 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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280 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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281 { |
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282 for (octave_idx_type i = 0; i < a.rows (); i++) |
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283 for (octave_idx_type j = 0; j < a.cols (); j++) |
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284 elem (i, j) = a.elem (i, j); |
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285 } |
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286 |
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287 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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288 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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289 { |
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290 for (octave_idx_type i = 0; i < a.rows (); i++) |
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291 for (octave_idx_type j = 0; j < a.cols (); j++) |
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292 elem (i, j) = a.elem (i, j); |
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293 } |
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294 |
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2384
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295 bool |
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458
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296 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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297 { |
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298 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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299 return false; |
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458
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300 |
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3769
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301 return mx_inline_equal (data (), a.data (), length ()); |
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458
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302 } |
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303 |
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2384
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304 bool |
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458
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305 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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306 { |
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307 return !(*this == a); |
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308 } |
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309 |
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2815
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310 bool |
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311 ComplexMatrix::is_hermitian (void) const |
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312 { |
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313 octave_idx_type nr = rows (); |
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314 octave_idx_type nc = cols (); |
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315 |
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316 if (is_square () && nr > 0) |
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317 { |
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318 for (octave_idx_type i = 0; i < nr; i++) |
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319 for (octave_idx_type j = i; j < nc; j++) |
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320 if (elem (i, j) != conj (elem (j, i))) |
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321 return false; |
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322 |
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323 return true; |
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324 } |
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325 |
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326 return false; |
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327 } |
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328 |
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458
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329 // destructive insert/delete/reorder operations |
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330 |
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331 ComplexMatrix& |
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5275
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332 ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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333 { |
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334 octave_idx_type a_nr = a.rows (); |
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335 octave_idx_type a_nc = a.cols (); |
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336 |
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337 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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338 { |
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339 (*current_liboctave_error_handler) ("range error for insert"); |
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340 return *this; |
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341 } |
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342 |
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4316
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343 if (a_nr >0 && a_nc > 0) |
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344 { |
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345 make_unique (); |
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346 |
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5275
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347 for (octave_idx_type j = 0; j < a_nc; j++) |
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348 for (octave_idx_type i = 0; i < a_nr; i++) |
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349 xelem (r+i, c+j) = a.elem (i, j); |
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350 } |
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458
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351 |
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352 return *this; |
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353 } |
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354 |
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355 ComplexMatrix& |
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5275
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356 ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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357 { |
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5275
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358 octave_idx_type a_len = a.length (); |
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4316
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359 |
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1699
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360 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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361 { |
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362 (*current_liboctave_error_handler) ("range error for insert"); |
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363 return *this; |
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364 } |
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365 |
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4316
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366 if (a_len > 0) |
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367 { |
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368 make_unique (); |
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369 |
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5275
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370 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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371 xelem (r, c+i) = a.elem (i); |
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372 } |
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458
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373 |
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374 return *this; |
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375 } |
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376 |
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377 ComplexMatrix& |
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5275
|
378 ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
|
458
|
379 { |
|
5275
|
380 octave_idx_type a_len = a.length (); |
|
4316
|
381 |
|
1699
|
382 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
|
458
|
383 { |
|
|
384 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
385 return *this; |
|
|
386 } |
|
|
387 |
|
4316
|
388 if (a_len > 0) |
|
|
389 { |
|
|
390 make_unique (); |
|
|
391 |
|
5275
|
392 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
393 xelem (r+i, c) = a.elem (i); |
|
|
394 } |
|
458
|
395 |
|
|
396 return *this; |
|
|
397 } |
|
|
398 |
|
|
399 ComplexMatrix& |
|
5275
|
400 ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
401 { |
|
5275
|
402 octave_idx_type a_nr = a.rows (); |
|
|
403 octave_idx_type a_nc = a.cols (); |
|
1699
|
404 |
|
|
405 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
406 { |
|
|
407 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
408 return *this; |
|
|
409 } |
|
|
410 |
|
1699
|
411 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
412 |
|
5275
|
413 octave_idx_type a_len = a.length (); |
|
4316
|
414 |
|
|
415 if (a_len > 0) |
|
|
416 { |
|
|
417 make_unique (); |
|
|
418 |
|
5275
|
419 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
420 xelem (r+i, c+i) = a.elem (i, i); |
|
|
421 } |
|
458
|
422 |
|
|
423 return *this; |
|
|
424 } |
|
|
425 |
|
|
426 ComplexMatrix& |
|
5275
|
427 ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
428 { |
|
1561
|
429 Array2<Complex>::insert (a, r, c); |
|
458
|
430 return *this; |
|
|
431 } |
|
|
432 |
|
|
433 ComplexMatrix& |
|
5275
|
434 ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) |
|
458
|
435 { |
|
5275
|
436 octave_idx_type a_len = a.length (); |
|
1699
|
437 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
|
458
|
438 { |
|
|
439 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
440 return *this; |
|
|
441 } |
|
|
442 |
|
5275
|
443 for (octave_idx_type i = 0; i < a_len; i++) |
|
458
|
444 elem (r, c+i) = a.elem (i); |
|
|
445 |
|
|
446 return *this; |
|
|
447 } |
|
|
448 |
|
|
449 ComplexMatrix& |
|
5275
|
450 ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) |
|
458
|
451 { |
|
5275
|
452 octave_idx_type a_len = a.length (); |
|
4316
|
453 |
|
1699
|
454 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
|
458
|
455 { |
|
|
456 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
457 return *this; |
|
|
458 } |
|
|
459 |
|
4316
|
460 if (a_len > 0) |
|
|
461 { |
|
|
462 make_unique (); |
|
|
463 |
|
5275
|
464 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
465 xelem (r+i, c) = a.elem (i); |
|
|
466 } |
|
458
|
467 |
|
|
468 return *this; |
|
|
469 } |
|
|
470 |
|
|
471 ComplexMatrix& |
|
5275
|
472 ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
473 { |
|
5275
|
474 octave_idx_type a_nr = a.rows (); |
|
|
475 octave_idx_type a_nc = a.cols (); |
|
1699
|
476 |
|
|
477 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
478 { |
|
|
479 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
480 return *this; |
|
|
481 } |
|
|
482 |
|
1699
|
483 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
484 |
|
5275
|
485 octave_idx_type a_len = a.length (); |
|
4316
|
486 |
|
|
487 if (a_len > 0) |
|
|
488 { |
|
|
489 make_unique (); |
|
|
490 |
|
5275
|
491 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
492 xelem (r+i, c+i) = a.elem (i, i); |
|
|
493 } |
|
458
|
494 |
|
|
495 return *this; |
|
|
496 } |
|
|
497 |
|
|
498 ComplexMatrix& |
|
|
499 ComplexMatrix::fill (double val) |
|
|
500 { |
|
5275
|
501 octave_idx_type nr = rows (); |
|
|
502 octave_idx_type nc = cols (); |
|
4316
|
503 |
|
458
|
504 if (nr > 0 && nc > 0) |
|
4316
|
505 { |
|
|
506 make_unique (); |
|
|
507 |
|
5275
|
508 for (octave_idx_type j = 0; j < nc; j++) |
|
|
509 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
510 xelem (i, j) = val; |
|
|
511 } |
|
458
|
512 |
|
|
513 return *this; |
|
|
514 } |
|
|
515 |
|
|
516 ComplexMatrix& |
|
|
517 ComplexMatrix::fill (const Complex& val) |
|
|
518 { |
|
5275
|
519 octave_idx_type nr = rows (); |
|
|
520 octave_idx_type nc = cols (); |
|
4316
|
521 |
|
458
|
522 if (nr > 0 && nc > 0) |
|
4316
|
523 { |
|
|
524 make_unique (); |
|
|
525 |
|
5275
|
526 for (octave_idx_type j = 0; j < nc; j++) |
|
|
527 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
528 xelem (i, j) = val; |
|
|
529 } |
|
458
|
530 |
|
|
531 return *this; |
|
|
532 } |
|
|
533 |
|
|
534 ComplexMatrix& |
|
5275
|
535 ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
536 { |
|
5275
|
537 octave_idx_type nr = rows (); |
|
|
538 octave_idx_type nc = cols (); |
|
4316
|
539 |
|
458
|
540 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
541 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
542 { |
|
|
543 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
544 return *this; |
|
|
545 } |
|
|
546 |
|
5275
|
547 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
548 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
549 |
|
4316
|
550 if (r2 >= r1 && c2 >= c1) |
|
|
551 { |
|
|
552 make_unique (); |
|
|
553 |
|
5275
|
554 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
555 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
556 xelem (i, j) = val; |
|
|
557 } |
|
458
|
558 |
|
|
559 return *this; |
|
|
560 } |
|
|
561 |
|
|
562 ComplexMatrix& |
|
5275
|
563 ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
564 { |
|
5275
|
565 octave_idx_type nr = rows (); |
|
|
566 octave_idx_type nc = cols (); |
|
4316
|
567 |
|
458
|
568 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
569 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
570 { |
|
|
571 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
572 return *this; |
|
|
573 } |
|
|
574 |
|
5275
|
575 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
576 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
577 |
|
4316
|
578 if (r2 >= r1 && c2 >=c1) |
|
|
579 { |
|
|
580 make_unique (); |
|
|
581 |
|
5275
|
582 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
583 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
584 xelem (i, j) = val; |
|
|
585 } |
|
458
|
586 |
|
|
587 return *this; |
|
|
588 } |
|
|
589 |
|
|
590 ComplexMatrix |
|
|
591 ComplexMatrix::append (const Matrix& a) const |
|
|
592 { |
|
5275
|
593 octave_idx_type nr = rows (); |
|
|
594 octave_idx_type nc = cols (); |
|
458
|
595 if (nr != a.rows ()) |
|
|
596 { |
|
|
597 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
598 return *this; |
|
|
599 } |
|
|
600 |
|
5275
|
601 octave_idx_type nc_insert = nc; |
|
458
|
602 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
603 retval.insert (*this, 0, 0); |
|
|
604 retval.insert (a, 0, nc_insert); |
|
|
605 return retval; |
|
|
606 } |
|
|
607 |
|
|
608 ComplexMatrix |
|
|
609 ComplexMatrix::append (const RowVector& a) const |
|
|
610 { |
|
5275
|
611 octave_idx_type nr = rows (); |
|
|
612 octave_idx_type nc = cols (); |
|
458
|
613 if (nr != 1) |
|
|
614 { |
|
|
615 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
616 return *this; |
|
|
617 } |
|
|
618 |
|
5275
|
619 octave_idx_type nc_insert = nc; |
|
458
|
620 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
621 retval.insert (*this, 0, 0); |
|
|
622 retval.insert (a, 0, nc_insert); |
|
|
623 return retval; |
|
|
624 } |
|
|
625 |
|
|
626 ComplexMatrix |
|
|
627 ComplexMatrix::append (const ColumnVector& a) const |
|
|
628 { |
|
5275
|
629 octave_idx_type nr = rows (); |
|
|
630 octave_idx_type nc = cols (); |
|
458
|
631 if (nr != a.length ()) |
|
|
632 { |
|
|
633 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
634 return *this; |
|
|
635 } |
|
|
636 |
|
5275
|
637 octave_idx_type nc_insert = nc; |
|
458
|
638 ComplexMatrix retval (nr, nc + 1); |
|
|
639 retval.insert (*this, 0, 0); |
|
|
640 retval.insert (a, 0, nc_insert); |
|
|
641 return retval; |
|
|
642 } |
|
|
643 |
|
|
644 ComplexMatrix |
|
|
645 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
646 { |
|
5275
|
647 octave_idx_type nr = rows (); |
|
|
648 octave_idx_type nc = cols (); |
|
458
|
649 if (nr != a.rows ()) |
|
|
650 { |
|
|
651 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
652 return *this; |
|
|
653 } |
|
|
654 |
|
5275
|
655 octave_idx_type nc_insert = nc; |
|
458
|
656 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
657 retval.insert (*this, 0, 0); |
|
|
658 retval.insert (a, 0, nc_insert); |
|
|
659 return retval; |
|
|
660 } |
|
|
661 |
|
|
662 ComplexMatrix |
|
|
663 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
664 { |
|
5275
|
665 octave_idx_type nr = rows (); |
|
|
666 octave_idx_type nc = cols (); |
|
458
|
667 if (nr != a.rows ()) |
|
|
668 { |
|
|
669 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
670 return *this; |
|
|
671 } |
|
|
672 |
|
5275
|
673 octave_idx_type nc_insert = nc; |
|
458
|
674 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
675 retval.insert (*this, 0, 0); |
|
|
676 retval.insert (a, 0, nc_insert); |
|
|
677 return retval; |
|
|
678 } |
|
|
679 |
|
|
680 ComplexMatrix |
|
|
681 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
682 { |
|
5275
|
683 octave_idx_type nr = rows (); |
|
|
684 octave_idx_type nc = cols (); |
|
458
|
685 if (nr != 1) |
|
|
686 { |
|
|
687 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
688 return *this; |
|
|
689 } |
|
|
690 |
|
5275
|
691 octave_idx_type nc_insert = nc; |
|
458
|
692 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
693 retval.insert (*this, 0, 0); |
|
|
694 retval.insert (a, 0, nc_insert); |
|
|
695 return retval; |
|
|
696 } |
|
|
697 |
|
|
698 ComplexMatrix |
|
|
699 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
700 { |
|
5275
|
701 octave_idx_type nr = rows (); |
|
|
702 octave_idx_type nc = cols (); |
|
458
|
703 if (nr != a.length ()) |
|
|
704 { |
|
|
705 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
706 return *this; |
|
|
707 } |
|
|
708 |
|
5275
|
709 octave_idx_type nc_insert = nc; |
|
458
|
710 ComplexMatrix retval (nr, nc + 1); |
|
|
711 retval.insert (*this, 0, 0); |
|
|
712 retval.insert (a, 0, nc_insert); |
|
|
713 return retval; |
|
|
714 } |
|
|
715 |
|
|
716 ComplexMatrix |
|
|
717 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
718 { |
|
5275
|
719 octave_idx_type nr = rows (); |
|
|
720 octave_idx_type nc = cols (); |
|
458
|
721 if (nr != a.rows ()) |
|
|
722 { |
|
|
723 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
724 return *this; |
|
|
725 } |
|
|
726 |
|
5275
|
727 octave_idx_type nc_insert = nc; |
|
458
|
728 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
729 retval.insert (*this, 0, 0); |
|
|
730 retval.insert (a, 0, nc_insert); |
|
|
731 return retval; |
|
|
732 } |
|
|
733 |
|
|
734 ComplexMatrix |
|
|
735 ComplexMatrix::stack (const Matrix& a) const |
|
|
736 { |
|
5275
|
737 octave_idx_type nr = rows (); |
|
|
738 octave_idx_type nc = cols (); |
|
458
|
739 if (nc != a.cols ()) |
|
|
740 { |
|
|
741 (*current_liboctave_error_handler) |
|
|
742 ("column dimension mismatch for stack"); |
|
|
743 return *this; |
|
|
744 } |
|
|
745 |
|
5275
|
746 octave_idx_type nr_insert = nr; |
|
458
|
747 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
748 retval.insert (*this, 0, 0); |
|
|
749 retval.insert (a, nr_insert, 0); |
|
|
750 return retval; |
|
|
751 } |
|
|
752 |
|
|
753 ComplexMatrix |
|
|
754 ComplexMatrix::stack (const RowVector& a) const |
|
|
755 { |
|
5275
|
756 octave_idx_type nr = rows (); |
|
|
757 octave_idx_type nc = cols (); |
|
458
|
758 if (nc != a.length ()) |
|
|
759 { |
|
|
760 (*current_liboctave_error_handler) |
|
|
761 ("column dimension mismatch for stack"); |
|
|
762 return *this; |
|
|
763 } |
|
|
764 |
|
5275
|
765 octave_idx_type nr_insert = nr; |
|
458
|
766 ComplexMatrix retval (nr + 1, nc); |
|
|
767 retval.insert (*this, 0, 0); |
|
|
768 retval.insert (a, nr_insert, 0); |
|
|
769 return retval; |
|
|
770 } |
|
|
771 |
|
|
772 ComplexMatrix |
|
|
773 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
774 { |
|
5275
|
775 octave_idx_type nr = rows (); |
|
|
776 octave_idx_type nc = cols (); |
|
458
|
777 if (nc != 1) |
|
|
778 { |
|
|
779 (*current_liboctave_error_handler) |
|
|
780 ("column dimension mismatch for stack"); |
|
|
781 return *this; |
|
|
782 } |
|
|
783 |
|
5275
|
784 octave_idx_type nr_insert = nr; |
|
458
|
785 ComplexMatrix retval (nr + a.length (), nc); |
|
|
786 retval.insert (*this, 0, 0); |
|
|
787 retval.insert (a, nr_insert, 0); |
|
|
788 return retval; |
|
|
789 } |
|
|
790 |
|
|
791 ComplexMatrix |
|
|
792 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
793 { |
|
5275
|
794 octave_idx_type nr = rows (); |
|
|
795 octave_idx_type nc = cols (); |
|
458
|
796 if (nc != a.cols ()) |
|
|
797 { |
|
|
798 (*current_liboctave_error_handler) |
|
|
799 ("column dimension mismatch for stack"); |
|
|
800 return *this; |
|
|
801 } |
|
|
802 |
|
5275
|
803 octave_idx_type nr_insert = nr; |
|
458
|
804 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
805 retval.insert (*this, 0, 0); |
|
|
806 retval.insert (a, nr_insert, 0); |
|
|
807 return retval; |
|
|
808 } |
|
|
809 |
|
|
810 ComplexMatrix |
|
|
811 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
812 { |
|
5275
|
813 octave_idx_type nr = rows (); |
|
|
814 octave_idx_type nc = cols (); |
|
458
|
815 if (nc != a.cols ()) |
|
|
816 { |
|
|
817 (*current_liboctave_error_handler) |
|
|
818 ("column dimension mismatch for stack"); |
|
|
819 return *this; |
|
|
820 } |
|
|
821 |
|
5275
|
822 octave_idx_type nr_insert = nr; |
|
458
|
823 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
824 retval.insert (*this, 0, 0); |
|
|
825 retval.insert (a, nr_insert, 0); |
|
|
826 return retval; |
|
|
827 } |
|
|
828 |
|
|
829 ComplexMatrix |
|
|
830 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
831 { |
|
5275
|
832 octave_idx_type nr = rows (); |
|
|
833 octave_idx_type nc = cols (); |
|
458
|
834 if (nc != a.length ()) |
|
|
835 { |
|
|
836 (*current_liboctave_error_handler) |
|
|
837 ("column dimension mismatch for stack"); |
|
|
838 return *this; |
|
|
839 } |
|
|
840 |
|
5275
|
841 octave_idx_type nr_insert = nr; |
|
458
|
842 ComplexMatrix retval (nr + 1, nc); |
|
|
843 retval.insert (*this, 0, 0); |
|
|
844 retval.insert (a, nr_insert, 0); |
|
|
845 return retval; |
|
|
846 } |
|
|
847 |
|
|
848 ComplexMatrix |
|
|
849 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
850 { |
|
5275
|
851 octave_idx_type nr = rows (); |
|
|
852 octave_idx_type nc = cols (); |
|
458
|
853 if (nc != 1) |
|
|
854 { |
|
|
855 (*current_liboctave_error_handler) |
|
|
856 ("column dimension mismatch for stack"); |
|
|
857 return *this; |
|
|
858 } |
|
|
859 |
|
5275
|
860 octave_idx_type nr_insert = nr; |
|
458
|
861 ComplexMatrix retval (nr + a.length (), nc); |
|
|
862 retval.insert (*this, 0, 0); |
|
|
863 retval.insert (a, nr_insert, 0); |
|
|
864 return retval; |
|
|
865 } |
|
|
866 |
|
|
867 ComplexMatrix |
|
|
868 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
869 { |
|
5275
|
870 octave_idx_type nr = rows (); |
|
|
871 octave_idx_type nc = cols (); |
|
458
|
872 if (nc != a.cols ()) |
|
|
873 { |
|
|
874 (*current_liboctave_error_handler) |
|
|
875 ("column dimension mismatch for stack"); |
|
|
876 return *this; |
|
|
877 } |
|
|
878 |
|
5275
|
879 octave_idx_type nr_insert = nr; |
|
458
|
880 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
881 retval.insert (*this, 0, 0); |
|
|
882 retval.insert (a, nr_insert, 0); |
|
|
883 return retval; |
|
|
884 } |
|
|
885 |
|
|
886 ComplexMatrix |
|
|
887 ComplexMatrix::hermitian (void) const |
|
|
888 { |
|
5275
|
889 octave_idx_type nr = rows (); |
|
|
890 octave_idx_type nc = cols (); |
|
458
|
891 ComplexMatrix result; |
|
|
892 if (length () > 0) |
|
|
893 { |
|
|
894 result.resize (nc, nr); |
|
5275
|
895 for (octave_idx_type j = 0; j < nc; j++) |
|
|
896 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
897 result.elem (j, i) = conj (elem (i, j)); |
|
|
898 } |
|
|
899 return result; |
|
|
900 } |
|
|
901 |
|
|
902 ComplexMatrix |
|
|
903 conj (const ComplexMatrix& a) |
|
|
904 { |
|
5275
|
905 octave_idx_type a_len = a.length (); |
|
458
|
906 ComplexMatrix retval; |
|
|
907 if (a_len > 0) |
|
3769
|
908 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
|
|
909 a.rows (), a.cols ()); |
|
458
|
910 return retval; |
|
|
911 } |
|
|
912 |
|
|
913 // resize is the destructive equivalent for this one |
|
|
914 |
|
|
915 ComplexMatrix |
|
5275
|
916 ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
917 { |
|
5275
|
918 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
919 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
920 |
|
|
921 octave_idx_type new_r = r2 - r1 + 1; |
|
|
922 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
923 |
|
|
924 ComplexMatrix result (new_r, new_c); |
|
|
925 |
|
5275
|
926 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
927 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
928 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
929 |
|
|
930 return result; |
|
|
931 } |
|
|
932 |
|
|
933 ComplexMatrix |
|
5275
|
934 ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
935 { |
|
|
936 ComplexMatrix result (nr, nc); |
|
|
937 |
|
5275
|
938 for (octave_idx_type j = 0; j < nc; j++) |
|
|
939 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
940 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
941 |
|
|
942 return result; |
|
|
943 } |
|
|
944 |
|
|
945 // extract row or column i. |
|
|
946 |
|
|
947 ComplexRowVector |
|
5275
|
948 ComplexMatrix::row (octave_idx_type i) const |
|
458
|
949 { |
|
5275
|
950 octave_idx_type nc = cols (); |
|
458
|
951 if (i < 0 || i >= rows ()) |
|
|
952 { |
|
|
953 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
954 return ComplexRowVector (); |
|
|
955 } |
|
|
956 |
|
|
957 ComplexRowVector retval (nc); |
|
5275
|
958 for (octave_idx_type j = 0; j < cols (); j++) |
|
4316
|
959 retval.xelem (j) = elem (i, j); |
|
458
|
960 |
|
|
961 return retval; |
|
|
962 } |
|
|
963 |
|
|
964 ComplexColumnVector |
|
5275
|
965 ComplexMatrix::column (octave_idx_type i) const |
|
458
|
966 { |
|
5275
|
967 octave_idx_type nr = rows (); |
|
458
|
968 if (i < 0 || i >= cols ()) |
|
|
969 { |
|
|
970 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
971 return ComplexColumnVector (); |
|
|
972 } |
|
|
973 |
|
|
974 ComplexColumnVector retval (nr); |
|
5275
|
975 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
976 retval.xelem (j) = elem (j, i); |
|
458
|
977 |
|
|
978 return retval; |
|
|
979 } |
|
|
980 |
|
|
981 ComplexMatrix |
|
|
982 ComplexMatrix::inverse (void) const |
|
|
983 { |
|
5275
|
984 octave_idx_type info; |
|
479
|
985 double rcond; |
|
6207
|
986 MatrixType mattype (*this); |
|
|
987 return inverse (mattype, info, rcond, 0, 0); |
|
|
988 } |
|
|
989 |
|
|
990 ComplexMatrix |
|
6479
|
991 ComplexMatrix::inverse (octave_idx_type& info) const |
|
|
992 { |
|
|
993 double rcond; |
|
|
994 MatrixType mattype (*this); |
|
|
995 return inverse (mattype, info, rcond, 0, 0); |
|
|
996 } |
|
|
997 |
|
|
998 ComplexMatrix |
|
|
999 ComplexMatrix::inverse (octave_idx_type& info, double& rcond, int force, |
|
|
1000 int calc_cond) const |
|
|
1001 { |
|
|
1002 MatrixType mattype (*this); |
|
6482
|
1003 return inverse (mattype, info, rcond, force, calc_cond); |
|
6479
|
1004 } |
|
|
1005 |
|
|
1006 ComplexMatrix |
|
6207
|
1007 ComplexMatrix::inverse (MatrixType &mattype) const |
|
|
1008 { |
|
|
1009 octave_idx_type info; |
|
|
1010 double rcond; |
|
|
1011 return inverse (mattype, info, rcond, 0, 0); |
|
|
1012 } |
|
|
1013 |
|
|
1014 ComplexMatrix |
|
|
1015 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const |
|
|
1016 { |
|
|
1017 double rcond; |
|
|
1018 return inverse (mattype, info, rcond, 0, 0); |
|
458
|
1019 } |
|
|
1020 |
|
|
1021 ComplexMatrix |
|
6207
|
1022 ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, |
|
|
1023 double& rcond, int force, int calc_cond) const |
|
458
|
1024 { |
|
6207
|
1025 ComplexMatrix retval; |
|
|
1026 |
|
|
1027 octave_idx_type nr = rows (); |
|
|
1028 octave_idx_type nc = cols (); |
|
|
1029 |
|
|
1030 if (nr != nc || nr == 0 || nc == 0) |
|
|
1031 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
1032 else |
|
|
1033 { |
|
|
1034 int typ = mattype.type (); |
|
|
1035 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); |
|
|
1036 char udiag = 'N'; |
|
|
1037 retval = *this; |
|
|
1038 Complex *tmp_data = retval.fortran_vec (); |
|
|
1039 |
|
|
1040 F77_XFCN (ztrtri, ZTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1041 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
1042 nr, tmp_data, nr, info |
|
|
1043 F77_CHAR_ARG_LEN (1) |
|
|
1044 F77_CHAR_ARG_LEN (1))); |
|
|
1045 |
|
|
1046 if (f77_exception_encountered) |
|
|
1047 (*current_liboctave_error_handler) ("unrecoverable error in ztrtri"); |
|
|
1048 else |
|
|
1049 { |
|
|
1050 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1051 rcond = 0.0; |
|
|
1052 if (info != 0) |
|
|
1053 info = -1; |
|
|
1054 else if (calc_cond) |
|
|
1055 { |
|
|
1056 octave_idx_type ztrcon_info = 0; |
|
|
1057 char job = '1'; |
|
|
1058 |
|
6482
|
1059 OCTAVE_LOCAL_BUFFER (Complex, cwork, 2*nr); |
|
6207
|
1060 OCTAVE_LOCAL_BUFFER (double, rwork, nr); |
|
|
1061 |
|
|
1062 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1063 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1064 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
1065 nr, tmp_data, nr, rcond, |
|
|
1066 cwork, rwork, ztrcon_info |
|
|
1067 F77_CHAR_ARG_LEN (1) |
|
|
1068 F77_CHAR_ARG_LEN (1) |
|
|
1069 F77_CHAR_ARG_LEN (1))); |
|
|
1070 |
|
|
1071 if (f77_exception_encountered) |
|
|
1072 (*current_liboctave_error_handler) |
|
|
1073 ("unrecoverable error in ztrcon"); |
|
|
1074 |
|
|
1075 if (ztrcon_info != 0) |
|
|
1076 info = -1; |
|
|
1077 } |
|
|
1078 } |
|
|
1079 |
|
|
1080 if (info == -1 && ! force) |
|
|
1081 retval = *this; // Restore matrix contents. |
|
|
1082 } |
|
|
1083 |
|
|
1084 return retval; |
|
458
|
1085 } |
|
|
1086 |
|
|
1087 ComplexMatrix |
|
6207
|
1088 ComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, |
|
|
1089 double& rcond, int force, int calc_cond) const |
|
458
|
1090 { |
|
1948
|
1091 ComplexMatrix retval; |
|
|
1092 |
|
5275
|
1093 octave_idx_type nr = rows (); |
|
|
1094 octave_idx_type nc = cols (); |
|
1948
|
1095 |
|
458
|
1096 if (nr != nc) |
|
1948
|
1097 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
1098 else |
|
|
1099 { |
|
5275
|
1100 Array<octave_idx_type> ipvt (nr); |
|
|
1101 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1102 |
|
|
1103 retval = *this; |
|
|
1104 Complex *tmp_data = retval.fortran_vec (); |
|
|
1105 |
|
4329
|
1106 Array<Complex> z(1); |
|
5275
|
1107 octave_idx_type lwork = -1; |
|
4330
|
1108 |
|
|
1109 // Query the optimum work array size. |
|
4329
|
1110 |
|
|
1111 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
|
1112 z.fortran_vec (), lwork, info)); |
|
|
1113 |
|
|
1114 if (f77_exception_encountered) |
|
|
1115 { |
|
|
1116 (*current_liboctave_error_handler) |
|
|
1117 ("unrecoverable error in zgetri"); |
|
|
1118 return retval; |
|
|
1119 } |
|
|
1120 |
|
5315
|
1121 lwork = static_cast<octave_idx_type> (std::real(z(0))); |
|
4329
|
1122 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
1123 z.resize (lwork); |
|
|
1124 Complex *pz = z.fortran_vec (); |
|
|
1125 |
|
|
1126 info = 0; |
|
|
1127 |
|
4330
|
1128 // Calculate the norm of the matrix, for later use. |
|
4329
|
1129 double anorm; |
|
|
1130 if (calc_cond) |
|
5275
|
1131 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1132 |
|
|
1133 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1134 |
|
|
1135 if (f77_exception_encountered) |
|
4329
|
1136 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1137 else |
|
|
1138 { |
|
4330
|
1139 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1140 rcond = 0.0; |
|
|
1141 if (info != 0) |
|
1948
|
1142 info = -1; |
|
4329
|
1143 else if (calc_cond) |
|
|
1144 { |
|
4330
|
1145 // Now calculate the condition number for non-singular matrix. |
|
5275
|
1146 octave_idx_type zgecon_info = 0; |
|
4329
|
1147 char job = '1'; |
|
|
1148 Array<double> rz (2 * nc); |
|
|
1149 double *prz = rz.fortran_vec (); |
|
4552
|
1150 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1151 nc, tmp_data, nr, anorm, |
|
5061
|
1152 rcond, pz, prz, zgecon_info |
|
4552
|
1153 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1154 |
|
|
1155 if (f77_exception_encountered) |
|
|
1156 (*current_liboctave_error_handler) |
|
|
1157 ("unrecoverable error in zgecon"); |
|
|
1158 |
|
5061
|
1159 if (zgecon_info != 0) |
|
4329
|
1160 info = -1; |
|
|
1161 } |
|
1948
|
1162 |
|
|
1163 if (info == -1 && ! force) |
|
|
1164 retval = *this; // Restore contents. |
|
|
1165 else |
|
|
1166 { |
|
5275
|
1167 octave_idx_type zgetri_info = 0; |
|
5061
|
1168 |
|
4329
|
1169 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
1170 pz, lwork, zgetri_info)); |
|
1948
|
1171 |
|
|
1172 if (f77_exception_encountered) |
|
|
1173 (*current_liboctave_error_handler) |
|
4329
|
1174 ("unrecoverable error in zgetri"); |
|
|
1175 |
|
5061
|
1176 if (zgetri_info != 0) |
|
4329
|
1177 info = -1; |
|
1948
|
1178 } |
|
|
1179 } |
|
6207
|
1180 |
|
|
1181 if (info != 0) |
|
|
1182 mattype.mark_as_rectangular(); |
|
458
|
1183 } |
|
4329
|
1184 |
|
1948
|
1185 return retval; |
|
458
|
1186 } |
|
|
1187 |
|
|
1188 ComplexMatrix |
|
6207
|
1189 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, |
|
|
1190 double& rcond, int force, int calc_cond) const |
|
|
1191 { |
|
|
1192 int typ = mattype.type (false); |
|
|
1193 ComplexMatrix ret; |
|
|
1194 |
|
|
1195 if (typ == MatrixType::Unknown) |
|
|
1196 typ = mattype.type (*this); |
|
|
1197 |
|
|
1198 if (typ == MatrixType::Upper || typ == MatrixType::Lower) |
|
|
1199 ret = tinverse (mattype, info, rcond, force, calc_cond); |
|
6840
|
1200 else |
|
6207
|
1201 { |
|
|
1202 if (mattype.is_hermitian ()) |
|
|
1203 { |
|
6486
|
1204 ComplexCHOL chol (*this, info, calc_cond); |
|
6207
|
1205 if (info == 0) |
|
6486
|
1206 { |
|
|
1207 if (calc_cond) |
|
|
1208 rcond = chol.rcond(); |
|
|
1209 else |
|
|
1210 rcond = 1.0; |
|
|
1211 ret = chol.inverse (); |
|
|
1212 } |
|
6207
|
1213 else |
|
|
1214 mattype.mark_as_unsymmetric (); |
|
|
1215 } |
|
|
1216 |
|
|
1217 if (!mattype.is_hermitian ()) |
|
|
1218 ret = finverse(mattype, info, rcond, force, calc_cond); |
|
6840
|
1219 |
|
7033
|
1220 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
|
6840
|
1221 ret = ComplexMatrix (rows (), columns (), Complex (octave_Inf, 0.)); |
|
6207
|
1222 } |
|
|
1223 |
|
|
1224 return ret; |
|
|
1225 } |
|
|
1226 |
|
|
1227 ComplexMatrix |
|
4384
|
1228 ComplexMatrix::pseudo_inverse (double tol) const |
|
740
|
1229 { |
|
1549
|
1230 ComplexMatrix retval; |
|
|
1231 |
|
3480
|
1232 ComplexSVD result (*this, SVD::economy); |
|
740
|
1233 |
|
|
1234 DiagMatrix S = result.singular_values (); |
|
|
1235 ComplexMatrix U = result.left_singular_matrix (); |
|
|
1236 ComplexMatrix V = result.right_singular_matrix (); |
|
|
1237 |
|
|
1238 ColumnVector sigma = S.diag (); |
|
|
1239 |
|
5275
|
1240 octave_idx_type r = sigma.length () - 1; |
|
|
1241 octave_idx_type nr = rows (); |
|
|
1242 octave_idx_type nc = cols (); |
|
740
|
1243 |
|
|
1244 if (tol <= 0.0) |
|
|
1245 { |
|
|
1246 if (nr > nc) |
|
|
1247 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
1248 else |
|
|
1249 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
1250 } |
|
|
1251 |
|
|
1252 while (r >= 0 && sigma.elem (r) < tol) |
|
|
1253 r--; |
|
|
1254 |
|
|
1255 if (r < 0) |
|
1549
|
1256 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
1257 else |
|
|
1258 { |
|
|
1259 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
1260 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
1261 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
1262 retval = Vr * D * Ur.hermitian (); |
|
740
|
1263 } |
|
1549
|
1264 |
|
|
1265 return retval; |
|
740
|
1266 } |
|
|
1267 |
|
4773
|
1268 #if defined (HAVE_FFTW3) |
|
3827
|
1269 |
|
|
1270 ComplexMatrix |
|
|
1271 ComplexMatrix::fourier (void) const |
|
|
1272 { |
|
|
1273 size_t nr = rows (); |
|
|
1274 size_t nc = cols (); |
|
|
1275 |
|
|
1276 ComplexMatrix retval (nr, nc); |
|
|
1277 |
|
|
1278 size_t npts, nsamples; |
|
|
1279 |
|
|
1280 if (nr == 1 || nc == 1) |
|
|
1281 { |
|
|
1282 npts = nr > nc ? nr : nc; |
|
|
1283 nsamples = 1; |
|
|
1284 } |
|
|
1285 else |
|
|
1286 { |
|
|
1287 npts = nr; |
|
|
1288 nsamples = nc; |
|
|
1289 } |
|
|
1290 |
|
|
1291 const Complex *in (data ()); |
|
|
1292 Complex *out (retval.fortran_vec ()); |
|
|
1293 |
|
4773
|
1294 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
1295 |
|
|
1296 return retval; |
|
|
1297 } |
|
|
1298 |
|
|
1299 ComplexMatrix |
|
|
1300 ComplexMatrix::ifourier (void) const |
|
|
1301 { |
|
|
1302 size_t nr = rows (); |
|
|
1303 size_t nc = cols (); |
|
|
1304 |
|
|
1305 ComplexMatrix retval (nr, nc); |
|
|
1306 |
|
|
1307 size_t npts, nsamples; |
|
|
1308 |
|
|
1309 if (nr == 1 || nc == 1) |
|
|
1310 { |
|
|
1311 npts = nr > nc ? nr : nc; |
|
|
1312 nsamples = 1; |
|
|
1313 } |
|
|
1314 else |
|
|
1315 { |
|
|
1316 npts = nr; |
|
|
1317 nsamples = nc; |
|
|
1318 } |
|
|
1319 |
|
|
1320 const Complex *in (data ()); |
|
|
1321 Complex *out (retval.fortran_vec ()); |
|
|
1322 |
|
4773
|
1323 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
1324 |
|
|
1325 return retval; |
|
|
1326 } |
|
|
1327 |
|
|
1328 ComplexMatrix |
|
|
1329 ComplexMatrix::fourier2d (void) const |
|
|
1330 { |
|
4773
|
1331 dim_vector dv(rows (), cols ()); |
|
|
1332 |
|
|
1333 ComplexMatrix retval (rows (), cols ()); |
|
|
1334 const Complex *in (data ()); |
|
|
1335 Complex *out (retval.fortran_vec ()); |
|
|
1336 |
|
|
1337 octave_fftw::fftNd (in, out, 2, dv); |
|
3827
|
1338 |
|
|
1339 return retval; |
|
|
1340 } |
|
|
1341 |
|
|
1342 ComplexMatrix |
|
|
1343 ComplexMatrix::ifourier2d (void) const |
|
|
1344 { |
|
4773
|
1345 dim_vector dv(rows (), cols ()); |
|
|
1346 |
|
|
1347 ComplexMatrix retval (rows (), cols ()); |
|
|
1348 const Complex *in (data ()); |
|
|
1349 Complex *out (retval.fortran_vec ()); |
|
|
1350 |
|
|
1351 octave_fftw::ifftNd (in, out, 2, dv); |
|
3827
|
1352 |
|
|
1353 return retval; |
|
|
1354 } |
|
|
1355 |
|
|
1356 #else |
|
|
1357 |
|
740
|
1358 ComplexMatrix |
|
458
|
1359 ComplexMatrix::fourier (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 (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1394 } |
|
1948
|
1395 |
|
|
1396 return retval; |
|
458
|
1397 } |
|
|
1398 |
|
|
1399 ComplexMatrix |
|
|
1400 ComplexMatrix::ifourier (void) const |
|
|
1401 { |
|
1948
|
1402 ComplexMatrix retval; |
|
|
1403 |
|
5275
|
1404 octave_idx_type nr = rows (); |
|
|
1405 octave_idx_type nc = cols (); |
|
|
1406 |
|
|
1407 octave_idx_type npts, nsamples; |
|
1948
|
1408 |
|
458
|
1409 if (nr == 1 || nc == 1) |
|
|
1410 { |
|
|
1411 npts = nr > nc ? nr : nc; |
|
|
1412 nsamples = 1; |
|
|
1413 } |
|
|
1414 else |
|
|
1415 { |
|
|
1416 npts = nr; |
|
|
1417 nsamples = nc; |
|
|
1418 } |
|
|
1419 |
|
5275
|
1420 octave_idx_type nn = 4*npts+15; |
|
1948
|
1421 |
|
|
1422 Array<Complex> wsave (nn); |
|
|
1423 Complex *pwsave = wsave.fortran_vec (); |
|
|
1424 |
|
|
1425 retval = *this; |
|
|
1426 Complex *tmp_data = retval.fortran_vec (); |
|
|
1427 |
|
3887
|
1428 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1429 |
|
5275
|
1430 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1431 { |
|
|
1432 OCTAVE_QUIT; |
|
|
1433 |
|
|
1434 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1435 } |
|
458
|
1436 |
|
5275
|
1437 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1438 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1439 |
|
1948
|
1440 return retval; |
|
458
|
1441 } |
|
|
1442 |
|
677
|
1443 ComplexMatrix |
|
|
1444 ComplexMatrix::fourier2d (void) const |
|
|
1445 { |
|
1948
|
1446 ComplexMatrix retval; |
|
|
1447 |
|
5275
|
1448 octave_idx_type nr = rows (); |
|
|
1449 octave_idx_type nc = cols (); |
|
|
1450 |
|
|
1451 octave_idx_type npts, nsamples; |
|
1948
|
1452 |
|
677
|
1453 if (nr == 1 || nc == 1) |
|
|
1454 { |
|
|
1455 npts = nr > nc ? nr : nc; |
|
|
1456 nsamples = 1; |
|
|
1457 } |
|
|
1458 else |
|
|
1459 { |
|
|
1460 npts = nr; |
|
|
1461 nsamples = nc; |
|
|
1462 } |
|
|
1463 |
|
5275
|
1464 octave_idx_type nn = 4*npts+15; |
|
1948
|
1465 |
|
|
1466 Array<Complex> wsave (nn); |
|
|
1467 Complex *pwsave = wsave.fortran_vec (); |
|
|
1468 |
|
|
1469 retval = *this; |
|
|
1470 Complex *tmp_data = retval.fortran_vec (); |
|
|
1471 |
|
3887
|
1472 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1473 |
|
5275
|
1474 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1475 { |
|
|
1476 OCTAVE_QUIT; |
|
|
1477 |
|
|
1478 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1479 } |
|
677
|
1480 |
|
|
1481 npts = nc; |
|
|
1482 nsamples = nr; |
|
|
1483 nn = 4*npts+15; |
|
1948
|
1484 |
|
|
1485 wsave.resize (nn); |
|
|
1486 pwsave = wsave.fortran_vec (); |
|
|
1487 |
|
4773
|
1488 Array<Complex> tmp (npts); |
|
|
1489 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1490 |
|
3887
|
1491 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1492 |
|
5275
|
1493 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1494 { |
|
4153
|
1495 OCTAVE_QUIT; |
|
|
1496 |
|
5275
|
1497 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1498 prow[i] = tmp_data[i*nr + j]; |
|
|
1499 |
|
3887
|
1500 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1501 |
|
5275
|
1502 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1503 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1504 } |
|
|
1505 |
|
1948
|
1506 return retval; |
|
677
|
1507 } |
|
|
1508 |
|
|
1509 ComplexMatrix |
|
|
1510 ComplexMatrix::ifourier2d (void) const |
|
|
1511 { |
|
1948
|
1512 ComplexMatrix retval; |
|
|
1513 |
|
5275
|
1514 octave_idx_type nr = rows (); |
|
|
1515 octave_idx_type nc = cols (); |
|
|
1516 |
|
|
1517 octave_idx_type npts, nsamples; |
|
1948
|
1518 |
|
677
|
1519 if (nr == 1 || nc == 1) |
|
|
1520 { |
|
|
1521 npts = nr > nc ? nr : nc; |
|
|
1522 nsamples = 1; |
|
|
1523 } |
|
|
1524 else |
|
|
1525 { |
|
|
1526 npts = nr; |
|
|
1527 nsamples = nc; |
|
|
1528 } |
|
|
1529 |
|
5275
|
1530 octave_idx_type nn = 4*npts+15; |
|
1948
|
1531 |
|
|
1532 Array<Complex> wsave (nn); |
|
|
1533 Complex *pwsave = wsave.fortran_vec (); |
|
|
1534 |
|
|
1535 retval = *this; |
|
|
1536 Complex *tmp_data = retval.fortran_vec (); |
|
|
1537 |
|
3887
|
1538 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1539 |
|
5275
|
1540 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1541 { |
|
|
1542 OCTAVE_QUIT; |
|
|
1543 |
|
|
1544 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1545 } |
|
677
|
1546 |
|
5275
|
1547 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1548 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1549 |
|
|
1550 npts = nc; |
|
|
1551 nsamples = nr; |
|
|
1552 nn = 4*npts+15; |
|
1948
|
1553 |
|
|
1554 wsave.resize (nn); |
|
|
1555 pwsave = wsave.fortran_vec (); |
|
|
1556 |
|
4773
|
1557 Array<Complex> tmp (npts); |
|
|
1558 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1559 |
|
3887
|
1560 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1561 |
|
5275
|
1562 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1563 { |
|
4153
|
1564 OCTAVE_QUIT; |
|
|
1565 |
|
5275
|
1566 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1567 prow[i] = tmp_data[i*nr + j]; |
|
|
1568 |
|
3887
|
1569 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1570 |
|
5275
|
1571 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1572 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1573 } |
|
|
1574 |
|
1948
|
1575 return retval; |
|
677
|
1576 } |
|
|
1577 |
|
3827
|
1578 #endif |
|
|
1579 |
|
458
|
1580 ComplexDET |
|
|
1581 ComplexMatrix::determinant (void) const |
|
|
1582 { |
|
5275
|
1583 octave_idx_type info; |
|
458
|
1584 double rcond; |
|
4329
|
1585 return determinant (info, rcond, 0); |
|
458
|
1586 } |
|
|
1587 |
|
|
1588 ComplexDET |
|
5275
|
1589 ComplexMatrix::determinant (octave_idx_type& info) const |
|
458
|
1590 { |
|
|
1591 double rcond; |
|
4329
|
1592 return determinant (info, rcond, 0); |
|
458
|
1593 } |
|
|
1594 |
|
|
1595 ComplexDET |
|
5275
|
1596 ComplexMatrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1597 { |
|
|
1598 ComplexDET retval; |
|
|
1599 |
|
5275
|
1600 octave_idx_type nr = rows (); |
|
|
1601 octave_idx_type nc = cols (); |
|
458
|
1602 |
|
|
1603 if (nr == 0 || nc == 0) |
|
|
1604 { |
|
5634
|
1605 retval = ComplexDET (1.0, 0); |
|
458
|
1606 } |
|
|
1607 else |
|
|
1608 { |
|
5275
|
1609 Array<octave_idx_type> ipvt (nr); |
|
|
1610 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1611 |
|
|
1612 ComplexMatrix atmp = *this; |
|
|
1613 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1614 |
|
4329
|
1615 info = 0; |
|
|
1616 |
|
4330
|
1617 // Calculate the norm of the matrix, for later use. |
|
4329
|
1618 double anorm = 0; |
|
|
1619 if (calc_cond) |
|
5275
|
1620 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1621 |
|
|
1622 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1623 |
|
|
1624 if (f77_exception_encountered) |
|
4329
|
1625 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
458
|
1626 else |
|
|
1627 { |
|
4330
|
1628 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1629 rcond = 0.0; |
|
|
1630 if (info != 0) |
|
1948
|
1631 { |
|
|
1632 info = -1; |
|
|
1633 retval = ComplexDET (); |
|
4329
|
1634 } |
|
|
1635 else |
|
1948
|
1636 { |
|
4329
|
1637 if (calc_cond) |
|
|
1638 { |
|
4330
|
1639 // Now calc the condition number for non-singular matrix. |
|
4329
|
1640 char job = '1'; |
|
|
1641 Array<Complex> z (2*nr); |
|
|
1642 Complex *pz = z.fortran_vec (); |
|
|
1643 Array<double> rz (2*nr); |
|
|
1644 double *prz = rz.fortran_vec (); |
|
|
1645 |
|
4552
|
1646 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1647 nc, tmp_data, nr, anorm, |
|
|
1648 rcond, pz, prz, info |
|
|
1649 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1650 |
|
|
1651 if (f77_exception_encountered) |
|
|
1652 (*current_liboctave_error_handler) |
|
|
1653 ("unrecoverable error in zgecon"); |
|
|
1654 } |
|
|
1655 |
|
4509
|
1656 if (info != 0) |
|
4329
|
1657 { |
|
|
1658 info = -1; |
|
|
1659 retval = ComplexDET (); |
|
|
1660 } |
|
|
1661 else |
|
|
1662 { |
|
5634
|
1663 Complex c = 1.0; |
|
|
1664 int e = 0; |
|
|
1665 |
|
|
1666 for (octave_idx_type i = 0; i < nc; i++) |
|
4329
|
1667 { |
|
5634
|
1668 if (ipvt(i) != (i+1)) |
|
|
1669 c = -c; |
|
|
1670 |
|
|
1671 c *= atmp(i,i); |
|
|
1672 |
|
|
1673 if (c == 0.0) |
|
|
1674 break; |
|
|
1675 |
|
|
1676 while (std::abs(c) < 0.5) |
|
4329
|
1677 { |
|
5634
|
1678 c *= 2.0; |
|
|
1679 e--; |
|
4329
|
1680 } |
|
5634
|
1681 |
|
|
1682 while (std::abs(c) >= 2.0) |
|
4329
|
1683 { |
|
5634
|
1684 c /= 2.0; |
|
|
1685 e++; |
|
4329
|
1686 } |
|
|
1687 } |
|
5634
|
1688 |
|
|
1689 retval = ComplexDET (c, e); |
|
4329
|
1690 } |
|
1948
|
1691 } |
|
458
|
1692 } |
|
|
1693 } |
|
4329
|
1694 |
|
458
|
1695 return retval; |
|
|
1696 } |
|
|
1697 |
|
|
1698 ComplexMatrix |
|
5785
|
1699 ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1700 octave_idx_type& info, double& rcond, |
|
|
1701 solve_singularity_handler sing_handler, |
|
|
1702 bool calc_cond) const |
|
|
1703 { |
|
|
1704 ComplexMatrix retval; |
|
|
1705 |
|
|
1706 octave_idx_type nr = rows (); |
|
|
1707 octave_idx_type nc = cols (); |
|
|
1708 |
|
6924
|
1709 if (nr != b.rows ()) |
|
5785
|
1710 (*current_liboctave_error_handler) |
|
|
1711 ("matrix dimension mismatch solution of linear equations"); |
|
6924
|
1712 else if (nr == 0 || nc == 0 || b.cols () == 0) |
|
|
1713 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); |
|
5785
|
1714 else |
|
|
1715 { |
|
|
1716 volatile int typ = mattype.type (); |
|
|
1717 |
|
|
1718 if (typ == MatrixType::Permuted_Upper || |
|
|
1719 typ == MatrixType::Upper) |
|
|
1720 { |
|
|
1721 octave_idx_type b_nc = b.cols (); |
|
|
1722 rcond = 1.; |
|
|
1723 info = 0; |
|
|
1724 |
|
|
1725 if (typ == MatrixType::Permuted_Upper) |
|
|
1726 { |
|
|
1727 (*current_liboctave_error_handler) |
|
6390
|
1728 ("permuted triangular matrix not implemented"); |
|
5785
|
1729 } |
|
|
1730 else |
|
|
1731 { |
|
|
1732 const Complex *tmp_data = fortran_vec (); |
|
|
1733 |
|
|
1734 if (calc_cond) |
|
|
1735 { |
|
|
1736 char norm = '1'; |
|
|
1737 char uplo = 'U'; |
|
|
1738 char dia = 'N'; |
|
|
1739 |
|
|
1740 Array<Complex> z (2 * nc); |
|
|
1741 Complex *pz = z.fortran_vec (); |
|
|
1742 Array<double> rz (nc); |
|
|
1743 double *prz = rz.fortran_vec (); |
|
|
1744 |
|
|
1745 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1746 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1747 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1748 nr, tmp_data, nr, rcond, |
|
|
1749 pz, prz, info |
|
|
1750 F77_CHAR_ARG_LEN (1) |
|
|
1751 F77_CHAR_ARG_LEN (1) |
|
|
1752 F77_CHAR_ARG_LEN (1))); |
|
|
1753 |
|
|
1754 if (f77_exception_encountered) |
|
|
1755 (*current_liboctave_error_handler) |
|
|
1756 ("unrecoverable error in ztrcon"); |
|
|
1757 |
|
|
1758 if (info != 0) |
|
|
1759 info = -2; |
|
|
1760 |
|
|
1761 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1762 |
|
|
1763 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1764 { |
|
|
1765 info = -2; |
|
|
1766 |
|
|
1767 if (sing_handler) |
|
|
1768 sing_handler (rcond); |
|
|
1769 else |
|
|
1770 (*current_liboctave_error_handler) |
|
|
1771 ("matrix singular to machine precision, rcond = %g", |
|
|
1772 rcond); |
|
|
1773 } |
|
|
1774 } |
|
|
1775 |
|
|
1776 if (info == 0) |
|
|
1777 { |
|
|
1778 retval = b; |
|
|
1779 Complex *result = retval.fortran_vec (); |
|
|
1780 |
|
|
1781 char uplo = 'U'; |
|
|
1782 char trans = 'N'; |
|
|
1783 char dia = 'N'; |
|
|
1784 |
|
|
1785 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1786 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1787 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1788 nr, b_nc, tmp_data, nr, |
|
|
1789 result, nr, info |
|
|
1790 F77_CHAR_ARG_LEN (1) |
|
|
1791 F77_CHAR_ARG_LEN (1) |
|
|
1792 F77_CHAR_ARG_LEN (1))); |
|
|
1793 |
|
|
1794 if (f77_exception_encountered) |
|
|
1795 (*current_liboctave_error_handler) |
|
|
1796 ("unrecoverable error in dtrtrs"); |
|
|
1797 } |
|
|
1798 } |
|
|
1799 } |
|
|
1800 else |
|
|
1801 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1802 } |
|
|
1803 |
|
|
1804 return retval; |
|
|
1805 } |
|
|
1806 |
|
|
1807 ComplexMatrix |
|
|
1808 ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1809 octave_idx_type& info, double& rcond, |
|
|
1810 solve_singularity_handler sing_handler, |
|
|
1811 bool calc_cond) const |
|
|
1812 { |
|
|
1813 ComplexMatrix retval; |
|
|
1814 |
|
|
1815 octave_idx_type nr = rows (); |
|
|
1816 octave_idx_type nc = cols (); |
|
|
1817 |
|
6924
|
1818 if (nr != b.rows ()) |
|
5785
|
1819 (*current_liboctave_error_handler) |
|
|
1820 ("matrix dimension mismatch solution of linear equations"); |
|
6924
|
1821 else if (nr == 0 || nc == 0 || b.cols () == 0) |
|
|
1822 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); |
|
5785
|
1823 else |
|
|
1824 { |
|
|
1825 volatile int typ = mattype.type (); |
|
|
1826 |
|
|
1827 if (typ == MatrixType::Permuted_Lower || |
|
|
1828 typ == MatrixType::Lower) |
|
|
1829 { |
|
|
1830 octave_idx_type b_nc = b.cols (); |
|
|
1831 rcond = 1.; |
|
|
1832 info = 0; |
|
|
1833 |
|
|
1834 if (typ == MatrixType::Permuted_Lower) |
|
|
1835 { |
|
|
1836 (*current_liboctave_error_handler) |
|
6390
|
1837 ("permuted triangular matrix not implemented"); |
|
5785
|
1838 } |
|
|
1839 else |
|
|
1840 { |
|
|
1841 const Complex *tmp_data = fortran_vec (); |
|
|
1842 |
|
|
1843 if (calc_cond) |
|
|
1844 { |
|
|
1845 char norm = '1'; |
|
|
1846 char uplo = 'L'; |
|
|
1847 char dia = 'N'; |
|
|
1848 |
|
|
1849 Array<Complex> z (2 * nc); |
|
|
1850 Complex *pz = z.fortran_vec (); |
|
|
1851 Array<double> rz (nc); |
|
|
1852 double *prz = rz.fortran_vec (); |
|
|
1853 |
|
|
1854 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1855 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1856 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1857 nr, tmp_data, nr, rcond, |
|
|
1858 pz, prz, info |
|
|
1859 F77_CHAR_ARG_LEN (1) |
|
|
1860 F77_CHAR_ARG_LEN (1) |
|
|
1861 F77_CHAR_ARG_LEN (1))); |
|
|
1862 |
|
|
1863 if (f77_exception_encountered) |
|
|
1864 (*current_liboctave_error_handler) |
|
|
1865 ("unrecoverable error in ztrcon"); |
|
|
1866 |
|
|
1867 if (info != 0) |
|
|
1868 info = -2; |
|
|
1869 |
|
|
1870 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1871 |
|
|
1872 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1873 { |
|
|
1874 info = -2; |
|
|
1875 |
|
|
1876 if (sing_handler) |
|
|
1877 sing_handler (rcond); |
|
|
1878 else |
|
|
1879 (*current_liboctave_error_handler) |
|
|
1880 ("matrix singular to machine precision, rcond = %g", |
|
|
1881 rcond); |
|
|
1882 } |
|
|
1883 } |
|
|
1884 |
|
|
1885 if (info == 0) |
|
|
1886 { |
|
|
1887 retval = b; |
|
|
1888 Complex *result = retval.fortran_vec (); |
|
|
1889 |
|
|
1890 char uplo = 'L'; |
|
|
1891 char trans = 'N'; |
|
|
1892 char dia = 'N'; |
|
|
1893 |
|
|
1894 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1895 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1896 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1897 nr, b_nc, tmp_data, nr, |
|
|
1898 result, nr, info |
|
|
1899 F77_CHAR_ARG_LEN (1) |
|
|
1900 F77_CHAR_ARG_LEN (1) |
|
|
1901 F77_CHAR_ARG_LEN (1))); |
|
|
1902 |
|
|
1903 if (f77_exception_encountered) |
|
|
1904 (*current_liboctave_error_handler) |
|
|
1905 ("unrecoverable error in dtrtrs"); |
|
|
1906 } |
|
|
1907 } |
|
|
1908 } |
|
|
1909 else |
|
|
1910 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1911 } |
|
|
1912 |
|
|
1913 return retval; |
|
|
1914 } |
|
|
1915 |
|
|
1916 ComplexMatrix |
|
|
1917 ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
1918 octave_idx_type& info, double& rcond, |
|
|
1919 solve_singularity_handler sing_handler, |
|
|
1920 bool calc_cond) const |
|
|
1921 { |
|
|
1922 ComplexMatrix retval; |
|
|
1923 |
|
|
1924 octave_idx_type nr = rows (); |
|
|
1925 octave_idx_type nc = cols (); |
|
|
1926 |
|
6924
|
1927 |
|
|
1928 if (nr != nc || nr != b.rows ()) |
|
5785
|
1929 (*current_liboctave_error_handler) |
|
6924
|
1930 ("matrix dimension mismatch solution of linear equations"); |
|
|
1931 else if (nr == 0 || b.cols () == 0) |
|
|
1932 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); |
|
5785
|
1933 else |
|
|
1934 { |
|
|
1935 volatile int typ = mattype.type (); |
|
|
1936 |
|
|
1937 // Calculate the norm of the matrix, for later use. |
|
|
1938 double anorm = -1.; |
|
|
1939 |
|
|
1940 if (typ == MatrixType::Hermitian) |
|
|
1941 { |
|
|
1942 info = 0; |
|
|
1943 char job = 'L'; |
|
|
1944 ComplexMatrix atmp = *this; |
|
|
1945 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1946 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1947 |
|
|
1948 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
|
1949 tmp_data, nr, info |
|
|
1950 F77_CHAR_ARG_LEN (1))); |
|
|
1951 |
|
|
1952 if (f77_exception_encountered) |
|
|
1953 (*current_liboctave_error_handler) |
|
|
1954 ("unrecoverable error in zpotrf"); |
|
|
1955 else |
|
|
1956 { |
|
|
1957 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1958 rcond = 0.0; |
|
|
1959 if (info != 0) |
|
|
1960 { |
|
|
1961 info = -2; |
|
|
1962 |
|
|
1963 mattype.mark_as_unsymmetric (); |
|
|
1964 typ = MatrixType::Full; |
|
|
1965 } |
|
|
1966 else |
|
|
1967 { |
|
|
1968 if (calc_cond) |
|
|
1969 { |
|
|
1970 Array<Complex> z (2 * nc); |
|
|
1971 Complex *pz = z.fortran_vec (); |
|
|
1972 Array<double> rz (nc); |
|
|
1973 double *prz = rz.fortran_vec (); |
|
|
1974 |
|
|
1975 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1976 nr, tmp_data, nr, anorm, |
|
|
1977 rcond, pz, prz, info |
|
|
1978 F77_CHAR_ARG_LEN (1))); |
|
|
1979 |
|
|
1980 if (f77_exception_encountered) |
|
|
1981 (*current_liboctave_error_handler) |
|
|
1982 ("unrecoverable error in zpocon"); |
|
|
1983 |
|
|
1984 if (info != 0) |
|
|
1985 info = -2; |
|
|
1986 |
|
|
1987 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1988 |
|
|
1989 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1990 { |
|
|
1991 info = -2; |
|
|
1992 |
|
|
1993 if (sing_handler) |
|
|
1994 sing_handler (rcond); |
|
|
1995 else |
|
|
1996 (*current_liboctave_error_handler) |
|
|
1997 ("matrix singular to machine precision, rcond = %g", |
|
|
1998 rcond); |
|
|
1999 } |
|
|
2000 } |
|
|
2001 |
|
|
2002 if (info == 0) |
|
|
2003 { |
|
|
2004 retval = b; |
|
|
2005 Complex *result = retval.fortran_vec (); |
|
|
2006 |
|
|
2007 octave_idx_type b_nc = b.cols (); |
|
|
2008 |
|
|
2009 F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2010 nr, b_nc, tmp_data, nr, |
|
|
2011 result, b.rows(), info |
|
|
2012 F77_CHAR_ARG_LEN (1))); |
|
|
2013 |
|
|
2014 if (f77_exception_encountered) |
|
|
2015 (*current_liboctave_error_handler) |
|
|
2016 ("unrecoverable error in zpotrs"); |
|
|
2017 } |
|
|
2018 else |
|
|
2019 { |
|
|
2020 mattype.mark_as_unsymmetric (); |
|
|
2021 typ = MatrixType::Full; |
|
|
2022 } |
|
|
2023 } |
|
|
2024 } |
|
|
2025 } |
|
|
2026 |
|
|
2027 if (typ == MatrixType::Full) |
|
|
2028 { |
|
|
2029 info = 0; |
|
|
2030 |
|
|
2031 Array<octave_idx_type> ipvt (nr); |
|
|
2032 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
|
2033 |
|
|
2034 ComplexMatrix atmp = *this; |
|
|
2035 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2036 |
|
|
2037 Array<Complex> z (2 * nc); |
|
|
2038 Complex *pz = z.fortran_vec (); |
|
|
2039 Array<double> rz (2 * nc); |
|
|
2040 double *prz = rz.fortran_vec (); |
|
|
2041 |
|
|
2042 // Calculate the norm of the matrix, for later use. |
|
|
2043 if (anorm < 0.) |
|
|
2044 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
2045 |
|
|
2046 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
|
2047 |
|
|
2048 if (f77_exception_encountered) |
|
|
2049 (*current_liboctave_error_handler) |
|
|
2050 ("unrecoverable error in zgetrf"); |
|
|
2051 else |
|
|
2052 { |
|
|
2053 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
2054 rcond = 0.0; |
|
|
2055 if (info != 0) |
|
|
2056 { |
|
|
2057 info = -2; |
|
|
2058 |
|
|
2059 if (sing_handler) |
|
|
2060 sing_handler (rcond); |
|
|
2061 else |
|
|
2062 (*current_liboctave_error_handler) |
|
|
2063 ("matrix singular to machine precision"); |
|
|
2064 |
|
|
2065 mattype.mark_as_rectangular (); |
|
|
2066 } |
|
|
2067 else |
|
|
2068 { |
|
|
2069 if (calc_cond) |
|
|
2070 { |
|
|
2071 // Now calculate the condition number for |
|
|
2072 // non-singular matrix. |
|
|
2073 char job = '1'; |
|
|
2074 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2075 nc, tmp_data, nr, anorm, |
|
|
2076 rcond, pz, prz, info |
|
|
2077 F77_CHAR_ARG_LEN (1))); |
|
|
2078 |
|
|
2079 if (f77_exception_encountered) |
|
|
2080 (*current_liboctave_error_handler) |
|
|
2081 ("unrecoverable error in zgecon"); |
|
|
2082 |
|
|
2083 if (info != 0) |
|
|
2084 info = -2; |
|
|
2085 |
|
|
2086 volatile double rcond_plus_one = rcond + 1.0; |
|
|
2087 |
|
|
2088 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
2089 { |
|
|
2090 info = -2; |
|
|
2091 |
|
|
2092 if (sing_handler) |
|
|
2093 sing_handler (rcond); |
|
|
2094 else |
|
|
2095 (*current_liboctave_error_handler) |
|
|
2096 ("matrix singular to machine precision, rcond = %g", |
|
|
2097 rcond); |
|
|
2098 } |
|
|
2099 } |
|
|
2100 |
|
|
2101 if (info == 0) |
|
|
2102 { |
|
|
2103 retval = b; |
|
|
2104 Complex *result = retval.fortran_vec (); |
|
|
2105 |
|
|
2106 octave_idx_type b_nc = b.cols (); |
|
|
2107 |
|
|
2108 char job = 'N'; |
|
|
2109 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2110 nr, b_nc, tmp_data, nr, |
|
|
2111 pipvt, result, b.rows(), info |
|
|
2112 F77_CHAR_ARG_LEN (1))); |
|
|
2113 |
|
|
2114 if (f77_exception_encountered) |
|
|
2115 (*current_liboctave_error_handler) |
|
|
2116 ("unrecoverable error in zgetrs"); |
|
|
2117 } |
|
|
2118 else |
|
|
2119 mattype.mark_as_rectangular (); |
|
|
2120 } |
|
|
2121 } |
|
|
2122 } |
|
|
2123 } |
|
|
2124 |
|
|
2125 return retval; |
|
|
2126 } |
|
|
2127 |
|
|
2128 ComplexMatrix |
|
|
2129 ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const |
|
|
2130 { |
|
|
2131 octave_idx_type info; |
|
|
2132 double rcond; |
|
|
2133 return solve (typ, b, info, rcond, 0); |
|
|
2134 } |
|
|
2135 |
|
|
2136 ComplexMatrix |
|
|
2137 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, |
|
|
2138 octave_idx_type& info) const |
|
|
2139 { |
|
|
2140 double rcond; |
|
|
2141 return solve (typ, b, info, rcond, 0); |
|
|
2142 } |
|
|
2143 |
|
|
2144 ComplexMatrix |
|
|
2145 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
2146 double& rcond) const |
|
|
2147 { |
|
|
2148 return solve (typ, b, info, rcond, 0); |
|
|
2149 } |
|
|
2150 |
|
|
2151 ComplexMatrix |
|
|
2152 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
2153 double& rcond, solve_singularity_handler sing_handler, |
|
|
2154 bool singular_fallback) const |
|
|
2155 { |
|
|
2156 ComplexMatrix tmp (b); |
|
|
2157 return solve (typ, tmp, info, rcond, sing_handler, singular_fallback); |
|
|
2158 } |
|
|
2159 |
|
|
2160 ComplexMatrix |
|
|
2161 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const |
|
|
2162 { |
|
|
2163 octave_idx_type info; |
|
|
2164 double rcond; |
|
|
2165 return solve (typ, b, info, rcond, 0); |
|
|
2166 } |
|
|
2167 |
|
|
2168 ComplexMatrix |
|
|
2169 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
2170 octave_idx_type& info) const |
|
|
2171 { |
|
|
2172 double rcond; |
|
|
2173 return solve (typ, b, info, rcond, 0); |
|
|
2174 } |
|
|
2175 |
|
|
2176 ComplexMatrix |
|
|
2177 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
2178 octave_idx_type& info, double& rcond) const |
|
|
2179 { |
|
|
2180 return solve (typ, b, info, rcond, 0); |
|
|
2181 } |
|
|
2182 |
|
|
2183 ComplexMatrix |
|
|
2184 ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, |
|
|
2185 octave_idx_type& info, double& rcond, |
|
|
2186 solve_singularity_handler sing_handler, |
|
|
2187 bool singular_fallback) const |
|
|
2188 { |
|
|
2189 ComplexMatrix retval; |
|
|
2190 int typ = mattype.type (); |
|
|
2191 |
|
|
2192 if (typ == MatrixType::Unknown) |
|
|
2193 typ = mattype.type (*this); |
|
|
2194 |
|
|
2195 // Only calculate the condition number for LU/Cholesky |
|
|
2196 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
|
2197 retval = utsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
2198 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
|
2199 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
2200 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
|
2201 retval = fsolve (mattype, b, info, rcond, sing_handler, true); |
|
|
2202 else if (typ != MatrixType::Rectangular) |
|
|
2203 { |
|
|
2204 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
|
2205 return ComplexMatrix (); |
|
|
2206 } |
|
|
2207 |
|
|
2208 // Rectangular or one of the above solvers flags a singular matrix |
|
|
2209 if (singular_fallback && mattype.type () == MatrixType::Rectangular) |
|
|
2210 { |
|
|
2211 octave_idx_type rank; |
|
7076
|
2212 retval = lssolve (b, info, rank, rcond); |
|
5785
|
2213 } |
|
|
2214 |
|
|
2215 return retval; |
|
|
2216 } |
|
|
2217 |
|
|
2218 ComplexColumnVector |
|
|
2219 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const |
|
|
2220 { |
|
|
2221 octave_idx_type info; |
|
|
2222 double rcond; |
|
|
2223 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2224 } |
|
|
2225 |
|
|
2226 ComplexColumnVector |
|
|
2227 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2228 octave_idx_type& info) const |
|
|
2229 { |
|
|
2230 double rcond; |
|
|
2231 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2232 } |
|
|
2233 |
|
|
2234 ComplexColumnVector |
|
|
2235 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2236 octave_idx_type& info, double& rcond) const |
|
|
2237 { |
|
|
2238 return solve (typ, ComplexColumnVector (b), info, rcond, 0); |
|
|
2239 } |
|
|
2240 |
|
|
2241 ComplexColumnVector |
|
|
2242 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
2243 octave_idx_type& info, double& rcond, |
|
|
2244 solve_singularity_handler sing_handler) const |
|
|
2245 { |
|
|
2246 return solve (typ, ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
2247 } |
|
|
2248 |
|
|
2249 ComplexColumnVector |
|
|
2250 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const |
|
|
2251 { |
|
|
2252 octave_idx_type info; |
|
|
2253 double rcond; |
|
|
2254 return solve (typ, b, info, rcond, 0); |
|
|
2255 } |
|
|
2256 |
|
|
2257 ComplexColumnVector |
|
|
2258 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2259 octave_idx_type& info) const |
|
|
2260 { |
|
|
2261 double rcond; |
|
|
2262 return solve (typ, b, info, rcond, 0); |
|
|
2263 } |
|
|
2264 |
|
|
2265 ComplexColumnVector |
|
|
2266 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2267 octave_idx_type& info, double& rcond) const |
|
|
2268 { |
|
|
2269 return solve (typ, b, info, rcond, 0); |
|
|
2270 } |
|
|
2271 |
|
|
2272 ComplexColumnVector |
|
|
2273 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
2274 octave_idx_type& info, double& rcond, |
|
|
2275 solve_singularity_handler sing_handler) const |
|
|
2276 { |
|
|
2277 |
|
|
2278 ComplexMatrix tmp (b); |
|
|
2279 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); |
|
|
2280 } |
|
|
2281 |
|
|
2282 ComplexMatrix |
|
458
|
2283 ComplexMatrix::solve (const Matrix& b) const |
|
|
2284 { |
|
5275
|
2285 octave_idx_type info; |
|
458
|
2286 double rcond; |
|
3480
|
2287 return solve (b, info, rcond, 0); |
|
458
|
2288 } |
|
|
2289 |
|
|
2290 ComplexMatrix |
|
5275
|
2291 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
2292 { |
|
|
2293 double rcond; |
|
3480
|
2294 return solve (b, info, rcond, 0); |
|
458
|
2295 } |
|
|
2296 |
|
|
2297 ComplexMatrix |
|
5275
|
2298 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
2299 { |
|
3480
|
2300 return solve (b, info, rcond, 0); |
|
|
2301 } |
|
|
2302 |
|
|
2303 ComplexMatrix |
|
5275
|
2304 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
2305 solve_singularity_handler sing_handler) const |
|
|
2306 { |
|
458
|
2307 ComplexMatrix tmp (b); |
|
3480
|
2308 return solve (tmp, info, rcond, sing_handler); |
|
458
|
2309 } |
|
|
2310 |
|
|
2311 ComplexMatrix |
|
|
2312 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
2313 { |
|
5275
|
2314 octave_idx_type info; |
|
458
|
2315 double rcond; |
|
3480
|
2316 return solve (b, info, rcond, 0); |
|
458
|
2317 } |
|
|
2318 |
|
|
2319 ComplexMatrix |
|
5275
|
2320 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
2321 { |
|
|
2322 double rcond; |
|
3480
|
2323 return solve (b, info, rcond, 0); |
|
458
|
2324 } |
|
3480
|
2325 |
|
458
|
2326 ComplexMatrix |
|
5275
|
2327 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
2328 { |
|
3480
|
2329 return solve (b, info, rcond, 0); |
|
|
2330 } |
|
|
2331 |
|
|
2332 ComplexMatrix |
|
5275
|
2333 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
2334 solve_singularity_handler sing_handler) const |
|
|
2335 { |
|
5785
|
2336 MatrixType mattype (*this); |
|
6060
|
2337 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
2338 } |
|
|
2339 |
|
|
2340 ComplexColumnVector |
|
3585
|
2341 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
2342 { |
|
5275
|
2343 octave_idx_type info; |
|
3585
|
2344 double rcond; |
|
|
2345 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2346 } |
|
|
2347 |
|
|
2348 ComplexColumnVector |
|
5275
|
2349 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
2350 { |
|
|
2351 double rcond; |
|
|
2352 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2353 } |
|
|
2354 |
|
|
2355 ComplexColumnVector |
|
5785
|
2356 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
|
|
2357 double& rcond) const |
|
3585
|
2358 { |
|
|
2359 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
2360 } |
|
|
2361 |
|
|
2362 ComplexColumnVector |
|
5785
|
2363 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
|
|
2364 double& rcond, |
|
3585
|
2365 solve_singularity_handler sing_handler) const |
|
|
2366 { |
|
|
2367 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
2368 } |
|
|
2369 |
|
|
2370 ComplexColumnVector |
|
458
|
2371 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
2372 { |
|
5275
|
2373 octave_idx_type info; |
|
458
|
2374 double rcond; |
|
3480
|
2375 return solve (b, info, rcond, 0); |
|
458
|
2376 } |
|
|
2377 |
|
|
2378 ComplexColumnVector |
|
5275
|
2379 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2380 { |
|
|
2381 double rcond; |
|
3480
|
2382 return solve (b, info, rcond, 0); |
|
458
|
2383 } |
|
|
2384 |
|
|
2385 ComplexColumnVector |
|
5275
|
2386 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
532
|
2387 double& rcond) const |
|
458
|
2388 { |
|
3480
|
2389 return solve (b, info, rcond, 0); |
|
|
2390 } |
|
|
2391 |
|
|
2392 ComplexColumnVector |
|
5275
|
2393 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
3480
|
2394 double& rcond, |
|
|
2395 solve_singularity_handler sing_handler) const |
|
|
2396 { |
|
5785
|
2397 MatrixType mattype (*this); |
|
|
2398 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
2399 } |
|
|
2400 |
|
|
2401 ComplexMatrix |
|
3585
|
2402 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
2403 { |
|
5275
|
2404 octave_idx_type info; |
|
|
2405 octave_idx_type rank; |
|
7076
|
2406 double rcond; |
|
|
2407 return lssolve (ComplexMatrix (b), info, rank, rcond); |
|
3585
|
2408 } |
|
|
2409 |
|
|
2410 ComplexMatrix |
|
5275
|
2411 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
3585
|
2412 { |
|
5275
|
2413 octave_idx_type rank; |
|
7076
|
2414 double rcond; |
|
|
2415 return lssolve (ComplexMatrix (b), info, rank, rcond); |
|
3585
|
2416 } |
|
|
2417 |
|
|
2418 ComplexMatrix |
|
7076
|
2419 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, |
|
|
2420 octave_idx_type& rank) const |
|
3585
|
2421 { |
|
7076
|
2422 double rcond; |
|
|
2423 return lssolve (ComplexMatrix (b), info, rank, rcond); |
|
|
2424 } |
|
|
2425 |
|
|
2426 ComplexMatrix |
|
|
2427 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, |
|
|
2428 octave_idx_type& rank, double& rcond) const |
|
|
2429 { |
|
|
2430 return lssolve (ComplexMatrix (b), info, rank, rcond); |
|
3585
|
2431 } |
|
|
2432 |
|
|
2433 ComplexMatrix |
|
458
|
2434 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
2435 { |
|
5275
|
2436 octave_idx_type info; |
|
|
2437 octave_idx_type rank; |
|
7076
|
2438 double rcond; |
|
|
2439 return lssolve (b, info, rank, rcond); |
|
458
|
2440 } |
|
|
2441 |
|
|
2442 ComplexMatrix |
|
5275
|
2443 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
2444 { |
|
5275
|
2445 octave_idx_type rank; |
|
7076
|
2446 double rcond; |
|
|
2447 return lssolve (b, info, rank, rcond); |
|
458
|
2448 } |
|
|
2449 |
|
|
2450 ComplexMatrix |
|
7076
|
2451 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
|
|
2452 octave_idx_type& rank) const |
|
|
2453 { |
|
|
2454 double rcond; |
|
|
2455 return lssolve (b, info, rank, rcond); |
|
|
2456 } |
|
|
2457 |
|
|
2458 ComplexMatrix |
|
|
2459 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
|
|
2460 octave_idx_type& rank, double& rcond) const |
|
458
|
2461 { |
|
1948
|
2462 ComplexMatrix retval; |
|
|
2463 |
|
5275
|
2464 octave_idx_type nrhs = b.cols (); |
|
|
2465 |
|
|
2466 octave_idx_type m = rows (); |
|
|
2467 octave_idx_type n = cols (); |
|
458
|
2468 |
|
6924
|
2469 if (m != b.rows ()) |
|
1948
|
2470 (*current_liboctave_error_handler) |
|
|
2471 ("matrix dimension mismatch solution of linear equations"); |
|
6924
|
2472 else if (m== 0 || n == 0 || b.cols () == 0) |
|
|
2473 retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); |
|
1948
|
2474 else |
|
458
|
2475 { |
|
7072
|
2476 volatile octave_idx_type minmn = (m < n ? m : n); |
|
|
2477 octave_idx_type maxmn = m > n ? m : n; |
|
7076
|
2478 rcond = -1.0; |
|
7072
|
2479 |
|
|
2480 if (m != n) |
|
|
2481 { |
|
|
2482 retval = ComplexMatrix (maxmn, nrhs); |
|
|
2483 |
|
|
2484 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
2485 for (octave_idx_type i = 0; i < m; i++) |
|
|
2486 retval.elem (i, j) = b.elem (i, j); |
|
|
2487 } |
|
|
2488 else |
|
|
2489 retval = b; |
|
|
2490 |
|
1948
|
2491 ComplexMatrix atmp = *this; |
|
|
2492 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2493 |
|
7072
|
2494 Complex *pretval = retval.fortran_vec (); |
|
|
2495 Array<double> s (minmn); |
|
7071
|
2496 double *ps = s.fortran_vec (); |
|
2563
|
2497 |
|
7072
|
2498 // Ask ZGELSD what the dimension of WORK should be. |
|
5275
|
2499 octave_idx_type lwork = -1; |
|
3752
|
2500 |
|
|
2501 Array<Complex> work (1); |
|
7079
|
2502 |
|
11646
|
2503 octave_idx_type smlsiz; |
|
|
2504 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
|
|
2505 F77_CONST_CHAR_ARG2 (" ", 1), |
|
|
2506 0, 0, 0, 0, smlsiz |
|
|
2507 F77_CHAR_ARG_LEN (6) |
|
|
2508 F77_CHAR_ARG_LEN (1)); |
|
7079
|
2509 |
|
|
2510 // We compute the size of rwork and iwork because ZGELSD in |
|
|
2511 // older versions of LAPACK does not return them on a query |
|
|
2512 // call. |
|
7124
|
2513 double dminmn = static_cast<double> (minmn); |
|
|
2514 double dsmlsizp1 = static_cast<double> (smlsiz+1); |
|
7079
|
2515 #if defined (HAVE_LOG2) |
|
7124
|
2516 double tmp = log2 (dminmn) / dsmlsizp1 + 1; |
|
7079
|
2517 #else |
|
7124
|
2518 double tmp = log (dminmn) / dsmlsizp1 / log (2.0) + 1; |
|
7079
|
2519 #endif |
|
|
2520 octave_idx_type nlvl = static_cast<int> (tmp); |
|
|
2521 if (nlvl < 0) |
|
|
2522 nlvl = 0; |
|
|
2523 |
|
|
2524 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) |
|
|
2525 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); |
|
|
2526 if (lrwork < 1) |
|
|
2527 lrwork = 1; |
|
|
2528 Array<double> rwork (lrwork); |
|
|
2529 double *prwork = rwork.fortran_vec (); |
|
|
2530 |
|
|
2531 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; |
|
|
2532 if (liwork < 1) |
|
|
2533 liwork = 1; |
|
|
2534 Array<octave_idx_type> iwork (liwork); |
|
|
2535 octave_idx_type* piwork = iwork.fortran_vec (); |
|
7072
|
2536 |
|
|
2537 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, |
|
|
2538 ps, rcond, rank, work.fortran_vec (), |
|
7079
|
2539 lwork, prwork, piwork, info)); |
|
1948
|
2540 |
|
11640
|
2541 // The workspace query is broken in at least LAPACK 3.0.0 |
|
|
2542 // through 3.1.1 when n > m. The obtuse formula below |
|
|
2543 // should provide sufficient workspace for DGELSD to operate |
|
|
2544 // efficiently. |
|
|
2545 if (n > m) |
|
|
2546 { |
|
|
2547 octave_idx_type addend = m; |
|
|
2548 |
|
|
2549 if (2*m-4 > addend) |
|
|
2550 addend = 2*m-4; |
|
|
2551 |
|
|
2552 if (nrhs > addend) |
|
|
2553 addend = nrhs; |
|
|
2554 |
|
|
2555 if (n-3*m > addend) |
|
|
2556 addend = n-3*m; |
|
|
2557 |
|
|
2558 const octave_idx_type lworkaround = 4*m + m*m + addend; |
|
|
2559 |
|
|
2560 if (std::real (work(0)) < lworkaround) |
|
|
2561 work(0) = lworkaround; |
|
|
2562 } |
|
|
2563 |
|
1948
|
2564 if (f77_exception_encountered) |
|
7072
|
2565 (*current_liboctave_error_handler) |
|
|
2566 ("unrecoverable error in zgelsd"); |
|
1948
|
2567 else |
|
|
2568 { |
|
5315
|
2569 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
|
3752
|
2570 work.resize (lwork); |
|
7072
|
2571 |
|
|
2572 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
|
|
2573 maxmn, ps, rcond, rank, |
|
|
2574 work.fortran_vec (), lwork, |
|
7079
|
2575 prwork, piwork, info)); |
|
3752
|
2576 |
|
|
2577 if (f77_exception_encountered) |
|
7072
|
2578 (*current_liboctave_error_handler) |
|
|
2579 ("unrecoverable error in zgelsd"); |
|
7076
|
2580 else |
|
|
2581 { |
|
|
2582 if (rank < minmn) |
|
|
2583 (*current_liboctave_warning_handler) |
|
|
2584 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
|
|
2585 m, n, rank, rcond); |
|
|
2586 |
|
|
2587 if (s.elem (0) == 0.0) |
|
|
2588 rcond = 0.0; |
|
|
2589 else |
|
|
2590 rcond = s.elem (minmn - 1) / s.elem (0); |
|
7079
|
2591 |
|
|
2592 retval.resize (n, nrhs); |
|
7076
|
2593 } |
|
1948
|
2594 } |
|
458
|
2595 } |
|
|
2596 |
|
|
2597 return retval; |
|
|
2598 } |
|
|
2599 |
|
|
2600 ComplexColumnVector |
|
3585
|
2601 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
2602 { |
|
5275
|
2603 octave_idx_type info; |
|
|
2604 octave_idx_type rank; |
|
7076
|
2605 double rcond; |
|
|
2606 return lssolve (ComplexColumnVector (b), info, rank, rcond); |
|
3585
|
2607 } |
|
|
2608 |
|
|
2609 ComplexColumnVector |
|
5275
|
2610 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
2611 { |
|
5275
|
2612 octave_idx_type rank; |
|
7076
|
2613 double rcond; |
|
|
2614 return lssolve (ComplexColumnVector (b), info, rank, rcond); |
|
3585
|
2615 } |
|
|
2616 |
|
|
2617 ComplexColumnVector |
|
7076
|
2618 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
|
|
2619 octave_idx_type& rank) const |
|
3585
|
2620 { |
|
7076
|
2621 double rcond; |
|
|
2622 return lssolve (ComplexColumnVector (b), info, rank, rcond); |
|
|
2623 } |
|
|
2624 |
|
|
2625 ComplexColumnVector |
|
|
2626 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
|
|
2627 octave_idx_type& rank, double& rcond) const |
|
|
2628 { |
|
|
2629 return lssolve (ComplexColumnVector (b), info, rank, rcond); |
|
3585
|
2630 } |
|
|
2631 |
|
|
2632 ComplexColumnVector |
|
458
|
2633 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
2634 { |
|
5275
|
2635 octave_idx_type info; |
|
|
2636 octave_idx_type rank; |
|
7076
|
2637 double rcond; |
|
|
2638 return lssolve (b, info, rank, rcond); |
|
458
|
2639 } |
|
|
2640 |
|
|
2641 ComplexColumnVector |
|
5275
|
2642 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2643 { |
|
5275
|
2644 octave_idx_type rank; |
|
7076
|
2645 double rcond; |
|
|
2646 return lssolve (b, info, rank, rcond); |
|
458
|
2647 } |
|
|
2648 |
|
|
2649 ComplexColumnVector |
|
5275
|
2650 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
|
|
2651 octave_idx_type& rank) const |
|
458
|
2652 { |
|
7076
|
2653 double rcond; |
|
|
2654 return lssolve (b, info, rank, rcond); |
|
|
2655 |
|
|
2656 } |
|
|
2657 |
|
|
2658 ComplexColumnVector |
|
|
2659 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
|
|
2660 octave_idx_type& rank, double& rcond) const |
|
|
2661 { |
|
1948
|
2662 ComplexColumnVector retval; |
|
|
2663 |
|
5275
|
2664 octave_idx_type nrhs = 1; |
|
|
2665 |
|
|
2666 octave_idx_type m = rows (); |
|
|
2667 octave_idx_type n = cols (); |
|
458
|
2668 |
|
6924
|
2669 if (m != b.length ()) |
|
1948
|
2670 (*current_liboctave_error_handler) |
|
6924
|
2671 ("matrix dimension mismatch solution of linear equations"); |
|
|
2672 else if (m == 0 || n == 0 || b.cols () == 0) |
|
|
2673 retval = ComplexColumnVector (n, Complex (0.0, 0.0)); |
|
1948
|
2674 else |
|
458
|
2675 { |
|
7072
|
2676 volatile octave_idx_type minmn = (m < n ? m : n); |
|
|
2677 octave_idx_type maxmn = m > n ? m : n; |
|
7076
|
2678 rcond = -1.0; |
|
7072
|
2679 |
|
|
2680 if (m != n) |
|
|
2681 { |
|
|
2682 retval = ComplexColumnVector (maxmn); |
|
|
2683 |
|
|
2684 for (octave_idx_type i = 0; i < m; i++) |
|
|
2685 retval.elem (i) = b.elem (i); |
|
|
2686 } |
|
|
2687 else |
|
|
2688 retval = b; |
|
|
2689 |
|
1948
|
2690 ComplexMatrix atmp = *this; |
|
|
2691 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2692 |
|
7072
|
2693 Complex *pretval = retval.fortran_vec (); |
|
|
2694 Array<double> s (minmn); |
|
7071
|
2695 double *ps = s.fortran_vec (); |
|
1948
|
2696 |
|
7072
|
2697 // Ask ZGELSD what the dimension of WORK should be. |
|
5275
|
2698 octave_idx_type lwork = -1; |
|
3752
|
2699 |
|
|
2700 Array<Complex> work (1); |
|
7079
|
2701 |
|
|
2702 // FIXME: Can SMLSIZ be other than 25? |
|
|
2703 octave_idx_type smlsiz = 25; |
|
|
2704 |
|
|
2705 // We compute the size of rwork and iwork because ZGELSD in |
|
|
2706 // older versions of LAPACK does not return them on a query |
|
|
2707 // call. |
|
7124
|
2708 double dminmn = static_cast<double> (minmn); |
|
|
2709 double dsmlsizp1 = static_cast<double> (smlsiz+1); |
|
7079
|
2710 #if defined (HAVE_LOG2) |
|
7124
|
2711 double tmp = log2 (dminmn) / dsmlsizp1 + 1; |
|
7079
|
2712 #else |
|
7124
|
2713 double tmp = log (dminmn) / dsmlsizp1 / log (2.0) + 1; |
|
7079
|
2714 #endif |
|
|
2715 octave_idx_type nlvl = static_cast<int> (tmp); |
|
|
2716 if (nlvl < 0) |
|
|
2717 nlvl = 0; |
|
|
2718 |
|
|
2719 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) |
|
|
2720 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); |
|
|
2721 if (lrwork < 1) |
|
|
2722 lrwork = 1; |
|
|
2723 Array<double> rwork (lrwork); |
|
|
2724 double *prwork = rwork.fortran_vec (); |
|
|
2725 |
|
|
2726 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; |
|
|
2727 if (liwork < 1) |
|
|
2728 liwork = 1; |
|
|
2729 Array<octave_idx_type> iwork (liwork); |
|
|
2730 octave_idx_type* piwork = iwork.fortran_vec (); |
|
7072
|
2731 |
|
|
2732 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, |
|
|
2733 ps, rcond, rank, work.fortran_vec (), |
|
7079
|
2734 lwork, prwork, piwork, info)); |
|
1948
|
2735 |
|
|
2736 if (f77_exception_encountered) |
|
7072
|
2737 (*current_liboctave_error_handler) |
|
|
2738 ("unrecoverable error in zgelsd"); |
|
1948
|
2739 else |
|
|
2740 { |
|
7072
|
2741 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
|
3752
|
2742 work.resize (lwork); |
|
7072
|
2743 rwork.resize (static_cast<octave_idx_type> (rwork(0))); |
|
|
2744 iwork.resize (iwork(0)); |
|
|
2745 |
|
|
2746 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
|
|
2747 maxmn, ps, rcond, rank, |
|
|
2748 work.fortran_vec (), lwork, |
|
7079
|
2749 prwork, piwork, info)); |
|
3752
|
2750 |
|
|
2751 if (f77_exception_encountered) |
|
7072
|
2752 (*current_liboctave_error_handler) |
|
|
2753 ("unrecoverable error in zgelsd"); |
|
|
2754 else if (rank < minmn) |
|
7076
|
2755 { |
|
|
2756 if (rank < minmn) |
|
|
2757 (*current_liboctave_warning_handler) |
|
|
2758 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
|
|
2759 m, n, rank, rcond); |
|
|
2760 |
|
|
2761 if (s.elem (0) == 0.0) |
|
|
2762 rcond = 0.0; |
|
|
2763 else |
|
|
2764 rcond = s.elem (minmn - 1) / s.elem (0); |
|
7079
|
2765 |
|
|
2766 retval.resize (n, nrhs); |
|
7076
|
2767 } |
|
1948
|
2768 } |
|
458
|
2769 } |
|
|
2770 |
|
|
2771 return retval; |
|
|
2772 } |
|
|
2773 |
|
1819
|
2774 // Constants for matrix exponential calculation. |
|
|
2775 |
|
|
2776 static double padec [] = |
|
|
2777 { |
|
|
2778 5.0000000000000000e-1, |
|
|
2779 1.1666666666666667e-1, |
|
|
2780 1.6666666666666667e-2, |
|
|
2781 1.6025641025641026e-3, |
|
|
2782 1.0683760683760684e-4, |
|
|
2783 4.8562548562548563e-6, |
|
|
2784 1.3875013875013875e-7, |
|
|
2785 1.9270852604185938e-9, |
|
|
2786 }; |
|
|
2787 |
|
|
2788 ComplexMatrix |
|
|
2789 ComplexMatrix::expm (void) const |
|
|
2790 { |
|
|
2791 ComplexMatrix retval; |
|
|
2792 |
|
|
2793 ComplexMatrix m = *this; |
|
|
2794 |
|
5275
|
2795 octave_idx_type nc = columns (); |
|
1819
|
2796 |
|
3130
|
2797 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2798 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2799 |
|
1819
|
2800 // trace shift value |
|
|
2801 Complex trshift = 0.0; |
|
|
2802 |
|
5275
|
2803 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2804 trshift += m.elem (i, i); |
|
|
2805 |
|
|
2806 trshift /= nc; |
|
|
2807 |
|
3130
|
2808 if (trshift.real () < 0.0) |
|
6958
|
2809 { |
|
|
2810 trshift = trshift.imag (); |
|
|
2811 if (trshift.real () > 709.0) |
|
|
2812 trshift = 709.0; |
|
|
2813 } |
|
3130
|
2814 |
|
5275
|
2815 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2816 m.elem (i, i) -= trshift; |
|
|
2817 |
|
|
2818 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
2819 // code follows development in AEPBAL |
|
|
2820 |
|
|
2821 Complex *mp = m.fortran_vec (); |
|
3467
|
2822 |
|
5275
|
2823 octave_idx_type info, ilo, ihi,ilos,ihis; |
|
3468
|
2824 Array<double> dpermute (nc); |
|
|
2825 Array<double> dscale (nc); |
|
|
2826 |
|
5775
|
2827 // FIXME -- should pass job as a parameter in expm |
|
3468
|
2828 |
|
|
2829 // Permute first |
|
|
2830 char job = 'P'; |
|
4552
|
2831 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2832 nc, mp, nc, ilo, ihi, |
|
|
2833 dpermute.fortran_vec (), info |
|
|
2834 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2835 |
|
|
2836 if (f77_exception_encountered) |
|
|
2837 { |
|
|
2838 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
2839 return retval; |
|
|
2840 } |
|
|
2841 |
|
3468
|
2842 // then scale |
|
|
2843 job = 'S'; |
|
4552
|
2844 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2845 nc, mp, nc, ilos, ihis, |
|
|
2846 dscale.fortran_vec (), info |
|
|
2847 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2848 |
|
|
2849 if (f77_exception_encountered) |
|
|
2850 { |
|
3467
|
2851 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
2852 return retval; |
|
|
2853 } |
|
1819
|
2854 |
|
|
2855 // Preconditioning step 3: scaling. |
|
|
2856 |
|
|
2857 ColumnVector work (nc); |
|
3130
|
2858 double inf_norm; |
|
|
2859 |
|
4552
|
2860 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2861 nc, nc, m.fortran_vec (), nc, |
|
|
2862 work.fortran_vec (), inf_norm |
|
|
2863 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2864 |
|
|
2865 if (f77_exception_encountered) |
|
|
2866 { |
|
|
2867 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
2868 return retval; |
|
|
2869 } |
|
1819
|
2870 |
|
2800
|
2871 int sqpow = (inf_norm > 0.0 |
|
|
2872 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
2873 |
|
|
2874 // Check whether we need to square at all. |
|
|
2875 |
|
|
2876 if (sqpow < 0) |
|
|
2877 sqpow = 0; |
|
|
2878 |
|
|
2879 if (sqpow > 0) |
|
|
2880 { |
|
|
2881 double scale_factor = 1.0; |
|
5275
|
2882 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2883 scale_factor *= 2.0; |
|
|
2884 |
|
|
2885 m = m / scale_factor; |
|
|
2886 } |
|
|
2887 |
|
|
2888 // npp, dpp: pade' approx polynomial matrices. |
|
|
2889 |
|
|
2890 ComplexMatrix npp (nc, nc, 0.0); |
|
6958
|
2891 Complex *pnpp = npp.fortran_vec (); |
|
1819
|
2892 ComplexMatrix dpp = npp; |
|
6958
|
2893 Complex *pdpp = dpp.fortran_vec (); |
|
1819
|
2894 |
|
|
2895 // Now powers a^8 ... a^1. |
|
|
2896 |
|
|
2897 int minus_one_j = -1; |
|
5275
|
2898 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2899 { |
|
6958
|
2900 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2901 { |
|
|
2902 octave_idx_type k = i * nc + i; |
|
7265
|
2903 pnpp[k] += padec[j]; |
|
|
2904 pdpp[k] += minus_one_j * padec[j]; |
|
6958
|
2905 } |
|
7265
|
2906 |
|
6958
|
2907 npp = m * npp; |
|
7265
|
2908 pnpp = npp.fortran_vec (); |
|
|
2909 |
|
6958
|
2910 dpp = m * dpp; |
|
7265
|
2911 pdpp = dpp.fortran_vec (); |
|
|
2912 |
|
1819
|
2913 minus_one_j *= -1; |
|
|
2914 } |
|
|
2915 |
|
|
2916 // Zero power. |
|
|
2917 |
|
|
2918 dpp = -dpp; |
|
5275
|
2919 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2920 { |
|
|
2921 npp.elem (j, j) += 1.0; |
|
|
2922 dpp.elem (j, j) += 1.0; |
|
|
2923 } |
|
|
2924 |
|
|
2925 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2926 |
|
|
2927 retval = dpp.solve (npp); |
|
|
2928 |
|
|
2929 // Reverse preconditioning step 3: repeated squaring. |
|
|
2930 |
|
|
2931 while (sqpow) |
|
|
2932 { |
|
|
2933 retval = retval * retval; |
|
|
2934 sqpow--; |
|
|
2935 } |
|
|
2936 |
|
|
2937 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
2938 // Done in two steps: inverse scaling, then inverse permutation |
|
|
2939 |
|
|
2940 // inverse scaling (diagonal transformation) |
|
5275
|
2941 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2942 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2943 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
2944 |
|
4153
|
2945 OCTAVE_QUIT; |
|
|
2946 |
|
3467
|
2947 // construct balancing permutation vector |
|
6867
|
2948 Array<octave_idx_type> iperm (nc); |
|
5275
|
2949 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2950 iperm(i) = i; // initialize to identity permutation |
|
3467
|
2951 |
|
|
2952 // leading permutations in forward order |
|
5275
|
2953 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2954 { |
|
6867
|
2955 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
5275
|
2956 octave_idx_type tmp = iperm(i); |
|
4593
|
2957 iperm(i) = iperm(swapidx); |
|
|
2958 iperm(swapidx) = tmp; |
|
3468
|
2959 } |
|
3467
|
2960 |
|
|
2961 // trailing permutations must be done in reverse order |
|
5275
|
2962 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2963 { |
|
6867
|
2964 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
5275
|
2965 octave_idx_type tmp = iperm(i); |
|
4593
|
2966 iperm(i) = iperm(swapidx); |
|
|
2967 iperm(swapidx) = tmp; |
|
3468
|
2968 } |
|
3467
|
2969 |
|
|
2970 // construct inverse balancing permutation vector |
|
6867
|
2971 Array<octave_idx_type> invpvec (nc); |
|
5275
|
2972 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2973 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
2974 |
|
4153
|
2975 OCTAVE_QUIT; |
|
|
2976 |
|
3467
|
2977 ComplexMatrix tmpMat = retval; |
|
5275
|
2978 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2979 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2980 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
2981 |
|
|
2982 // Reverse preconditioning step 1: fix trace normalization. |
|
|
2983 |
|
3130
|
2984 return exp (trshift) * retval; |
|
1819
|
2985 } |
|
|
2986 |
|
1205
|
2987 // column vector by row vector -> matrix operations |
|
|
2988 |
|
|
2989 ComplexMatrix |
|
|
2990 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
2991 { |
|
|
2992 ComplexColumnVector tmp (v); |
|
|
2993 return tmp * a; |
|
|
2994 } |
|
|
2995 |
|
|
2996 ComplexMatrix |
|
|
2997 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
2998 { |
|
|
2999 ComplexRowVector tmp (b); |
|
|
3000 return a * tmp; |
|
|
3001 } |
|
|
3002 |
|
|
3003 ComplexMatrix |
|
|
3004 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
3005 { |
|
1948
|
3006 ComplexMatrix retval; |
|
|
3007 |
|
5275
|
3008 octave_idx_type len = v.length (); |
|
3233
|
3009 |
|
|
3010 if (len != 0) |
|
1205
|
3011 { |
|
5275
|
3012 octave_idx_type a_len = a.length (); |
|
3233
|
3013 |
|
|
3014 retval.resize (len, a_len); |
|
|
3015 Complex *c = retval.fortran_vec (); |
|
|
3016 |
|
4552
|
3017 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3018 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3019 len, a_len, 1, 1.0, v.data (), len, |
|
|
3020 a.data (), 1, 0.0, c, len |
|
|
3021 F77_CHAR_ARG_LEN (1) |
|
|
3022 F77_CHAR_ARG_LEN (1))); |
|
3233
|
3023 |
|
|
3024 if (f77_exception_encountered) |
|
|
3025 (*current_liboctave_error_handler) |
|
|
3026 ("unrecoverable error in zgemm"); |
|
1205
|
3027 } |
|
|
3028 |
|
1948
|
3029 return retval; |
|
1205
|
3030 } |
|
|
3031 |
|
458
|
3032 // matrix by diagonal matrix -> matrix operations |
|
|
3033 |
|
|
3034 ComplexMatrix& |
|
|
3035 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
3036 { |
|
5275
|
3037 octave_idx_type nr = rows (); |
|
|
3038 octave_idx_type nc = cols (); |
|
|
3039 |
|
|
3040 octave_idx_type a_nr = rows (); |
|
|
3041 octave_idx_type a_nc = cols (); |
|
2384
|
3042 |
|
|
3043 if (nr != a_nr || nc != a_nc) |
|
458
|
3044 { |
|
2384
|
3045 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
3046 return *this; |
|
458
|
3047 } |
|
|
3048 |
|
5275
|
3049 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
3050 elem (i, i) += a.elem (i, i); |
|
|
3051 |
|
|
3052 return *this; |
|
|
3053 } |
|
|
3054 |
|
|
3055 ComplexMatrix& |
|
|
3056 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
3057 { |
|
5275
|
3058 octave_idx_type nr = rows (); |
|
|
3059 octave_idx_type nc = cols (); |
|
|
3060 |
|
|
3061 octave_idx_type a_nr = rows (); |
|
|
3062 octave_idx_type a_nc = cols (); |
|
2384
|
3063 |
|
|
3064 if (nr != a_nr || nc != a_nc) |
|
458
|
3065 { |
|
2384
|
3066 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
3067 return *this; |
|
458
|
3068 } |
|
|
3069 |
|
5275
|
3070 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
3071 elem (i, i) -= a.elem (i, i); |
|
|
3072 |
|
|
3073 return *this; |
|
|
3074 } |
|
|
3075 |
|
|
3076 ComplexMatrix& |
|
|
3077 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
3078 { |
|
5275
|
3079 octave_idx_type nr = rows (); |
|
|
3080 octave_idx_type nc = cols (); |
|
|
3081 |
|
|
3082 octave_idx_type a_nr = rows (); |
|
|
3083 octave_idx_type a_nc = cols (); |
|
2384
|
3084 |
|
|
3085 if (nr != a_nr || nc != a_nc) |
|
458
|
3086 { |
|
2384
|
3087 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
3088 return *this; |
|
458
|
3089 } |
|
|
3090 |
|
5275
|
3091 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
3092 elem (i, i) += a.elem (i, i); |
|
|
3093 |
|
|
3094 return *this; |
|
|
3095 } |
|
|
3096 |
|
|
3097 ComplexMatrix& |
|
|
3098 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
3099 { |
|
5275
|
3100 octave_idx_type nr = rows (); |
|
|
3101 octave_idx_type nc = cols (); |
|
|
3102 |
|
|
3103 octave_idx_type a_nr = rows (); |
|
|
3104 octave_idx_type a_nc = cols (); |
|
2384
|
3105 |
|
|
3106 if (nr != a_nr || nc != a_nc) |
|
458
|
3107 { |
|
2384
|
3108 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
3109 return *this; |
|
458
|
3110 } |
|
|
3111 |
|
5275
|
3112 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
3113 elem (i, i) -= a.elem (i, i); |
|
|
3114 |
|
|
3115 return *this; |
|
|
3116 } |
|
|
3117 |
|
|
3118 // matrix by matrix -> matrix operations |
|
|
3119 |
|
|
3120 ComplexMatrix& |
|
|
3121 ComplexMatrix::operator += (const Matrix& a) |
|
|
3122 { |
|
5275
|
3123 octave_idx_type nr = rows (); |
|
|
3124 octave_idx_type nc = cols (); |
|
|
3125 |
|
|
3126 octave_idx_type a_nr = a.rows (); |
|
|
3127 octave_idx_type a_nc = a.cols (); |
|
2384
|
3128 |
|
|
3129 if (nr != a_nr || nc != a_nc) |
|
458
|
3130 { |
|
2384
|
3131 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
3132 return *this; |
|
|
3133 } |
|
|
3134 |
|
|
3135 if (nr == 0 || nc == 0) |
|
|
3136 return *this; |
|
|
3137 |
|
|
3138 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
3139 |
|
3769
|
3140 mx_inline_add2 (d, a.data (), length ()); |
|
458
|
3141 return *this; |
|
|
3142 } |
|
|
3143 |
|
|
3144 ComplexMatrix& |
|
|
3145 ComplexMatrix::operator -= (const Matrix& a) |
|
|
3146 { |
|
5275
|
3147 octave_idx_type nr = rows (); |
|
|
3148 octave_idx_type nc = cols (); |
|
|
3149 |
|
|
3150 octave_idx_type a_nr = a.rows (); |
|
|
3151 octave_idx_type a_nc = a.cols (); |
|
2384
|
3152 |
|
|
3153 if (nr != a_nr || nc != a_nc) |
|
458
|
3154 { |
|
2384
|
3155 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
3156 return *this; |
|
|
3157 } |
|
|
3158 |
|
|
3159 if (nr == 0 || nc == 0) |
|
|
3160 return *this; |
|
|
3161 |
|
|
3162 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
3163 |
|
3769
|
3164 mx_inline_subtract2 (d, a.data (), length ()); |
|
458
|
3165 return *this; |
|
|
3166 } |
|
|
3167 |
|
|
3168 // unary operations |
|
|
3169 |
|
2964
|
3170 boolMatrix |
|
458
|
3171 ComplexMatrix::operator ! (void) const |
|
|
3172 { |
|
5275
|
3173 octave_idx_type nr = rows (); |
|
|
3174 octave_idx_type nc = cols (); |
|
2964
|
3175 |
|
|
3176 boolMatrix b (nr, nc); |
|
|
3177 |
|
5275
|
3178 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3179 for (octave_idx_type i = 0; i < nr; i++) |
|
5139
|
3180 b.elem (i, j) = elem (i, j) == 0.0; |
|
2964
|
3181 |
|
|
3182 return b; |
|
458
|
3183 } |
|
|
3184 |
|
|
3185 // other operations |
|
|
3186 |
|
|
3187 ComplexMatrix |
|
2676
|
3188 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
3189 { |
|
2676
|
3190 ComplexMatrix b (*this); |
|
|
3191 return b.apply (f); |
|
458
|
3192 } |
|
|
3193 |
|
2676
|
3194 Matrix |
|
|
3195 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
3196 { |
|
5275
|
3197 octave_idx_type nr = rows (); |
|
|
3198 octave_idx_type nc = cols (); |
|
3248
|
3199 |
|
|
3200 Matrix retval (nr, nc); |
|
|
3201 |
|
5275
|
3202 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3203 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
3204 retval(i,j) = f (elem(i,j)); |
|
|
3205 |
|
|
3206 return retval; |
|
|
3207 } |
|
|
3208 |
|
|
3209 boolMatrix |
|
|
3210 ComplexMatrix::map (b_c_Mapper f) const |
|
|
3211 { |
|
5275
|
3212 octave_idx_type nr = rows (); |
|
|
3213 octave_idx_type nc = cols (); |
|
3248
|
3214 |
|
|
3215 boolMatrix retval (nr, nc); |
|
|
3216 |
|
5275
|
3217 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3218 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
3219 retval(i,j) = f (elem(i,j)); |
|
2676
|
3220 |
|
|
3221 return retval; |
|
|
3222 } |
|
|
3223 |
|
|
3224 ComplexMatrix& |
|
|
3225 ComplexMatrix::apply (c_c_Mapper f) |
|
|
3226 { |
|
|
3227 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
3228 |
|
5275
|
3229 for (octave_idx_type i = 0; i < length (); i++) |
|
2676
|
3230 d[i] = f (d[i]); |
|
|
3231 |
|
|
3232 return *this; |
|
458
|
3233 } |
|
|
3234 |
|
2384
|
3235 bool |
|
|
3236 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
3237 { |
|
5275
|
3238 octave_idx_type nr = rows (); |
|
|
3239 octave_idx_type nc = cols (); |
|
|
3240 |
|
|
3241 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3242 for (octave_idx_type i = 0; i < nr; i++) |
|
2384
|
3243 { |
|
|
3244 Complex val = elem (i, j); |
|
|
3245 if (xisinf (val) || xisnan (val)) |
|
|
3246 return true; |
|
|
3247 } |
|
|
3248 |
|
|
3249 return false; |
|
|
3250 } |
|
|
3251 |
|
2408
|
3252 // Return true if no elements have imaginary components. |
|
|
3253 |
|
|
3254 bool |
|
|
3255 ComplexMatrix::all_elements_are_real (void) const |
|
|
3256 { |
|
5275
|
3257 octave_idx_type nr = rows (); |
|
|
3258 octave_idx_type nc = cols (); |
|
|
3259 |
|
|
3260 for (octave_idx_type j = 0; j < nc; j++) |
|
4349
|
3261 { |
|
5275
|
3262 for (octave_idx_type i = 0; i < nr; i++) |
|
4349
|
3263 { |
|
5315
|
3264 double ip = std::imag (elem (i, j)); |
|
4349
|
3265 |
|
|
3266 if (ip != 0.0 || lo_ieee_signbit (ip)) |
|
|
3267 return false; |
|
|
3268 } |
|
|
3269 } |
|
2408
|
3270 |
|
|
3271 return true; |
|
|
3272 } |
|
|
3273 |
|
1968
|
3274 // Return nonzero if any element of CM has a non-integer real or |
|
|
3275 // imaginary part. Also extract the largest and smallest (real or |
|
|
3276 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
3277 |
|
2384
|
3278 bool |
|
1968
|
3279 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
3280 { |
|
5275
|
3281 octave_idx_type nr = rows (); |
|
|
3282 octave_idx_type nc = cols (); |
|
1968
|
3283 |
|
|
3284 if (nr > 0 && nc > 0) |
|
|
3285 { |
|
|
3286 Complex val = elem (0, 0); |
|
|
3287 |
|
5315
|
3288 double r_val = std::real (val); |
|
|
3289 double i_val = std::imag (val); |
|
1968
|
3290 |
|
|
3291 max_val = r_val; |
|
|
3292 min_val = r_val; |
|
|
3293 |
|
|
3294 if (i_val > max_val) |
|
|
3295 max_val = i_val; |
|
|
3296 |
|
|
3297 if (i_val < max_val) |
|
|
3298 min_val = i_val; |
|
|
3299 } |
|
|
3300 else |
|
2384
|
3301 return false; |
|
1968
|
3302 |
|
5275
|
3303 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3304 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
3305 { |
|
|
3306 Complex val = elem (i, j); |
|
|
3307 |
|
5315
|
3308 double r_val = std::real (val); |
|
|
3309 double i_val = std::imag (val); |
|
1968
|
3310 |
|
|
3311 if (r_val > max_val) |
|
|
3312 max_val = r_val; |
|
|
3313 |
|
|
3314 if (i_val > max_val) |
|
|
3315 max_val = i_val; |
|
|
3316 |
|
|
3317 if (r_val < min_val) |
|
|
3318 min_val = r_val; |
|
|
3319 |
|
|
3320 if (i_val < min_val) |
|
|
3321 min_val = i_val; |
|
|
3322 |
|
|
3323 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
3324 return false; |
|
1968
|
3325 } |
|
2384
|
3326 |
|
|
3327 return true; |
|
1968
|
3328 } |
|
|
3329 |
|
2384
|
3330 bool |
|
1968
|
3331 ComplexMatrix::too_large_for_float (void) const |
|
|
3332 { |
|
5275
|
3333 octave_idx_type nr = rows (); |
|
|
3334 octave_idx_type nc = cols (); |
|
|
3335 |
|
|
3336 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3337 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
3338 { |
|
|
3339 Complex val = elem (i, j); |
|
|
3340 |
|
5315
|
3341 double r_val = std::real (val); |
|
|
3342 double i_val = std::imag (val); |
|
1968
|
3343 |
|
5389
|
3344 if ((! (xisnan (r_val) || xisinf (r_val)) |
|
5387
|
3345 && fabs (r_val) > FLT_MAX) |
|
5389
|
3346 || (! (xisnan (i_val) || xisinf (i_val)) |
|
5387
|
3347 && fabs (i_val) > FLT_MAX)) |
|
2384
|
3348 return true; |
|
1968
|
3349 } |
|
|
3350 |
|
2384
|
3351 return false; |
|
1968
|
3352 } |
|
|
3353 |
|
5775
|
3354 // FIXME Do these really belong here? Maybe they should be |
|
4015
|
3355 // in a base class? |
|
|
3356 |
|
2832
|
3357 boolMatrix |
|
4015
|
3358 ComplexMatrix::all (int dim) const |
|
458
|
3359 { |
|
4015
|
3360 MX_ALL_OP (dim); |
|
458
|
3361 } |
|
|
3362 |
|
2832
|
3363 boolMatrix |
|
4015
|
3364 ComplexMatrix::any (int dim) const |
|
458
|
3365 { |
|
4015
|
3366 MX_ANY_OP (dim); |
|
458
|
3367 } |
|
|
3368 |
|
|
3369 ComplexMatrix |
|
3723
|
3370 ComplexMatrix::cumprod (int dim) const |
|
458
|
3371 { |
|
4015
|
3372 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
|
458
|
3373 } |
|
|
3374 |
|
|
3375 ComplexMatrix |
|
3723
|
3376 ComplexMatrix::cumsum (int dim) const |
|
458
|
3377 { |
|
4015
|
3378 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
|
458
|
3379 } |
|
|
3380 |
|
|
3381 ComplexMatrix |
|
3723
|
3382 ComplexMatrix::prod (int dim) const |
|
458
|
3383 { |
|
3864
|
3384 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
|
458
|
3385 } |
|
|
3386 |
|
|
3387 ComplexMatrix |
|
3723
|
3388 ComplexMatrix::sum (int dim) const |
|
458
|
3389 { |
|
3864
|
3390 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
|
458
|
3391 } |
|
|
3392 |
|
|
3393 ComplexMatrix |
|
3723
|
3394 ComplexMatrix::sumsq (int dim) const |
|
458
|
3395 { |
|
3864
|
3396 #define ROW_EXPR \ |
|
|
3397 Complex d = elem (i, j); \ |
|
|
3398 retval.elem (i, 0) += d * conj (d) |
|
|
3399 |
|
|
3400 #define COL_EXPR \ |
|
|
3401 Complex d = elem (i, j); \ |
|
|
3402 retval.elem (0, j) += d * conj (d) |
|
|
3403 |
|
|
3404 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
3405 |
|
|
3406 #undef ROW_EXPR |
|
|
3407 #undef COL_EXPR |
|
458
|
3408 } |
|
|
3409 |
|
4329
|
3410 Matrix ComplexMatrix::abs (void) const |
|
|
3411 { |
|
5275
|
3412 octave_idx_type nr = rows (); |
|
|
3413 octave_idx_type nc = cols (); |
|
4329
|
3414 |
|
|
3415 Matrix retval (nr, nc); |
|
|
3416 |
|
5275
|
3417 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3418 for (octave_idx_type i = 0; i < nr; i++) |
|
5315
|
3419 retval (i, j) = std::abs (elem (i, j)); |
|
4329
|
3420 |
|
|
3421 return retval; |
|
|
3422 } |
|
|
3423 |
|
458
|
3424 ComplexColumnVector |
|
|
3425 ComplexMatrix::diag (void) const |
|
|
3426 { |
|
|
3427 return diag (0); |
|
|
3428 } |
|
|
3429 |
|
|
3430 ComplexColumnVector |
|
5275
|
3431 ComplexMatrix::diag (octave_idx_type k) const |
|
458
|
3432 { |
|
5275
|
3433 octave_idx_type nnr = rows (); |
|
|
3434 octave_idx_type nnc = cols (); |
|
458
|
3435 if (k > 0) |
|
|
3436 nnc -= k; |
|
|
3437 else if (k < 0) |
|
|
3438 nnr += k; |
|
|
3439 |
|
|
3440 ComplexColumnVector d; |
|
|
3441 |
|
|
3442 if (nnr > 0 && nnc > 0) |
|
|
3443 { |
|
5275
|
3444 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
3445 |
|
|
3446 d.resize (ndiag); |
|
|
3447 |
|
|
3448 if (k > 0) |
|
|
3449 { |
|
5275
|
3450 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3451 d.elem (i) = elem (i, i+k); |
|
|
3452 } |
|
4509
|
3453 else if (k < 0) |
|
458
|
3454 { |
|
5275
|
3455 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3456 d.elem (i) = elem (i-k, i); |
|
|
3457 } |
|
|
3458 else |
|
|
3459 { |
|
5275
|
3460 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
3461 d.elem (i) = elem (i, i); |
|
|
3462 } |
|
|
3463 } |
|
|
3464 else |
|
4513
|
3465 (*current_liboctave_error_handler) |
|
|
3466 ("diag: requested diagonal out of range"); |
|
458
|
3467 |
|
|
3468 return d; |
|
|
3469 } |
|
|
3470 |
|
2354
|
3471 bool |
|
5275
|
3472 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
|
2354
|
3473 { |
|
|
3474 bool retval = true; |
|
|
3475 |
|
5275
|
3476 octave_idx_type nc = columns (); |
|
|
3477 |
|
|
3478 for (octave_idx_type j = 0; j < nc; j++) |
|
2354
|
3479 { |
|
5315
|
3480 if (std::imag (elem (i, j)) != 0.0) |
|
2354
|
3481 { |
|
|
3482 retval = false; |
|
|
3483 break; |
|
|
3484 } |
|
|
3485 } |
|
|
3486 |
|
|
3487 return retval; |
|
|
3488 } |
|
|
3489 |
|
|
3490 bool |
|
5275
|
3491 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
|
2354
|
3492 { |
|
|
3493 bool retval = true; |
|
|
3494 |
|
5275
|
3495 octave_idx_type nr = rows (); |
|
|
3496 |
|
|
3497 for (octave_idx_type i = 0; i < nr; i++) |
|
2354
|
3498 { |
|
5315
|
3499 if (std::imag (elem (i, j)) != 0.0) |
|
2354
|
3500 { |
|
|
3501 retval = false; |
|
|
3502 break; |
|
|
3503 } |
|
|
3504 } |
|
|
3505 |
|
|
3506 return retval; |
|
|
3507 } |
|
891
|
3508 |
|
458
|
3509 ComplexColumnVector |
|
|
3510 ComplexMatrix::row_min (void) const |
|
|
3511 { |
|
5275
|
3512 Array<octave_idx_type> dummy_idx; |
|
4587
|
3513 return row_min (dummy_idx); |
|
458
|
3514 } |
|
|
3515 |
|
|
3516 ComplexColumnVector |
|
5275
|
3517 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
3518 { |
|
|
3519 ComplexColumnVector result; |
|
|
3520 |
|
5275
|
3521 octave_idx_type nr = rows (); |
|
|
3522 octave_idx_type nc = cols (); |
|
458
|
3523 |
|
|
3524 if (nr > 0 && nc > 0) |
|
|
3525 { |
|
|
3526 result.resize (nr); |
|
4587
|
3527 idx_arg.resize (nr); |
|
458
|
3528 |
|
5275
|
3529 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
3530 { |
|
2354
|
3531 bool real_only = row_is_real_only (i); |
|
|
3532 |
|
5275
|
3533 octave_idx_type idx_j; |
|
4469
|
3534 |
|
|
3535 Complex tmp_min; |
|
|
3536 |
|
|
3537 double abs_min = octave_NaN; |
|
|
3538 |
|
|
3539 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
3540 { |
|
|
3541 tmp_min = elem (i, idx_j); |
|
|
3542 |
|
5389
|
3543 if (! xisnan (tmp_min)) |
|
4469
|
3544 { |
|
5315
|
3545 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
|
4469
|
3546 break; |
|
|
3547 } |
|
|
3548 } |
|
|
3549 |
|
5275
|
3550 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
3551 { |
|
|
3552 Complex tmp = elem (i, j); |
|
|
3553 |
|
5389
|
3554 if (xisnan (tmp)) |
|
4469
|
3555 continue; |
|
|
3556 |
|
5315
|
3557 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3558 |
|
|
3559 if (abs_tmp < abs_min) |
|
|
3560 { |
|
|
3561 idx_j = j; |
|
|
3562 tmp_min = tmp; |
|
|
3563 abs_min = abs_tmp; |
|
|
3564 } |
|
|
3565 } |
|
|
3566 |
|
5389
|
3567 if (xisnan (tmp_min)) |
|
4469
|
3568 { |
|
|
3569 result.elem (i) = Complex_NaN_result; |
|
4587
|
3570 idx_arg.elem (i) = 0; |
|
4469
|
3571 } |
|
891
|
3572 else |
|
|
3573 { |
|
4469
|
3574 result.elem (i) = tmp_min; |
|
4587
|
3575 idx_arg.elem (i) = idx_j; |
|
891
|
3576 } |
|
458
|
3577 } |
|
|
3578 } |
|
|
3579 |
|
|
3580 return result; |
|
|
3581 } |
|
|
3582 |
|
|
3583 ComplexColumnVector |
|
|
3584 ComplexMatrix::row_max (void) const |
|
|
3585 { |
|
5275
|
3586 Array<octave_idx_type> dummy_idx; |
|
4587
|
3587 return row_max (dummy_idx); |
|
458
|
3588 } |
|
|
3589 |
|
|
3590 ComplexColumnVector |
|
5275
|
3591 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
3592 { |
|
|
3593 ComplexColumnVector result; |
|
|
3594 |
|
5275
|
3595 octave_idx_type nr = rows (); |
|
|
3596 octave_idx_type nc = cols (); |
|
458
|
3597 |
|
|
3598 if (nr > 0 && nc > 0) |
|
|
3599 { |
|
|
3600 result.resize (nr); |
|
4587
|
3601 idx_arg.resize (nr); |
|
458
|
3602 |
|
5275
|
3603 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
3604 { |
|
2354
|
3605 bool real_only = row_is_real_only (i); |
|
|
3606 |
|
5275
|
3607 octave_idx_type idx_j; |
|
4469
|
3608 |
|
|
3609 Complex tmp_max; |
|
|
3610 |
|
|
3611 double abs_max = octave_NaN; |
|
|
3612 |
|
|
3613 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
3614 { |
|
|
3615 tmp_max = elem (i, idx_j); |
|
|
3616 |
|
5389
|
3617 if (! xisnan (tmp_max)) |
|
4469
|
3618 { |
|
5315
|
3619 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
|
4469
|
3620 break; |
|
|
3621 } |
|
|
3622 } |
|
|
3623 |
|
5275
|
3624 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
3625 { |
|
|
3626 Complex tmp = elem (i, j); |
|
|
3627 |
|
5389
|
3628 if (xisnan (tmp)) |
|
4469
|
3629 continue; |
|
|
3630 |
|
5315
|
3631 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3632 |
|
|
3633 if (abs_tmp > abs_max) |
|
|
3634 { |
|
|
3635 idx_j = j; |
|
|
3636 tmp_max = tmp; |
|
|
3637 abs_max = abs_tmp; |
|
|
3638 } |
|
|
3639 } |
|
|
3640 |
|
5389
|
3641 if (xisnan (tmp_max)) |
|
4469
|
3642 { |
|
|
3643 result.elem (i) = Complex_NaN_result; |
|
4587
|
3644 idx_arg.elem (i) = 0; |
|
4469
|
3645 } |
|
891
|
3646 else |
|
|
3647 { |
|
4469
|
3648 result.elem (i) = tmp_max; |
|
4587
|
3649 idx_arg.elem (i) = idx_j; |
|
891
|
3650 } |
|
458
|
3651 } |
|
|
3652 } |
|
|
3653 |
|
|
3654 return result; |
|
|
3655 } |
|
|
3656 |
|
|
3657 ComplexRowVector |
|
|
3658 ComplexMatrix::column_min (void) const |
|
|
3659 { |
|
5275
|
3660 Array<octave_idx_type> dummy_idx; |
|
4587
|
3661 return column_min (dummy_idx); |
|
458
|
3662 } |
|
|
3663 |
|
|
3664 ComplexRowVector |
|
5275
|
3665 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
3666 { |
|
|
3667 ComplexRowVector result; |
|
|
3668 |
|
5275
|
3669 octave_idx_type nr = rows (); |
|
|
3670 octave_idx_type nc = cols (); |
|
458
|
3671 |
|
|
3672 if (nr > 0 && nc > 0) |
|
|
3673 { |
|
|
3674 result.resize (nc); |
|
4587
|
3675 idx_arg.resize (nc); |
|
458
|
3676 |
|
5275
|
3677 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3678 { |
|
2354
|
3679 bool real_only = column_is_real_only (j); |
|
|
3680 |
|
5275
|
3681 octave_idx_type idx_i; |
|
4469
|
3682 |
|
|
3683 Complex tmp_min; |
|
|
3684 |
|
|
3685 double abs_min = octave_NaN; |
|
|
3686 |
|
|
3687 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3688 { |
|
|
3689 tmp_min = elem (idx_i, j); |
|
|
3690 |
|
5389
|
3691 if (! xisnan (tmp_min)) |
|
4469
|
3692 { |
|
5315
|
3693 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
|
4469
|
3694 break; |
|
|
3695 } |
|
|
3696 } |
|
|
3697 |
|
5275
|
3698 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
3699 { |
|
|
3700 Complex tmp = elem (i, j); |
|
|
3701 |
|
5389
|
3702 if (xisnan (tmp)) |
|
4469
|
3703 continue; |
|
|
3704 |
|
5315
|
3705 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3706 |
|
|
3707 if (abs_tmp < abs_min) |
|
|
3708 { |
|
|
3709 idx_i = i; |
|
|
3710 tmp_min = tmp; |
|
|
3711 abs_min = abs_tmp; |
|
|
3712 } |
|
|
3713 } |
|
|
3714 |
|
5389
|
3715 if (xisnan (tmp_min)) |
|
4469
|
3716 { |
|
|
3717 result.elem (j) = Complex_NaN_result; |
|
4587
|
3718 idx_arg.elem (j) = 0; |
|
4469
|
3719 } |
|
891
|
3720 else |
|
|
3721 { |
|
4469
|
3722 result.elem (j) = tmp_min; |
|
4587
|
3723 idx_arg.elem (j) = idx_i; |
|
891
|
3724 } |
|
458
|
3725 } |
|
|
3726 } |
|
|
3727 |
|
|
3728 return result; |
|
|
3729 } |
|
|
3730 |
|
|
3731 ComplexRowVector |
|
|
3732 ComplexMatrix::column_max (void) const |
|
|
3733 { |
|
5275
|
3734 Array<octave_idx_type> dummy_idx; |
|
4587
|
3735 return column_max (dummy_idx); |
|
458
|
3736 } |
|
|
3737 |
|
|
3738 ComplexRowVector |
|
5275
|
3739 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
3740 { |
|
|
3741 ComplexRowVector result; |
|
|
3742 |
|
5275
|
3743 octave_idx_type nr = rows (); |
|
|
3744 octave_idx_type nc = cols (); |
|
458
|
3745 |
|
|
3746 if (nr > 0 && nc > 0) |
|
|
3747 { |
|
|
3748 result.resize (nc); |
|
4587
|
3749 idx_arg.resize (nc); |
|
458
|
3750 |
|
5275
|
3751 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3752 { |
|
2354
|
3753 bool real_only = column_is_real_only (j); |
|
|
3754 |
|
5275
|
3755 octave_idx_type idx_i; |
|
4469
|
3756 |
|
|
3757 Complex tmp_max; |
|
|
3758 |
|
|
3759 double abs_max = octave_NaN; |
|
|
3760 |
|
|
3761 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3762 { |
|
|
3763 tmp_max = elem (idx_i, j); |
|
|
3764 |
|
5389
|
3765 if (! xisnan (tmp_max)) |
|
4469
|
3766 { |
|
5315
|
3767 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
|
4469
|
3768 break; |
|
|
3769 } |
|
|
3770 } |
|
|
3771 |
|
5275
|
3772 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
3773 { |
|
|
3774 Complex tmp = elem (i, j); |
|
|
3775 |
|
5389
|
3776 if (xisnan (tmp)) |
|
4469
|
3777 continue; |
|
|
3778 |
|
5315
|
3779 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
|
4469
|
3780 |
|
|
3781 if (abs_tmp > abs_max) |
|
|
3782 { |
|
|
3783 idx_i = i; |
|
|
3784 tmp_max = tmp; |
|
|
3785 abs_max = abs_tmp; |
|
|
3786 } |
|
|
3787 } |
|
|
3788 |
|
5389
|
3789 if (xisnan (tmp_max)) |
|
4469
|
3790 { |
|
|
3791 result.elem (j) = Complex_NaN_result; |
|
4587
|
3792 idx_arg.elem (j) = 0; |
|
4469
|
3793 } |
|
891
|
3794 else |
|
|
3795 { |
|
4469
|
3796 result.elem (j) = tmp_max; |
|
4587
|
3797 idx_arg.elem (j) = idx_i; |
|
891
|
3798 } |
|
458
|
3799 } |
|
|
3800 } |
|
|
3801 |
|
|
3802 return result; |
|
|
3803 } |
|
|
3804 |
|
|
3805 // i/o |
|
|
3806 |
|
3504
|
3807 std::ostream& |
|
|
3808 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
3809 { |
|
5275
|
3810 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
3811 { |
|
5275
|
3812 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
3813 { |
|
|
3814 os << " "; |
|
|
3815 octave_write_complex (os, a.elem (i, j)); |
|
|
3816 } |
|
458
|
3817 os << "\n"; |
|
|
3818 } |
|
|
3819 return os; |
|
|
3820 } |
|
|
3821 |
|
3504
|
3822 std::istream& |
|
|
3823 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
3824 { |
|
5275
|
3825 octave_idx_type nr = a.rows (); |
|
|
3826 octave_idx_type nc = a.cols (); |
|
458
|
3827 |
|
|
3828 if (nr < 1 || nc < 1) |
|
3504
|
3829 is.clear (std::ios::badbit); |
|
458
|
3830 else |
|
|
3831 { |
|
|
3832 Complex tmp; |
|
5275
|
3833 for (octave_idx_type i = 0; i < nr; i++) |
|
|
3834 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3835 { |
|
4130
|
3836 tmp = octave_read_complex (is); |
|
458
|
3837 if (is) |
|
|
3838 a.elem (i, j) = tmp; |
|
|
3839 else |
|
2993
|
3840 goto done; |
|
458
|
3841 } |
|
|
3842 } |
|
|
3843 |
|
2993
|
3844 done: |
|
|
3845 |
|
458
|
3846 return is; |
|
|
3847 } |
|
|
3848 |
|
1819
|
3849 ComplexMatrix |
|
|
3850 Givens (const Complex& x, const Complex& y) |
|
|
3851 { |
|
|
3852 double cc; |
|
|
3853 Complex cs, temp_r; |
|
|
3854 |
|
3887
|
3855 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
1819
|
3856 |
|
|
3857 ComplexMatrix g (2, 2); |
|
|
3858 |
|
|
3859 g.elem (0, 0) = cc; |
|
|
3860 g.elem (1, 1) = cc; |
|
|
3861 g.elem (0, 1) = cs; |
|
|
3862 g.elem (1, 0) = -conj (cs); |
|
|
3863 |
|
|
3864 return g; |
|
|
3865 } |
|
|
3866 |
|
|
3867 ComplexMatrix |
|
|
3868 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
3869 const ComplexMatrix& c) |
|
|
3870 { |
|
|
3871 ComplexMatrix retval; |
|
|
3872 |
|
5775
|
3873 // FIXME -- need to check that a, b, and c are all the same |
|
1819
|
3874 // size. |
|
|
3875 |
|
|
3876 // Compute Schur decompositions |
|
|
3877 |
|
|
3878 ComplexSCHUR as (a, "U"); |
|
|
3879 ComplexSCHUR bs (b, "U"); |
|
|
3880 |
|
|
3881 // Transform c to new coordinates. |
|
|
3882 |
|
|
3883 ComplexMatrix ua = as.unitary_matrix (); |
|
|
3884 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
3885 |
|
|
3886 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
3887 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
3888 |
|
|
3889 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
3890 |
|
|
3891 // Solve the sylvester equation, back-transform, and return the |
|
|
3892 // solution. |
|
|
3893 |
|
5275
|
3894 octave_idx_type a_nr = a.rows (); |
|
|
3895 octave_idx_type b_nr = b.rows (); |
|
1819
|
3896 |
|
|
3897 double scale; |
|
5275
|
3898 octave_idx_type info; |
|
1950
|
3899 |
|
|
3900 Complex *pa = sch_a.fortran_vec (); |
|
|
3901 Complex *pb = sch_b.fortran_vec (); |
|
|
3902 Complex *px = cx.fortran_vec (); |
|
1819
|
3903 |
|
4552
|
3904 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3905 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3906 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3907 b_nr, px, a_nr, scale, info |
|
|
3908 F77_CHAR_ARG_LEN (1) |
|
|
3909 F77_CHAR_ARG_LEN (1))); |
|
1950
|
3910 |
|
|
3911 if (f77_exception_encountered) |
|
|
3912 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
3913 else |
|
|
3914 { |
|
5775
|
3915 // FIXME -- check info? |
|
1950
|
3916 |
|
|
3917 retval = -ua * cx * ub.hermitian (); |
|
|
3918 } |
|
1819
|
3919 |
|
|
3920 return retval; |
|
|
3921 } |
|
|
3922 |
|
2828
|
3923 ComplexMatrix |
|
|
3924 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
3925 { |
|
|
3926 ComplexMatrix tmp (a); |
|
|
3927 return m * tmp; |
|
|
3928 } |
|
|
3929 |
|
|
3930 ComplexMatrix |
|
|
3931 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
3932 { |
|
|
3933 ComplexMatrix tmp (m); |
|
|
3934 return tmp * a; |
|
|
3935 } |
|
|
3936 |
|
6162
|
3937 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
|
|
3938 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) |
|
|
3939 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) |
|
|
3940 %!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) |
|
|
3941 */ |
|
|
3942 |
|
|
3943 /* Test some simple identities |
|
|
3944 %!shared M, cv, rv |
|
|
3945 %! M = randn(10,10)+i*rand(10,10); |
|
|
3946 %! cv = randn(10,1)+i*rand(10,1); |
|
|
3947 %! rv = randn(1,10)+i*rand(1,10); |
|
|
3948 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) |
|
|
3949 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) |
|
|
3950 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) |
|
|
3951 */ |
|
|
3952 |
|
2828
|
3953 ComplexMatrix |
|
|
3954 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
3955 { |
|
|
3956 ComplexMatrix retval; |
|
|
3957 |
|
5275
|
3958 octave_idx_type nr = m.rows (); |
|
|
3959 octave_idx_type nc = m.cols (); |
|
|
3960 |
|
|
3961 octave_idx_type a_nr = a.rows (); |
|
|
3962 octave_idx_type a_nc = a.cols (); |
|
2828
|
3963 |
|
|
3964 if (nc != a_nr) |
|
|
3965 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3966 else |
|
|
3967 { |
|
|
3968 if (nr == 0 || nc == 0 || a_nc == 0) |
|
3760
|
3969 retval.resize (nr, a_nc, 0.0); |
|
2828
|
3970 else |
|
|
3971 { |
|
5275
|
3972 octave_idx_type ld = nr; |
|
|
3973 octave_idx_type lda = a.rows (); |
|
2828
|
3974 |
|
|
3975 retval.resize (nr, a_nc); |
|
|
3976 Complex *c = retval.fortran_vec (); |
|
|
3977 |
|
5983
|
3978 if (a_nc == 1) |
|
|
3979 { |
|
|
3980 if (nr == 1) |
|
|
3981 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); |
|
|
3982 else |
|
6390
|
3983 { |
|
|
3984 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3985 nr, nc, 1.0, m.data (), ld, |
|
|
3986 a.data (), 1, 0.0, c, 1 |
|
|
3987 F77_CHAR_ARG_LEN (1))); |
|
|
3988 |
|
|
3989 if (f77_exception_encountered) |
|
|
3990 (*current_liboctave_error_handler) |
|
|
3991 ("unrecoverable error in zgemv"); |
|
|
3992 } |
|
5983
|
3993 } |
|
|
3994 else |
|
6390
|
3995 { |
|
|
3996 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3997 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3998 nr, a_nc, nc, 1.0, m.data (), |
|
|
3999 ld, a.data (), lda, 0.0, c, nr |
|
|
4000 F77_CHAR_ARG_LEN (1) |
|
|
4001 F77_CHAR_ARG_LEN (1))); |
|
|
4002 |
|
|
4003 if (f77_exception_encountered) |
|
|
4004 (*current_liboctave_error_handler) |
|
|
4005 ("unrecoverable error in zgemm"); |
|
|
4006 } |
|
2828
|
4007 } |
|
|
4008 } |
|
|
4009 |
|
|
4010 return retval; |
|
|
4011 } |
|
|
4012 |
|
5775
|
4013 // FIXME -- it would be nice to share code among the min/max |
|
4309
|
4014 // functions below. |
|
|
4015 |
|
|
4016 #define EMPTY_RETURN_CHECK(T) \ |
|
|
4017 if (nr == 0 || nc == 0) \ |
|
|
4018 return T (nr, nc); |
|
|
4019 |
|
|
4020 ComplexMatrix |
|
|
4021 min (const Complex& c, const ComplexMatrix& m) |
|
|
4022 { |
|
5275
|
4023 octave_idx_type nr = m.rows (); |
|
|
4024 octave_idx_type nc = m.columns (); |
|
4309
|
4025 |
|
|
4026 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4027 |
|
|
4028 ComplexMatrix result (nr, nc); |
|
|
4029 |
|
5275
|
4030 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4031 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4032 { |
|
|
4033 OCTAVE_QUIT; |
|
|
4034 result (i, j) = xmin (c, m (i, j)); |
|
|
4035 } |
|
|
4036 |
|
|
4037 return result; |
|
|
4038 } |
|
|
4039 |
|
|
4040 ComplexMatrix |
|
|
4041 min (const ComplexMatrix& m, const Complex& c) |
|
|
4042 { |
|
5275
|
4043 octave_idx_type nr = m.rows (); |
|
|
4044 octave_idx_type nc = m.columns (); |
|
4309
|
4045 |
|
|
4046 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4047 |
|
|
4048 ComplexMatrix result (nr, nc); |
|
|
4049 |
|
5275
|
4050 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4051 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4052 { |
|
|
4053 OCTAVE_QUIT; |
|
|
4054 result (i, j) = xmin (m (i, j), c); |
|
|
4055 } |
|
|
4056 |
|
|
4057 return result; |
|
|
4058 } |
|
|
4059 |
|
|
4060 ComplexMatrix |
|
|
4061 min (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
4062 { |
|
5275
|
4063 octave_idx_type nr = a.rows (); |
|
|
4064 octave_idx_type nc = a.columns (); |
|
4309
|
4065 |
|
|
4066 if (nr != b.rows () || nc != b.columns ()) |
|
|
4067 { |
|
|
4068 (*current_liboctave_error_handler) |
|
|
4069 ("two-arg min expecting args of same size"); |
|
|
4070 return ComplexMatrix (); |
|
|
4071 } |
|
|
4072 |
|
|
4073 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4074 |
|
|
4075 ComplexMatrix result (nr, nc); |
|
|
4076 |
|
5275
|
4077 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
4078 { |
|
|
4079 int columns_are_real_only = 1; |
|
5275
|
4080 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4081 { |
|
|
4082 OCTAVE_QUIT; |
|
5315
|
4083 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
|
4309
|
4084 { |
|
|
4085 columns_are_real_only = 0; |
|
|
4086 break; |
|
|
4087 } |
|
|
4088 } |
|
|
4089 |
|
|
4090 if (columns_are_real_only) |
|
|
4091 { |
|
5275
|
4092 for (octave_idx_type i = 0; i < nr; i++) |
|
5315
|
4093 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
|
4309
|
4094 } |
|
|
4095 else |
|
|
4096 { |
|
5275
|
4097 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4098 { |
|
|
4099 OCTAVE_QUIT; |
|
|
4100 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
4101 } |
|
|
4102 } |
|
|
4103 } |
|
|
4104 |
|
|
4105 return result; |
|
|
4106 } |
|
|
4107 |
|
|
4108 ComplexMatrix |
|
|
4109 max (const Complex& c, const ComplexMatrix& m) |
|
|
4110 { |
|
5275
|
4111 octave_idx_type nr = m.rows (); |
|
|
4112 octave_idx_type nc = m.columns (); |
|
4309
|
4113 |
|
|
4114 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4115 |
|
|
4116 ComplexMatrix result (nr, nc); |
|
|
4117 |
|
5275
|
4118 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4119 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4120 { |
|
|
4121 OCTAVE_QUIT; |
|
|
4122 result (i, j) = xmax (c, m (i, j)); |
|
|
4123 } |
|
|
4124 |
|
|
4125 return result; |
|
|
4126 } |
|
|
4127 |
|
|
4128 ComplexMatrix |
|
|
4129 max (const ComplexMatrix& m, const Complex& c) |
|
|
4130 { |
|
5275
|
4131 octave_idx_type nr = m.rows (); |
|
|
4132 octave_idx_type nc = m.columns (); |
|
4309
|
4133 |
|
|
4134 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4135 |
|
|
4136 ComplexMatrix result (nr, nc); |
|
|
4137 |
|
5275
|
4138 for (octave_idx_type j = 0; j < nc; j++) |
|
|
4139 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4140 { |
|
|
4141 OCTAVE_QUIT; |
|
|
4142 result (i, j) = xmax (m (i, j), c); |
|
|
4143 } |
|
|
4144 |
|
|
4145 return result; |
|
|
4146 } |
|
|
4147 |
|
|
4148 ComplexMatrix |
|
|
4149 max (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
4150 { |
|
5275
|
4151 octave_idx_type nr = a.rows (); |
|
|
4152 octave_idx_type nc = a.columns (); |
|
4309
|
4153 |
|
|
4154 if (nr != b.rows () || nc != b.columns ()) |
|
|
4155 { |
|
|
4156 (*current_liboctave_error_handler) |
|
|
4157 ("two-arg max expecting args of same size"); |
|
|
4158 return ComplexMatrix (); |
|
|
4159 } |
|
|
4160 |
|
|
4161 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
4162 |
|
|
4163 ComplexMatrix result (nr, nc); |
|
|
4164 |
|
5275
|
4165 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
4166 { |
|
|
4167 int columns_are_real_only = 1; |
|
5275
|
4168 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4169 { |
|
|
4170 OCTAVE_QUIT; |
|
5315
|
4171 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
|
4309
|
4172 { |
|
|
4173 columns_are_real_only = 0; |
|
|
4174 break; |
|
|
4175 } |
|
|
4176 } |
|
|
4177 |
|
|
4178 if (columns_are_real_only) |
|
|
4179 { |
|
5275
|
4180 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4181 { |
|
|
4182 OCTAVE_QUIT; |
|
5315
|
4183 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
|
4309
|
4184 } |
|
|
4185 } |
|
|
4186 else |
|
|
4187 { |
|
5275
|
4188 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
4189 { |
|
|
4190 OCTAVE_QUIT; |
|
|
4191 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
4192 } |
|
|
4193 } |
|
|
4194 } |
|
|
4195 |
|
|
4196 return result; |
|
|
4197 } |
|
|
4198 |
|
5315
|
4199 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
|
3504
|
4200 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
4201 |
|
5315
|
4202 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
|
3504
|
4203 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
4204 |
|
5315
|
4205 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
|
3504
|
4206 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
4207 |
|
458
|
4208 /* |
|
|
4209 ;;; Local Variables: *** |
|
|
4210 ;;; mode: C++ *** |
|
|
4211 ;;; End: *** |
|
|
4212 */ |
