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1 #define STD_OCTAVE std |
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2 |
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1993
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3 // Matrix manipulations. |
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4 /* |
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5 |
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6 Copyright (C) 1996, 1997 John W. Eaton |
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7 |
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8 This file is part of Octave. |
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9 |
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10 Octave is free software; you can redistribute it and/or modify it |
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11 under the terms of the GNU General Public License as published by the |
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12 Free Software Foundation; either version 2, or (at your option) any |
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13 later version. |
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14 |
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15 Octave is distributed in the hope that it will be useful, but WITHOUT |
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16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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17 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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18 for more details. |
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19 |
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20 You should have received a copy of the GNU General Public License |
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21 along with Octave; see the file COPYING. If not, write to the Free |
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22 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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23 02110-1301, USA. |
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24 |
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25 */ |
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26 |
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27 #ifdef HAVE_CONFIG_H |
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1192
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28 #include <config.h> |
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29 #endif |
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30 |
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31 #include <cfloat> |
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32 |
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3503
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33 #include <iostream> |
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34 |
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2443
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35 // XXX FIXME XXX |
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36 #ifdef HAVE_SYS_TYPES_H |
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37 #include <sys/types.h> |
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38 #endif |
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39 |
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4669
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40 #include "Array-util.h" |
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2828
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41 #include "CMatrix.h" |
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1819
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42 #include "CmplxAEPBAL.h" |
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458
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43 #include "CmplxDET.h" |
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1819
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44 #include "CmplxSCHUR.h" |
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740
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45 #include "CmplxSVD.h" |
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1847
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46 #include "f77-fcn.h" |
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458
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47 #include "lo-error.h" |
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2354
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48 #include "lo-ieee.h" |
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49 #include "lo-mappers.h" |
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1968
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50 #include "lo-utils.h" |
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1367
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51 #include "mx-base.h" |
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2828
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52 #include "mx-cm-dm.h" |
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3176
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53 #include "mx-dm-cm.h" |
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2828
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54 #include "mx-cm-s.h" |
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1367
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55 #include "mx-inlines.cc" |
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1650
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56 #include "oct-cmplx.h" |
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458
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57 |
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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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458
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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 (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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5275
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68 const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, |
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69 octave_idx_type&, double*, octave_idx_type& |
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70 F77_CHAR_ARG_LEN_DECL); |
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71 |
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72 F77_RET_T |
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73 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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74 F77_CONST_CHAR_ARG_DECL, |
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5275
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75 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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76 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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77 F77_CHAR_ARG_LEN_DECL |
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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 (zgemm, ZGEMM) (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&, |
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84 const Complex&, const Complex*, const octave_idx_type&, |
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85 const Complex*, const octave_idx_type&, const Complex&, |
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86 Complex*, const octave_idx_type& |
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87 F77_CHAR_ARG_LEN_DECL |
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88 F77_CHAR_ARG_LEN_DECL); |
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89 |
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90 F77_RET_T |
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91 F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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92 octave_idx_type*, octave_idx_type&); |
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93 |
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94 F77_RET_T |
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95 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, |
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96 const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
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97 const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& |
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98 F77_CHAR_ARG_LEN_DECL); |
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99 |
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100 F77_RET_T |
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101 F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, |
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102 Complex*, const octave_idx_type&, octave_idx_type&); |
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103 |
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104 F77_RET_T |
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105 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, |
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5275
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106 const octave_idx_type&, Complex*, |
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107 const octave_idx_type&, const double&, double&, |
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108 Complex*, double*, octave_idx_type& |
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109 F77_CHAR_ARG_LEN_DECL); |
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110 |
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111 F77_RET_T |
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112 F77_FUNC (zgelss, ZGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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113 Complex*, const octave_idx_type&, Complex*, |
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114 const octave_idx_type&, double*, double&, octave_idx_type&, |
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115 Complex*, const octave_idx_type&, double*, octave_idx_type&); |
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116 |
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1360
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117 // Note that the original complex fft routines were not written for |
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118 // double complex arguments. They have been modified by adding an |
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119 // implicit double precision (a-h,o-z) statement at the beginning of |
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120 // each subroutine. |
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121 |
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122 F77_RET_T |
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123 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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124 |
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125 F77_RET_T |
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5275
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126 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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127 |
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128 F77_RET_T |
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129 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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130 |
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131 F77_RET_T |
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132 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, |
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133 double&, Complex&, Complex&); |
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134 |
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135 F77_RET_T |
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136 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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137 F77_CONST_CHAR_ARG_DECL, |
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5275
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138 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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139 const Complex*, const octave_idx_type&, |
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140 const Complex*, const octave_idx_type&, |
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141 const Complex*, const octave_idx_type&, double&, octave_idx_type& |
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4552
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142 F77_CHAR_ARG_LEN_DECL |
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143 F77_CHAR_ARG_LEN_DECL); |
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144 |
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145 F77_RET_T |
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146 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, |
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5275
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147 const octave_idx_type&, const octave_idx_type&, const Complex*, |
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148 const octave_idx_type&, double*, double& |
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4552
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149 F77_CHAR_ARG_LEN_DECL); |
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458
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150 } |
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151 |
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2354
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152 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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153 |
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1360
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154 // Complex Matrix class |
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458
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155 |
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156 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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1214
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157 : MArray2<Complex> (a.rows (), a.cols ()) |
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458
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158 { |
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5275
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159 for (octave_idx_type j = 0; j < cols (); j++) |
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160 for (octave_idx_type i = 0; i < rows (); i++) |
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458
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161 elem (i, j) = a.elem (i, j); |
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162 } |
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163 |
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164 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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165 : MArray2<Complex> (1, rv.length (), 0.0) |
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166 { |
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5275
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167 for (octave_idx_type i = 0; i < rv.length (); i++) |
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168 elem (0, i) = rv.elem (i); |
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169 } |
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170 |
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171 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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172 : MArray2<Complex> (cv.length (), 1, 0.0) |
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173 { |
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5275
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174 for (octave_idx_type i = 0; i < cv.length (); i++) |
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175 elem (i, 0) = cv.elem (i); |
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176 } |
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177 |
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458
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178 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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179 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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180 { |
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181 for (octave_idx_type i = 0; i < a.length (); i++) |
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182 elem (i, i) = a.elem (i, i); |
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183 } |
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184 |
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185 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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186 : MArray2<Complex> (1, rv.length (), 0.0) |
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187 { |
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188 for (octave_idx_type i = 0; i < rv.length (); i++) |
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189 elem (0, i) = rv.elem (i); |
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190 } |
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191 |
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192 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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193 : MArray2<Complex> (cv.length (), 1, 0.0) |
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194 { |
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195 for (octave_idx_type i = 0; i < cv.length (); i++) |
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196 elem (i, 0) = cv.elem (i); |
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197 } |
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198 |
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199 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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200 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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201 { |
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202 for (octave_idx_type i = 0; i < a.length (); i++) |
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203 elem (i, i) = a.elem (i, i); |
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204 } |
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205 |
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1574
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206 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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207 // here? |
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208 |
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209 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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3180
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210 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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211 { |
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212 for (octave_idx_type i = 0; i < a.rows (); i++) |
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213 for (octave_idx_type j = 0; j < a.cols (); j++) |
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214 elem (i, j) = a.elem (i, j); |
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215 } |
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216 |
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1574
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217 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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218 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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219 { |
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220 for (octave_idx_type i = 0; i < a.rows (); i++) |
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221 for (octave_idx_type j = 0; j < a.cols (); j++) |
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1574
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222 elem (i, j) = a.elem (i, j); |
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223 } |
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224 |
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2384
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225 bool |
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458
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226 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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227 { |
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228 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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229 return false; |
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458
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230 |
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3769
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231 return mx_inline_equal (data (), a.data (), length ()); |
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458
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232 } |
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233 |
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2384
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234 bool |
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458
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235 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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236 { |
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237 return !(*this == a); |
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238 } |
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239 |
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2815
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240 bool |
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241 ComplexMatrix::is_hermitian (void) const |
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242 { |
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243 octave_idx_type nr = rows (); |
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244 octave_idx_type nc = cols (); |
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245 |
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246 if (is_square () && nr > 0) |
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247 { |
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5275
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248 for (octave_idx_type i = 0; i < nr; i++) |
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249 for (octave_idx_type j = i; j < nc; j++) |
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2815
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250 if (elem (i, j) != conj (elem (j, i))) |
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251 return false; |
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252 |
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253 return true; |
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254 } |
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255 |
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256 return false; |
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257 } |
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258 |
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458
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259 // destructive insert/delete/reorder operations |
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260 |
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261 ComplexMatrix& |
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262 ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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263 { |
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264 octave_idx_type a_nr = a.rows (); |
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265 octave_idx_type a_nc = a.cols (); |
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266 |
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267 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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268 { |
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269 (*current_liboctave_error_handler) ("range error for insert"); |
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270 return *this; |
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271 } |
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272 |
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4316
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273 if (a_nr >0 && a_nc > 0) |
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274 { |
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275 make_unique (); |
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276 |
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5275
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277 for (octave_idx_type j = 0; j < a_nc; j++) |
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278 for (octave_idx_type i = 0; i < a_nr; i++) |
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4316
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279 xelem (r+i, c+j) = a.elem (i, j); |
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280 } |
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458
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281 |
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282 return *this; |
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283 } |
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284 |
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285 ComplexMatrix& |
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5275
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286 ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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287 { |
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5275
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288 octave_idx_type a_len = a.length (); |
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4316
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289 |
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1699
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290 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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291 { |
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292 (*current_liboctave_error_handler) ("range error for insert"); |
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293 return *this; |
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294 } |
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295 |
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4316
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296 if (a_len > 0) |
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297 { |
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298 make_unique (); |
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299 |
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5275
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300 for (octave_idx_type i = 0; i < a_len; i++) |
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301 xelem (r, c+i) = a.elem (i); |
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302 } |
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458
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303 |
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304 return *this; |
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305 } |
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306 |
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307 ComplexMatrix& |
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5275
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308 ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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309 { |
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5275
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310 octave_idx_type a_len = a.length (); |
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4316
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311 |
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1699
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312 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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313 { |
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314 (*current_liboctave_error_handler) ("range error for insert"); |
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315 return *this; |
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316 } |
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317 |
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4316
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318 if (a_len > 0) |
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319 { |
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320 make_unique (); |
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321 |
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5275
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322 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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323 xelem (r+i, c) = a.elem (i); |
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324 } |
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458
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325 |
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326 return *this; |
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327 } |
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328 |
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329 ComplexMatrix& |
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5275
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330 ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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331 { |
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5275
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332 octave_idx_type a_nr = a.rows (); |
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333 octave_idx_type a_nc = a.cols (); |
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1699
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334 |
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335 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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336 { |
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337 (*current_liboctave_error_handler) ("range error for insert"); |
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338 return *this; |
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339 } |
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340 |
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1699
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341 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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342 |
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5275
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343 octave_idx_type a_len = a.length (); |
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4316
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344 |
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345 if (a_len > 0) |
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346 { |
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347 make_unique (); |
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348 |
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5275
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349 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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350 xelem (r+i, c+i) = a.elem (i, i); |
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351 } |
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458
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352 |
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353 return *this; |
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354 } |
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355 |
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356 ComplexMatrix& |
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5275
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357 ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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358 { |
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1561
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359 Array2<Complex>::insert (a, r, c); |
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458
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360 return *this; |
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361 } |
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362 |
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363 ComplexMatrix& |
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5275
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364 ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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365 { |
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5275
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366 octave_idx_type a_len = a.length (); |
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1699
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367 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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368 { |
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369 (*current_liboctave_error_handler) ("range error for insert"); |
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370 return *this; |
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371 } |
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372 |
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5275
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373 for (octave_idx_type i = 0; i < a_len; i++) |
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458
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374 elem (r, c+i) = a.elem (i); |
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375 |
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376 return *this; |
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377 } |
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378 |
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379 ComplexMatrix& |
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5275
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380 ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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381 { |
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5275
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382 octave_idx_type a_len = a.length (); |
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4316
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383 |
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1699
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384 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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385 { |
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386 (*current_liboctave_error_handler) ("range error for insert"); |
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387 return *this; |
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388 } |
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389 |
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4316
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390 if (a_len > 0) |
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391 { |
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392 make_unique (); |
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393 |
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5275
|
394 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
|
395 xelem (r+i, c) = a.elem (i); |
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396 } |
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458
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397 |
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398 return *this; |
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|
399 } |
|
|
400 |
|
|
401 ComplexMatrix& |
|
5275
|
402 ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) |
|
458
|
403 { |
|
5275
|
404 octave_idx_type a_nr = a.rows (); |
|
|
405 octave_idx_type a_nc = a.cols (); |
|
1699
|
406 |
|
|
407 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
408 { |
|
|
409 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
410 return *this; |
|
|
411 } |
|
|
412 |
|
1699
|
413 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
414 |
|
5275
|
415 octave_idx_type a_len = a.length (); |
|
4316
|
416 |
|
|
417 if (a_len > 0) |
|
|
418 { |
|
|
419 make_unique (); |
|
|
420 |
|
5275
|
421 for (octave_idx_type i = 0; i < a_len; i++) |
|
4316
|
422 xelem (r+i, c+i) = a.elem (i, i); |
|
|
423 } |
|
458
|
424 |
|
|
425 return *this; |
|
|
426 } |
|
|
427 |
|
|
428 ComplexMatrix& |
|
|
429 ComplexMatrix::fill (double val) |
|
|
430 { |
|
5275
|
431 octave_idx_type nr = rows (); |
|
|
432 octave_idx_type nc = cols (); |
|
4316
|
433 |
|
458
|
434 if (nr > 0 && nc > 0) |
|
4316
|
435 { |
|
|
436 make_unique (); |
|
|
437 |
|
5275
|
438 for (octave_idx_type j = 0; j < nc; j++) |
|
|
439 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
440 xelem (i, j) = val; |
|
|
441 } |
|
458
|
442 |
|
|
443 return *this; |
|
|
444 } |
|
|
445 |
|
|
446 ComplexMatrix& |
|
|
447 ComplexMatrix::fill (const Complex& val) |
|
|
448 { |
|
5275
|
449 octave_idx_type nr = rows (); |
|
|
450 octave_idx_type nc = cols (); |
|
4316
|
451 |
|
458
|
452 if (nr > 0 && nc > 0) |
|
4316
|
453 { |
|
|
454 make_unique (); |
|
|
455 |
|
5275
|
456 for (octave_idx_type j = 0; j < nc; j++) |
|
|
457 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
458 xelem (i, j) = val; |
|
|
459 } |
|
458
|
460 |
|
|
461 return *this; |
|
|
462 } |
|
|
463 |
|
|
464 ComplexMatrix& |
|
5275
|
465 ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
466 { |
|
5275
|
467 octave_idx_type nr = rows (); |
|
|
468 octave_idx_type nc = cols (); |
|
4316
|
469 |
|
458
|
470 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
471 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
472 { |
|
|
473 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
474 return *this; |
|
|
475 } |
|
|
476 |
|
5275
|
477 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
478 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
479 |
|
4316
|
480 if (r2 >= r1 && c2 >= c1) |
|
|
481 { |
|
|
482 make_unique (); |
|
|
483 |
|
5275
|
484 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
485 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
486 xelem (i, j) = val; |
|
|
487 } |
|
458
|
488 |
|
|
489 return *this; |
|
|
490 } |
|
|
491 |
|
|
492 ComplexMatrix& |
|
5275
|
493 ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
|
458
|
494 { |
|
5275
|
495 octave_idx_type nr = rows (); |
|
|
496 octave_idx_type nc = cols (); |
|
4316
|
497 |
|
458
|
498 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
499 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
500 { |
|
|
501 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
502 return *this; |
|
|
503 } |
|
|
504 |
|
5275
|
505 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
506 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
458
|
507 |
|
4316
|
508 if (r2 >= r1 && c2 >=c1) |
|
|
509 { |
|
|
510 make_unique (); |
|
|
511 |
|
5275
|
512 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
513 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
514 xelem (i, j) = val; |
|
|
515 } |
|
458
|
516 |
|
|
517 return *this; |
|
|
518 } |
|
|
519 |
|
|
520 ComplexMatrix |
|
|
521 ComplexMatrix::append (const Matrix& a) const |
|
|
522 { |
|
5275
|
523 octave_idx_type nr = rows (); |
|
|
524 octave_idx_type nc = cols (); |
|
458
|
525 if (nr != a.rows ()) |
|
|
526 { |
|
|
527 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
528 return *this; |
|
|
529 } |
|
|
530 |
|
5275
|
531 octave_idx_type nc_insert = nc; |
|
458
|
532 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
533 retval.insert (*this, 0, 0); |
|
|
534 retval.insert (a, 0, nc_insert); |
|
|
535 return retval; |
|
|
536 } |
|
|
537 |
|
|
538 ComplexMatrix |
|
|
539 ComplexMatrix::append (const RowVector& a) const |
|
|
540 { |
|
5275
|
541 octave_idx_type nr = rows (); |
|
|
542 octave_idx_type nc = cols (); |
|
458
|
543 if (nr != 1) |
|
|
544 { |
|
|
545 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
546 return *this; |
|
|
547 } |
|
|
548 |
|
5275
|
549 octave_idx_type nc_insert = nc; |
|
458
|
550 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
551 retval.insert (*this, 0, 0); |
|
|
552 retval.insert (a, 0, nc_insert); |
|
|
553 return retval; |
|
|
554 } |
|
|
555 |
|
|
556 ComplexMatrix |
|
|
557 ComplexMatrix::append (const ColumnVector& a) const |
|
|
558 { |
|
5275
|
559 octave_idx_type nr = rows (); |
|
|
560 octave_idx_type nc = cols (); |
|
458
|
561 if (nr != a.length ()) |
|
|
562 { |
|
|
563 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
564 return *this; |
|
|
565 } |
|
|
566 |
|
5275
|
567 octave_idx_type nc_insert = nc; |
|
458
|
568 ComplexMatrix retval (nr, nc + 1); |
|
|
569 retval.insert (*this, 0, 0); |
|
|
570 retval.insert (a, 0, nc_insert); |
|
|
571 return retval; |
|
|
572 } |
|
|
573 |
|
|
574 ComplexMatrix |
|
|
575 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
576 { |
|
5275
|
577 octave_idx_type nr = rows (); |
|
|
578 octave_idx_type nc = cols (); |
|
458
|
579 if (nr != a.rows ()) |
|
|
580 { |
|
|
581 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
582 return *this; |
|
|
583 } |
|
|
584 |
|
5275
|
585 octave_idx_type nc_insert = nc; |
|
458
|
586 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
587 retval.insert (*this, 0, 0); |
|
|
588 retval.insert (a, 0, nc_insert); |
|
|
589 return retval; |
|
|
590 } |
|
|
591 |
|
|
592 ComplexMatrix |
|
|
593 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
594 { |
|
5275
|
595 octave_idx_type nr = rows (); |
|
|
596 octave_idx_type nc = cols (); |
|
458
|
597 if (nr != a.rows ()) |
|
|
598 { |
|
|
599 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
600 return *this; |
|
|
601 } |
|
|
602 |
|
5275
|
603 octave_idx_type nc_insert = nc; |
|
458
|
604 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
605 retval.insert (*this, 0, 0); |
|
|
606 retval.insert (a, 0, nc_insert); |
|
|
607 return retval; |
|
|
608 } |
|
|
609 |
|
|
610 ComplexMatrix |
|
|
611 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
612 { |
|
5275
|
613 octave_idx_type nr = rows (); |
|
|
614 octave_idx_type nc = cols (); |
|
458
|
615 if (nr != 1) |
|
|
616 { |
|
|
617 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
618 return *this; |
|
|
619 } |
|
|
620 |
|
5275
|
621 octave_idx_type nc_insert = nc; |
|
458
|
622 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
623 retval.insert (*this, 0, 0); |
|
|
624 retval.insert (a, 0, nc_insert); |
|
|
625 return retval; |
|
|
626 } |
|
|
627 |
|
|
628 ComplexMatrix |
|
|
629 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
630 { |
|
5275
|
631 octave_idx_type nr = rows (); |
|
|
632 octave_idx_type nc = cols (); |
|
458
|
633 if (nr != a.length ()) |
|
|
634 { |
|
|
635 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
636 return *this; |
|
|
637 } |
|
|
638 |
|
5275
|
639 octave_idx_type nc_insert = nc; |
|
458
|
640 ComplexMatrix retval (nr, nc + 1); |
|
|
641 retval.insert (*this, 0, 0); |
|
|
642 retval.insert (a, 0, nc_insert); |
|
|
643 return retval; |
|
|
644 } |
|
|
645 |
|
|
646 ComplexMatrix |
|
|
647 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
648 { |
|
5275
|
649 octave_idx_type nr = rows (); |
|
|
650 octave_idx_type nc = cols (); |
|
458
|
651 if (nr != a.rows ()) |
|
|
652 { |
|
|
653 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
654 return *this; |
|
|
655 } |
|
|
656 |
|
5275
|
657 octave_idx_type nc_insert = nc; |
|
458
|
658 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
659 retval.insert (*this, 0, 0); |
|
|
660 retval.insert (a, 0, nc_insert); |
|
|
661 return retval; |
|
|
662 } |
|
|
663 |
|
|
664 ComplexMatrix |
|
|
665 ComplexMatrix::stack (const Matrix& a) const |
|
|
666 { |
|
5275
|
667 octave_idx_type nr = rows (); |
|
|
668 octave_idx_type nc = cols (); |
|
458
|
669 if (nc != a.cols ()) |
|
|
670 { |
|
|
671 (*current_liboctave_error_handler) |
|
|
672 ("column dimension mismatch for stack"); |
|
|
673 return *this; |
|
|
674 } |
|
|
675 |
|
5275
|
676 octave_idx_type nr_insert = nr; |
|
458
|
677 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
678 retval.insert (*this, 0, 0); |
|
|
679 retval.insert (a, nr_insert, 0); |
|
|
680 return retval; |
|
|
681 } |
|
|
682 |
|
|
683 ComplexMatrix |
|
|
684 ComplexMatrix::stack (const RowVector& a) const |
|
|
685 { |
|
5275
|
686 octave_idx_type nr = rows (); |
|
|
687 octave_idx_type nc = cols (); |
|
458
|
688 if (nc != a.length ()) |
|
|
689 { |
|
|
690 (*current_liboctave_error_handler) |
|
|
691 ("column dimension mismatch for stack"); |
|
|
692 return *this; |
|
|
693 } |
|
|
694 |
|
5275
|
695 octave_idx_type nr_insert = nr; |
|
458
|
696 ComplexMatrix retval (nr + 1, nc); |
|
|
697 retval.insert (*this, 0, 0); |
|
|
698 retval.insert (a, nr_insert, 0); |
|
|
699 return retval; |
|
|
700 } |
|
|
701 |
|
|
702 ComplexMatrix |
|
|
703 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
704 { |
|
5275
|
705 octave_idx_type nr = rows (); |
|
|
706 octave_idx_type nc = cols (); |
|
458
|
707 if (nc != 1) |
|
|
708 { |
|
|
709 (*current_liboctave_error_handler) |
|
|
710 ("column dimension mismatch for stack"); |
|
|
711 return *this; |
|
|
712 } |
|
|
713 |
|
5275
|
714 octave_idx_type nr_insert = nr; |
|
458
|
715 ComplexMatrix retval (nr + a.length (), nc); |
|
|
716 retval.insert (*this, 0, 0); |
|
|
717 retval.insert (a, nr_insert, 0); |
|
|
718 return retval; |
|
|
719 } |
|
|
720 |
|
|
721 ComplexMatrix |
|
|
722 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
723 { |
|
5275
|
724 octave_idx_type nr = rows (); |
|
|
725 octave_idx_type nc = cols (); |
|
458
|
726 if (nc != a.cols ()) |
|
|
727 { |
|
|
728 (*current_liboctave_error_handler) |
|
|
729 ("column dimension mismatch for stack"); |
|
|
730 return *this; |
|
|
731 } |
|
|
732 |
|
5275
|
733 octave_idx_type nr_insert = nr; |
|
458
|
734 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
735 retval.insert (*this, 0, 0); |
|
|
736 retval.insert (a, nr_insert, 0); |
|
|
737 return retval; |
|
|
738 } |
|
|
739 |
|
|
740 ComplexMatrix |
|
|
741 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
742 { |
|
5275
|
743 octave_idx_type nr = rows (); |
|
|
744 octave_idx_type nc = cols (); |
|
458
|
745 if (nc != a.cols ()) |
|
|
746 { |
|
|
747 (*current_liboctave_error_handler) |
|
|
748 ("column dimension mismatch for stack"); |
|
|
749 return *this; |
|
|
750 } |
|
|
751 |
|
5275
|
752 octave_idx_type nr_insert = nr; |
|
458
|
753 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
754 retval.insert (*this, 0, 0); |
|
|
755 retval.insert (a, nr_insert, 0); |
|
|
756 return retval; |
|
|
757 } |
|
|
758 |
|
|
759 ComplexMatrix |
|
|
760 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
761 { |
|
5275
|
762 octave_idx_type nr = rows (); |
|
|
763 octave_idx_type nc = cols (); |
|
458
|
764 if (nc != a.length ()) |
|
|
765 { |
|
|
766 (*current_liboctave_error_handler) |
|
|
767 ("column dimension mismatch for stack"); |
|
|
768 return *this; |
|
|
769 } |
|
|
770 |
|
5275
|
771 octave_idx_type nr_insert = nr; |
|
458
|
772 ComplexMatrix retval (nr + 1, nc); |
|
|
773 retval.insert (*this, 0, 0); |
|
|
774 retval.insert (a, nr_insert, 0); |
|
|
775 return retval; |
|
|
776 } |
|
|
777 |
|
|
778 ComplexMatrix |
|
|
779 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
780 { |
|
5275
|
781 octave_idx_type nr = rows (); |
|
|
782 octave_idx_type nc = cols (); |
|
458
|
783 if (nc != 1) |
|
|
784 { |
|
|
785 (*current_liboctave_error_handler) |
|
|
786 ("column dimension mismatch for stack"); |
|
|
787 return *this; |
|
|
788 } |
|
|
789 |
|
5275
|
790 octave_idx_type nr_insert = nr; |
|
458
|
791 ComplexMatrix retval (nr + a.length (), nc); |
|
|
792 retval.insert (*this, 0, 0); |
|
|
793 retval.insert (a, nr_insert, 0); |
|
|
794 return retval; |
|
|
795 } |
|
|
796 |
|
|
797 ComplexMatrix |
|
|
798 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
799 { |
|
5275
|
800 octave_idx_type nr = rows (); |
|
|
801 octave_idx_type nc = cols (); |
|
458
|
802 if (nc != a.cols ()) |
|
|
803 { |
|
|
804 (*current_liboctave_error_handler) |
|
|
805 ("column dimension mismatch for stack"); |
|
|
806 return *this; |
|
|
807 } |
|
|
808 |
|
5275
|
809 octave_idx_type nr_insert = nr; |
|
458
|
810 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
811 retval.insert (*this, 0, 0); |
|
|
812 retval.insert (a, nr_insert, 0); |
|
|
813 return retval; |
|
|
814 } |
|
|
815 |
|
|
816 ComplexMatrix |
|
|
817 ComplexMatrix::hermitian (void) const |
|
|
818 { |
|
5275
|
819 octave_idx_type nr = rows (); |
|
|
820 octave_idx_type nc = cols (); |
|
458
|
821 ComplexMatrix result; |
|
|
822 if (length () > 0) |
|
|
823 { |
|
|
824 result.resize (nc, nr); |
|
5275
|
825 for (octave_idx_type j = 0; j < nc; j++) |
|
|
826 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
827 result.elem (j, i) = conj (elem (i, j)); |
|
|
828 } |
|
|
829 return result; |
|
|
830 } |
|
|
831 |
|
|
832 ComplexMatrix |
|
|
833 conj (const ComplexMatrix& a) |
|
|
834 { |
|
5275
|
835 octave_idx_type a_len = a.length (); |
|
458
|
836 ComplexMatrix retval; |
|
|
837 if (a_len > 0) |
|
3769
|
838 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
|
|
839 a.rows (), a.cols ()); |
|
458
|
840 return retval; |
|
|
841 } |
|
|
842 |
|
|
843 // resize is the destructive equivalent for this one |
|
|
844 |
|
|
845 ComplexMatrix |
|
5275
|
846 ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
847 { |
|
5275
|
848 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
849 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
850 |
|
|
851 octave_idx_type new_r = r2 - r1 + 1; |
|
|
852 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
853 |
|
|
854 ComplexMatrix result (new_r, new_c); |
|
|
855 |
|
5275
|
856 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
857 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
858 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
859 |
|
|
860 return result; |
|
|
861 } |
|
|
862 |
|
|
863 ComplexMatrix |
|
5275
|
864 ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
865 { |
|
|
866 ComplexMatrix result (nr, nc); |
|
|
867 |
|
5275
|
868 for (octave_idx_type j = 0; j < nc; j++) |
|
|
869 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
870 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
871 |
|
|
872 return result; |
|
|
873 } |
|
|
874 |
|
|
875 // extract row or column i. |
|
|
876 |
|
|
877 ComplexRowVector |
|
5275
|
878 ComplexMatrix::row (octave_idx_type i) const |
|
458
|
879 { |
|
5275
|
880 octave_idx_type nc = cols (); |
|
458
|
881 if (i < 0 || i >= rows ()) |
|
|
882 { |
|
|
883 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
884 return ComplexRowVector (); |
|
|
885 } |
|
|
886 |
|
|
887 ComplexRowVector retval (nc); |
|
5275
|
888 for (octave_idx_type j = 0; j < cols (); j++) |
|
4316
|
889 retval.xelem (j) = elem (i, j); |
|
458
|
890 |
|
|
891 return retval; |
|
|
892 } |
|
|
893 |
|
|
894 ComplexRowVector |
|
|
895 ComplexMatrix::row (char *s) const |
|
|
896 { |
|
533
|
897 if (! s) |
|
458
|
898 { |
|
|
899 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
900 return ComplexRowVector (); |
|
|
901 } |
|
|
902 |
|
|
903 char c = *s; |
|
|
904 if (c == 'f' || c == 'F') |
|
5275
|
905 return row (static_cast<octave_idx_type>(0)); |
|
458
|
906 else if (c == 'l' || c == 'L') |
|
|
907 return row (rows () - 1); |
|
|
908 else |
|
|
909 { |
|
|
910 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
911 return ComplexRowVector (); |
|
|
912 } |
|
|
913 } |
|
|
914 |
|
|
915 ComplexColumnVector |
|
5275
|
916 ComplexMatrix::column (octave_idx_type i) const |
|
458
|
917 { |
|
5275
|
918 octave_idx_type nr = rows (); |
|
458
|
919 if (i < 0 || i >= cols ()) |
|
|
920 { |
|
|
921 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
922 return ComplexColumnVector (); |
|
|
923 } |
|
|
924 |
|
|
925 ComplexColumnVector retval (nr); |
|
5275
|
926 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
927 retval.xelem (j) = elem (j, i); |
|
458
|
928 |
|
|
929 return retval; |
|
|
930 } |
|
|
931 |
|
|
932 ComplexColumnVector |
|
|
933 ComplexMatrix::column (char *s) const |
|
|
934 { |
|
533
|
935 if (! s) |
|
458
|
936 { |
|
|
937 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
938 return ComplexColumnVector (); |
|
|
939 } |
|
|
940 |
|
|
941 char c = *s; |
|
|
942 if (c == 'f' || c == 'F') |
|
5275
|
943 return column (static_cast<octave_idx_type>(0)); |
|
458
|
944 else if (c == 'l' || c == 'L') |
|
|
945 return column (cols () - 1); |
|
|
946 else |
|
|
947 { |
|
|
948 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
949 return ComplexColumnVector (); |
|
|
950 } |
|
|
951 } |
|
|
952 |
|
|
953 ComplexMatrix |
|
|
954 ComplexMatrix::inverse (void) const |
|
|
955 { |
|
5275
|
956 octave_idx_type info; |
|
479
|
957 double rcond; |
|
4329
|
958 return inverse (info, rcond, 0, 0); |
|
458
|
959 } |
|
|
960 |
|
|
961 ComplexMatrix |
|
5275
|
962 ComplexMatrix::inverse (octave_idx_type& info) const |
|
458
|
963 { |
|
|
964 double rcond; |
|
4329
|
965 return inverse (info, rcond, 0, 0); |
|
458
|
966 } |
|
|
967 |
|
|
968 ComplexMatrix |
|
5275
|
969 ComplexMatrix::inverse (octave_idx_type& info, double& rcond, int force, |
|
4329
|
970 int calc_cond) const |
|
458
|
971 { |
|
1948
|
972 ComplexMatrix retval; |
|
|
973 |
|
5275
|
974 octave_idx_type nr = rows (); |
|
|
975 octave_idx_type nc = cols (); |
|
1948
|
976 |
|
458
|
977 if (nr != nc) |
|
1948
|
978 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
979 else |
|
|
980 { |
|
5275
|
981 Array<octave_idx_type> ipvt (nr); |
|
|
982 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
983 |
|
|
984 retval = *this; |
|
|
985 Complex *tmp_data = retval.fortran_vec (); |
|
|
986 |
|
4329
|
987 Array<Complex> z(1); |
|
5275
|
988 octave_idx_type lwork = -1; |
|
4330
|
989 |
|
|
990 // Query the optimum work array size. |
|
4329
|
991 |
|
|
992 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
|
993 z.fortran_vec (), lwork, info)); |
|
|
994 |
|
|
995 if (f77_exception_encountered) |
|
|
996 { |
|
|
997 (*current_liboctave_error_handler) |
|
|
998 ("unrecoverable error in zgetri"); |
|
|
999 return retval; |
|
|
1000 } |
|
|
1001 |
|
5275
|
1002 lwork = static_cast<octave_idx_type> (STD_OCTAVE::real(z(0))); |
|
4329
|
1003 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
1004 z.resize (lwork); |
|
|
1005 Complex *pz = z.fortran_vec (); |
|
|
1006 |
|
|
1007 info = 0; |
|
|
1008 |
|
4330
|
1009 // Calculate the norm of the matrix, for later use. |
|
4329
|
1010 double anorm; |
|
|
1011 if (calc_cond) |
|
5275
|
1012 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1013 |
|
|
1014 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1015 |
|
|
1016 if (f77_exception_encountered) |
|
4329
|
1017 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1018 else |
|
|
1019 { |
|
4330
|
1020 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1021 rcond = 0.0; |
|
|
1022 if (info != 0) |
|
1948
|
1023 info = -1; |
|
4329
|
1024 else if (calc_cond) |
|
|
1025 { |
|
4330
|
1026 // Now calculate the condition number for non-singular matrix. |
|
5275
|
1027 octave_idx_type zgecon_info = 0; |
|
4329
|
1028 char job = '1'; |
|
|
1029 Array<double> rz (2 * nc); |
|
|
1030 double *prz = rz.fortran_vec (); |
|
4552
|
1031 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1032 nc, tmp_data, nr, anorm, |
|
5061
|
1033 rcond, pz, prz, zgecon_info |
|
4552
|
1034 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1035 |
|
|
1036 if (f77_exception_encountered) |
|
|
1037 (*current_liboctave_error_handler) |
|
|
1038 ("unrecoverable error in zgecon"); |
|
|
1039 |
|
5061
|
1040 if (zgecon_info != 0) |
|
4329
|
1041 info = -1; |
|
|
1042 } |
|
1948
|
1043 |
|
|
1044 if (info == -1 && ! force) |
|
|
1045 retval = *this; // Restore contents. |
|
|
1046 else |
|
|
1047 { |
|
5275
|
1048 octave_idx_type zgetri_info = 0; |
|
5061
|
1049 |
|
4329
|
1050 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
1051 pz, lwork, zgetri_info)); |
|
1948
|
1052 |
|
|
1053 if (f77_exception_encountered) |
|
|
1054 (*current_liboctave_error_handler) |
|
4329
|
1055 ("unrecoverable error in zgetri"); |
|
|
1056 |
|
5061
|
1057 if (zgetri_info != 0) |
|
4329
|
1058 info = -1; |
|
1948
|
1059 } |
|
|
1060 } |
|
458
|
1061 } |
|
4329
|
1062 |
|
1948
|
1063 return retval; |
|
458
|
1064 } |
|
|
1065 |
|
|
1066 ComplexMatrix |
|
4384
|
1067 ComplexMatrix::pseudo_inverse (double tol) const |
|
740
|
1068 { |
|
1549
|
1069 ComplexMatrix retval; |
|
|
1070 |
|
3480
|
1071 ComplexSVD result (*this, SVD::economy); |
|
740
|
1072 |
|
|
1073 DiagMatrix S = result.singular_values (); |
|
|
1074 ComplexMatrix U = result.left_singular_matrix (); |
|
|
1075 ComplexMatrix V = result.right_singular_matrix (); |
|
|
1076 |
|
|
1077 ColumnVector sigma = S.diag (); |
|
|
1078 |
|
5275
|
1079 octave_idx_type r = sigma.length () - 1; |
|
|
1080 octave_idx_type nr = rows (); |
|
|
1081 octave_idx_type nc = cols (); |
|
740
|
1082 |
|
|
1083 if (tol <= 0.0) |
|
|
1084 { |
|
|
1085 if (nr > nc) |
|
|
1086 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
1087 else |
|
|
1088 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
1089 } |
|
|
1090 |
|
|
1091 while (r >= 0 && sigma.elem (r) < tol) |
|
|
1092 r--; |
|
|
1093 |
|
|
1094 if (r < 0) |
|
1549
|
1095 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
1096 else |
|
|
1097 { |
|
|
1098 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
1099 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
1100 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
1101 retval = Vr * D * Ur.hermitian (); |
|
740
|
1102 } |
|
1549
|
1103 |
|
|
1104 return retval; |
|
740
|
1105 } |
|
|
1106 |
|
4773
|
1107 #if defined (HAVE_FFTW3) |
|
3827
|
1108 |
|
|
1109 ComplexMatrix |
|
|
1110 ComplexMatrix::fourier (void) const |
|
|
1111 { |
|
|
1112 size_t nr = rows (); |
|
|
1113 size_t nc = cols (); |
|
|
1114 |
|
|
1115 ComplexMatrix retval (nr, nc); |
|
|
1116 |
|
|
1117 size_t npts, nsamples; |
|
|
1118 |
|
|
1119 if (nr == 1 || nc == 1) |
|
|
1120 { |
|
|
1121 npts = nr > nc ? nr : nc; |
|
|
1122 nsamples = 1; |
|
|
1123 } |
|
|
1124 else |
|
|
1125 { |
|
|
1126 npts = nr; |
|
|
1127 nsamples = nc; |
|
|
1128 } |
|
|
1129 |
|
|
1130 const Complex *in (data ()); |
|
|
1131 Complex *out (retval.fortran_vec ()); |
|
|
1132 |
|
4773
|
1133 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
1134 |
|
|
1135 return retval; |
|
|
1136 } |
|
|
1137 |
|
|
1138 ComplexMatrix |
|
|
1139 ComplexMatrix::ifourier (void) const |
|
|
1140 { |
|
|
1141 size_t nr = rows (); |
|
|
1142 size_t nc = cols (); |
|
|
1143 |
|
|
1144 ComplexMatrix retval (nr, nc); |
|
|
1145 |
|
|
1146 size_t npts, nsamples; |
|
|
1147 |
|
|
1148 if (nr == 1 || nc == 1) |
|
|
1149 { |
|
|
1150 npts = nr > nc ? nr : nc; |
|
|
1151 nsamples = 1; |
|
|
1152 } |
|
|
1153 else |
|
|
1154 { |
|
|
1155 npts = nr; |
|
|
1156 nsamples = nc; |
|
|
1157 } |
|
|
1158 |
|
|
1159 const Complex *in (data ()); |
|
|
1160 Complex *out (retval.fortran_vec ()); |
|
|
1161 |
|
4773
|
1162 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
1163 |
|
|
1164 return retval; |
|
|
1165 } |
|
|
1166 |
|
|
1167 ComplexMatrix |
|
|
1168 ComplexMatrix::fourier2d (void) const |
|
|
1169 { |
|
4773
|
1170 dim_vector dv(rows (), cols ()); |
|
|
1171 |
|
|
1172 ComplexMatrix retval (rows (), cols ()); |
|
|
1173 const Complex *in (data ()); |
|
|
1174 Complex *out (retval.fortran_vec ()); |
|
|
1175 |
|
|
1176 octave_fftw::fftNd (in, out, 2, dv); |
|
3827
|
1177 |
|
|
1178 return retval; |
|
|
1179 } |
|
|
1180 |
|
|
1181 ComplexMatrix |
|
|
1182 ComplexMatrix::ifourier2d (void) const |
|
|
1183 { |
|
4773
|
1184 dim_vector dv(rows (), cols ()); |
|
|
1185 |
|
|
1186 ComplexMatrix retval (rows (), cols ()); |
|
|
1187 const Complex *in (data ()); |
|
|
1188 Complex *out (retval.fortran_vec ()); |
|
|
1189 |
|
|
1190 octave_fftw::ifftNd (in, out, 2, dv); |
|
3827
|
1191 |
|
|
1192 return retval; |
|
|
1193 } |
|
|
1194 |
|
|
1195 #else |
|
|
1196 |
|
740
|
1197 ComplexMatrix |
|
458
|
1198 ComplexMatrix::fourier (void) const |
|
|
1199 { |
|
1948
|
1200 ComplexMatrix retval; |
|
|
1201 |
|
5275
|
1202 octave_idx_type nr = rows (); |
|
|
1203 octave_idx_type nc = cols (); |
|
|
1204 |
|
|
1205 octave_idx_type npts, nsamples; |
|
1948
|
1206 |
|
458
|
1207 if (nr == 1 || nc == 1) |
|
|
1208 { |
|
|
1209 npts = nr > nc ? nr : nc; |
|
|
1210 nsamples = 1; |
|
|
1211 } |
|
|
1212 else |
|
|
1213 { |
|
|
1214 npts = nr; |
|
|
1215 nsamples = nc; |
|
|
1216 } |
|
|
1217 |
|
5275
|
1218 octave_idx_type nn = 4*npts+15; |
|
1948
|
1219 |
|
|
1220 Array<Complex> wsave (nn); |
|
|
1221 Complex *pwsave = wsave.fortran_vec (); |
|
|
1222 |
|
|
1223 retval = *this; |
|
|
1224 Complex *tmp_data = retval.fortran_vec (); |
|
|
1225 |
|
3887
|
1226 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1227 |
|
5275
|
1228 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1229 { |
|
|
1230 OCTAVE_QUIT; |
|
|
1231 |
|
|
1232 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1233 } |
|
1948
|
1234 |
|
|
1235 return retval; |
|
458
|
1236 } |
|
|
1237 |
|
|
1238 ComplexMatrix |
|
|
1239 ComplexMatrix::ifourier (void) const |
|
|
1240 { |
|
1948
|
1241 ComplexMatrix retval; |
|
|
1242 |
|
5275
|
1243 octave_idx_type nr = rows (); |
|
|
1244 octave_idx_type nc = cols (); |
|
|
1245 |
|
|
1246 octave_idx_type npts, nsamples; |
|
1948
|
1247 |
|
458
|
1248 if (nr == 1 || nc == 1) |
|
|
1249 { |
|
|
1250 npts = nr > nc ? nr : nc; |
|
|
1251 nsamples = 1; |
|
|
1252 } |
|
|
1253 else |
|
|
1254 { |
|
|
1255 npts = nr; |
|
|
1256 nsamples = nc; |
|
|
1257 } |
|
|
1258 |
|
5275
|
1259 octave_idx_type nn = 4*npts+15; |
|
1948
|
1260 |
|
|
1261 Array<Complex> wsave (nn); |
|
|
1262 Complex *pwsave = wsave.fortran_vec (); |
|
|
1263 |
|
|
1264 retval = *this; |
|
|
1265 Complex *tmp_data = retval.fortran_vec (); |
|
|
1266 |
|
3887
|
1267 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1268 |
|
5275
|
1269 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1270 { |
|
|
1271 OCTAVE_QUIT; |
|
|
1272 |
|
|
1273 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1274 } |
|
458
|
1275 |
|
5275
|
1276 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1277 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1278 |
|
1948
|
1279 return retval; |
|
458
|
1280 } |
|
|
1281 |
|
677
|
1282 ComplexMatrix |
|
|
1283 ComplexMatrix::fourier2d (void) const |
|
|
1284 { |
|
1948
|
1285 ComplexMatrix retval; |
|
|
1286 |
|
5275
|
1287 octave_idx_type nr = rows (); |
|
|
1288 octave_idx_type nc = cols (); |
|
|
1289 |
|
|
1290 octave_idx_type npts, nsamples; |
|
1948
|
1291 |
|
677
|
1292 if (nr == 1 || nc == 1) |
|
|
1293 { |
|
|
1294 npts = nr > nc ? nr : nc; |
|
|
1295 nsamples = 1; |
|
|
1296 } |
|
|
1297 else |
|
|
1298 { |
|
|
1299 npts = nr; |
|
|
1300 nsamples = nc; |
|
|
1301 } |
|
|
1302 |
|
5275
|
1303 octave_idx_type nn = 4*npts+15; |
|
1948
|
1304 |
|
|
1305 Array<Complex> wsave (nn); |
|
|
1306 Complex *pwsave = wsave.fortran_vec (); |
|
|
1307 |
|
|
1308 retval = *this; |
|
|
1309 Complex *tmp_data = retval.fortran_vec (); |
|
|
1310 |
|
3887
|
1311 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1312 |
|
5275
|
1313 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1314 { |
|
|
1315 OCTAVE_QUIT; |
|
|
1316 |
|
|
1317 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1318 } |
|
677
|
1319 |
|
|
1320 npts = nc; |
|
|
1321 nsamples = nr; |
|
|
1322 nn = 4*npts+15; |
|
1948
|
1323 |
|
|
1324 wsave.resize (nn); |
|
|
1325 pwsave = wsave.fortran_vec (); |
|
|
1326 |
|
4773
|
1327 Array<Complex> tmp (npts); |
|
|
1328 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1329 |
|
3887
|
1330 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1331 |
|
5275
|
1332 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1333 { |
|
4153
|
1334 OCTAVE_QUIT; |
|
|
1335 |
|
5275
|
1336 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1337 prow[i] = tmp_data[i*nr + j]; |
|
|
1338 |
|
3887
|
1339 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1340 |
|
5275
|
1341 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1342 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1343 } |
|
|
1344 |
|
1948
|
1345 return retval; |
|
677
|
1346 } |
|
|
1347 |
|
|
1348 ComplexMatrix |
|
|
1349 ComplexMatrix::ifourier2d (void) const |
|
|
1350 { |
|
1948
|
1351 ComplexMatrix retval; |
|
|
1352 |
|
5275
|
1353 octave_idx_type nr = rows (); |
|
|
1354 octave_idx_type nc = cols (); |
|
|
1355 |
|
|
1356 octave_idx_type npts, nsamples; |
|
1948
|
1357 |
|
677
|
1358 if (nr == 1 || nc == 1) |
|
|
1359 { |
|
|
1360 npts = nr > nc ? nr : nc; |
|
|
1361 nsamples = 1; |
|
|
1362 } |
|
|
1363 else |
|
|
1364 { |
|
|
1365 npts = nr; |
|
|
1366 nsamples = nc; |
|
|
1367 } |
|
|
1368 |
|
5275
|
1369 octave_idx_type nn = 4*npts+15; |
|
1948
|
1370 |
|
|
1371 Array<Complex> wsave (nn); |
|
|
1372 Complex *pwsave = wsave.fortran_vec (); |
|
|
1373 |
|
|
1374 retval = *this; |
|
|
1375 Complex *tmp_data = retval.fortran_vec (); |
|
|
1376 |
|
3887
|
1377 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1378 |
|
5275
|
1379 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1380 { |
|
|
1381 OCTAVE_QUIT; |
|
|
1382 |
|
|
1383 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1384 } |
|
677
|
1385 |
|
5275
|
1386 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1387 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1388 |
|
|
1389 npts = nc; |
|
|
1390 nsamples = nr; |
|
|
1391 nn = 4*npts+15; |
|
1948
|
1392 |
|
|
1393 wsave.resize (nn); |
|
|
1394 pwsave = wsave.fortran_vec (); |
|
|
1395 |
|
4773
|
1396 Array<Complex> tmp (npts); |
|
|
1397 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1398 |
|
3887
|
1399 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1400 |
|
5275
|
1401 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1402 { |
|
4153
|
1403 OCTAVE_QUIT; |
|
|
1404 |
|
5275
|
1405 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1406 prow[i] = tmp_data[i*nr + j]; |
|
|
1407 |
|
3887
|
1408 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1409 |
|
5275
|
1410 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1411 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1412 } |
|
|
1413 |
|
1948
|
1414 return retval; |
|
677
|
1415 } |
|
|
1416 |
|
3827
|
1417 #endif |
|
|
1418 |
|
458
|
1419 ComplexDET |
|
|
1420 ComplexMatrix::determinant (void) const |
|
|
1421 { |
|
5275
|
1422 octave_idx_type info; |
|
458
|
1423 double rcond; |
|
4329
|
1424 return determinant (info, rcond, 0); |
|
458
|
1425 } |
|
|
1426 |
|
|
1427 ComplexDET |
|
5275
|
1428 ComplexMatrix::determinant (octave_idx_type& info) const |
|
458
|
1429 { |
|
|
1430 double rcond; |
|
4329
|
1431 return determinant (info, rcond, 0); |
|
458
|
1432 } |
|
|
1433 |
|
|
1434 ComplexDET |
|
5275
|
1435 ComplexMatrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1436 { |
|
|
1437 ComplexDET retval; |
|
|
1438 |
|
5275
|
1439 octave_idx_type nr = rows (); |
|
|
1440 octave_idx_type nc = cols (); |
|
458
|
1441 |
|
|
1442 if (nr == 0 || nc == 0) |
|
|
1443 { |
|
|
1444 Complex d[2]; |
|
|
1445 d[0] = 1.0; |
|
|
1446 d[1] = 0.0; |
|
|
1447 retval = ComplexDET (d); |
|
|
1448 } |
|
|
1449 else |
|
|
1450 { |
|
5275
|
1451 Array<octave_idx_type> ipvt (nr); |
|
|
1452 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1453 |
|
|
1454 ComplexMatrix atmp = *this; |
|
|
1455 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1456 |
|
4329
|
1457 info = 0; |
|
|
1458 |
|
4330
|
1459 // Calculate the norm of the matrix, for later use. |
|
4329
|
1460 double anorm = 0; |
|
|
1461 if (calc_cond) |
|
5275
|
1462 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1463 |
|
|
1464 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
1465 |
|
|
1466 if (f77_exception_encountered) |
|
4329
|
1467 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
458
|
1468 else |
|
|
1469 { |
|
4330
|
1470 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1471 rcond = 0.0; |
|
|
1472 if (info != 0) |
|
1948
|
1473 { |
|
|
1474 info = -1; |
|
|
1475 retval = ComplexDET (); |
|
4329
|
1476 } |
|
|
1477 else |
|
1948
|
1478 { |
|
4329
|
1479 if (calc_cond) |
|
|
1480 { |
|
4330
|
1481 // Now calc the condition number for non-singular matrix. |
|
4329
|
1482 char job = '1'; |
|
|
1483 Array<Complex> z (2*nr); |
|
|
1484 Complex *pz = z.fortran_vec (); |
|
|
1485 Array<double> rz (2*nr); |
|
|
1486 double *prz = rz.fortran_vec (); |
|
|
1487 |
|
4552
|
1488 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1489 nc, tmp_data, nr, anorm, |
|
|
1490 rcond, pz, prz, info |
|
|
1491 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1492 |
|
|
1493 if (f77_exception_encountered) |
|
|
1494 (*current_liboctave_error_handler) |
|
|
1495 ("unrecoverable error in zgecon"); |
|
|
1496 } |
|
|
1497 |
|
4509
|
1498 if (info != 0) |
|
4329
|
1499 { |
|
|
1500 info = -1; |
|
|
1501 retval = ComplexDET (); |
|
|
1502 } |
|
|
1503 else |
|
|
1504 { |
|
|
1505 Complex d[2] = { 1., 0.}; |
|
5275
|
1506 for (octave_idx_type i=0; i<nc; i++) |
|
4329
|
1507 { |
|
|
1508 if (ipvt(i) != (i+1)) d[0] = -d[0]; |
|
|
1509 d[0] = d[0] * atmp(i,i); |
|
|
1510 if (d[0] == 0.) break; |
|
5260
|
1511 while (STD_OCTAVE::abs(d[0]) < 1.) |
|
4329
|
1512 { |
|
|
1513 d[0] = 10. * d[0]; |
|
4509
|
1514 d[1] = d[1] - 1.0; |
|
4329
|
1515 } |
|
5260
|
1516 while (STD_OCTAVE::abs(d[0]) >= 10.) |
|
4329
|
1517 { |
|
|
1518 d[0] = 0.1 * d[0]; |
|
4509
|
1519 d[1] = d[1] + 1.0; |
|
4329
|
1520 } |
|
|
1521 } |
|
|
1522 retval = ComplexDET (d); |
|
|
1523 } |
|
1948
|
1524 } |
|
458
|
1525 } |
|
|
1526 } |
|
4329
|
1527 |
|
458
|
1528 return retval; |
|
|
1529 } |
|
|
1530 |
|
|
1531 ComplexMatrix |
|
|
1532 ComplexMatrix::solve (const Matrix& b) const |
|
|
1533 { |
|
5275
|
1534 octave_idx_type info; |
|
458
|
1535 double rcond; |
|
3480
|
1536 return solve (b, info, rcond, 0); |
|
458
|
1537 } |
|
|
1538 |
|
|
1539 ComplexMatrix |
|
5275
|
1540 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1541 { |
|
|
1542 double rcond; |
|
3480
|
1543 return solve (b, info, rcond, 0); |
|
458
|
1544 } |
|
|
1545 |
|
|
1546 ComplexMatrix |
|
5275
|
1547 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1548 { |
|
3480
|
1549 return solve (b, info, rcond, 0); |
|
|
1550 } |
|
|
1551 |
|
|
1552 ComplexMatrix |
|
5275
|
1553 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1554 solve_singularity_handler sing_handler) const |
|
|
1555 { |
|
458
|
1556 ComplexMatrix tmp (b); |
|
3480
|
1557 return solve (tmp, info, rcond, sing_handler); |
|
458
|
1558 } |
|
|
1559 |
|
|
1560 ComplexMatrix |
|
|
1561 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1562 { |
|
5275
|
1563 octave_idx_type info; |
|
458
|
1564 double rcond; |
|
3480
|
1565 return solve (b, info, rcond, 0); |
|
458
|
1566 } |
|
|
1567 |
|
|
1568 ComplexMatrix |
|
5275
|
1569 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1570 { |
|
|
1571 double rcond; |
|
3480
|
1572 return solve (b, info, rcond, 0); |
|
458
|
1573 } |
|
3480
|
1574 |
|
458
|
1575 ComplexMatrix |
|
5275
|
1576 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1577 { |
|
3480
|
1578 return solve (b, info, rcond, 0); |
|
|
1579 } |
|
|
1580 |
|
|
1581 ComplexMatrix |
|
5275
|
1582 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1583 solve_singularity_handler sing_handler) const |
|
|
1584 { |
|
458
|
1585 ComplexMatrix retval; |
|
|
1586 |
|
5275
|
1587 octave_idx_type nr = rows (); |
|
|
1588 octave_idx_type nc = cols (); |
|
1948
|
1589 |
|
|
1590 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1591 (*current_liboctave_error_handler) |
|
|
1592 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1593 else |
|
|
1594 { |
|
1948
|
1595 info = 0; |
|
|
1596 |
|
5275
|
1597 Array<octave_idx_type> ipvt (nr); |
|
|
1598 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1599 |
|
|
1600 ComplexMatrix atmp = *this; |
|
|
1601 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1602 |
|
4329
|
1603 Array<Complex> z (2 * nc); |
|
|
1604 Complex *pz = z.fortran_vec (); |
|
|
1605 Array<double> rz (2 * nc); |
|
|
1606 double *prz = rz.fortran_vec (); |
|
|
1607 |
|
4330
|
1608 // Calculate the norm of the matrix, for later use. |
|
5275
|
1609 double anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1610 |
|
|
1611 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1612 |
|
|
1613 if (f77_exception_encountered) |
|
4329
|
1614 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1615 else |
|
|
1616 { |
|
4330
|
1617 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1618 rcond = 0.0; |
|
|
1619 if (info != 0) |
|
4329
|
1620 { |
|
1948
|
1621 info = -2; |
|
3480
|
1622 |
|
|
1623 if (sing_handler) |
|
|
1624 sing_handler (rcond); |
|
|
1625 else |
|
|
1626 (*current_liboctave_error_handler) |
|
4329
|
1627 ("matrix singular to machine precision"); |
|
|
1628 |
|
|
1629 } |
|
|
1630 else |
|
1948
|
1631 { |
|
4330
|
1632 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1633 char job = '1'; |
|
4552
|
1634 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1635 nc, tmp_data, nr, anorm, |
|
|
1636 rcond, pz, prz, info |
|
|
1637 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1638 |
|
|
1639 if (f77_exception_encountered) |
|
|
1640 (*current_liboctave_error_handler) |
|
|
1641 ("unrecoverable error in zgecon"); |
|
|
1642 |
|
4509
|
1643 if (info != 0) |
|
4329
|
1644 info = -2; |
|
|
1645 |
|
|
1646 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1647 |
|
|
1648 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1649 { |
|
4329
|
1650 info = -2; |
|
|
1651 |
|
|
1652 if (sing_handler) |
|
|
1653 sing_handler (rcond); |
|
|
1654 else |
|
|
1655 (*current_liboctave_error_handler) |
|
|
1656 ("matrix singular to machine precision, rcond = %g", |
|
|
1657 rcond); |
|
|
1658 } |
|
|
1659 else |
|
|
1660 { |
|
|
1661 retval = b; |
|
|
1662 Complex *result = retval.fortran_vec (); |
|
|
1663 |
|
5275
|
1664 octave_idx_type b_nc = b.cols (); |
|
4329
|
1665 |
|
4587
|
1666 job = 'N'; |
|
4552
|
1667 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1668 nr, b_nc, tmp_data, nr, |
|
|
1669 pipvt, result, b.rows(), info |
|
|
1670 F77_CHAR_ARG_LEN (1))); |
|
1948
|
1671 |
|
|
1672 if (f77_exception_encountered) |
|
4329
|
1673 (*current_liboctave_error_handler) |
|
|
1674 ("unrecoverable error in zgetrs"); |
|
1948
|
1675 } |
|
|
1676 } |
|
|
1677 } |
|
458
|
1678 } |
|
4329
|
1679 |
|
458
|
1680 return retval; |
|
|
1681 } |
|
|
1682 |
|
|
1683 ComplexColumnVector |
|
3585
|
1684 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
1685 { |
|
5275
|
1686 octave_idx_type info; |
|
3585
|
1687 double rcond; |
|
|
1688 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1689 } |
|
|
1690 |
|
|
1691 ComplexColumnVector |
|
5275
|
1692 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
1693 { |
|
|
1694 double rcond; |
|
|
1695 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1696 } |
|
|
1697 |
|
|
1698 ComplexColumnVector |
|
5275
|
1699 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
3585
|
1700 { |
|
|
1701 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1702 } |
|
|
1703 |
|
|
1704 ComplexColumnVector |
|
5275
|
1705 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
3585
|
1706 solve_singularity_handler sing_handler) const |
|
|
1707 { |
|
|
1708 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
1709 } |
|
|
1710 |
|
|
1711 ComplexColumnVector |
|
458
|
1712 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1713 { |
|
5275
|
1714 octave_idx_type info; |
|
458
|
1715 double rcond; |
|
3480
|
1716 return solve (b, info, rcond, 0); |
|
458
|
1717 } |
|
|
1718 |
|
|
1719 ComplexColumnVector |
|
5275
|
1720 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1721 { |
|
|
1722 double rcond; |
|
3480
|
1723 return solve (b, info, rcond, 0); |
|
458
|
1724 } |
|
|
1725 |
|
|
1726 ComplexColumnVector |
|
5275
|
1727 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
532
|
1728 double& rcond) const |
|
458
|
1729 { |
|
3480
|
1730 return solve (b, info, rcond, 0); |
|
|
1731 } |
|
|
1732 |
|
|
1733 ComplexColumnVector |
|
5275
|
1734 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
|
3480
|
1735 double& rcond, |
|
|
1736 solve_singularity_handler sing_handler) const |
|
|
1737 { |
|
458
|
1738 ComplexColumnVector retval; |
|
|
1739 |
|
5275
|
1740 octave_idx_type nr = rows (); |
|
|
1741 octave_idx_type nc = cols (); |
|
1948
|
1742 |
|
|
1743 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
1744 (*current_liboctave_error_handler) |
|
|
1745 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1746 else |
|
|
1747 { |
|
1948
|
1748 info = 0; |
|
|
1749 |
|
5275
|
1750 Array<octave_idx_type> ipvt (nr); |
|
|
1751 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1752 |
|
|
1753 ComplexMatrix atmp = *this; |
|
|
1754 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1755 |
|
4329
|
1756 Array<Complex> z (2 * nc); |
|
|
1757 Complex *pz = z.fortran_vec (); |
|
|
1758 Array<double> rz (2 * nc); |
|
|
1759 double *prz = rz.fortran_vec (); |
|
|
1760 |
|
4330
|
1761 // Calculate the norm of the matrix, for later use. |
|
5275
|
1762 double anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1763 |
|
|
1764 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1765 |
|
|
1766 if (f77_exception_encountered) |
|
4329
|
1767 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
|
1948
|
1768 else |
|
|
1769 { |
|
4330
|
1770 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1771 rcond = 0.0; |
|
|
1772 if (info != 0) |
|
4329
|
1773 { |
|
1948
|
1774 info = -2; |
|
3480
|
1775 |
|
|
1776 if (sing_handler) |
|
|
1777 sing_handler (rcond); |
|
|
1778 else |
|
|
1779 (*current_liboctave_error_handler) |
|
|
1780 ("matrix singular to machine precision, rcond = %g", |
|
|
1781 rcond); |
|
4329
|
1782 } |
|
|
1783 else |
|
1948
|
1784 { |
|
4330
|
1785 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1786 char job = '1'; |
|
4552
|
1787 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1788 nc, tmp_data, nr, anorm, |
|
|
1789 rcond, pz, prz, info |
|
|
1790 F77_CHAR_ARG_LEN (1))); |
|
1948
|
1791 |
|
|
1792 if (f77_exception_encountered) |
|
4329
|
1793 (*current_liboctave_error_handler) |
|
|
1794 ("unrecoverable error in zgecon"); |
|
|
1795 |
|
4509
|
1796 if (info != 0) |
|
4329
|
1797 info = -2; |
|
|
1798 |
|
|
1799 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1800 |
|
|
1801 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1802 { |
|
|
1803 info = -2; |
|
|
1804 |
|
|
1805 if (sing_handler) |
|
|
1806 sing_handler (rcond); |
|
|
1807 else |
|
|
1808 (*current_liboctave_error_handler) |
|
|
1809 ("matrix singular to machine precision, rcond = %g", |
|
|
1810 rcond); |
|
|
1811 } |
|
|
1812 else |
|
|
1813 { |
|
|
1814 retval = b; |
|
|
1815 Complex *result = retval.fortran_vec (); |
|
|
1816 |
|
4587
|
1817 job = 'N'; |
|
4552
|
1818 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1819 nr, 1, tmp_data, nr, pipvt, |
|
|
1820 result, b.length(), info |
|
|
1821 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1822 |
|
|
1823 if (f77_exception_encountered) |
|
|
1824 (*current_liboctave_error_handler) |
|
|
1825 ("unrecoverable error in zgetrs"); |
|
|
1826 |
|
|
1827 } |
|
1948
|
1828 } |
|
|
1829 } |
|
458
|
1830 } |
|
|
1831 return retval; |
|
|
1832 } |
|
|
1833 |
|
|
1834 ComplexMatrix |
|
3585
|
1835 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
1836 { |
|
5275
|
1837 octave_idx_type info; |
|
|
1838 octave_idx_type rank; |
|
3585
|
1839 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1840 } |
|
|
1841 |
|
|
1842 ComplexMatrix |
|
5275
|
1843 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
3585
|
1844 { |
|
5275
|
1845 octave_idx_type rank; |
|
3585
|
1846 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1847 } |
|
|
1848 |
|
|
1849 ComplexMatrix |
|
5275
|
1850 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
3585
|
1851 { |
|
|
1852 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1853 } |
|
|
1854 |
|
|
1855 ComplexMatrix |
|
458
|
1856 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1857 { |
|
5275
|
1858 octave_idx_type info; |
|
|
1859 octave_idx_type rank; |
|
458
|
1860 return lssolve (b, info, rank); |
|
|
1861 } |
|
|
1862 |
|
|
1863 ComplexMatrix |
|
5275
|
1864 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1865 { |
|
5275
|
1866 octave_idx_type rank; |
|
458
|
1867 return lssolve (b, info, rank); |
|
|
1868 } |
|
|
1869 |
|
|
1870 ComplexMatrix |
|
5275
|
1871 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1872 { |
|
1948
|
1873 ComplexMatrix retval; |
|
|
1874 |
|
5275
|
1875 octave_idx_type nrhs = b.cols (); |
|
|
1876 |
|
|
1877 octave_idx_type m = rows (); |
|
|
1878 octave_idx_type n = cols (); |
|
458
|
1879 |
|
|
1880 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1881 (*current_liboctave_error_handler) |
|
|
1882 ("matrix dimension mismatch solution of linear equations"); |
|
|
1883 else |
|
458
|
1884 { |
|
1948
|
1885 ComplexMatrix atmp = *this; |
|
|
1886 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1887 |
|
5275
|
1888 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
1889 ComplexMatrix result (nrr, nrhs); |
|
|
1890 |
|
5275
|
1891 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1892 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
1893 result.elem (i, j) = b.elem (i, j); |
|
|
1894 |
|
|
1895 Complex *presult = result.fortran_vec (); |
|
|
1896 |
|
5275
|
1897 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
1898 Array<double> s (len_s); |
|
|
1899 double *ps = s.fortran_vec (); |
|
2563
|
1900 |
|
1948
|
1901 double rcond = -1.0; |
|
2563
|
1902 |
|
5275
|
1903 octave_idx_type lrwork = (5 * (m < n ? m : n)) - 4; |
|
1948
|
1904 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1905 Array<double> rwork (lrwork); |
|
|
1906 double *prwork = rwork.fortran_vec (); |
|
|
1907 |
|
3752
|
1908 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1909 |
|
5275
|
1910 octave_idx_type lwork = -1; |
|
3752
|
1911 |
|
|
1912 Array<Complex> work (1); |
|
|
1913 |
|
1948
|
1914 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1915 nrr, ps, rcond, rank, |
|
|
1916 work.fortran_vec (), lwork, prwork, |
|
|
1917 info)); |
|
1948
|
1918 |
|
|
1919 if (f77_exception_encountered) |
|
|
1920 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1921 else |
|
|
1922 { |
|
5275
|
1923 lwork = static_cast<octave_idx_type> (STD_OCTAVE::real (work(0))); |
|
3752
|
1924 work.resize (lwork); |
|
|
1925 |
|
|
1926 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1927 nrr, ps, rcond, rank, |
|
|
1928 work.fortran_vec (), lwork, |
|
|
1929 prwork, info)); |
|
|
1930 |
|
|
1931 if (f77_exception_encountered) |
|
|
1932 (*current_liboctave_error_handler) |
|
|
1933 ("unrecoverable error in zgelss"); |
|
|
1934 else |
|
|
1935 { |
|
|
1936 retval.resize (n, nrhs); |
|
5275
|
1937 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1938 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
1939 retval.elem (i, j) = result.elem (i, j); |
|
|
1940 } |
|
1948
|
1941 } |
|
458
|
1942 } |
|
|
1943 |
|
|
1944 return retval; |
|
|
1945 } |
|
|
1946 |
|
|
1947 ComplexColumnVector |
|
3585
|
1948 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
1949 { |
|
5275
|
1950 octave_idx_type info; |
|
|
1951 octave_idx_type rank; |
|
3585
|
1952 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1953 } |
|
|
1954 |
|
|
1955 ComplexColumnVector |
|
5275
|
1956 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
3585
|
1957 { |
|
5275
|
1958 octave_idx_type rank; |
|
3585
|
1959 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1960 } |
|
|
1961 |
|
|
1962 ComplexColumnVector |
|
5275
|
1963 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
3585
|
1964 { |
|
|
1965 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1966 } |
|
|
1967 |
|
|
1968 ComplexColumnVector |
|
458
|
1969 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1970 { |
|
5275
|
1971 octave_idx_type info; |
|
|
1972 octave_idx_type rank; |
|
458
|
1973 return lssolve (b, info, rank); |
|
|
1974 } |
|
|
1975 |
|
|
1976 ComplexColumnVector |
|
5275
|
1977 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1978 { |
|
5275
|
1979 octave_idx_type rank; |
|
458
|
1980 return lssolve (b, info, rank); |
|
|
1981 } |
|
|
1982 |
|
|
1983 ComplexColumnVector |
|
5275
|
1984 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
|
|
1985 octave_idx_type& rank) const |
|
458
|
1986 { |
|
1948
|
1987 ComplexColumnVector retval; |
|
|
1988 |
|
5275
|
1989 octave_idx_type nrhs = 1; |
|
|
1990 |
|
|
1991 octave_idx_type m = rows (); |
|
|
1992 octave_idx_type n = cols (); |
|
458
|
1993 |
|
|
1994 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1995 (*current_liboctave_error_handler) |
|
|
1996 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1997 else |
|
458
|
1998 { |
|
1948
|
1999 ComplexMatrix atmp = *this; |
|
|
2000 Complex *tmp_data = atmp.fortran_vec (); |
|
|
2001 |
|
5275
|
2002 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2003 ComplexColumnVector result (nrr); |
|
|
2004 |
|
5275
|
2005 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2006 result.elem (i) = b.elem (i); |
|
|
2007 |
|
|
2008 Complex *presult = result.fortran_vec (); |
|
|
2009 |
|
5275
|
2010 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2011 Array<double> s (len_s); |
|
|
2012 double *ps = s.fortran_vec (); |
|
|
2013 |
|
|
2014 double rcond = -1.0; |
|
|
2015 |
|
5275
|
2016 octave_idx_type lrwork = (5 * (m < n ? m : n)) - 4; |
|
1948
|
2017 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
2018 Array<double> rwork (lrwork); |
|
|
2019 double *prwork = rwork.fortran_vec (); |
|
|
2020 |
|
3752
|
2021 // Ask ZGELSS what the dimension of WORK should be. |
|
|
2022 |
|
5275
|
2023 octave_idx_type lwork = -1; |
|
3752
|
2024 |
|
|
2025 Array<Complex> work (1); |
|
|
2026 |
|
1948
|
2027 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
2028 nrr, ps, rcond, rank, |
|
|
2029 work.fortran_vec (), lwork, prwork, |
|
|
2030 info)); |
|
1948
|
2031 |
|
|
2032 if (f77_exception_encountered) |
|
|
2033 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
2034 else |
|
|
2035 { |
|
5260
|
2036 lwork = static_cast<int> (STD_OCTAVE::real (work(0))); |
|
3752
|
2037 work.resize (lwork); |
|
|
2038 |
|
|
2039 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2040 nrr, ps, rcond, rank, |
|
|
2041 work.fortran_vec (), lwork, |
|
|
2042 prwork, info)); |
|
|
2043 |
|
|
2044 if (f77_exception_encountered) |
|
|
2045 (*current_liboctave_error_handler) |
|
|
2046 ("unrecoverable error in zgelss"); |
|
|
2047 else |
|
|
2048 { |
|
|
2049 retval.resize (n); |
|
5275
|
2050 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2051 retval.elem (i) = result.elem (i); |
|
|
2052 } |
|
1948
|
2053 } |
|
458
|
2054 } |
|
|
2055 |
|
|
2056 return retval; |
|
|
2057 } |
|
|
2058 |
|
1819
|
2059 // Constants for matrix exponential calculation. |
|
|
2060 |
|
|
2061 static double padec [] = |
|
|
2062 { |
|
|
2063 5.0000000000000000e-1, |
|
|
2064 1.1666666666666667e-1, |
|
|
2065 1.6666666666666667e-2, |
|
|
2066 1.6025641025641026e-3, |
|
|
2067 1.0683760683760684e-4, |
|
|
2068 4.8562548562548563e-6, |
|
|
2069 1.3875013875013875e-7, |
|
|
2070 1.9270852604185938e-9, |
|
|
2071 }; |
|
|
2072 |
|
|
2073 ComplexMatrix |
|
|
2074 ComplexMatrix::expm (void) const |
|
|
2075 { |
|
|
2076 ComplexMatrix retval; |
|
|
2077 |
|
|
2078 ComplexMatrix m = *this; |
|
|
2079 |
|
5275
|
2080 octave_idx_type nc = columns (); |
|
1819
|
2081 |
|
3130
|
2082 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2083 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2084 |
|
1819
|
2085 // trace shift value |
|
|
2086 Complex trshift = 0.0; |
|
|
2087 |
|
5275
|
2088 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2089 trshift += m.elem (i, i); |
|
|
2090 |
|
|
2091 trshift /= nc; |
|
|
2092 |
|
3130
|
2093 if (trshift.real () < 0.0) |
|
|
2094 trshift = trshift.imag (); |
|
|
2095 |
|
5275
|
2096 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2097 m.elem (i, i) -= trshift; |
|
|
2098 |
|
|
2099 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
2100 // code follows development in AEPBAL |
|
|
2101 |
|
|
2102 Complex *mp = m.fortran_vec (); |
|
3467
|
2103 |
|
5275
|
2104 octave_idx_type info, ilo, ihi,ilos,ihis; |
|
3468
|
2105 Array<double> dpermute (nc); |
|
|
2106 Array<double> dscale (nc); |
|
|
2107 |
|
|
2108 // XXX FIXME XXX -- should pass job as a parameter in expm |
|
|
2109 |
|
|
2110 // Permute first |
|
|
2111 char job = 'P'; |
|
4552
|
2112 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2113 nc, mp, nc, ilo, ihi, |
|
|
2114 dpermute.fortran_vec (), info |
|
|
2115 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2116 |
|
|
2117 if (f77_exception_encountered) |
|
|
2118 { |
|
|
2119 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
2120 return retval; |
|
|
2121 } |
|
|
2122 |
|
3468
|
2123 // then scale |
|
|
2124 job = 'S'; |
|
4552
|
2125 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2126 nc, mp, nc, ilos, ihis, |
|
|
2127 dscale.fortran_vec (), info |
|
|
2128 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2129 |
|
|
2130 if (f77_exception_encountered) |
|
|
2131 { |
|
3467
|
2132 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
2133 return retval; |
|
|
2134 } |
|
1819
|
2135 |
|
|
2136 // Preconditioning step 3: scaling. |
|
|
2137 |
|
|
2138 ColumnVector work (nc); |
|
3130
|
2139 double inf_norm; |
|
|
2140 |
|
4552
|
2141 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2142 nc, nc, m.fortran_vec (), nc, |
|
|
2143 work.fortran_vec (), inf_norm |
|
|
2144 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2145 |
|
|
2146 if (f77_exception_encountered) |
|
|
2147 { |
|
|
2148 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
2149 return retval; |
|
|
2150 } |
|
1819
|
2151 |
|
2800
|
2152 int sqpow = (inf_norm > 0.0 |
|
|
2153 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
2154 |
|
|
2155 // Check whether we need to square at all. |
|
|
2156 |
|
|
2157 if (sqpow < 0) |
|
|
2158 sqpow = 0; |
|
|
2159 |
|
|
2160 if (sqpow > 0) |
|
|
2161 { |
|
|
2162 double scale_factor = 1.0; |
|
5275
|
2163 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2164 scale_factor *= 2.0; |
|
|
2165 |
|
|
2166 m = m / scale_factor; |
|
|
2167 } |
|
|
2168 |
|
|
2169 // npp, dpp: pade' approx polynomial matrices. |
|
|
2170 |
|
|
2171 ComplexMatrix npp (nc, nc, 0.0); |
|
|
2172 ComplexMatrix dpp = npp; |
|
|
2173 |
|
|
2174 // Now powers a^8 ... a^1. |
|
|
2175 |
|
|
2176 int minus_one_j = -1; |
|
5275
|
2177 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2178 { |
|
|
2179 npp = m * npp + m * padec[j]; |
|
|
2180 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
2181 minus_one_j *= -1; |
|
|
2182 } |
|
|
2183 |
|
|
2184 // Zero power. |
|
|
2185 |
|
|
2186 dpp = -dpp; |
|
5275
|
2187 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2188 { |
|
|
2189 npp.elem (j, j) += 1.0; |
|
|
2190 dpp.elem (j, j) += 1.0; |
|
|
2191 } |
|
|
2192 |
|
|
2193 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2194 |
|
|
2195 retval = dpp.solve (npp); |
|
|
2196 |
|
|
2197 // Reverse preconditioning step 3: repeated squaring. |
|
|
2198 |
|
|
2199 while (sqpow) |
|
|
2200 { |
|
|
2201 retval = retval * retval; |
|
|
2202 sqpow--; |
|
|
2203 } |
|
|
2204 |
|
|
2205 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
2206 // Done in two steps: inverse scaling, then inverse permutation |
|
|
2207 |
|
|
2208 // inverse scaling (diagonal transformation) |
|
5275
|
2209 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2210 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2211 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
2212 |
|
4153
|
2213 OCTAVE_QUIT; |
|
|
2214 |
|
3467
|
2215 // construct balancing permutation vector |
|
4593
|
2216 Array<int> iperm (nc); |
|
5275
|
2217 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2218 iperm(i) = i; // initialize to identity permutation |
|
3467
|
2219 |
|
|
2220 // leading permutations in forward order |
|
5275
|
2221 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2222 { |
|
5275
|
2223 octave_idx_type swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
2224 octave_idx_type tmp = iperm(i); |
|
4593
|
2225 iperm(i) = iperm(swapidx); |
|
|
2226 iperm(swapidx) = tmp; |
|
3468
|
2227 } |
|
3467
|
2228 |
|
|
2229 // trailing permutations must be done in reverse order |
|
5275
|
2230 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2231 { |
|
5275
|
2232 octave_idx_type swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
2233 octave_idx_type tmp = iperm(i); |
|
4593
|
2234 iperm(i) = iperm(swapidx); |
|
|
2235 iperm(swapidx) = tmp; |
|
3468
|
2236 } |
|
3467
|
2237 |
|
|
2238 // construct inverse balancing permutation vector |
|
3468
|
2239 Array<int> invpvec (nc); |
|
5275
|
2240 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2241 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
2242 |
|
4153
|
2243 OCTAVE_QUIT; |
|
|
2244 |
|
3467
|
2245 ComplexMatrix tmpMat = retval; |
|
5275
|
2246 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2247 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2248 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
2249 |
|
|
2250 // Reverse preconditioning step 1: fix trace normalization. |
|
|
2251 |
|
3130
|
2252 return exp (trshift) * retval; |
|
1819
|
2253 } |
|
|
2254 |
|
1205
|
2255 // column vector by row vector -> matrix operations |
|
|
2256 |
|
|
2257 ComplexMatrix |
|
|
2258 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
2259 { |
|
|
2260 ComplexColumnVector tmp (v); |
|
|
2261 return tmp * a; |
|
|
2262 } |
|
|
2263 |
|
|
2264 ComplexMatrix |
|
|
2265 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
2266 { |
|
|
2267 ComplexRowVector tmp (b); |
|
|
2268 return a * tmp; |
|
|
2269 } |
|
|
2270 |
|
|
2271 ComplexMatrix |
|
|
2272 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
2273 { |
|
1948
|
2274 ComplexMatrix retval; |
|
|
2275 |
|
5275
|
2276 octave_idx_type len = v.length (); |
|
3233
|
2277 |
|
|
2278 if (len != 0) |
|
1205
|
2279 { |
|
5275
|
2280 octave_idx_type a_len = a.length (); |
|
3233
|
2281 |
|
|
2282 retval.resize (len, a_len); |
|
|
2283 Complex *c = retval.fortran_vec (); |
|
|
2284 |
|
4552
|
2285 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2286 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2287 len, a_len, 1, 1.0, v.data (), len, |
|
|
2288 a.data (), 1, 0.0, c, len |
|
|
2289 F77_CHAR_ARG_LEN (1) |
|
|
2290 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2291 |
|
|
2292 if (f77_exception_encountered) |
|
|
2293 (*current_liboctave_error_handler) |
|
|
2294 ("unrecoverable error in zgemm"); |
|
1205
|
2295 } |
|
|
2296 |
|
1948
|
2297 return retval; |
|
1205
|
2298 } |
|
|
2299 |
|
458
|
2300 // matrix by diagonal matrix -> matrix operations |
|
|
2301 |
|
|
2302 ComplexMatrix& |
|
|
2303 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
2304 { |
|
5275
|
2305 octave_idx_type nr = rows (); |
|
|
2306 octave_idx_type nc = cols (); |
|
|
2307 |
|
|
2308 octave_idx_type a_nr = rows (); |
|
|
2309 octave_idx_type a_nc = cols (); |
|
2384
|
2310 |
|
|
2311 if (nr != a_nr || nc != a_nc) |
|
458
|
2312 { |
|
2384
|
2313 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2314 return *this; |
|
458
|
2315 } |
|
|
2316 |
|
5275
|
2317 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2318 elem (i, i) += a.elem (i, i); |
|
|
2319 |
|
|
2320 return *this; |
|
|
2321 } |
|
|
2322 |
|
|
2323 ComplexMatrix& |
|
|
2324 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
2325 { |
|
5275
|
2326 octave_idx_type nr = rows (); |
|
|
2327 octave_idx_type nc = cols (); |
|
|
2328 |
|
|
2329 octave_idx_type a_nr = rows (); |
|
|
2330 octave_idx_type a_nc = cols (); |
|
2384
|
2331 |
|
|
2332 if (nr != a_nr || nc != a_nc) |
|
458
|
2333 { |
|
2384
|
2334 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2335 return *this; |
|
458
|
2336 } |
|
|
2337 |
|
5275
|
2338 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2339 elem (i, i) -= a.elem (i, i); |
|
|
2340 |
|
|
2341 return *this; |
|
|
2342 } |
|
|
2343 |
|
|
2344 ComplexMatrix& |
|
|
2345 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
2346 { |
|
5275
|
2347 octave_idx_type nr = rows (); |
|
|
2348 octave_idx_type nc = cols (); |
|
|
2349 |
|
|
2350 octave_idx_type a_nr = rows (); |
|
|
2351 octave_idx_type a_nc = cols (); |
|
2384
|
2352 |
|
|
2353 if (nr != a_nr || nc != a_nc) |
|
458
|
2354 { |
|
2384
|
2355 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2356 return *this; |
|
458
|
2357 } |
|
|
2358 |
|
5275
|
2359 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2360 elem (i, i) += a.elem (i, i); |
|
|
2361 |
|
|
2362 return *this; |
|
|
2363 } |
|
|
2364 |
|
|
2365 ComplexMatrix& |
|
|
2366 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
2367 { |
|
5275
|
2368 octave_idx_type nr = rows (); |
|
|
2369 octave_idx_type nc = cols (); |
|
|
2370 |
|
|
2371 octave_idx_type a_nr = rows (); |
|
|
2372 octave_idx_type a_nc = cols (); |
|
2384
|
2373 |
|
|
2374 if (nr != a_nr || nc != a_nc) |
|
458
|
2375 { |
|
2384
|
2376 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2377 return *this; |
|
458
|
2378 } |
|
|
2379 |
|
5275
|
2380 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2381 elem (i, i) -= a.elem (i, i); |
|
|
2382 |
|
|
2383 return *this; |
|
|
2384 } |
|
|
2385 |
|
|
2386 // matrix by matrix -> matrix operations |
|
|
2387 |
|
|
2388 ComplexMatrix& |
|
|
2389 ComplexMatrix::operator += (const Matrix& a) |
|
|
2390 { |
|
5275
|
2391 octave_idx_type nr = rows (); |
|
|
2392 octave_idx_type nc = cols (); |
|
|
2393 |
|
|
2394 octave_idx_type a_nr = a.rows (); |
|
|
2395 octave_idx_type a_nc = a.cols (); |
|
2384
|
2396 |
|
|
2397 if (nr != a_nr || nc != a_nc) |
|
458
|
2398 { |
|
2384
|
2399 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2400 return *this; |
|
|
2401 } |
|
|
2402 |
|
|
2403 if (nr == 0 || nc == 0) |
|
|
2404 return *this; |
|
|
2405 |
|
|
2406 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2407 |
|
3769
|
2408 mx_inline_add2 (d, a.data (), length ()); |
|
458
|
2409 return *this; |
|
|
2410 } |
|
|
2411 |
|
|
2412 ComplexMatrix& |
|
|
2413 ComplexMatrix::operator -= (const Matrix& a) |
|
|
2414 { |
|
5275
|
2415 octave_idx_type nr = rows (); |
|
|
2416 octave_idx_type nc = cols (); |
|
|
2417 |
|
|
2418 octave_idx_type a_nr = a.rows (); |
|
|
2419 octave_idx_type a_nc = a.cols (); |
|
2384
|
2420 |
|
|
2421 if (nr != a_nr || nc != a_nc) |
|
458
|
2422 { |
|
2384
|
2423 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2424 return *this; |
|
|
2425 } |
|
|
2426 |
|
|
2427 if (nr == 0 || nc == 0) |
|
|
2428 return *this; |
|
|
2429 |
|
|
2430 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2431 |
|
3769
|
2432 mx_inline_subtract2 (d, a.data (), length ()); |
|
458
|
2433 return *this; |
|
|
2434 } |
|
|
2435 |
|
|
2436 // unary operations |
|
|
2437 |
|
2964
|
2438 boolMatrix |
|
458
|
2439 ComplexMatrix::operator ! (void) const |
|
|
2440 { |
|
5275
|
2441 octave_idx_type nr = rows (); |
|
|
2442 octave_idx_type nc = cols (); |
|
2964
|
2443 |
|
|
2444 boolMatrix b (nr, nc); |
|
|
2445 |
|
5275
|
2446 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2447 for (octave_idx_type i = 0; i < nr; i++) |
|
5139
|
2448 b.elem (i, j) = elem (i, j) == 0.0; |
|
2964
|
2449 |
|
|
2450 return b; |
|
458
|
2451 } |
|
|
2452 |
|
|
2453 // other operations |
|
|
2454 |
|
|
2455 ComplexMatrix |
|
2676
|
2456 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
2457 { |
|
2676
|
2458 ComplexMatrix b (*this); |
|
|
2459 return b.apply (f); |
|
458
|
2460 } |
|
|
2461 |
|
2676
|
2462 Matrix |
|
|
2463 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
2464 { |
|
5275
|
2465 octave_idx_type nr = rows (); |
|
|
2466 octave_idx_type nc = cols (); |
|
3248
|
2467 |
|
|
2468 Matrix retval (nr, nc); |
|
|
2469 |
|
5275
|
2470 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2471 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2472 retval(i,j) = f (elem(i,j)); |
|
|
2473 |
|
|
2474 return retval; |
|
|
2475 } |
|
|
2476 |
|
|
2477 boolMatrix |
|
|
2478 ComplexMatrix::map (b_c_Mapper f) const |
|
|
2479 { |
|
5275
|
2480 octave_idx_type nr = rows (); |
|
|
2481 octave_idx_type nc = cols (); |
|
3248
|
2482 |
|
|
2483 boolMatrix retval (nr, nc); |
|
|
2484 |
|
5275
|
2485 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2486 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2487 retval(i,j) = f (elem(i,j)); |
|
2676
|
2488 |
|
|
2489 return retval; |
|
|
2490 } |
|
|
2491 |
|
|
2492 ComplexMatrix& |
|
|
2493 ComplexMatrix::apply (c_c_Mapper f) |
|
|
2494 { |
|
|
2495 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2496 |
|
5275
|
2497 for (octave_idx_type i = 0; i < length (); i++) |
|
2676
|
2498 d[i] = f (d[i]); |
|
|
2499 |
|
|
2500 return *this; |
|
458
|
2501 } |
|
|
2502 |
|
2384
|
2503 bool |
|
|
2504 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
2505 { |
|
5275
|
2506 octave_idx_type nr = rows (); |
|
|
2507 octave_idx_type nc = cols (); |
|
|
2508 |
|
|
2509 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2510 for (octave_idx_type i = 0; i < nr; i++) |
|
2384
|
2511 { |
|
|
2512 Complex val = elem (i, j); |
|
|
2513 if (xisinf (val) || xisnan (val)) |
|
|
2514 return true; |
|
|
2515 } |
|
|
2516 |
|
|
2517 return false; |
|
|
2518 } |
|
|
2519 |
|
2408
|
2520 // Return true if no elements have imaginary components. |
|
|
2521 |
|
|
2522 bool |
|
|
2523 ComplexMatrix::all_elements_are_real (void) const |
|
|
2524 { |
|
5275
|
2525 octave_idx_type nr = rows (); |
|
|
2526 octave_idx_type nc = cols (); |
|
|
2527 |
|
|
2528 for (octave_idx_type j = 0; j < nc; j++) |
|
4349
|
2529 { |
|
5275
|
2530 for (octave_idx_type i = 0; i < nr; i++) |
|
4349
|
2531 { |
|
5260
|
2532 double ip = STD_OCTAVE::imag (elem (i, j)); |
|
4349
|
2533 |
|
|
2534 if (ip != 0.0 || lo_ieee_signbit (ip)) |
|
|
2535 return false; |
|
|
2536 } |
|
|
2537 } |
|
2408
|
2538 |
|
|
2539 return true; |
|
|
2540 } |
|
|
2541 |
|
1968
|
2542 // Return nonzero if any element of CM has a non-integer real or |
|
|
2543 // imaginary part. Also extract the largest and smallest (real or |
|
|
2544 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
2545 |
|
2384
|
2546 bool |
|
1968
|
2547 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
2548 { |
|
5275
|
2549 octave_idx_type nr = rows (); |
|
|
2550 octave_idx_type nc = cols (); |
|
1968
|
2551 |
|
|
2552 if (nr > 0 && nc > 0) |
|
|
2553 { |
|
|
2554 Complex val = elem (0, 0); |
|
|
2555 |
|
5260
|
2556 double r_val = STD_OCTAVE::real (val); |
|
|
2557 double i_val = STD_OCTAVE::imag (val); |
|
1968
|
2558 |
|
|
2559 max_val = r_val; |
|
|
2560 min_val = r_val; |
|
|
2561 |
|
|
2562 if (i_val > max_val) |
|
|
2563 max_val = i_val; |
|
|
2564 |
|
|
2565 if (i_val < max_val) |
|
|
2566 min_val = i_val; |
|
|
2567 } |
|
|
2568 else |
|
2384
|
2569 return false; |
|
1968
|
2570 |
|
5275
|
2571 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2572 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
2573 { |
|
|
2574 Complex val = elem (i, j); |
|
|
2575 |
|
5260
|
2576 double r_val = STD_OCTAVE::real (val); |
|
|
2577 double i_val = STD_OCTAVE::imag (val); |
|
1968
|
2578 |
|
|
2579 if (r_val > max_val) |
|
|
2580 max_val = r_val; |
|
|
2581 |
|
|
2582 if (i_val > max_val) |
|
|
2583 max_val = i_val; |
|
|
2584 |
|
|
2585 if (r_val < min_val) |
|
|
2586 min_val = r_val; |
|
|
2587 |
|
|
2588 if (i_val < min_val) |
|
|
2589 min_val = i_val; |
|
|
2590 |
|
|
2591 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
2592 return false; |
|
1968
|
2593 } |
|
2384
|
2594 |
|
|
2595 return true; |
|
1968
|
2596 } |
|
|
2597 |
|
2384
|
2598 bool |
|
1968
|
2599 ComplexMatrix::too_large_for_float (void) const |
|
|
2600 { |
|
5275
|
2601 octave_idx_type nr = rows (); |
|
|
2602 octave_idx_type nc = cols (); |
|
|
2603 |
|
|
2604 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2605 for (octave_idx_type i = 0; i < nr; i++) |
|
1968
|
2606 { |
|
|
2607 Complex val = elem (i, j); |
|
|
2608 |
|
5260
|
2609 double r_val = STD_OCTAVE::real (val); |
|
|
2610 double i_val = STD_OCTAVE::imag (val); |
|
1968
|
2611 |
|
|
2612 if (r_val > FLT_MAX |
|
|
2613 || i_val > FLT_MAX |
|
|
2614 || r_val < FLT_MIN |
|
|
2615 || i_val < FLT_MIN) |
|
2384
|
2616 return true; |
|
1968
|
2617 } |
|
|
2618 |
|
2384
|
2619 return false; |
|
1968
|
2620 } |
|
|
2621 |
|
4015
|
2622 // XXX FIXME XXX Do these really belong here? Maybe they should be |
|
|
2623 // in a base class? |
|
|
2624 |
|
2832
|
2625 boolMatrix |
|
4015
|
2626 ComplexMatrix::all (int dim) const |
|
458
|
2627 { |
|
4015
|
2628 MX_ALL_OP (dim); |
|
458
|
2629 } |
|
|
2630 |
|
2832
|
2631 boolMatrix |
|
4015
|
2632 ComplexMatrix::any (int dim) const |
|
458
|
2633 { |
|
4015
|
2634 MX_ANY_OP (dim); |
|
458
|
2635 } |
|
|
2636 |
|
|
2637 ComplexMatrix |
|
3723
|
2638 ComplexMatrix::cumprod (int dim) const |
|
458
|
2639 { |
|
4015
|
2640 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
|
458
|
2641 } |
|
|
2642 |
|
|
2643 ComplexMatrix |
|
3723
|
2644 ComplexMatrix::cumsum (int dim) const |
|
458
|
2645 { |
|
4015
|
2646 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
|
458
|
2647 } |
|
|
2648 |
|
|
2649 ComplexMatrix |
|
3723
|
2650 ComplexMatrix::prod (int dim) const |
|
458
|
2651 { |
|
3864
|
2652 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
|
458
|
2653 } |
|
|
2654 |
|
|
2655 ComplexMatrix |
|
3723
|
2656 ComplexMatrix::sum (int dim) const |
|
458
|
2657 { |
|
3864
|
2658 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
|
458
|
2659 } |
|
|
2660 |
|
|
2661 ComplexMatrix |
|
3723
|
2662 ComplexMatrix::sumsq (int dim) const |
|
458
|
2663 { |
|
3864
|
2664 #define ROW_EXPR \ |
|
|
2665 Complex d = elem (i, j); \ |
|
|
2666 retval.elem (i, 0) += d * conj (d) |
|
|
2667 |
|
|
2668 #define COL_EXPR \ |
|
|
2669 Complex d = elem (i, j); \ |
|
|
2670 retval.elem (0, j) += d * conj (d) |
|
|
2671 |
|
|
2672 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2673 |
|
|
2674 #undef ROW_EXPR |
|
|
2675 #undef COL_EXPR |
|
458
|
2676 } |
|
|
2677 |
|
4329
|
2678 Matrix ComplexMatrix::abs (void) const |
|
|
2679 { |
|
5275
|
2680 octave_idx_type nr = rows (); |
|
|
2681 octave_idx_type nc = cols (); |
|
4329
|
2682 |
|
|
2683 Matrix retval (nr, nc); |
|
|
2684 |
|
5275
|
2685 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2686 for (octave_idx_type i = 0; i < nr; i++) |
|
5260
|
2687 retval (i, j) = STD_OCTAVE::abs (elem (i, j)); |
|
4329
|
2688 |
|
|
2689 return retval; |
|
|
2690 } |
|
|
2691 |
|
458
|
2692 ComplexColumnVector |
|
|
2693 ComplexMatrix::diag (void) const |
|
|
2694 { |
|
|
2695 return diag (0); |
|
|
2696 } |
|
|
2697 |
|
|
2698 ComplexColumnVector |
|
5275
|
2699 ComplexMatrix::diag (octave_idx_type k) const |
|
458
|
2700 { |
|
5275
|
2701 octave_idx_type nnr = rows (); |
|
|
2702 octave_idx_type nnc = cols (); |
|
458
|
2703 if (k > 0) |
|
|
2704 nnc -= k; |
|
|
2705 else if (k < 0) |
|
|
2706 nnr += k; |
|
|
2707 |
|
|
2708 ComplexColumnVector d; |
|
|
2709 |
|
|
2710 if (nnr > 0 && nnc > 0) |
|
|
2711 { |
|
5275
|
2712 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
2713 |
|
|
2714 d.resize (ndiag); |
|
|
2715 |
|
|
2716 if (k > 0) |
|
|
2717 { |
|
5275
|
2718 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2719 d.elem (i) = elem (i, i+k); |
|
|
2720 } |
|
4509
|
2721 else if (k < 0) |
|
458
|
2722 { |
|
5275
|
2723 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2724 d.elem (i) = elem (i-k, i); |
|
|
2725 } |
|
|
2726 else |
|
|
2727 { |
|
5275
|
2728 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2729 d.elem (i) = elem (i, i); |
|
|
2730 } |
|
|
2731 } |
|
|
2732 else |
|
4513
|
2733 (*current_liboctave_error_handler) |
|
|
2734 ("diag: requested diagonal out of range"); |
|
458
|
2735 |
|
|
2736 return d; |
|
|
2737 } |
|
|
2738 |
|
2354
|
2739 bool |
|
5275
|
2740 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
|
2354
|
2741 { |
|
|
2742 bool retval = true; |
|
|
2743 |
|
5275
|
2744 octave_idx_type nc = columns (); |
|
|
2745 |
|
|
2746 for (octave_idx_type j = 0; j < nc; j++) |
|
2354
|
2747 { |
|
5260
|
2748 if (STD_OCTAVE::imag (elem (i, j)) != 0.0) |
|
2354
|
2749 { |
|
|
2750 retval = false; |
|
|
2751 break; |
|
|
2752 } |
|
|
2753 } |
|
|
2754 |
|
|
2755 return retval; |
|
|
2756 } |
|
|
2757 |
|
|
2758 bool |
|
5275
|
2759 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
|
2354
|
2760 { |
|
|
2761 bool retval = true; |
|
|
2762 |
|
5275
|
2763 octave_idx_type nr = rows (); |
|
|
2764 |
|
|
2765 for (octave_idx_type i = 0; i < nr; i++) |
|
2354
|
2766 { |
|
5260
|
2767 if (STD_OCTAVE::imag (elem (i, j)) != 0.0) |
|
2354
|
2768 { |
|
|
2769 retval = false; |
|
|
2770 break; |
|
|
2771 } |
|
|
2772 } |
|
|
2773 |
|
|
2774 return retval; |
|
|
2775 } |
|
891
|
2776 |
|
458
|
2777 ComplexColumnVector |
|
|
2778 ComplexMatrix::row_min (void) const |
|
|
2779 { |
|
5275
|
2780 Array<octave_idx_type> dummy_idx; |
|
4587
|
2781 return row_min (dummy_idx); |
|
458
|
2782 } |
|
|
2783 |
|
|
2784 ComplexColumnVector |
|
5275
|
2785 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2786 { |
|
|
2787 ComplexColumnVector result; |
|
|
2788 |
|
5275
|
2789 octave_idx_type nr = rows (); |
|
|
2790 octave_idx_type nc = cols (); |
|
458
|
2791 |
|
|
2792 if (nr > 0 && nc > 0) |
|
|
2793 { |
|
|
2794 result.resize (nr); |
|
4587
|
2795 idx_arg.resize (nr); |
|
458
|
2796 |
|
5275
|
2797 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2798 { |
|
2354
|
2799 bool real_only = row_is_real_only (i); |
|
|
2800 |
|
5275
|
2801 octave_idx_type idx_j; |
|
4469
|
2802 |
|
|
2803 Complex tmp_min; |
|
|
2804 |
|
|
2805 double abs_min = octave_NaN; |
|
|
2806 |
|
|
2807 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
2808 { |
|
|
2809 tmp_min = elem (i, idx_j); |
|
|
2810 |
|
|
2811 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2812 { |
|
5260
|
2813 abs_min = real_only ? STD_OCTAVE::real (tmp_min) : STD_OCTAVE::abs (tmp_min); |
|
4469
|
2814 break; |
|
|
2815 } |
|
|
2816 } |
|
|
2817 |
|
5275
|
2818 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2819 { |
|
|
2820 Complex tmp = elem (i, j); |
|
|
2821 |
|
|
2822 if (octave_is_NaN_or_NA (tmp)) |
|
|
2823 continue; |
|
|
2824 |
|
5260
|
2825 double abs_tmp = real_only ? STD_OCTAVE::real (tmp) : STD_OCTAVE::abs (tmp); |
|
4469
|
2826 |
|
|
2827 if (abs_tmp < abs_min) |
|
|
2828 { |
|
|
2829 idx_j = j; |
|
|
2830 tmp_min = tmp; |
|
|
2831 abs_min = abs_tmp; |
|
|
2832 } |
|
|
2833 } |
|
|
2834 |
|
|
2835 if (octave_is_NaN_or_NA (tmp_min)) |
|
|
2836 { |
|
|
2837 result.elem (i) = Complex_NaN_result; |
|
4587
|
2838 idx_arg.elem (i) = 0; |
|
4469
|
2839 } |
|
891
|
2840 else |
|
|
2841 { |
|
4469
|
2842 result.elem (i) = tmp_min; |
|
4587
|
2843 idx_arg.elem (i) = idx_j; |
|
891
|
2844 } |
|
458
|
2845 } |
|
|
2846 } |
|
|
2847 |
|
|
2848 return result; |
|
|
2849 } |
|
|
2850 |
|
|
2851 ComplexColumnVector |
|
|
2852 ComplexMatrix::row_max (void) const |
|
|
2853 { |
|
5275
|
2854 Array<octave_idx_type> dummy_idx; |
|
4587
|
2855 return row_max (dummy_idx); |
|
458
|
2856 } |
|
|
2857 |
|
|
2858 ComplexColumnVector |
|
5275
|
2859 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2860 { |
|
|
2861 ComplexColumnVector result; |
|
|
2862 |
|
5275
|
2863 octave_idx_type nr = rows (); |
|
|
2864 octave_idx_type nc = cols (); |
|
458
|
2865 |
|
|
2866 if (nr > 0 && nc > 0) |
|
|
2867 { |
|
|
2868 result.resize (nr); |
|
4587
|
2869 idx_arg.resize (nr); |
|
458
|
2870 |
|
5275
|
2871 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2872 { |
|
2354
|
2873 bool real_only = row_is_real_only (i); |
|
|
2874 |
|
5275
|
2875 octave_idx_type idx_j; |
|
4469
|
2876 |
|
|
2877 Complex tmp_max; |
|
|
2878 |
|
|
2879 double abs_max = octave_NaN; |
|
|
2880 |
|
|
2881 for (idx_j = 0; idx_j < nc; idx_j++) |
|
|
2882 { |
|
|
2883 tmp_max = elem (i, idx_j); |
|
|
2884 |
|
|
2885 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
2886 { |
|
5260
|
2887 abs_max = real_only ? STD_OCTAVE::real (tmp_max) : STD_OCTAVE::abs (tmp_max); |
|
4469
|
2888 break; |
|
|
2889 } |
|
|
2890 } |
|
|
2891 |
|
5275
|
2892 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2893 { |
|
|
2894 Complex tmp = elem (i, j); |
|
|
2895 |
|
|
2896 if (octave_is_NaN_or_NA (tmp)) |
|
|
2897 continue; |
|
|
2898 |
|
5260
|
2899 double abs_tmp = real_only ? STD_OCTAVE::real (tmp) : STD_OCTAVE::abs (tmp); |
|
4469
|
2900 |
|
|
2901 if (abs_tmp > abs_max) |
|
|
2902 { |
|
|
2903 idx_j = j; |
|
|
2904 tmp_max = tmp; |
|
|
2905 abs_max = abs_tmp; |
|
|
2906 } |
|
|
2907 } |
|
|
2908 |
|
|
2909 if (octave_is_NaN_or_NA (tmp_max)) |
|
|
2910 { |
|
|
2911 result.elem (i) = Complex_NaN_result; |
|
4587
|
2912 idx_arg.elem (i) = 0; |
|
4469
|
2913 } |
|
891
|
2914 else |
|
|
2915 { |
|
4469
|
2916 result.elem (i) = tmp_max; |
|
4587
|
2917 idx_arg.elem (i) = idx_j; |
|
891
|
2918 } |
|
458
|
2919 } |
|
|
2920 } |
|
|
2921 |
|
|
2922 return result; |
|
|
2923 } |
|
|
2924 |
|
|
2925 ComplexRowVector |
|
|
2926 ComplexMatrix::column_min (void) const |
|
|
2927 { |
|
5275
|
2928 Array<octave_idx_type> dummy_idx; |
|
4587
|
2929 return column_min (dummy_idx); |
|
458
|
2930 } |
|
|
2931 |
|
|
2932 ComplexRowVector |
|
5275
|
2933 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2934 { |
|
|
2935 ComplexRowVector result; |
|
|
2936 |
|
5275
|
2937 octave_idx_type nr = rows (); |
|
|
2938 octave_idx_type nc = cols (); |
|
458
|
2939 |
|
|
2940 if (nr > 0 && nc > 0) |
|
|
2941 { |
|
|
2942 result.resize (nc); |
|
4587
|
2943 idx_arg.resize (nc); |
|
458
|
2944 |
|
5275
|
2945 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2946 { |
|
2354
|
2947 bool real_only = column_is_real_only (j); |
|
|
2948 |
|
5275
|
2949 octave_idx_type idx_i; |
|
4469
|
2950 |
|
|
2951 Complex tmp_min; |
|
|
2952 |
|
|
2953 double abs_min = octave_NaN; |
|
|
2954 |
|
|
2955 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
2956 { |
|
|
2957 tmp_min = elem (idx_i, j); |
|
|
2958 |
|
|
2959 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2960 { |
|
5260
|
2961 abs_min = real_only ? STD_OCTAVE::real (tmp_min) : STD_OCTAVE::abs (tmp_min); |
|
4469
|
2962 break; |
|
|
2963 } |
|
|
2964 } |
|
|
2965 |
|
5275
|
2966 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2967 { |
|
|
2968 Complex tmp = elem (i, j); |
|
|
2969 |
|
|
2970 if (octave_is_NaN_or_NA (tmp)) |
|
|
2971 continue; |
|
|
2972 |
|
5260
|
2973 double abs_tmp = real_only ? STD_OCTAVE::real (tmp) : STD_OCTAVE::abs (tmp); |
|
4469
|
2974 |
|
|
2975 if (abs_tmp < abs_min) |
|
|
2976 { |
|
|
2977 idx_i = i; |
|
|
2978 tmp_min = tmp; |
|
|
2979 abs_min = abs_tmp; |
|
|
2980 } |
|
|
2981 } |
|
|
2982 |
|
|
2983 if (octave_is_NaN_or_NA (tmp_min)) |
|
|
2984 { |
|
|
2985 result.elem (j) = Complex_NaN_result; |
|
4587
|
2986 idx_arg.elem (j) = 0; |
|
4469
|
2987 } |
|
891
|
2988 else |
|
|
2989 { |
|
4469
|
2990 result.elem (j) = tmp_min; |
|
4587
|
2991 idx_arg.elem (j) = idx_i; |
|
891
|
2992 } |
|
458
|
2993 } |
|
|
2994 } |
|
|
2995 |
|
|
2996 return result; |
|
|
2997 } |
|
|
2998 |
|
|
2999 ComplexRowVector |
|
|
3000 ComplexMatrix::column_max (void) const |
|
|
3001 { |
|
5275
|
3002 Array<octave_idx_type> dummy_idx; |
|
4587
|
3003 return column_max (dummy_idx); |
|
458
|
3004 } |
|
|
3005 |
|
|
3006 ComplexRowVector |
|
5275
|
3007 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
3008 { |
|
|
3009 ComplexRowVector result; |
|
|
3010 |
|
5275
|
3011 octave_idx_type nr = rows (); |
|
|
3012 octave_idx_type nc = cols (); |
|
458
|
3013 |
|
|
3014 if (nr > 0 && nc > 0) |
|
|
3015 { |
|
|
3016 result.resize (nc); |
|
4587
|
3017 idx_arg.resize (nc); |
|
458
|
3018 |
|
5275
|
3019 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3020 { |
|
2354
|
3021 bool real_only = column_is_real_only (j); |
|
|
3022 |
|
5275
|
3023 octave_idx_type idx_i; |
|
4469
|
3024 |
|
|
3025 Complex tmp_max; |
|
|
3026 |
|
|
3027 double abs_max = octave_NaN; |
|
|
3028 |
|
|
3029 for (idx_i = 0; idx_i < nr; idx_i++) |
|
|
3030 { |
|
|
3031 tmp_max = elem (idx_i, j); |
|
|
3032 |
|
|
3033 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
3034 { |
|
5260
|
3035 abs_max = real_only ? STD_OCTAVE::real (tmp_max) : STD_OCTAVE::abs (tmp_max); |
|
4469
|
3036 break; |
|
|
3037 } |
|
|
3038 } |
|
|
3039 |
|
5275
|
3040 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
3041 { |
|
|
3042 Complex tmp = elem (i, j); |
|
|
3043 |
|
|
3044 if (octave_is_NaN_or_NA (tmp)) |
|
|
3045 continue; |
|
|
3046 |
|
5260
|
3047 double abs_tmp = real_only ? STD_OCTAVE::real (tmp) : STD_OCTAVE::abs (tmp); |
|
4469
|
3048 |
|
|
3049 if (abs_tmp > abs_max) |
|
|
3050 { |
|
|
3051 idx_i = i; |
|
|
3052 tmp_max = tmp; |
|
|
3053 abs_max = abs_tmp; |
|
|
3054 } |
|
|
3055 } |
|
|
3056 |
|
|
3057 if (octave_is_NaN_or_NA (tmp_max)) |
|
|
3058 { |
|
|
3059 result.elem (j) = Complex_NaN_result; |
|
4587
|
3060 idx_arg.elem (j) = 0; |
|
4469
|
3061 } |
|
891
|
3062 else |
|
|
3063 { |
|
4469
|
3064 result.elem (j) = tmp_max; |
|
4587
|
3065 idx_arg.elem (j) = idx_i; |
|
891
|
3066 } |
|
458
|
3067 } |
|
|
3068 } |
|
|
3069 |
|
|
3070 return result; |
|
|
3071 } |
|
|
3072 |
|
|
3073 // i/o |
|
|
3074 |
|
3504
|
3075 std::ostream& |
|
|
3076 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
3077 { |
|
5275
|
3078 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
3079 { |
|
5275
|
3080 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
3081 { |
|
|
3082 os << " "; |
|
|
3083 octave_write_complex (os, a.elem (i, j)); |
|
|
3084 } |
|
458
|
3085 os << "\n"; |
|
|
3086 } |
|
|
3087 return os; |
|
|
3088 } |
|
|
3089 |
|
3504
|
3090 std::istream& |
|
|
3091 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
3092 { |
|
5275
|
3093 octave_idx_type nr = a.rows (); |
|
|
3094 octave_idx_type nc = a.cols (); |
|
458
|
3095 |
|
|
3096 if (nr < 1 || nc < 1) |
|
3504
|
3097 is.clear (std::ios::badbit); |
|
458
|
3098 else |
|
|
3099 { |
|
|
3100 Complex tmp; |
|
5275
|
3101 for (octave_idx_type i = 0; i < nr; i++) |
|
|
3102 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3103 { |
|
4130
|
3104 tmp = octave_read_complex (is); |
|
458
|
3105 if (is) |
|
|
3106 a.elem (i, j) = tmp; |
|
|
3107 else |
|
2993
|
3108 goto done; |
|
458
|
3109 } |
|
|
3110 } |
|
|
3111 |
|
2993
|
3112 done: |
|
|
3113 |
|
458
|
3114 return is; |
|
|
3115 } |
|
|
3116 |
|
1819
|
3117 ComplexMatrix |
|
|
3118 Givens (const Complex& x, const Complex& y) |
|
|
3119 { |
|
|
3120 double cc; |
|
|
3121 Complex cs, temp_r; |
|
|
3122 |
|
3887
|
3123 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
1819
|
3124 |
|
|
3125 ComplexMatrix g (2, 2); |
|
|
3126 |
|
|
3127 g.elem (0, 0) = cc; |
|
|
3128 g.elem (1, 1) = cc; |
|
|
3129 g.elem (0, 1) = cs; |
|
|
3130 g.elem (1, 0) = -conj (cs); |
|
|
3131 |
|
|
3132 return g; |
|
|
3133 } |
|
|
3134 |
|
|
3135 ComplexMatrix |
|
|
3136 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
3137 const ComplexMatrix& c) |
|
|
3138 { |
|
|
3139 ComplexMatrix retval; |
|
|
3140 |
|
|
3141 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
3142 // size. |
|
|
3143 |
|
|
3144 // Compute Schur decompositions |
|
|
3145 |
|
|
3146 ComplexSCHUR as (a, "U"); |
|
|
3147 ComplexSCHUR bs (b, "U"); |
|
|
3148 |
|
|
3149 // Transform c to new coordinates. |
|
|
3150 |
|
|
3151 ComplexMatrix ua = as.unitary_matrix (); |
|
|
3152 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
3153 |
|
|
3154 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
3155 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
3156 |
|
|
3157 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
3158 |
|
|
3159 // Solve the sylvester equation, back-transform, and return the |
|
|
3160 // solution. |
|
|
3161 |
|
5275
|
3162 octave_idx_type a_nr = a.rows (); |
|
|
3163 octave_idx_type b_nr = b.rows (); |
|
1819
|
3164 |
|
|
3165 double scale; |
|
5275
|
3166 octave_idx_type info; |
|
1950
|
3167 |
|
|
3168 Complex *pa = sch_a.fortran_vec (); |
|
|
3169 Complex *pb = sch_b.fortran_vec (); |
|
|
3170 Complex *px = cx.fortran_vec (); |
|
1819
|
3171 |
|
4552
|
3172 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3173 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3174 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3175 b_nr, px, a_nr, scale, info |
|
|
3176 F77_CHAR_ARG_LEN (1) |
|
|
3177 F77_CHAR_ARG_LEN (1))); |
|
1950
|
3178 |
|
|
3179 if (f77_exception_encountered) |
|
|
3180 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
3181 else |
|
|
3182 { |
|
|
3183 // XXX FIXME XXX -- check info? |
|
|
3184 |
|
|
3185 retval = -ua * cx * ub.hermitian (); |
|
|
3186 } |
|
1819
|
3187 |
|
|
3188 return retval; |
|
|
3189 } |
|
|
3190 |
|
2828
|
3191 ComplexMatrix |
|
|
3192 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
3193 { |
|
|
3194 ComplexMatrix tmp (a); |
|
|
3195 return m * tmp; |
|
|
3196 } |
|
|
3197 |
|
|
3198 ComplexMatrix |
|
|
3199 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
3200 { |
|
|
3201 ComplexMatrix tmp (m); |
|
|
3202 return tmp * a; |
|
|
3203 } |
|
|
3204 |
|
|
3205 ComplexMatrix |
|
|
3206 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
3207 { |
|
|
3208 ComplexMatrix retval; |
|
|
3209 |
|
5275
|
3210 octave_idx_type nr = m.rows (); |
|
|
3211 octave_idx_type nc = m.cols (); |
|
|
3212 |
|
|
3213 octave_idx_type a_nr = a.rows (); |
|
|
3214 octave_idx_type a_nc = a.cols (); |
|
2828
|
3215 |
|
|
3216 if (nc != a_nr) |
|
|
3217 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3218 else |
|
|
3219 { |
|
|
3220 if (nr == 0 || nc == 0 || a_nc == 0) |
|
3760
|
3221 retval.resize (nr, a_nc, 0.0); |
|
2828
|
3222 else |
|
|
3223 { |
|
5275
|
3224 octave_idx_type ld = nr; |
|
|
3225 octave_idx_type lda = a.rows (); |
|
2828
|
3226 |
|
|
3227 retval.resize (nr, a_nc); |
|
|
3228 Complex *c = retval.fortran_vec (); |
|
|
3229 |
|
4552
|
3230 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3231 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3232 nr, a_nc, nc, 1.0, m.data (), |
|
|
3233 ld, a.data (), lda, 0.0, c, nr |
|
|
3234 F77_CHAR_ARG_LEN (1) |
|
|
3235 F77_CHAR_ARG_LEN (1))); |
|
2828
|
3236 |
|
|
3237 if (f77_exception_encountered) |
|
|
3238 (*current_liboctave_error_handler) |
|
|
3239 ("unrecoverable error in zgemm"); |
|
|
3240 } |
|
|
3241 } |
|
|
3242 |
|
|
3243 return retval; |
|
|
3244 } |
|
|
3245 |
|
4309
|
3246 // XXX FIXME XXX -- it would be nice to share code among the min/max |
|
|
3247 // functions below. |
|
|
3248 |
|
|
3249 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3250 if (nr == 0 || nc == 0) \ |
|
|
3251 return T (nr, nc); |
|
|
3252 |
|
|
3253 ComplexMatrix |
|
|
3254 min (const Complex& c, const ComplexMatrix& m) |
|
|
3255 { |
|
5275
|
3256 octave_idx_type nr = m.rows (); |
|
|
3257 octave_idx_type nc = m.columns (); |
|
4309
|
3258 |
|
|
3259 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3260 |
|
|
3261 ComplexMatrix result (nr, nc); |
|
|
3262 |
|
5275
|
3263 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3264 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3265 { |
|
|
3266 OCTAVE_QUIT; |
|
|
3267 result (i, j) = xmin (c, m (i, j)); |
|
|
3268 } |
|
|
3269 |
|
|
3270 return result; |
|
|
3271 } |
|
|
3272 |
|
|
3273 ComplexMatrix |
|
|
3274 min (const ComplexMatrix& m, const Complex& c) |
|
|
3275 { |
|
5275
|
3276 octave_idx_type nr = m.rows (); |
|
|
3277 octave_idx_type nc = m.columns (); |
|
4309
|
3278 |
|
|
3279 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3280 |
|
|
3281 ComplexMatrix result (nr, nc); |
|
|
3282 |
|
5275
|
3283 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3284 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3285 { |
|
|
3286 OCTAVE_QUIT; |
|
|
3287 result (i, j) = xmin (m (i, j), c); |
|
|
3288 } |
|
|
3289 |
|
|
3290 return result; |
|
|
3291 } |
|
|
3292 |
|
|
3293 ComplexMatrix |
|
|
3294 min (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3295 { |
|
5275
|
3296 octave_idx_type nr = a.rows (); |
|
|
3297 octave_idx_type nc = a.columns (); |
|
4309
|
3298 |
|
|
3299 if (nr != b.rows () || nc != b.columns ()) |
|
|
3300 { |
|
|
3301 (*current_liboctave_error_handler) |
|
|
3302 ("two-arg min expecting args of same size"); |
|
|
3303 return ComplexMatrix (); |
|
|
3304 } |
|
|
3305 |
|
|
3306 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3307 |
|
|
3308 ComplexMatrix result (nr, nc); |
|
|
3309 |
|
5275
|
3310 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
3311 { |
|
|
3312 int columns_are_real_only = 1; |
|
5275
|
3313 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3314 { |
|
|
3315 OCTAVE_QUIT; |
|
5260
|
3316 if (STD_OCTAVE::imag (a (i, j)) != 0.0 || STD_OCTAVE::imag (b (i, j)) != 0.0) |
|
4309
|
3317 { |
|
|
3318 columns_are_real_only = 0; |
|
|
3319 break; |
|
|
3320 } |
|
|
3321 } |
|
|
3322 |
|
|
3323 if (columns_are_real_only) |
|
|
3324 { |
|
5275
|
3325 for (octave_idx_type i = 0; i < nr; i++) |
|
5260
|
3326 result (i, j) = xmin (STD_OCTAVE::real (a (i, j)), STD_OCTAVE::real (b (i, j))); |
|
4309
|
3327 } |
|
|
3328 else |
|
|
3329 { |
|
5275
|
3330 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3331 { |
|
|
3332 OCTAVE_QUIT; |
|
|
3333 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3334 } |
|
|
3335 } |
|
|
3336 } |
|
|
3337 |
|
|
3338 return result; |
|
|
3339 } |
|
|
3340 |
|
|
3341 ComplexMatrix |
|
|
3342 max (const Complex& c, const ComplexMatrix& m) |
|
|
3343 { |
|
5275
|
3344 octave_idx_type nr = m.rows (); |
|
|
3345 octave_idx_type nc = m.columns (); |
|
4309
|
3346 |
|
|
3347 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3348 |
|
|
3349 ComplexMatrix result (nr, nc); |
|
|
3350 |
|
5275
|
3351 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3352 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3353 { |
|
|
3354 OCTAVE_QUIT; |
|
|
3355 result (i, j) = xmax (c, m (i, j)); |
|
|
3356 } |
|
|
3357 |
|
|
3358 return result; |
|
|
3359 } |
|
|
3360 |
|
|
3361 ComplexMatrix |
|
|
3362 max (const ComplexMatrix& m, const Complex& c) |
|
|
3363 { |
|
5275
|
3364 octave_idx_type nr = m.rows (); |
|
|
3365 octave_idx_type nc = m.columns (); |
|
4309
|
3366 |
|
|
3367 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3368 |
|
|
3369 ComplexMatrix result (nr, nc); |
|
|
3370 |
|
5275
|
3371 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3372 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3373 { |
|
|
3374 OCTAVE_QUIT; |
|
|
3375 result (i, j) = xmax (m (i, j), c); |
|
|
3376 } |
|
|
3377 |
|
|
3378 return result; |
|
|
3379 } |
|
|
3380 |
|
|
3381 ComplexMatrix |
|
|
3382 max (const ComplexMatrix& a, const ComplexMatrix& b) |
|
|
3383 { |
|
5275
|
3384 octave_idx_type nr = a.rows (); |
|
|
3385 octave_idx_type nc = a.columns (); |
|
4309
|
3386 |
|
|
3387 if (nr != b.rows () || nc != b.columns ()) |
|
|
3388 { |
|
|
3389 (*current_liboctave_error_handler) |
|
|
3390 ("two-arg max expecting args of same size"); |
|
|
3391 return ComplexMatrix (); |
|
|
3392 } |
|
|
3393 |
|
|
3394 EMPTY_RETURN_CHECK (ComplexMatrix); |
|
|
3395 |
|
|
3396 ComplexMatrix result (nr, nc); |
|
|
3397 |
|
5275
|
3398 for (octave_idx_type j = 0; j < nc; j++) |
|
4309
|
3399 { |
|
|
3400 int columns_are_real_only = 1; |
|
5275
|
3401 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3402 { |
|
|
3403 OCTAVE_QUIT; |
|
5260
|
3404 if (STD_OCTAVE::imag (a (i, j)) != 0.0 || STD_OCTAVE::imag (b (i, j)) != 0.0) |
|
4309
|
3405 { |
|
|
3406 columns_are_real_only = 0; |
|
|
3407 break; |
|
|
3408 } |
|
|
3409 } |
|
|
3410 |
|
|
3411 if (columns_are_real_only) |
|
|
3412 { |
|
5275
|
3413 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3414 { |
|
|
3415 OCTAVE_QUIT; |
|
5260
|
3416 result (i, j) = xmax (STD_OCTAVE::real (a (i, j)), STD_OCTAVE::real (b (i, j))); |
|
4309
|
3417 } |
|
|
3418 } |
|
|
3419 else |
|
|
3420 { |
|
5275
|
3421 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3422 { |
|
|
3423 OCTAVE_QUIT; |
|
|
3424 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3425 } |
|
|
3426 } |
|
|
3427 } |
|
|
3428 |
|
|
3429 return result; |
|
|
3430 } |
|
|
3431 |
|
5260
|
3432 MS_CMP_OPS(ComplexMatrix, STD_OCTAVE::real, Complex, STD_OCTAVE::real) |
|
3504
|
3433 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
3434 |
|
5260
|
3435 SM_CMP_OPS(Complex, STD_OCTAVE::real, ComplexMatrix, STD_OCTAVE::real) |
|
3504
|
3436 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
3437 |
|
5260
|
3438 MM_CMP_OPS(ComplexMatrix, STD_OCTAVE::real, ComplexMatrix, STD_OCTAVE::real) |
|
3504
|
3439 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
3440 |
|
458
|
3441 /* |
|
|
3442 ;;; Local Variables: *** |
|
|
3443 ;;; mode: C++ *** |
|
|
3444 ;;; End: *** |
|
|
3445 */ |
