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1993
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1 // Matrix manipulations. |
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458
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2 /* |
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3 |
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2847
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4 Copyright (C) 1996, 1997 John W. Eaton |
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458
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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21 |
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22 */ |
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23 |
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24 #if defined (__GNUG__) && ! defined (NO_PRAGMA_INTERFACE_IMPLEMENTATION) |
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1296
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25 #pragma implementation |
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26 #endif |
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27 |
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458
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28 #ifdef HAVE_CONFIG_H |
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1192
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29 #include <config.h> |
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458
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30 #endif |
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31 |
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1367
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32 #include <cfloat> |
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33 |
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3503
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34 #include <iostream> |
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35 |
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2443
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36 // XXX FIXME XXX |
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37 #ifdef HAVE_SYS_TYPES_H |
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38 #include <sys/types.h> |
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39 #endif |
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458
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40 |
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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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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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3827
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58 #ifdef HAVE_FFTW |
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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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3887
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66 int F77_FUNC (zgebal, ZGEBAL) (const char*, const int&, Complex*, |
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3331
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67 const int&, int&, int&, double*, int&, |
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68 long, long); |
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69 |
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70 int F77_FUNC (dgebak, DGEBAK) (const char*, const char*, const int&, |
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3331
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71 const int&, const int&, double*, |
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72 const int&, double*, const int&, |
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73 int&, long, long); |
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74 |
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3887
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75 int F77_FUNC (zgemm, ZGEMM) (const char*, const char*, const int&, |
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1253
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76 const int&, const int&, const Complex&, |
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77 const Complex*, const int&, |
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78 const Complex*, const int&, |
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79 const Complex&, Complex*, const int&, |
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80 long, long); |
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81 |
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3887
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82 int F77_FUNC (zgeco, ZGECO) (Complex*, const int&, const int&, int*, |
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83 double&, Complex*); |
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84 |
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85 int F77_FUNC (zgedi, ZGEDI) (Complex*, const int&, const int&, int*, |
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86 Complex*, Complex*, const int&); |
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87 |
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88 int F77_FUNC (zgesl, ZGESL) (Complex*, const int&, const int&, int*, |
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1253
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89 Complex*, const int&); |
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90 |
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91 int F77_FUNC (zgelss, ZGELSS) (const int&, const int&, const int&, |
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1253
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92 Complex*, const int&, Complex*, |
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93 const int&, double*, double&, int&, |
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94 Complex*, const int&, double*, int&); |
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95 |
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1360
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96 // Note that the original complex fft routines were not written for |
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97 // double complex arguments. They have been modified by adding an |
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98 // implicit double precision (a-h,o-z) statement at the beginning of |
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99 // each subroutine. |
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100 |
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3887
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101 int F77_FUNC (cffti, CFFTI) (const int&, Complex*); |
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102 |
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103 int F77_FUNC (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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104 |
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105 int F77_FUNC (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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106 |
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107 int F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, |
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1819
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108 double&, Complex&, Complex&); |
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109 |
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3887
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110 int F77_FUNC (ztrsyl, ZTRSYL) (const char*, const char*, const int&, |
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1819
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111 const int&, const int&, |
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112 const Complex*, const int&, |
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113 const Complex*, const int&, |
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114 const Complex*, const int&, double&, |
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115 int&, long, long); |
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116 |
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3887
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117 int F77_FUNC (xzlange, XZLANGE) (const char*, const int&, |
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3130
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118 const int&, const Complex*, |
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119 const int&, double*, double&); |
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120 } |
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121 |
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2354
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122 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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123 |
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1360
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124 // Complex Matrix class |
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458
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125 |
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126 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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1214
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127 : MArray2<Complex> (a.rows (), a.cols ()) |
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458
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128 { |
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129 for (int j = 0; j < cols (); j++) |
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130 for (int i = 0; i < rows (); i++) |
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131 elem (i, j) = a.elem (i, j); |
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132 } |
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133 |
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2349
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134 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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135 : MArray2<Complex> (1, rv.length (), 0.0) |
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136 { |
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137 for (int i = 0; i < rv.length (); i++) |
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138 elem (0, i) = rv.elem (i); |
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139 } |
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140 |
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141 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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142 : MArray2<Complex> (cv.length (), 1, 0.0) |
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143 { |
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144 for (int i = 0; i < cv.length (); i++) |
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145 elem (i, 0) = cv.elem (i); |
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146 } |
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147 |
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458
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148 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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149 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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150 { |
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151 for (int i = 0; i < a.length (); i++) |
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152 elem (i, i) = a.elem (i, i); |
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153 } |
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154 |
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2349
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155 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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156 : MArray2<Complex> (1, rv.length (), 0.0) |
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157 { |
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158 for (int i = 0; i < rv.length (); i++) |
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159 elem (0, i) = rv.elem (i); |
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160 } |
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161 |
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162 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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163 : MArray2<Complex> (cv.length (), 1, 0.0) |
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164 { |
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165 for (int i = 0; i < cv.length (); i++) |
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166 elem (i, 0) = cv.elem (i); |
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167 } |
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168 |
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458
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169 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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170 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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171 { |
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172 for (int i = 0; i < a.length (); i++) |
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173 elem (i, i) = a.elem (i, i); |
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174 } |
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175 |
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1574
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176 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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177 // here? |
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178 |
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179 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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3180
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180 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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181 { |
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182 for (int i = 0; i < a.rows (); i++) |
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183 for (int j = 0; j < a.cols (); j++) |
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2828
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184 elem (i, j) = a.elem (i, j); |
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185 } |
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186 |
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1574
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187 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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3180
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188 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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1574
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189 { |
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3998
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190 for (int i = 0; i < a.rows (); i++) |
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191 for (int j = 0; j < a.cols (); j++) |
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1574
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192 elem (i, j) = a.elem (i, j); |
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193 } |
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194 |
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2384
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195 bool |
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196 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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197 { |
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198 if (rows () != a.rows () || cols () != a.cols ()) |
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2384
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199 return false; |
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200 |
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3769
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201 return mx_inline_equal (data (), a.data (), length ()); |
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202 } |
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203 |
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2384
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204 bool |
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205 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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206 { |
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207 return !(*this == a); |
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208 } |
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209 |
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2815
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210 bool |
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211 ComplexMatrix::is_hermitian (void) const |
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212 { |
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213 int nr = rows (); |
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214 int nc = cols (); |
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215 |
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216 if (is_square () && nr > 0) |
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217 { |
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218 for (int i = 0; i < nr; i++) |
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219 for (int j = i; j < nc; j++) |
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220 if (elem (i, j) != conj (elem (j, i))) |
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221 return false; |
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222 |
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223 return true; |
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224 } |
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225 |
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226 return false; |
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227 } |
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228 |
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458
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229 // destructive insert/delete/reorder operations |
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230 |
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231 ComplexMatrix& |
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232 ComplexMatrix::insert (const Matrix& a, int r, int c) |
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233 { |
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234 int a_nr = a.rows (); |
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235 int a_nc = a.cols (); |
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236 |
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237 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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238 { |
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239 (*current_liboctave_error_handler) ("range error for insert"); |
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240 return *this; |
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241 } |
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242 |
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243 for (int j = 0; j < a_nc; j++) |
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244 for (int i = 0; i < a_nr; i++) |
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245 elem (r+i, c+j) = a.elem (i, j); |
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246 |
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247 return *this; |
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248 } |
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249 |
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250 ComplexMatrix& |
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251 ComplexMatrix::insert (const RowVector& a, int r, int c) |
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252 { |
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253 int a_len = a.length (); |
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254 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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255 { |
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256 (*current_liboctave_error_handler) ("range error for insert"); |
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257 return *this; |
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258 } |
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259 |
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260 for (int i = 0; i < a_len; i++) |
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261 elem (r, c+i) = a.elem (i); |
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262 |
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263 return *this; |
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264 } |
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265 |
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266 ComplexMatrix& |
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267 ComplexMatrix::insert (const ColumnVector& a, int r, int c) |
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268 { |
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269 int a_len = a.length (); |
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270 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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271 { |
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272 (*current_liboctave_error_handler) ("range error for insert"); |
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273 return *this; |
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274 } |
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275 |
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276 for (int i = 0; i < a_len; i++) |
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277 elem (r+i, c) = a.elem (i); |
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278 |
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279 return *this; |
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280 } |
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281 |
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282 ComplexMatrix& |
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283 ComplexMatrix::insert (const DiagMatrix& a, int r, int c) |
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284 { |
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285 int a_nr = a.rows (); |
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286 int a_nc = a.cols (); |
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287 |
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288 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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289 { |
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290 (*current_liboctave_error_handler) ("range error for insert"); |
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291 return *this; |
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292 } |
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293 |
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294 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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295 |
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458
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296 for (int i = 0; i < a.length (); i++) |
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297 elem (r+i, c+i) = a.elem (i, i); |
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298 |
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299 return *this; |
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300 } |
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301 |
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302 ComplexMatrix& |
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303 ComplexMatrix::insert (const ComplexMatrix& a, int r, int c) |
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304 { |
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1561
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305 Array2<Complex>::insert (a, r, c); |
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458
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306 return *this; |
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307 } |
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308 |
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309 ComplexMatrix& |
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310 ComplexMatrix::insert (const ComplexRowVector& a, int r, int c) |
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311 { |
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312 int a_len = a.length (); |
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1699
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313 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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314 { |
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315 (*current_liboctave_error_handler) ("range error for insert"); |
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316 return *this; |
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317 } |
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318 |
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319 for (int i = 0; i < a_len; i++) |
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320 elem (r, c+i) = a.elem (i); |
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321 |
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322 return *this; |
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323 } |
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324 |
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325 ComplexMatrix& |
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326 ComplexMatrix::insert (const ComplexColumnVector& a, int r, int c) |
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327 { |
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328 int a_len = a.length (); |
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329 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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330 { |
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331 (*current_liboctave_error_handler) ("range error for insert"); |
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332 return *this; |
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333 } |
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334 |
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335 for (int i = 0; i < a_len; i++) |
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336 elem (r+i, c) = a.elem (i); |
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337 |
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338 return *this; |
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339 } |
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340 |
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341 ComplexMatrix& |
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342 ComplexMatrix::insert (const ComplexDiagMatrix& a, int r, int c) |
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343 { |
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1699
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344 int a_nr = a.rows (); |
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345 int a_nc = a.cols (); |
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346 |
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347 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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348 { |
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349 (*current_liboctave_error_handler) ("range error for insert"); |
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350 return *this; |
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351 } |
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352 |
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1699
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353 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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354 |
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458
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355 for (int i = 0; i < a.length (); i++) |
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356 elem (r+i, c+i) = a.elem (i, i); |
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357 |
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358 return *this; |
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359 } |
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360 |
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361 ComplexMatrix& |
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362 ComplexMatrix::fill (double val) |
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363 { |
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364 int nr = rows (); |
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365 int nc = cols (); |
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366 if (nr > 0 && nc > 0) |
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367 for (int j = 0; j < nc; j++) |
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368 for (int i = 0; i < nr; i++) |
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369 elem (i, j) = val; |
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370 |
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371 return *this; |
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372 } |
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373 |
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374 ComplexMatrix& |
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375 ComplexMatrix::fill (const Complex& val) |
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376 { |
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377 int nr = rows (); |
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378 int nc = cols (); |
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379 if (nr > 0 && nc > 0) |
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380 for (int j = 0; j < nc; j++) |
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381 for (int i = 0; i < nr; i++) |
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382 elem (i, j) = val; |
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383 |
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384 return *this; |
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385 } |
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386 |
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387 ComplexMatrix& |
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388 ComplexMatrix::fill (double val, int r1, int c1, int r2, int c2) |
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389 { |
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390 int nr = rows (); |
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391 int nc = cols (); |
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392 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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393 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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394 { |
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395 (*current_liboctave_error_handler) ("range error for fill"); |
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396 return *this; |
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397 } |
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398 |
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399 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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400 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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401 |
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402 for (int j = c1; j <= c2; j++) |
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403 for (int i = r1; i <= r2; i++) |
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404 elem (i, j) = val; |
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405 |
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406 return *this; |
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407 } |
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408 |
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409 ComplexMatrix& |
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410 ComplexMatrix::fill (const Complex& val, int r1, int c1, int r2, int c2) |
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411 { |
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412 int nr = rows (); |
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413 int nc = cols (); |
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414 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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415 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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416 { |
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417 (*current_liboctave_error_handler) ("range error for fill"); |
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418 return *this; |
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419 } |
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420 |
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421 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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422 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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423 |
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424 for (int j = c1; j <= c2; j++) |
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425 for (int i = r1; i <= r2; i++) |
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426 elem (i, j) = val; |
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427 |
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428 return *this; |
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429 } |
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430 |
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431 ComplexMatrix |
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432 ComplexMatrix::append (const Matrix& a) const |
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433 { |
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434 int nr = rows (); |
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435 int nc = cols (); |
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436 if (nr != a.rows ()) |
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|
437 { |
|
|
438 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
439 return *this; |
|
|
440 } |
|
|
441 |
|
|
442 int nc_insert = nc; |
|
|
443 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
444 retval.insert (*this, 0, 0); |
|
|
445 retval.insert (a, 0, nc_insert); |
|
|
446 return retval; |
|
|
447 } |
|
|
448 |
|
|
449 ComplexMatrix |
|
|
450 ComplexMatrix::append (const RowVector& a) const |
|
|
451 { |
|
|
452 int nr = rows (); |
|
|
453 int nc = cols (); |
|
|
454 if (nr != 1) |
|
|
455 { |
|
|
456 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
457 return *this; |
|
|
458 } |
|
|
459 |
|
|
460 int nc_insert = nc; |
|
|
461 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
462 retval.insert (*this, 0, 0); |
|
|
463 retval.insert (a, 0, nc_insert); |
|
|
464 return retval; |
|
|
465 } |
|
|
466 |
|
|
467 ComplexMatrix |
|
|
468 ComplexMatrix::append (const ColumnVector& a) const |
|
|
469 { |
|
|
470 int nr = rows (); |
|
|
471 int nc = cols (); |
|
|
472 if (nr != a.length ()) |
|
|
473 { |
|
|
474 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
475 return *this; |
|
|
476 } |
|
|
477 |
|
|
478 int nc_insert = nc; |
|
|
479 ComplexMatrix retval (nr, nc + 1); |
|
|
480 retval.insert (*this, 0, 0); |
|
|
481 retval.insert (a, 0, nc_insert); |
|
|
482 return retval; |
|
|
483 } |
|
|
484 |
|
|
485 ComplexMatrix |
|
|
486 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
487 { |
|
|
488 int nr = rows (); |
|
|
489 int nc = cols (); |
|
|
490 if (nr != a.rows ()) |
|
|
491 { |
|
|
492 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
493 return *this; |
|
|
494 } |
|
|
495 |
|
|
496 int nc_insert = nc; |
|
|
497 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
498 retval.insert (*this, 0, 0); |
|
|
499 retval.insert (a, 0, nc_insert); |
|
|
500 return retval; |
|
|
501 } |
|
|
502 |
|
|
503 ComplexMatrix |
|
|
504 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
505 { |
|
|
506 int nr = rows (); |
|
|
507 int nc = cols (); |
|
|
508 if (nr != a.rows ()) |
|
|
509 { |
|
|
510 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
511 return *this; |
|
|
512 } |
|
|
513 |
|
|
514 int nc_insert = nc; |
|
|
515 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
516 retval.insert (*this, 0, 0); |
|
|
517 retval.insert (a, 0, nc_insert); |
|
|
518 return retval; |
|
|
519 } |
|
|
520 |
|
|
521 ComplexMatrix |
|
|
522 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
523 { |
|
|
524 int nr = rows (); |
|
|
525 int nc = cols (); |
|
|
526 if (nr != 1) |
|
|
527 { |
|
|
528 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
529 return *this; |
|
|
530 } |
|
|
531 |
|
|
532 int nc_insert = nc; |
|
|
533 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
534 retval.insert (*this, 0, 0); |
|
|
535 retval.insert (a, 0, nc_insert); |
|
|
536 return retval; |
|
|
537 } |
|
|
538 |
|
|
539 ComplexMatrix |
|
|
540 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
541 { |
|
|
542 int nr = rows (); |
|
|
543 int nc = cols (); |
|
|
544 if (nr != a.length ()) |
|
|
545 { |
|
|
546 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
547 return *this; |
|
|
548 } |
|
|
549 |
|
|
550 int nc_insert = nc; |
|
|
551 ComplexMatrix retval (nr, nc + 1); |
|
|
552 retval.insert (*this, 0, 0); |
|
|
553 retval.insert (a, 0, nc_insert); |
|
|
554 return retval; |
|
|
555 } |
|
|
556 |
|
|
557 ComplexMatrix |
|
|
558 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
559 { |
|
|
560 int nr = rows (); |
|
|
561 int nc = cols (); |
|
|
562 if (nr != a.rows ()) |
|
|
563 { |
|
|
564 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
565 return *this; |
|
|
566 } |
|
|
567 |
|
|
568 int nc_insert = nc; |
|
|
569 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
570 retval.insert (*this, 0, 0); |
|
|
571 retval.insert (a, 0, nc_insert); |
|
|
572 return retval; |
|
|
573 } |
|
|
574 |
|
|
575 ComplexMatrix |
|
|
576 ComplexMatrix::stack (const Matrix& a) const |
|
|
577 { |
|
|
578 int nr = rows (); |
|
|
579 int nc = cols (); |
|
|
580 if (nc != a.cols ()) |
|
|
581 { |
|
|
582 (*current_liboctave_error_handler) |
|
|
583 ("column dimension mismatch for stack"); |
|
|
584 return *this; |
|
|
585 } |
|
|
586 |
|
|
587 int nr_insert = nr; |
|
|
588 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
589 retval.insert (*this, 0, 0); |
|
|
590 retval.insert (a, nr_insert, 0); |
|
|
591 return retval; |
|
|
592 } |
|
|
593 |
|
|
594 ComplexMatrix |
|
|
595 ComplexMatrix::stack (const RowVector& a) const |
|
|
596 { |
|
|
597 int nr = rows (); |
|
|
598 int nc = cols (); |
|
|
599 if (nc != a.length ()) |
|
|
600 { |
|
|
601 (*current_liboctave_error_handler) |
|
|
602 ("column dimension mismatch for stack"); |
|
|
603 return *this; |
|
|
604 } |
|
|
605 |
|
|
606 int nr_insert = nr; |
|
|
607 ComplexMatrix retval (nr + 1, nc); |
|
|
608 retval.insert (*this, 0, 0); |
|
|
609 retval.insert (a, nr_insert, 0); |
|
|
610 return retval; |
|
|
611 } |
|
|
612 |
|
|
613 ComplexMatrix |
|
|
614 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
615 { |
|
|
616 int nr = rows (); |
|
|
617 int nc = cols (); |
|
|
618 if (nc != 1) |
|
|
619 { |
|
|
620 (*current_liboctave_error_handler) |
|
|
621 ("column dimension mismatch for stack"); |
|
|
622 return *this; |
|
|
623 } |
|
|
624 |
|
|
625 int nr_insert = nr; |
|
|
626 ComplexMatrix retval (nr + a.length (), nc); |
|
|
627 retval.insert (*this, 0, 0); |
|
|
628 retval.insert (a, nr_insert, 0); |
|
|
629 return retval; |
|
|
630 } |
|
|
631 |
|
|
632 ComplexMatrix |
|
|
633 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
634 { |
|
|
635 int nr = rows (); |
|
|
636 int nc = cols (); |
|
|
637 if (nc != a.cols ()) |
|
|
638 { |
|
|
639 (*current_liboctave_error_handler) |
|
|
640 ("column dimension mismatch for stack"); |
|
|
641 return *this; |
|
|
642 } |
|
|
643 |
|
|
644 int nr_insert = nr; |
|
|
645 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
646 retval.insert (*this, 0, 0); |
|
|
647 retval.insert (a, nr_insert, 0); |
|
|
648 return retval; |
|
|
649 } |
|
|
650 |
|
|
651 ComplexMatrix |
|
|
652 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
653 { |
|
|
654 int nr = rows (); |
|
|
655 int nc = cols (); |
|
|
656 if (nc != a.cols ()) |
|
|
657 { |
|
|
658 (*current_liboctave_error_handler) |
|
|
659 ("column dimension mismatch for stack"); |
|
|
660 return *this; |
|
|
661 } |
|
|
662 |
|
|
663 int nr_insert = nr; |
|
|
664 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
665 retval.insert (*this, 0, 0); |
|
|
666 retval.insert (a, nr_insert, 0); |
|
|
667 return retval; |
|
|
668 } |
|
|
669 |
|
|
670 ComplexMatrix |
|
|
671 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
672 { |
|
|
673 int nr = rows (); |
|
|
674 int nc = cols (); |
|
|
675 if (nc != a.length ()) |
|
|
676 { |
|
|
677 (*current_liboctave_error_handler) |
|
|
678 ("column dimension mismatch for stack"); |
|
|
679 return *this; |
|
|
680 } |
|
|
681 |
|
|
682 int nr_insert = nr; |
|
|
683 ComplexMatrix retval (nr + 1, nc); |
|
|
684 retval.insert (*this, 0, 0); |
|
|
685 retval.insert (a, nr_insert, 0); |
|
|
686 return retval; |
|
|
687 } |
|
|
688 |
|
|
689 ComplexMatrix |
|
|
690 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
691 { |
|
|
692 int nr = rows (); |
|
|
693 int nc = cols (); |
|
|
694 if (nc != 1) |
|
|
695 { |
|
|
696 (*current_liboctave_error_handler) |
|
|
697 ("column dimension mismatch for stack"); |
|
|
698 return *this; |
|
|
699 } |
|
|
700 |
|
|
701 int nr_insert = nr; |
|
|
702 ComplexMatrix retval (nr + a.length (), nc); |
|
|
703 retval.insert (*this, 0, 0); |
|
|
704 retval.insert (a, nr_insert, 0); |
|
|
705 return retval; |
|
|
706 } |
|
|
707 |
|
|
708 ComplexMatrix |
|
|
709 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
710 { |
|
|
711 int nr = rows (); |
|
|
712 int nc = cols (); |
|
|
713 if (nc != a.cols ()) |
|
|
714 { |
|
|
715 (*current_liboctave_error_handler) |
|
|
716 ("column dimension mismatch for stack"); |
|
|
717 return *this; |
|
|
718 } |
|
|
719 |
|
|
720 int nr_insert = nr; |
|
|
721 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
722 retval.insert (*this, 0, 0); |
|
|
723 retval.insert (a, nr_insert, 0); |
|
|
724 return retval; |
|
|
725 } |
|
|
726 |
|
|
727 ComplexMatrix |
|
|
728 ComplexMatrix::hermitian (void) const |
|
|
729 { |
|
|
730 int nr = rows (); |
|
|
731 int nc = cols (); |
|
|
732 ComplexMatrix result; |
|
|
733 if (length () > 0) |
|
|
734 { |
|
|
735 result.resize (nc, nr); |
|
|
736 for (int j = 0; j < nc; j++) |
|
|
737 for (int i = 0; i < nr; i++) |
|
|
738 result.elem (j, i) = conj (elem (i, j)); |
|
|
739 } |
|
|
740 return result; |
|
|
741 } |
|
|
742 |
|
|
743 ComplexMatrix |
|
|
744 conj (const ComplexMatrix& a) |
|
|
745 { |
|
|
746 int a_len = a.length (); |
|
|
747 ComplexMatrix retval; |
|
|
748 if (a_len > 0) |
|
3769
|
749 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
|
|
750 a.rows (), a.cols ()); |
|
458
|
751 return retval; |
|
|
752 } |
|
|
753 |
|
|
754 // resize is the destructive equivalent for this one |
|
|
755 |
|
|
756 ComplexMatrix |
|
|
757 ComplexMatrix::extract (int r1, int c1, int r2, int c2) const |
|
|
758 { |
|
|
759 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
760 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
761 |
|
|
762 int new_r = r2 - r1 + 1; |
|
|
763 int new_c = c2 - c1 + 1; |
|
|
764 |
|
|
765 ComplexMatrix result (new_r, new_c); |
|
|
766 |
|
|
767 for (int j = 0; j < new_c; j++) |
|
|
768 for (int i = 0; i < new_r; i++) |
|
|
769 result.elem (i, j) = elem (r1+i, c1+j); |
|
|
770 |
|
|
771 return result; |
|
|
772 } |
|
|
773 |
|
|
774 // extract row or column i. |
|
|
775 |
|
|
776 ComplexRowVector |
|
|
777 ComplexMatrix::row (int i) const |
|
|
778 { |
|
|
779 int nc = cols (); |
|
|
780 if (i < 0 || i >= rows ()) |
|
|
781 { |
|
|
782 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
783 return ComplexRowVector (); |
|
|
784 } |
|
|
785 |
|
|
786 ComplexRowVector retval (nc); |
|
|
787 for (int j = 0; j < cols (); j++) |
|
|
788 retval.elem (j) = elem (i, j); |
|
|
789 |
|
|
790 return retval; |
|
|
791 } |
|
|
792 |
|
|
793 ComplexRowVector |
|
|
794 ComplexMatrix::row (char *s) const |
|
|
795 { |
|
533
|
796 if (! s) |
|
458
|
797 { |
|
|
798 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
799 return ComplexRowVector (); |
|
|
800 } |
|
|
801 |
|
|
802 char c = *s; |
|
|
803 if (c == 'f' || c == 'F') |
|
|
804 return row (0); |
|
|
805 else if (c == 'l' || c == 'L') |
|
|
806 return row (rows () - 1); |
|
|
807 else |
|
|
808 { |
|
|
809 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
810 return ComplexRowVector (); |
|
|
811 } |
|
|
812 } |
|
|
813 |
|
|
814 ComplexColumnVector |
|
|
815 ComplexMatrix::column (int i) const |
|
|
816 { |
|
|
817 int nr = rows (); |
|
|
818 if (i < 0 || i >= cols ()) |
|
|
819 { |
|
|
820 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
821 return ComplexColumnVector (); |
|
|
822 } |
|
|
823 |
|
|
824 ComplexColumnVector retval (nr); |
|
|
825 for (int j = 0; j < nr; j++) |
|
|
826 retval.elem (j) = elem (j, i); |
|
|
827 |
|
|
828 return retval; |
|
|
829 } |
|
|
830 |
|
|
831 ComplexColumnVector |
|
|
832 ComplexMatrix::column (char *s) const |
|
|
833 { |
|
533
|
834 if (! s) |
|
458
|
835 { |
|
|
836 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
837 return ComplexColumnVector (); |
|
|
838 } |
|
|
839 |
|
|
840 char c = *s; |
|
|
841 if (c == 'f' || c == 'F') |
|
|
842 return column (0); |
|
|
843 else if (c == 'l' || c == 'L') |
|
|
844 return column (cols () - 1); |
|
|
845 else |
|
|
846 { |
|
|
847 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
848 return ComplexColumnVector (); |
|
|
849 } |
|
|
850 } |
|
|
851 |
|
|
852 ComplexMatrix |
|
|
853 ComplexMatrix::inverse (void) const |
|
|
854 { |
|
|
855 int info; |
|
479
|
856 double rcond; |
|
|
857 return inverse (info, rcond); |
|
458
|
858 } |
|
|
859 |
|
|
860 ComplexMatrix |
|
|
861 ComplexMatrix::inverse (int& info) const |
|
|
862 { |
|
|
863 double rcond; |
|
|
864 return inverse (info, rcond); |
|
|
865 } |
|
|
866 |
|
|
867 ComplexMatrix |
|
1656
|
868 ComplexMatrix::inverse (int& info, double& rcond, int force) const |
|
458
|
869 { |
|
1948
|
870 ComplexMatrix retval; |
|
|
871 |
|
458
|
872 int nr = rows (); |
|
|
873 int nc = cols (); |
|
1948
|
874 |
|
458
|
875 if (nr != nc) |
|
1948
|
876 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
877 else |
|
|
878 { |
|
1948
|
879 info = 0; |
|
|
880 |
|
|
881 Array<int> ipvt (nr); |
|
|
882 int *pipvt = ipvt.fortran_vec (); |
|
|
883 |
|
|
884 Array<Complex> z (nr); |
|
|
885 Complex *pz = z.fortran_vec (); |
|
|
886 |
|
|
887 retval = *this; |
|
|
888 Complex *tmp_data = retval.fortran_vec (); |
|
|
889 |
|
|
890 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nc, pipvt, rcond, pz)); |
|
|
891 |
|
|
892 if (f77_exception_encountered) |
|
|
893 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
894 else |
|
|
895 { |
|
|
896 volatile double rcond_plus_one = rcond + 1.0; |
|
|
897 |
|
3838
|
898 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
899 info = -1; |
|
|
900 |
|
|
901 if (info == -1 && ! force) |
|
|
902 retval = *this; // Restore contents. |
|
|
903 else |
|
|
904 { |
|
|
905 Complex *dummy = 0; |
|
|
906 |
|
|
907 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nc, pipvt, dummy, |
|
|
908 pz, 1)); |
|
|
909 |
|
|
910 if (f77_exception_encountered) |
|
|
911 (*current_liboctave_error_handler) |
|
|
912 ("unrecoverable error in zgedi"); |
|
|
913 } |
|
|
914 } |
|
458
|
915 } |
|
|
916 |
|
1948
|
917 return retval; |
|
458
|
918 } |
|
|
919 |
|
|
920 ComplexMatrix |
|
740
|
921 ComplexMatrix::pseudo_inverse (double tol) |
|
|
922 { |
|
1549
|
923 ComplexMatrix retval; |
|
|
924 |
|
3480
|
925 ComplexSVD result (*this, SVD::economy); |
|
740
|
926 |
|
|
927 DiagMatrix S = result.singular_values (); |
|
|
928 ComplexMatrix U = result.left_singular_matrix (); |
|
|
929 ComplexMatrix V = result.right_singular_matrix (); |
|
|
930 |
|
|
931 ColumnVector sigma = S.diag (); |
|
|
932 |
|
|
933 int r = sigma.length () - 1; |
|
|
934 int nr = rows (); |
|
|
935 int nc = cols (); |
|
|
936 |
|
|
937 if (tol <= 0.0) |
|
|
938 { |
|
|
939 if (nr > nc) |
|
|
940 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
941 else |
|
|
942 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
943 } |
|
|
944 |
|
|
945 while (r >= 0 && sigma.elem (r) < tol) |
|
|
946 r--; |
|
|
947 |
|
|
948 if (r < 0) |
|
1549
|
949 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
950 else |
|
|
951 { |
|
|
952 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
953 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
954 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
955 retval = Vr * D * Ur.hermitian (); |
|
740
|
956 } |
|
1549
|
957 |
|
|
958 return retval; |
|
740
|
959 } |
|
|
960 |
|
3827
|
961 #ifdef HAVE_FFTW |
|
|
962 |
|
|
963 ComplexMatrix |
|
|
964 ComplexMatrix::fourier (void) const |
|
|
965 { |
|
|
966 size_t nr = rows (); |
|
|
967 size_t nc = cols (); |
|
|
968 |
|
|
969 ComplexMatrix retval (nr, nc); |
|
|
970 |
|
|
971 size_t npts, nsamples; |
|
|
972 |
|
|
973 if (nr == 1 || nc == 1) |
|
|
974 { |
|
|
975 npts = nr > nc ? nr : nc; |
|
|
976 nsamples = 1; |
|
|
977 } |
|
|
978 else |
|
|
979 { |
|
|
980 npts = nr; |
|
|
981 nsamples = nc; |
|
|
982 } |
|
|
983 |
|
|
984 const Complex *in (data ()); |
|
|
985 Complex *out (retval.fortran_vec ()); |
|
|
986 |
|
|
987 for (size_t i = 0; i < nsamples; i++) |
|
|
988 { |
|
|
989 octave_fftw::fft (&in[npts * i], &out[npts * i], npts); |
|
|
990 } |
|
|
991 |
|
|
992 return retval; |
|
|
993 } |
|
|
994 |
|
|
995 ComplexMatrix |
|
|
996 ComplexMatrix::ifourier (void) const |
|
|
997 { |
|
|
998 size_t nr = rows (); |
|
|
999 size_t nc = cols (); |
|
|
1000 |
|
|
1001 ComplexMatrix retval (nr, nc); |
|
|
1002 |
|
|
1003 size_t npts, nsamples; |
|
|
1004 |
|
|
1005 if (nr == 1 || nc == 1) |
|
|
1006 { |
|
|
1007 npts = nr > nc ? nr : nc; |
|
|
1008 nsamples = 1; |
|
|
1009 } |
|
|
1010 else |
|
|
1011 { |
|
|
1012 npts = nr; |
|
|
1013 nsamples = nc; |
|
|
1014 } |
|
|
1015 |
|
|
1016 const Complex *in (data ()); |
|
|
1017 Complex *out (retval.fortran_vec ()); |
|
|
1018 |
|
|
1019 for (size_t i = 0; i < nsamples; i++) |
|
|
1020 { |
|
|
1021 octave_fftw::ifft (&in[npts * i], &out[npts * i], npts); |
|
|
1022 } |
|
|
1023 |
|
|
1024 return retval; |
|
|
1025 } |
|
|
1026 |
|
|
1027 ComplexMatrix |
|
|
1028 ComplexMatrix::fourier2d (void) const |
|
|
1029 { |
|
|
1030 int nr = rows (); |
|
|
1031 int nc = cols (); |
|
|
1032 |
|
|
1033 ComplexMatrix retval (*this); |
|
|
1034 // Note the order of passing the rows and columns to account for |
|
|
1035 // column-major storage. |
|
|
1036 octave_fftw::fft2d (retval.fortran_vec (), nc, nr); |
|
|
1037 |
|
|
1038 return retval; |
|
|
1039 } |
|
|
1040 |
|
|
1041 ComplexMatrix |
|
|
1042 ComplexMatrix::ifourier2d (void) const |
|
|
1043 { |
|
|
1044 int nr = rows (); |
|
|
1045 int nc = cols (); |
|
|
1046 |
|
|
1047 ComplexMatrix retval (*this); |
|
|
1048 // Note the order of passing the rows and columns to account for |
|
|
1049 // column-major storage. |
|
|
1050 octave_fftw::ifft2d (retval.fortran_vec (), nc, nr); |
|
|
1051 |
|
|
1052 return retval; |
|
|
1053 } |
|
|
1054 |
|
|
1055 #else |
|
|
1056 |
|
740
|
1057 ComplexMatrix |
|
458
|
1058 ComplexMatrix::fourier (void) const |
|
|
1059 { |
|
1948
|
1060 ComplexMatrix retval; |
|
|
1061 |
|
458
|
1062 int nr = rows (); |
|
|
1063 int nc = cols (); |
|
1948
|
1064 |
|
458
|
1065 int npts, nsamples; |
|
1948
|
1066 |
|
458
|
1067 if (nr == 1 || nc == 1) |
|
|
1068 { |
|
|
1069 npts = nr > nc ? nr : nc; |
|
|
1070 nsamples = 1; |
|
|
1071 } |
|
|
1072 else |
|
|
1073 { |
|
|
1074 npts = nr; |
|
|
1075 nsamples = nc; |
|
|
1076 } |
|
|
1077 |
|
|
1078 int nn = 4*npts+15; |
|
1948
|
1079 |
|
|
1080 Array<Complex> wsave (nn); |
|
|
1081 Complex *pwsave = wsave.fortran_vec (); |
|
|
1082 |
|
|
1083 retval = *this; |
|
|
1084 Complex *tmp_data = retval.fortran_vec (); |
|
|
1085 |
|
3887
|
1086 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1087 |
|
|
1088 for (int j = 0; j < nsamples; j++) |
|
3887
|
1089 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
1948
|
1090 |
|
|
1091 return retval; |
|
458
|
1092 } |
|
|
1093 |
|
|
1094 ComplexMatrix |
|
|
1095 ComplexMatrix::ifourier (void) const |
|
|
1096 { |
|
1948
|
1097 ComplexMatrix retval; |
|
|
1098 |
|
458
|
1099 int nr = rows (); |
|
|
1100 int nc = cols (); |
|
1948
|
1101 |
|
458
|
1102 int npts, nsamples; |
|
1948
|
1103 |
|
458
|
1104 if (nr == 1 || nc == 1) |
|
|
1105 { |
|
|
1106 npts = nr > nc ? nr : nc; |
|
|
1107 nsamples = 1; |
|
|
1108 } |
|
|
1109 else |
|
|
1110 { |
|
|
1111 npts = nr; |
|
|
1112 nsamples = nc; |
|
|
1113 } |
|
|
1114 |
|
|
1115 int nn = 4*npts+15; |
|
1948
|
1116 |
|
|
1117 Array<Complex> wsave (nn); |
|
|
1118 Complex *pwsave = wsave.fortran_vec (); |
|
|
1119 |
|
|
1120 retval = *this; |
|
|
1121 Complex *tmp_data = retval.fortran_vec (); |
|
|
1122 |
|
3887
|
1123 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1124 |
|
|
1125 for (int j = 0; j < nsamples; j++) |
|
3887
|
1126 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
458
|
1127 |
|
1321
|
1128 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1129 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1130 |
|
1948
|
1131 return retval; |
|
458
|
1132 } |
|
|
1133 |
|
677
|
1134 ComplexMatrix |
|
|
1135 ComplexMatrix::fourier2d (void) const |
|
|
1136 { |
|
1948
|
1137 ComplexMatrix retval; |
|
|
1138 |
|
677
|
1139 int nr = rows (); |
|
|
1140 int nc = cols (); |
|
1948
|
1141 |
|
677
|
1142 int npts, nsamples; |
|
1948
|
1143 |
|
677
|
1144 if (nr == 1 || nc == 1) |
|
|
1145 { |
|
|
1146 npts = nr > nc ? nr : nc; |
|
|
1147 nsamples = 1; |
|
|
1148 } |
|
|
1149 else |
|
|
1150 { |
|
|
1151 npts = nr; |
|
|
1152 nsamples = nc; |
|
|
1153 } |
|
|
1154 |
|
|
1155 int nn = 4*npts+15; |
|
1948
|
1156 |
|
|
1157 Array<Complex> wsave (nn); |
|
|
1158 Complex *pwsave = wsave.fortran_vec (); |
|
|
1159 |
|
|
1160 retval = *this; |
|
|
1161 Complex *tmp_data = retval.fortran_vec (); |
|
|
1162 |
|
3887
|
1163 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1164 |
|
|
1165 for (int j = 0; j < nsamples; j++) |
|
3887
|
1166 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1167 |
|
|
1168 npts = nc; |
|
|
1169 nsamples = nr; |
|
|
1170 nn = 4*npts+15; |
|
1948
|
1171 |
|
|
1172 wsave.resize (nn); |
|
|
1173 pwsave = wsave.fortran_vec (); |
|
|
1174 |
|
|
1175 Array<Complex> row (npts); |
|
|
1176 Complex *prow = row.fortran_vec (); |
|
|
1177 |
|
3887
|
1178 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1179 |
|
1321
|
1180 for (int j = 0; j < nsamples; j++) |
|
677
|
1181 { |
|
|
1182 for (int i = 0; i < npts; i++) |
|
1948
|
1183 prow[i] = tmp_data[i*nr + j]; |
|
|
1184 |
|
3887
|
1185 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1186 |
|
1321
|
1187 for (int i = 0; i < npts; i++) |
|
1948
|
1188 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1189 } |
|
|
1190 |
|
1948
|
1191 return retval; |
|
677
|
1192 } |
|
|
1193 |
|
|
1194 ComplexMatrix |
|
|
1195 ComplexMatrix::ifourier2d (void) const |
|
|
1196 { |
|
1948
|
1197 ComplexMatrix retval; |
|
|
1198 |
|
677
|
1199 int nr = rows (); |
|
|
1200 int nc = cols (); |
|
1948
|
1201 |
|
677
|
1202 int npts, nsamples; |
|
1948
|
1203 |
|
677
|
1204 if (nr == 1 || nc == 1) |
|
|
1205 { |
|
|
1206 npts = nr > nc ? nr : nc; |
|
|
1207 nsamples = 1; |
|
|
1208 } |
|
|
1209 else |
|
|
1210 { |
|
|
1211 npts = nr; |
|
|
1212 nsamples = nc; |
|
|
1213 } |
|
|
1214 |
|
|
1215 int nn = 4*npts+15; |
|
1948
|
1216 |
|
|
1217 Array<Complex> wsave (nn); |
|
|
1218 Complex *pwsave = wsave.fortran_vec (); |
|
|
1219 |
|
|
1220 retval = *this; |
|
|
1221 Complex *tmp_data = retval.fortran_vec (); |
|
|
1222 |
|
3887
|
1223 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1224 |
|
|
1225 for (int j = 0; j < nsamples; j++) |
|
3887
|
1226 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1227 |
|
1321
|
1228 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1229 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1230 |
|
|
1231 npts = nc; |
|
|
1232 nsamples = nr; |
|
|
1233 nn = 4*npts+15; |
|
1948
|
1234 |
|
|
1235 wsave.resize (nn); |
|
|
1236 pwsave = wsave.fortran_vec (); |
|
|
1237 |
|
|
1238 Array<Complex> row (npts); |
|
|
1239 Complex *prow = row.fortran_vec (); |
|
|
1240 |
|
3887
|
1241 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1242 |
|
1321
|
1243 for (int j = 0; j < nsamples; j++) |
|
677
|
1244 { |
|
|
1245 for (int i = 0; i < npts; i++) |
|
1948
|
1246 prow[i] = tmp_data[i*nr + j]; |
|
|
1247 |
|
3887
|
1248 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1249 |
|
1321
|
1250 for (int i = 0; i < npts; i++) |
|
3572
|
1251 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1252 } |
|
|
1253 |
|
1948
|
1254 return retval; |
|
677
|
1255 } |
|
|
1256 |
|
3827
|
1257 #endif |
|
|
1258 |
|
458
|
1259 ComplexDET |
|
|
1260 ComplexMatrix::determinant (void) const |
|
|
1261 { |
|
|
1262 int info; |
|
|
1263 double rcond; |
|
|
1264 return determinant (info, rcond); |
|
|
1265 } |
|
|
1266 |
|
|
1267 ComplexDET |
|
|
1268 ComplexMatrix::determinant (int& info) const |
|
|
1269 { |
|
|
1270 double rcond; |
|
|
1271 return determinant (info, rcond); |
|
|
1272 } |
|
|
1273 |
|
|
1274 ComplexDET |
|
532
|
1275 ComplexMatrix::determinant (int& info, double& rcond) const |
|
458
|
1276 { |
|
|
1277 ComplexDET retval; |
|
|
1278 |
|
|
1279 int nr = rows (); |
|
|
1280 int nc = cols (); |
|
|
1281 |
|
|
1282 if (nr == 0 || nc == 0) |
|
|
1283 { |
|
|
1284 Complex d[2]; |
|
|
1285 d[0] = 1.0; |
|
|
1286 d[1] = 0.0; |
|
|
1287 retval = ComplexDET (d); |
|
|
1288 } |
|
|
1289 else |
|
|
1290 { |
|
|
1291 info = 0; |
|
1948
|
1292 |
|
|
1293 Array<int> ipvt (nr); |
|
|
1294 int *pipvt = ipvt.fortran_vec (); |
|
|
1295 |
|
|
1296 Array<Complex> z (nr); |
|
|
1297 Complex *pz = z.fortran_vec (); |
|
|
1298 |
|
|
1299 ComplexMatrix atmp = *this; |
|
|
1300 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1301 |
|
|
1302 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1303 |
|
|
1304 if (f77_exception_encountered) |
|
|
1305 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
458
|
1306 else |
|
|
1307 { |
|
1948
|
1308 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1309 |
|
3838
|
1310 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1311 { |
|
|
1312 info = -1; |
|
|
1313 retval = ComplexDET (); |
|
|
1314 } |
|
|
1315 else |
|
|
1316 { |
|
|
1317 Complex d[2]; |
|
|
1318 |
|
|
1319 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nr, pipvt, d, pz, 10)); |
|
|
1320 |
|
|
1321 if (f77_exception_encountered) |
|
|
1322 (*current_liboctave_error_handler) |
|
|
1323 ("unrecoverable error in dgedi"); |
|
|
1324 else |
|
|
1325 retval = ComplexDET (d); |
|
|
1326 } |
|
458
|
1327 } |
|
|
1328 } |
|
|
1329 |
|
|
1330 return retval; |
|
|
1331 } |
|
|
1332 |
|
|
1333 ComplexMatrix |
|
|
1334 ComplexMatrix::solve (const Matrix& b) const |
|
|
1335 { |
|
|
1336 int info; |
|
|
1337 double rcond; |
|
3480
|
1338 return solve (b, info, rcond, 0); |
|
458
|
1339 } |
|
|
1340 |
|
|
1341 ComplexMatrix |
|
|
1342 ComplexMatrix::solve (const Matrix& b, int& info) const |
|
|
1343 { |
|
|
1344 double rcond; |
|
3480
|
1345 return solve (b, info, rcond, 0); |
|
458
|
1346 } |
|
|
1347 |
|
|
1348 ComplexMatrix |
|
|
1349 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond) const |
|
|
1350 { |
|
3480
|
1351 return solve (b, info, rcond, 0); |
|
|
1352 } |
|
|
1353 |
|
|
1354 ComplexMatrix |
|
|
1355 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond, |
|
|
1356 solve_singularity_handler sing_handler) const |
|
|
1357 { |
|
458
|
1358 ComplexMatrix tmp (b); |
|
3480
|
1359 return solve (tmp, info, rcond, sing_handler); |
|
458
|
1360 } |
|
|
1361 |
|
|
1362 ComplexMatrix |
|
|
1363 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1364 { |
|
|
1365 int info; |
|
|
1366 double rcond; |
|
3480
|
1367 return solve (b, info, rcond, 0); |
|
458
|
1368 } |
|
|
1369 |
|
|
1370 ComplexMatrix |
|
|
1371 ComplexMatrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1372 { |
|
|
1373 double rcond; |
|
3480
|
1374 return solve (b, info, rcond, 0); |
|
458
|
1375 } |
|
3480
|
1376 |
|
458
|
1377 ComplexMatrix |
|
532
|
1378 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
458
|
1379 { |
|
3480
|
1380 return solve (b, info, rcond, 0); |
|
|
1381 } |
|
|
1382 |
|
|
1383 ComplexMatrix |
|
|
1384 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond, |
|
|
1385 solve_singularity_handler sing_handler) const |
|
|
1386 { |
|
458
|
1387 ComplexMatrix retval; |
|
|
1388 |
|
|
1389 int nr = rows (); |
|
|
1390 int nc = cols (); |
|
1948
|
1391 |
|
|
1392 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1393 (*current_liboctave_error_handler) |
|
|
1394 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1395 else |
|
|
1396 { |
|
1948
|
1397 info = 0; |
|
|
1398 |
|
|
1399 Array<int> ipvt (nr); |
|
|
1400 int *pipvt = ipvt.fortran_vec (); |
|
|
1401 |
|
|
1402 Array<Complex> z (nr); |
|
|
1403 Complex *pz = z.fortran_vec (); |
|
|
1404 |
|
|
1405 ComplexMatrix atmp = *this; |
|
|
1406 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1407 |
|
|
1408 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1409 |
|
|
1410 if (f77_exception_encountered) |
|
|
1411 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
1412 else |
|
|
1413 { |
|
|
1414 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1415 |
|
3838
|
1416 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1417 { |
|
|
1418 info = -2; |
|
3480
|
1419 |
|
|
1420 if (sing_handler) |
|
|
1421 sing_handler (rcond); |
|
|
1422 else |
|
|
1423 (*current_liboctave_error_handler) |
|
|
1424 ("matrix singular to machine precision, rcond = %g", |
|
|
1425 rcond); |
|
1948
|
1426 } |
|
|
1427 else |
|
|
1428 { |
|
|
1429 retval = b; |
|
|
1430 Complex *result = retval.fortran_vec (); |
|
|
1431 |
|
|
1432 int b_nc = b.cols (); |
|
|
1433 |
|
|
1434 for (volatile int j = 0; j < b_nc; j++) |
|
|
1435 { |
|
|
1436 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, |
|
|
1437 &result[nr*j], 0)); |
|
|
1438 |
|
|
1439 if (f77_exception_encountered) |
|
|
1440 { |
|
|
1441 (*current_liboctave_error_handler) |
|
|
1442 ("unrecoverable error in dgesl"); |
|
|
1443 |
|
|
1444 break; |
|
|
1445 } |
|
|
1446 } |
|
|
1447 } |
|
|
1448 } |
|
458
|
1449 } |
|
|
1450 |
|
|
1451 return retval; |
|
|
1452 } |
|
|
1453 |
|
|
1454 ComplexColumnVector |
|
3585
|
1455 ComplexMatrix::solve (const ColumnVector& b) const |
|
|
1456 { |
|
|
1457 int info; |
|
|
1458 double rcond; |
|
|
1459 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1460 } |
|
|
1461 |
|
|
1462 ComplexColumnVector |
|
|
1463 ComplexMatrix::solve (const ColumnVector& b, int& info) const |
|
|
1464 { |
|
|
1465 double rcond; |
|
|
1466 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1467 } |
|
|
1468 |
|
|
1469 ComplexColumnVector |
|
|
1470 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
|
1471 { |
|
|
1472 return solve (ComplexColumnVector (b), info, rcond, 0); |
|
|
1473 } |
|
|
1474 |
|
|
1475 ComplexColumnVector |
|
|
1476 ComplexMatrix::solve (const ColumnVector& b, int& info, double& rcond, |
|
|
1477 solve_singularity_handler sing_handler) const |
|
|
1478 { |
|
|
1479 return solve (ComplexColumnVector (b), info, rcond, sing_handler); |
|
|
1480 } |
|
|
1481 |
|
|
1482 ComplexColumnVector |
|
458
|
1483 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1484 { |
|
|
1485 int info; |
|
|
1486 double rcond; |
|
3480
|
1487 return solve (b, info, rcond, 0); |
|
458
|
1488 } |
|
|
1489 |
|
|
1490 ComplexColumnVector |
|
|
1491 ComplexMatrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1492 { |
|
|
1493 double rcond; |
|
3480
|
1494 return solve (b, info, rcond, 0); |
|
458
|
1495 } |
|
|
1496 |
|
|
1497 ComplexColumnVector |
|
|
1498 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
532
|
1499 double& rcond) const |
|
458
|
1500 { |
|
3480
|
1501 return solve (b, info, rcond, 0); |
|
|
1502 } |
|
|
1503 |
|
|
1504 ComplexColumnVector |
|
|
1505 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
|
1506 double& rcond, |
|
|
1507 solve_singularity_handler sing_handler) const |
|
|
1508 { |
|
458
|
1509 ComplexColumnVector retval; |
|
|
1510 |
|
|
1511 int nr = rows (); |
|
|
1512 int nc = cols (); |
|
1948
|
1513 |
|
|
1514 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
1515 (*current_liboctave_error_handler) |
|
|
1516 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1517 else |
|
|
1518 { |
|
1948
|
1519 info = 0; |
|
|
1520 |
|
|
1521 Array<int> ipvt (nr); |
|
|
1522 int *pipvt = ipvt.fortran_vec (); |
|
|
1523 |
|
|
1524 Array<Complex> z (nr); |
|
|
1525 Complex *pz = z.fortran_vec (); |
|
|
1526 |
|
|
1527 ComplexMatrix atmp = *this; |
|
|
1528 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1529 |
|
|
1530 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1531 |
|
|
1532 if (f77_exception_encountered) |
|
|
1533 (*current_liboctave_error_handler) |
|
3838
|
1534 ("unrecoverable error in zgeco"); |
|
1948
|
1535 else |
|
|
1536 { |
|
|
1537 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1538 |
|
3838
|
1539 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1540 { |
|
|
1541 info = -2; |
|
3480
|
1542 |
|
|
1543 if (sing_handler) |
|
|
1544 sing_handler (rcond); |
|
|
1545 else |
|
|
1546 (*current_liboctave_error_handler) |
|
|
1547 ("matrix singular to machine precision, rcond = %g", |
|
|
1548 rcond); |
|
1948
|
1549 } |
|
|
1550 else |
|
|
1551 { |
|
|
1552 retval = b; |
|
|
1553 Complex *result = retval.fortran_vec (); |
|
|
1554 |
|
|
1555 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, result, 0)); |
|
|
1556 |
|
|
1557 if (f77_exception_encountered) |
|
|
1558 (*current_liboctave_error_handler) |
|
|
1559 ("unrecoverable error in dgesl"); |
|
|
1560 } |
|
|
1561 } |
|
458
|
1562 } |
|
|
1563 |
|
|
1564 return retval; |
|
|
1565 } |
|
|
1566 |
|
|
1567 ComplexMatrix |
|
3585
|
1568 ComplexMatrix::lssolve (const Matrix& b) const |
|
|
1569 { |
|
|
1570 int info; |
|
|
1571 int rank; |
|
|
1572 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1573 } |
|
|
1574 |
|
|
1575 ComplexMatrix |
|
|
1576 ComplexMatrix::lssolve (const Matrix& b, int& info) const |
|
|
1577 { |
|
|
1578 int rank; |
|
|
1579 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1580 } |
|
|
1581 |
|
|
1582 ComplexMatrix |
|
|
1583 ComplexMatrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1584 { |
|
|
1585 return lssolve (ComplexMatrix (b), info, rank); |
|
|
1586 } |
|
|
1587 |
|
|
1588 ComplexMatrix |
|
458
|
1589 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1590 { |
|
|
1591 int info; |
|
|
1592 int rank; |
|
|
1593 return lssolve (b, info, rank); |
|
|
1594 } |
|
|
1595 |
|
|
1596 ComplexMatrix |
|
|
1597 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1598 { |
|
|
1599 int rank; |
|
|
1600 return lssolve (b, info, rank); |
|
|
1601 } |
|
|
1602 |
|
|
1603 ComplexMatrix |
|
|
1604 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1605 { |
|
1948
|
1606 ComplexMatrix retval; |
|
|
1607 |
|
458
|
1608 int nrhs = b.cols (); |
|
|
1609 |
|
|
1610 int m = rows (); |
|
|
1611 int n = cols (); |
|
|
1612 |
|
|
1613 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1614 (*current_liboctave_error_handler) |
|
|
1615 ("matrix dimension mismatch solution of linear equations"); |
|
|
1616 else |
|
458
|
1617 { |
|
1948
|
1618 ComplexMatrix atmp = *this; |
|
|
1619 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1620 |
|
|
1621 int nrr = m > n ? m : n; |
|
|
1622 ComplexMatrix result (nrr, nrhs); |
|
|
1623 |
|
|
1624 for (int j = 0; j < nrhs; j++) |
|
|
1625 for (int i = 0; i < m; i++) |
|
|
1626 result.elem (i, j) = b.elem (i, j); |
|
|
1627 |
|
|
1628 Complex *presult = result.fortran_vec (); |
|
|
1629 |
|
|
1630 int len_s = m < n ? m : n; |
|
|
1631 Array<double> s (len_s); |
|
|
1632 double *ps = s.fortran_vec (); |
|
2563
|
1633 |
|
1948
|
1634 double rcond = -1.0; |
|
2563
|
1635 |
|
1948
|
1636 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1637 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1638 Array<double> rwork (lrwork); |
|
|
1639 double *prwork = rwork.fortran_vec (); |
|
|
1640 |
|
3752
|
1641 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1642 |
|
|
1643 int lwork = -1; |
|
|
1644 |
|
|
1645 Array<Complex> work (1); |
|
|
1646 |
|
1948
|
1647 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1648 nrr, ps, rcond, rank, |
|
|
1649 work.fortran_vec (), lwork, prwork, |
|
|
1650 info)); |
|
1948
|
1651 |
|
|
1652 if (f77_exception_encountered) |
|
|
1653 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1654 else |
|
|
1655 { |
|
3752
|
1656 lwork = static_cast<int> (real (work(0))); |
|
|
1657 work.resize (lwork); |
|
|
1658 |
|
|
1659 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1660 nrr, ps, rcond, rank, |
|
|
1661 work.fortran_vec (), lwork, |
|
|
1662 prwork, info)); |
|
|
1663 |
|
|
1664 if (f77_exception_encountered) |
|
|
1665 (*current_liboctave_error_handler) |
|
|
1666 ("unrecoverable error in zgelss"); |
|
|
1667 else |
|
|
1668 { |
|
|
1669 retval.resize (n, nrhs); |
|
|
1670 for (int j = 0; j < nrhs; j++) |
|
|
1671 for (int i = 0; i < n; i++) |
|
|
1672 retval.elem (i, j) = result.elem (i, j); |
|
|
1673 } |
|
1948
|
1674 } |
|
458
|
1675 } |
|
|
1676 |
|
|
1677 return retval; |
|
|
1678 } |
|
|
1679 |
|
|
1680 ComplexColumnVector |
|
3585
|
1681 ComplexMatrix::lssolve (const ColumnVector& b) const |
|
|
1682 { |
|
|
1683 int info; |
|
|
1684 int rank; |
|
|
1685 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1686 } |
|
|
1687 |
|
|
1688 ComplexColumnVector |
|
|
1689 ComplexMatrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1690 { |
|
|
1691 int rank; |
|
|
1692 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1693 } |
|
|
1694 |
|
|
1695 ComplexColumnVector |
|
|
1696 ComplexMatrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1697 { |
|
|
1698 return lssolve (ComplexColumnVector (b), info, rank); |
|
|
1699 } |
|
|
1700 |
|
|
1701 ComplexColumnVector |
|
458
|
1702 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1703 { |
|
|
1704 int info; |
|
|
1705 int rank; |
|
|
1706 return lssolve (b, info, rank); |
|
|
1707 } |
|
|
1708 |
|
|
1709 ComplexColumnVector |
|
|
1710 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1711 { |
|
|
1712 int rank; |
|
|
1713 return lssolve (b, info, rank); |
|
|
1714 } |
|
|
1715 |
|
|
1716 ComplexColumnVector |
|
|
1717 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info, |
|
|
1718 int& rank) const |
|
|
1719 { |
|
1948
|
1720 ComplexColumnVector retval; |
|
|
1721 |
|
458
|
1722 int nrhs = 1; |
|
|
1723 |
|
|
1724 int m = rows (); |
|
|
1725 int n = cols (); |
|
|
1726 |
|
|
1727 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1728 (*current_liboctave_error_handler) |
|
|
1729 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1730 else |
|
458
|
1731 { |
|
1948
|
1732 ComplexMatrix atmp = *this; |
|
|
1733 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1734 |
|
|
1735 int nrr = m > n ? m : n; |
|
|
1736 ComplexColumnVector result (nrr); |
|
|
1737 |
|
|
1738 for (int i = 0; i < m; i++) |
|
|
1739 result.elem (i) = b.elem (i); |
|
|
1740 |
|
|
1741 Complex *presult = result.fortran_vec (); |
|
|
1742 |
|
|
1743 int len_s = m < n ? m : n; |
|
|
1744 Array<double> s (len_s); |
|
|
1745 double *ps = s.fortran_vec (); |
|
|
1746 |
|
|
1747 double rcond = -1.0; |
|
|
1748 |
|
|
1749 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1750 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1751 Array<double> rwork (lrwork); |
|
|
1752 double *prwork = rwork.fortran_vec (); |
|
|
1753 |
|
3752
|
1754 // Ask ZGELSS what the dimension of WORK should be. |
|
|
1755 |
|
|
1756 int lwork = -1; |
|
|
1757 |
|
|
1758 Array<Complex> work (1); |
|
|
1759 |
|
1948
|
1760 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
3752
|
1761 nrr, ps, rcond, rank, |
|
|
1762 work.fortran_vec (), lwork, prwork, |
|
|
1763 info)); |
|
1948
|
1764 |
|
|
1765 if (f77_exception_encountered) |
|
|
1766 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1767 else |
|
|
1768 { |
|
3752
|
1769 lwork = static_cast<int> (real (work(0))); |
|
|
1770 work.resize (lwork); |
|
|
1771 |
|
|
1772 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1773 nrr, ps, rcond, rank, |
|
|
1774 work.fortran_vec (), lwork, |
|
|
1775 prwork, info)); |
|
|
1776 |
|
|
1777 if (f77_exception_encountered) |
|
|
1778 (*current_liboctave_error_handler) |
|
|
1779 ("unrecoverable error in zgelss"); |
|
|
1780 else |
|
|
1781 { |
|
|
1782 retval.resize (n); |
|
|
1783 for (int i = 0; i < n; i++) |
|
|
1784 retval.elem (i) = result.elem (i); |
|
|
1785 } |
|
1948
|
1786 } |
|
458
|
1787 } |
|
|
1788 |
|
|
1789 return retval; |
|
|
1790 } |
|
|
1791 |
|
1819
|
1792 // Constants for matrix exponential calculation. |
|
|
1793 |
|
|
1794 static double padec [] = |
|
|
1795 { |
|
|
1796 5.0000000000000000e-1, |
|
|
1797 1.1666666666666667e-1, |
|
|
1798 1.6666666666666667e-2, |
|
|
1799 1.6025641025641026e-3, |
|
|
1800 1.0683760683760684e-4, |
|
|
1801 4.8562548562548563e-6, |
|
|
1802 1.3875013875013875e-7, |
|
|
1803 1.9270852604185938e-9, |
|
|
1804 }; |
|
|
1805 |
|
|
1806 ComplexMatrix |
|
|
1807 ComplexMatrix::expm (void) const |
|
|
1808 { |
|
|
1809 ComplexMatrix retval; |
|
|
1810 |
|
|
1811 ComplexMatrix m = *this; |
|
|
1812 |
|
|
1813 int nc = columns (); |
|
|
1814 |
|
3130
|
1815 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1816 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1817 |
|
1819
|
1818 // trace shift value |
|
|
1819 Complex trshift = 0.0; |
|
|
1820 |
|
|
1821 for (int i = 0; i < nc; i++) |
|
|
1822 trshift += m.elem (i, i); |
|
|
1823 |
|
|
1824 trshift /= nc; |
|
|
1825 |
|
3130
|
1826 if (trshift.real () < 0.0) |
|
|
1827 trshift = trshift.imag (); |
|
|
1828 |
|
1819
|
1829 for (int i = 0; i < nc; i++) |
|
|
1830 m.elem (i, i) -= trshift; |
|
|
1831 |
|
|
1832 // Preconditioning step 2: eigenvalue balancing. |
|
3331
|
1833 // code follows development in AEPBAL |
|
|
1834 |
|
|
1835 Complex *mp = m.fortran_vec (); |
|
3467
|
1836 |
|
|
1837 int info, ilo, ihi,ilos,ihis; |
|
3468
|
1838 Array<double> dpermute (nc); |
|
|
1839 Array<double> dscale (nc); |
|
|
1840 |
|
|
1841 // XXX FIXME XXX -- should pass job as a parameter in expm |
|
|
1842 |
|
|
1843 // Permute first |
|
|
1844 char job = 'P'; |
|
3467
|
1845 F77_XFCN (zgebal, ZGEBAL, (&job, nc, mp, nc, ilo, ihi, |
|
3469
|
1846 dpermute.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1847 |
|
|
1848 if (f77_exception_encountered) |
|
|
1849 { |
|
|
1850 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
|
1851 return retval; |
|
|
1852 } |
|
|
1853 |
|
3468
|
1854 // then scale |
|
|
1855 job = 'S'; |
|
3467
|
1856 F77_XFCN (zgebal, ZGEBAL, (&job, nc, mp, nc, ilos, ihis, |
|
3469
|
1857 dscale.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1858 |
|
|
1859 if (f77_exception_encountered) |
|
|
1860 { |
|
3467
|
1861 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
|
3331
|
1862 return retval; |
|
|
1863 } |
|
1819
|
1864 |
|
|
1865 // Preconditioning step 3: scaling. |
|
|
1866 |
|
|
1867 ColumnVector work (nc); |
|
3130
|
1868 double inf_norm; |
|
|
1869 |
|
3331
|
1870 F77_XFCN (xzlange, XZLANGE, ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1871 work.fortran_vec (), inf_norm)); |
|
|
1872 |
|
|
1873 if (f77_exception_encountered) |
|
|
1874 { |
|
|
1875 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); |
|
|
1876 return retval; |
|
|
1877 } |
|
1819
|
1878 |
|
2800
|
1879 int sqpow = (inf_norm > 0.0 |
|
|
1880 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
1881 |
|
|
1882 // Check whether we need to square at all. |
|
|
1883 |
|
|
1884 if (sqpow < 0) |
|
|
1885 sqpow = 0; |
|
|
1886 |
|
|
1887 if (sqpow > 0) |
|
|
1888 { |
|
|
1889 double scale_factor = 1.0; |
|
|
1890 for (int i = 0; i < sqpow; i++) |
|
|
1891 scale_factor *= 2.0; |
|
|
1892 |
|
|
1893 m = m / scale_factor; |
|
|
1894 } |
|
|
1895 |
|
|
1896 // npp, dpp: pade' approx polynomial matrices. |
|
|
1897 |
|
|
1898 ComplexMatrix npp (nc, nc, 0.0); |
|
|
1899 ComplexMatrix dpp = npp; |
|
|
1900 |
|
|
1901 // Now powers a^8 ... a^1. |
|
|
1902 |
|
|
1903 int minus_one_j = -1; |
|
|
1904 for (int j = 7; j >= 0; j--) |
|
|
1905 { |
|
|
1906 npp = m * npp + m * padec[j]; |
|
|
1907 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
1908 minus_one_j *= -1; |
|
|
1909 } |
|
|
1910 |
|
|
1911 // Zero power. |
|
|
1912 |
|
|
1913 dpp = -dpp; |
|
|
1914 for (int j = 0; j < nc; j++) |
|
|
1915 { |
|
|
1916 npp.elem (j, j) += 1.0; |
|
|
1917 dpp.elem (j, j) += 1.0; |
|
|
1918 } |
|
|
1919 |
|
|
1920 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1921 |
|
|
1922 retval = dpp.solve (npp); |
|
|
1923 |
|
|
1924 // Reverse preconditioning step 3: repeated squaring. |
|
|
1925 |
|
|
1926 while (sqpow) |
|
|
1927 { |
|
|
1928 retval = retval * retval; |
|
|
1929 sqpow--; |
|
|
1930 } |
|
|
1931 |
|
|
1932 // Reverse preconditioning step 2: inverse balancing. |
|
3467
|
1933 // Done in two steps: inverse scaling, then inverse permutation |
|
|
1934 |
|
|
1935 // inverse scaling (diagonal transformation) |
|
3468
|
1936 for (int i = 0; i < nc; i++) |
|
|
1937 for (int j = 0; j < nc; j++) |
|
|
1938 retval(i,j) *= dscale(i) / dscale(j); |
|
3467
|
1939 |
|
|
1940 // construct balancing permutation vector |
|
3468
|
1941 Array<int> ipermute (nc); |
|
|
1942 for (int i = 0; i < nc; i++) |
|
|
1943 ipermute(i) = i; // initialize to identity permutation |
|
3467
|
1944 |
|
|
1945 // leading permutations in forward order |
|
3468
|
1946 for (int i = 0; i < (ilo-1); i++) |
|
|
1947 { |
|
|
1948 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1949 int tmp = ipermute(i); |
|
|
1950 ipermute(i) = ipermute(swapidx); |
|
|
1951 ipermute(swapidx) = tmp; |
|
|
1952 } |
|
3467
|
1953 |
|
|
1954 // trailing permutations must be done in reverse order |
|
3468
|
1955 for (int i = nc - 1; i >= ihi; i--) |
|
|
1956 { |
|
|
1957 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1958 int tmp = ipermute(i); |
|
|
1959 ipermute(i) = ipermute(swapidx); |
|
|
1960 ipermute(swapidx) = tmp; |
|
|
1961 } |
|
3467
|
1962 |
|
|
1963 // construct inverse balancing permutation vector |
|
3468
|
1964 Array<int> invpvec (nc); |
|
|
1965 for (int i = 0; i < nc; i++) |
|
|
1966 invpvec(ipermute(i)) = i; // Thanks to R. A. Lippert for this method |
|
3467
|
1967 |
|
|
1968 ComplexMatrix tmpMat = retval; |
|
3468
|
1969 for (int i = 0; i < nc; i++) |
|
|
1970 for (int j = 0; j < nc; j++) |
|
|
1971 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
1819
|
1972 |
|
|
1973 // Reverse preconditioning step 1: fix trace normalization. |
|
|
1974 |
|
3130
|
1975 return exp (trshift) * retval; |
|
1819
|
1976 } |
|
|
1977 |
|
1205
|
1978 // column vector by row vector -> matrix operations |
|
|
1979 |
|
|
1980 ComplexMatrix |
|
|
1981 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
1982 { |
|
|
1983 ComplexColumnVector tmp (v); |
|
|
1984 return tmp * a; |
|
|
1985 } |
|
|
1986 |
|
|
1987 ComplexMatrix |
|
|
1988 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
1989 { |
|
|
1990 ComplexRowVector tmp (b); |
|
|
1991 return a * tmp; |
|
|
1992 } |
|
|
1993 |
|
|
1994 ComplexMatrix |
|
|
1995 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
1996 { |
|
1948
|
1997 ComplexMatrix retval; |
|
|
1998 |
|
1205
|
1999 int len = v.length (); |
|
3233
|
2000 |
|
|
2001 if (len != 0) |
|
1205
|
2002 { |
|
3233
|
2003 int a_len = a.length (); |
|
|
2004 |
|
|
2005 retval.resize (len, a_len); |
|
|
2006 Complex *c = retval.fortran_vec (); |
|
|
2007 |
|
|
2008 F77_XFCN (zgemm, ZGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
2009 v.data (), len, a.data (), 1, 0.0, |
|
|
2010 c, len, 1L, 1L)); |
|
|
2011 |
|
|
2012 if (f77_exception_encountered) |
|
|
2013 (*current_liboctave_error_handler) |
|
|
2014 ("unrecoverable error in zgemm"); |
|
1205
|
2015 } |
|
|
2016 |
|
1948
|
2017 return retval; |
|
1205
|
2018 } |
|
|
2019 |
|
458
|
2020 // matrix by diagonal matrix -> matrix operations |
|
|
2021 |
|
|
2022 ComplexMatrix& |
|
|
2023 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
2024 { |
|
|
2025 int nr = rows (); |
|
|
2026 int nc = cols (); |
|
2384
|
2027 |
|
|
2028 int a_nr = rows (); |
|
|
2029 int a_nc = cols (); |
|
|
2030 |
|
|
2031 if (nr != a_nr || nc != a_nc) |
|
458
|
2032 { |
|
2384
|
2033 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2034 return *this; |
|
458
|
2035 } |
|
|
2036 |
|
|
2037 for (int i = 0; i < a.length (); i++) |
|
|
2038 elem (i, i) += a.elem (i, i); |
|
|
2039 |
|
|
2040 return *this; |
|
|
2041 } |
|
|
2042 |
|
|
2043 ComplexMatrix& |
|
|
2044 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
2045 { |
|
|
2046 int nr = rows (); |
|
|
2047 int nc = cols (); |
|
2384
|
2048 |
|
|
2049 int a_nr = rows (); |
|
|
2050 int a_nc = cols (); |
|
|
2051 |
|
|
2052 if (nr != a_nr || nc != a_nc) |
|
458
|
2053 { |
|
2384
|
2054 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2055 return *this; |
|
458
|
2056 } |
|
|
2057 |
|
|
2058 for (int i = 0; i < a.length (); i++) |
|
|
2059 elem (i, i) -= a.elem (i, i); |
|
|
2060 |
|
|
2061 return *this; |
|
|
2062 } |
|
|
2063 |
|
|
2064 ComplexMatrix& |
|
|
2065 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
2066 { |
|
|
2067 int nr = rows (); |
|
|
2068 int nc = cols (); |
|
2384
|
2069 |
|
|
2070 int a_nr = rows (); |
|
|
2071 int a_nc = cols (); |
|
|
2072 |
|
|
2073 if (nr != a_nr || nc != a_nc) |
|
458
|
2074 { |
|
2384
|
2075 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
2076 return *this; |
|
458
|
2077 } |
|
|
2078 |
|
|
2079 for (int i = 0; i < a.length (); i++) |
|
|
2080 elem (i, i) += a.elem (i, i); |
|
|
2081 |
|
|
2082 return *this; |
|
|
2083 } |
|
|
2084 |
|
|
2085 ComplexMatrix& |
|
|
2086 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
2087 { |
|
|
2088 int nr = rows (); |
|
|
2089 int nc = cols (); |
|
2384
|
2090 |
|
|
2091 int a_nr = rows (); |
|
|
2092 int a_nc = cols (); |
|
|
2093 |
|
|
2094 if (nr != a_nr || nc != a_nc) |
|
458
|
2095 { |
|
2384
|
2096 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
2097 return *this; |
|
458
|
2098 } |
|
|
2099 |
|
|
2100 for (int i = 0; i < a.length (); i++) |
|
|
2101 elem (i, i) -= a.elem (i, i); |
|
|
2102 |
|
|
2103 return *this; |
|
|
2104 } |
|
|
2105 |
|
|
2106 // matrix by matrix -> matrix operations |
|
|
2107 |
|
|
2108 ComplexMatrix& |
|
|
2109 ComplexMatrix::operator += (const Matrix& a) |
|
|
2110 { |
|
|
2111 int nr = rows (); |
|
|
2112 int nc = cols (); |
|
2384
|
2113 |
|
|
2114 int a_nr = a.rows (); |
|
|
2115 int a_nc = a.cols (); |
|
|
2116 |
|
|
2117 if (nr != a_nr || nc != a_nc) |
|
458
|
2118 { |
|
2384
|
2119 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2120 return *this; |
|
|
2121 } |
|
|
2122 |
|
|
2123 if (nr == 0 || nc == 0) |
|
|
2124 return *this; |
|
|
2125 |
|
|
2126 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2127 |
|
3769
|
2128 mx_inline_add2 (d, a.data (), length ()); |
|
458
|
2129 return *this; |
|
|
2130 } |
|
|
2131 |
|
|
2132 ComplexMatrix& |
|
|
2133 ComplexMatrix::operator -= (const Matrix& a) |
|
|
2134 { |
|
|
2135 int nr = rows (); |
|
|
2136 int nc = cols (); |
|
2384
|
2137 |
|
|
2138 int a_nr = a.rows (); |
|
|
2139 int a_nc = a.cols (); |
|
|
2140 |
|
|
2141 if (nr != a_nr || nc != a_nc) |
|
458
|
2142 { |
|
2384
|
2143 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2144 return *this; |
|
|
2145 } |
|
|
2146 |
|
|
2147 if (nr == 0 || nc == 0) |
|
|
2148 return *this; |
|
|
2149 |
|
|
2150 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2151 |
|
3769
|
2152 mx_inline_subtract2 (d, a.data (), length ()); |
|
458
|
2153 return *this; |
|
|
2154 } |
|
|
2155 |
|
|
2156 // unary operations |
|
|
2157 |
|
2964
|
2158 boolMatrix |
|
458
|
2159 ComplexMatrix::operator ! (void) const |
|
|
2160 { |
|
2964
|
2161 int nr = rows (); |
|
|
2162 int nc = cols (); |
|
|
2163 |
|
|
2164 boolMatrix b (nr, nc); |
|
|
2165 |
|
|
2166 for (int j = 0; j < nc; j++) |
|
|
2167 for (int i = 0; i < nr; i++) |
|
|
2168 b.elem (i, j) = elem (i, j) != 0.0; |
|
|
2169 |
|
|
2170 return b; |
|
458
|
2171 } |
|
|
2172 |
|
|
2173 // other operations |
|
|
2174 |
|
|
2175 ComplexMatrix |
|
2676
|
2176 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
2177 { |
|
2676
|
2178 ComplexMatrix b (*this); |
|
|
2179 return b.apply (f); |
|
458
|
2180 } |
|
|
2181 |
|
2676
|
2182 Matrix |
|
|
2183 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
2184 { |
|
3248
|
2185 int nr = rows (); |
|
|
2186 int nc = cols (); |
|
|
2187 |
|
|
2188 Matrix retval (nr, nc); |
|
|
2189 |
|
|
2190 for (int j = 0; j < nc; j++) |
|
|
2191 for (int i = 0; i < nr; i++) |
|
|
2192 retval(i,j) = f (elem(i,j)); |
|
|
2193 |
|
|
2194 return retval; |
|
|
2195 } |
|
|
2196 |
|
|
2197 boolMatrix |
|
|
2198 ComplexMatrix::map (b_c_Mapper f) const |
|
|
2199 { |
|
|
2200 int nr = rows (); |
|
|
2201 int nc = cols (); |
|
|
2202 |
|
|
2203 boolMatrix retval (nr, nc); |
|
|
2204 |
|
|
2205 for (int j = 0; j < nc; j++) |
|
|
2206 for (int i = 0; i < nr; i++) |
|
|
2207 retval(i,j) = f (elem(i,j)); |
|
2676
|
2208 |
|
|
2209 return retval; |
|
|
2210 } |
|
|
2211 |
|
|
2212 ComplexMatrix& |
|
|
2213 ComplexMatrix::apply (c_c_Mapper f) |
|
|
2214 { |
|
|
2215 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2216 |
|
|
2217 for (int i = 0; i < length (); i++) |
|
|
2218 d[i] = f (d[i]); |
|
|
2219 |
|
|
2220 return *this; |
|
458
|
2221 } |
|
|
2222 |
|
2384
|
2223 bool |
|
|
2224 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
2225 { |
|
|
2226 int nr = rows (); |
|
|
2227 int nc = cols (); |
|
|
2228 |
|
|
2229 for (int j = 0; j < nc; j++) |
|
|
2230 for (int i = 0; i < nr; i++) |
|
|
2231 { |
|
|
2232 Complex val = elem (i, j); |
|
|
2233 if (xisinf (val) || xisnan (val)) |
|
|
2234 return true; |
|
|
2235 } |
|
|
2236 |
|
|
2237 return false; |
|
|
2238 } |
|
|
2239 |
|
2408
|
2240 // Return true if no elements have imaginary components. |
|
|
2241 |
|
|
2242 bool |
|
|
2243 ComplexMatrix::all_elements_are_real (void) const |
|
|
2244 { |
|
|
2245 int nr = rows (); |
|
|
2246 int nc = cols (); |
|
|
2247 |
|
|
2248 for (int j = 0; j < nc; j++) |
|
|
2249 for (int i = 0; i < nr; i++) |
|
|
2250 if (imag (elem (i, j)) != 0.0) |
|
|
2251 return false; |
|
|
2252 |
|
|
2253 return true; |
|
|
2254 } |
|
|
2255 |
|
1968
|
2256 // Return nonzero if any element of CM has a non-integer real or |
|
|
2257 // imaginary part. Also extract the largest and smallest (real or |
|
|
2258 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
2259 |
|
2384
|
2260 bool |
|
1968
|
2261 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
2262 { |
|
|
2263 int nr = rows (); |
|
2384
|
2264 int nc = cols (); |
|
1968
|
2265 |
|
|
2266 if (nr > 0 && nc > 0) |
|
|
2267 { |
|
|
2268 Complex val = elem (0, 0); |
|
|
2269 |
|
|
2270 double r_val = real (val); |
|
|
2271 double i_val = imag (val); |
|
|
2272 |
|
|
2273 max_val = r_val; |
|
|
2274 min_val = r_val; |
|
|
2275 |
|
|
2276 if (i_val > max_val) |
|
|
2277 max_val = i_val; |
|
|
2278 |
|
|
2279 if (i_val < max_val) |
|
|
2280 min_val = i_val; |
|
|
2281 } |
|
|
2282 else |
|
2384
|
2283 return false; |
|
1968
|
2284 |
|
|
2285 for (int j = 0; j < nc; j++) |
|
|
2286 for (int i = 0; i < nr; i++) |
|
|
2287 { |
|
|
2288 Complex val = elem (i, j); |
|
|
2289 |
|
|
2290 double r_val = real (val); |
|
|
2291 double i_val = imag (val); |
|
|
2292 |
|
|
2293 if (r_val > max_val) |
|
|
2294 max_val = r_val; |
|
|
2295 |
|
|
2296 if (i_val > max_val) |
|
|
2297 max_val = i_val; |
|
|
2298 |
|
|
2299 if (r_val < min_val) |
|
|
2300 min_val = r_val; |
|
|
2301 |
|
|
2302 if (i_val < min_val) |
|
|
2303 min_val = i_val; |
|
|
2304 |
|
|
2305 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
2306 return false; |
|
1968
|
2307 } |
|
2384
|
2308 |
|
|
2309 return true; |
|
1968
|
2310 } |
|
|
2311 |
|
2384
|
2312 bool |
|
1968
|
2313 ComplexMatrix::too_large_for_float (void) const |
|
|
2314 { |
|
|
2315 int nr = rows (); |
|
2384
|
2316 int nc = cols (); |
|
1968
|
2317 |
|
|
2318 for (int j = 0; j < nc; j++) |
|
|
2319 for (int i = 0; i < nr; i++) |
|
|
2320 { |
|
|
2321 Complex val = elem (i, j); |
|
|
2322 |
|
|
2323 double r_val = real (val); |
|
|
2324 double i_val = imag (val); |
|
|
2325 |
|
|
2326 if (r_val > FLT_MAX |
|
|
2327 || i_val > FLT_MAX |
|
|
2328 || r_val < FLT_MIN |
|
|
2329 || i_val < FLT_MIN) |
|
2384
|
2330 return true; |
|
1968
|
2331 } |
|
|
2332 |
|
2384
|
2333 return false; |
|
1968
|
2334 } |
|
|
2335 |
|
4015
|
2336 // XXX FIXME XXX Do these really belong here? Maybe they should be |
|
|
2337 // in a base class? |
|
|
2338 |
|
2832
|
2339 boolMatrix |
|
4015
|
2340 ComplexMatrix::all (int dim) const |
|
458
|
2341 { |
|
4015
|
2342 MX_ALL_OP (dim); |
|
458
|
2343 } |
|
|
2344 |
|
2832
|
2345 boolMatrix |
|
4015
|
2346 ComplexMatrix::any (int dim) const |
|
458
|
2347 { |
|
4015
|
2348 MX_ANY_OP (dim); |
|
458
|
2349 } |
|
|
2350 |
|
|
2351 ComplexMatrix |
|
3723
|
2352 ComplexMatrix::cumprod (int dim) const |
|
458
|
2353 { |
|
4015
|
2354 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
|
458
|
2355 } |
|
|
2356 |
|
|
2357 ComplexMatrix |
|
3723
|
2358 ComplexMatrix::cumsum (int dim) const |
|
458
|
2359 { |
|
4015
|
2360 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
|
458
|
2361 } |
|
|
2362 |
|
|
2363 ComplexMatrix |
|
3723
|
2364 ComplexMatrix::prod (int dim) const |
|
458
|
2365 { |
|
3864
|
2366 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
|
458
|
2367 } |
|
|
2368 |
|
|
2369 ComplexMatrix |
|
3723
|
2370 ComplexMatrix::sum (int dim) const |
|
458
|
2371 { |
|
3864
|
2372 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
|
458
|
2373 } |
|
|
2374 |
|
|
2375 ComplexMatrix |
|
3723
|
2376 ComplexMatrix::sumsq (int dim) const |
|
458
|
2377 { |
|
3864
|
2378 #define ROW_EXPR \ |
|
|
2379 Complex d = elem (i, j); \ |
|
|
2380 retval.elem (i, 0) += d * conj (d) |
|
|
2381 |
|
|
2382 #define COL_EXPR \ |
|
|
2383 Complex d = elem (i, j); \ |
|
|
2384 retval.elem (0, j) += d * conj (d) |
|
|
2385 |
|
|
2386 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2387 |
|
|
2388 #undef ROW_EXPR |
|
|
2389 #undef COL_EXPR |
|
458
|
2390 } |
|
|
2391 |
|
|
2392 ComplexColumnVector |
|
|
2393 ComplexMatrix::diag (void) const |
|
|
2394 { |
|
|
2395 return diag (0); |
|
|
2396 } |
|
|
2397 |
|
|
2398 ComplexColumnVector |
|
|
2399 ComplexMatrix::diag (int k) const |
|
|
2400 { |
|
|
2401 int nnr = rows (); |
|
|
2402 int nnc = cols (); |
|
|
2403 if (k > 0) |
|
|
2404 nnc -= k; |
|
|
2405 else if (k < 0) |
|
|
2406 nnr += k; |
|
|
2407 |
|
|
2408 ComplexColumnVector d; |
|
|
2409 |
|
|
2410 if (nnr > 0 && nnc > 0) |
|
|
2411 { |
|
|
2412 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2413 |
|
|
2414 d.resize (ndiag); |
|
|
2415 |
|
|
2416 if (k > 0) |
|
|
2417 { |
|
|
2418 for (int i = 0; i < ndiag; i++) |
|
|
2419 d.elem (i) = elem (i, i+k); |
|
|
2420 } |
|
|
2421 else if ( k < 0) |
|
|
2422 { |
|
|
2423 for (int i = 0; i < ndiag; i++) |
|
|
2424 d.elem (i) = elem (i-k, i); |
|
|
2425 } |
|
|
2426 else |
|
|
2427 { |
|
|
2428 for (int i = 0; i < ndiag; i++) |
|
|
2429 d.elem (i) = elem (i, i); |
|
|
2430 } |
|
|
2431 } |
|
|
2432 else |
|
3504
|
2433 std::cerr << "diag: requested diagonal out of range\n"; |
|
458
|
2434 |
|
|
2435 return d; |
|
|
2436 } |
|
|
2437 |
|
2354
|
2438 bool |
|
|
2439 ComplexMatrix::row_is_real_only (int i) const |
|
|
2440 { |
|
|
2441 bool retval = true; |
|
|
2442 |
|
|
2443 int nc = columns (); |
|
|
2444 |
|
|
2445 for (int j = 0; j < nc; j++) |
|
|
2446 { |
|
|
2447 if (imag (elem (i, j)) != 0.0) |
|
|
2448 { |
|
|
2449 retval = false; |
|
|
2450 break; |
|
|
2451 } |
|
|
2452 } |
|
|
2453 |
|
|
2454 return retval; |
|
|
2455 } |
|
|
2456 |
|
|
2457 bool |
|
|
2458 ComplexMatrix::column_is_real_only (int j) const |
|
|
2459 { |
|
|
2460 bool retval = true; |
|
|
2461 |
|
|
2462 int nr = rows (); |
|
|
2463 |
|
|
2464 for (int i = 0; i < nr; i++) |
|
|
2465 { |
|
|
2466 if (imag (elem (i, j)) != 0.0) |
|
|
2467 { |
|
|
2468 retval = false; |
|
|
2469 break; |
|
|
2470 } |
|
|
2471 } |
|
|
2472 |
|
|
2473 return retval; |
|
|
2474 } |
|
891
|
2475 |
|
458
|
2476 ComplexColumnVector |
|
|
2477 ComplexMatrix::row_min (void) const |
|
|
2478 { |
|
2354
|
2479 Array<int> index; |
|
|
2480 return row_min (index); |
|
458
|
2481 } |
|
|
2482 |
|
|
2483 ComplexColumnVector |
|
2354
|
2484 ComplexMatrix::row_min (Array<int>& index) const |
|
458
|
2485 { |
|
|
2486 ComplexColumnVector result; |
|
|
2487 |
|
|
2488 int nr = rows (); |
|
|
2489 int nc = cols (); |
|
|
2490 |
|
|
2491 if (nr > 0 && nc > 0) |
|
|
2492 { |
|
|
2493 result.resize (nr); |
|
2354
|
2494 index.resize (nr); |
|
458
|
2495 |
|
|
2496 for (int i = 0; i < nr; i++) |
|
|
2497 { |
|
3504
|
2498 int idx_j = 0; |
|
|
2499 |
|
|
2500 Complex tmp_min = elem (i, idx_j); |
|
2354
|
2501 |
|
|
2502 bool real_only = row_is_real_only (i); |
|
|
2503 |
|
|
2504 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2505 |
|
|
2506 if (xisnan (tmp_min)) |
|
3504
|
2507 idx_j = -1; |
|
891
|
2508 else |
|
|
2509 { |
|
|
2510 for (int j = 1; j < nc; j++) |
|
2354
|
2511 { |
|
|
2512 Complex tmp = elem (i, j); |
|
|
2513 |
|
|
2514 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2515 |
|
|
2516 if (xisnan (tmp)) |
|
|
2517 { |
|
3504
|
2518 idx_j = -1; |
|
2354
|
2519 break; |
|
|
2520 } |
|
|
2521 else if (abs_tmp < abs_min) |
|
|
2522 { |
|
3504
|
2523 idx_j = j; |
|
2354
|
2524 tmp_min = tmp; |
|
|
2525 abs_min = abs_tmp; |
|
|
2526 } |
|
|
2527 } |
|
|
2528 |
|
3504
|
2529 result.elem (i) = (idx_j < 0) ? Complex_NaN_result : tmp_min; |
|
|
2530 index.elem (i) = idx_j; |
|
891
|
2531 } |
|
458
|
2532 } |
|
|
2533 } |
|
|
2534 |
|
|
2535 return result; |
|
|
2536 } |
|
|
2537 |
|
|
2538 ComplexColumnVector |
|
|
2539 ComplexMatrix::row_max (void) const |
|
|
2540 { |
|
2354
|
2541 Array<int> index; |
|
|
2542 return row_max (index); |
|
458
|
2543 } |
|
|
2544 |
|
|
2545 ComplexColumnVector |
|
2354
|
2546 ComplexMatrix::row_max (Array<int>& index) const |
|
458
|
2547 { |
|
|
2548 ComplexColumnVector result; |
|
|
2549 |
|
|
2550 int nr = rows (); |
|
|
2551 int nc = cols (); |
|
|
2552 |
|
|
2553 if (nr > 0 && nc > 0) |
|
|
2554 { |
|
|
2555 result.resize (nr); |
|
2354
|
2556 index.resize (nr); |
|
458
|
2557 |
|
|
2558 for (int i = 0; i < nr; i++) |
|
|
2559 { |
|
3504
|
2560 int idx_j = 0; |
|
|
2561 |
|
|
2562 Complex tmp_max = elem (i, idx_j); |
|
2354
|
2563 |
|
|
2564 bool real_only = row_is_real_only (i); |
|
|
2565 |
|
|
2566 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2567 |
|
|
2568 if (xisnan (tmp_max)) |
|
3504
|
2569 idx_j = -1; |
|
891
|
2570 else |
|
|
2571 { |
|
|
2572 for (int j = 1; j < nc; j++) |
|
2354
|
2573 { |
|
|
2574 Complex tmp = elem (i, j); |
|
|
2575 |
|
|
2576 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2577 |
|
|
2578 if (xisnan (tmp)) |
|
|
2579 { |
|
3504
|
2580 idx_j = -1; |
|
2354
|
2581 break; |
|
|
2582 } |
|
|
2583 else if (abs_tmp > abs_max) |
|
|
2584 { |
|
3504
|
2585 idx_j = j; |
|
2354
|
2586 tmp_max = tmp; |
|
|
2587 abs_max = abs_tmp; |
|
|
2588 } |
|
|
2589 } |
|
|
2590 |
|
3504
|
2591 result.elem (i) = (idx_j < 0) ? Complex_NaN_result : tmp_max; |
|
|
2592 index.elem (i) = idx_j; |
|
891
|
2593 } |
|
458
|
2594 } |
|
|
2595 } |
|
|
2596 |
|
|
2597 return result; |
|
|
2598 } |
|
|
2599 |
|
|
2600 ComplexRowVector |
|
|
2601 ComplexMatrix::column_min (void) const |
|
|
2602 { |
|
2354
|
2603 Array<int> index; |
|
|
2604 return column_min (index); |
|
458
|
2605 } |
|
|
2606 |
|
|
2607 ComplexRowVector |
|
2354
|
2608 ComplexMatrix::column_min (Array<int>& index) const |
|
458
|
2609 { |
|
|
2610 ComplexRowVector result; |
|
|
2611 |
|
|
2612 int nr = rows (); |
|
|
2613 int nc = cols (); |
|
|
2614 |
|
|
2615 if (nr > 0 && nc > 0) |
|
|
2616 { |
|
|
2617 result.resize (nc); |
|
2354
|
2618 index.resize (nc); |
|
458
|
2619 |
|
|
2620 for (int j = 0; j < nc; j++) |
|
|
2621 { |
|
3504
|
2622 int idx_i = 0; |
|
|
2623 |
|
|
2624 Complex tmp_min = elem (idx_i, j); |
|
2354
|
2625 |
|
|
2626 bool real_only = column_is_real_only (j); |
|
|
2627 |
|
|
2628 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2629 |
|
|
2630 if (xisnan (tmp_min)) |
|
3504
|
2631 idx_i = -1; |
|
891
|
2632 else |
|
|
2633 { |
|
|
2634 for (int i = 1; i < nr; i++) |
|
2354
|
2635 { |
|
|
2636 Complex tmp = elem (i, j); |
|
|
2637 |
|
|
2638 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2639 |
|
|
2640 if (xisnan (tmp)) |
|
|
2641 { |
|
3504
|
2642 idx_i = -1; |
|
2354
|
2643 break; |
|
|
2644 } |
|
|
2645 else if (abs_tmp < abs_min) |
|
|
2646 { |
|
3504
|
2647 idx_i = i; |
|
2354
|
2648 tmp_min = tmp; |
|
|
2649 abs_min = abs_tmp; |
|
|
2650 } |
|
|
2651 } |
|
|
2652 |
|
3504
|
2653 result.elem (j) = (idx_i < 0) ? Complex_NaN_result : tmp_min; |
|
|
2654 index.elem (j) = idx_i; |
|
891
|
2655 } |
|
458
|
2656 } |
|
|
2657 } |
|
|
2658 |
|
|
2659 return result; |
|
|
2660 } |
|
|
2661 |
|
|
2662 ComplexRowVector |
|
|
2663 ComplexMatrix::column_max (void) const |
|
|
2664 { |
|
2354
|
2665 Array<int> index; |
|
|
2666 return column_max (index); |
|
458
|
2667 } |
|
|
2668 |
|
|
2669 ComplexRowVector |
|
2354
|
2670 ComplexMatrix::column_max (Array<int>& index) const |
|
458
|
2671 { |
|
|
2672 ComplexRowVector result; |
|
|
2673 |
|
|
2674 int nr = rows (); |
|
|
2675 int nc = cols (); |
|
|
2676 |
|
|
2677 if (nr > 0 && nc > 0) |
|
|
2678 { |
|
|
2679 result.resize (nc); |
|
2354
|
2680 index.resize (nc); |
|
458
|
2681 |
|
|
2682 for (int j = 0; j < nc; j++) |
|
|
2683 { |
|
3504
|
2684 int idx_i = 0; |
|
|
2685 |
|
|
2686 Complex tmp_max = elem (idx_i, j); |
|
2354
|
2687 |
|
|
2688 bool real_only = column_is_real_only (j); |
|
|
2689 |
|
|
2690 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2691 |
|
|
2692 if (xisnan (tmp_max)) |
|
3504
|
2693 idx_i = -1; |
|
891
|
2694 else |
|
|
2695 { |
|
|
2696 for (int i = 1; i < nr; i++) |
|
2354
|
2697 { |
|
|
2698 Complex tmp = elem (i, j); |
|
|
2699 |
|
|
2700 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2701 |
|
|
2702 if (xisnan (tmp)) |
|
|
2703 { |
|
3504
|
2704 idx_i = -1; |
|
2354
|
2705 break; |
|
|
2706 } |
|
|
2707 else if (abs_tmp > abs_max) |
|
|
2708 { |
|
3504
|
2709 idx_i = i; |
|
2354
|
2710 tmp_max = tmp; |
|
|
2711 abs_max = abs_tmp; |
|
|
2712 } |
|
|
2713 } |
|
|
2714 |
|
3504
|
2715 result.elem (j) = (idx_i < 0) ? Complex_NaN_result : tmp_max; |
|
|
2716 index.elem (j) = idx_i; |
|
891
|
2717 } |
|
458
|
2718 } |
|
|
2719 } |
|
|
2720 |
|
|
2721 return result; |
|
|
2722 } |
|
|
2723 |
|
|
2724 // i/o |
|
|
2725 |
|
3504
|
2726 std::ostream& |
|
|
2727 operator << (std::ostream& os, const ComplexMatrix& a) |
|
458
|
2728 { |
|
|
2729 for (int i = 0; i < a.rows (); i++) |
|
|
2730 { |
|
|
2731 for (int j = 0; j < a.cols (); j++) |
|
4130
|
2732 { |
|
|
2733 os << " "; |
|
|
2734 octave_write_complex (os, a.elem (i, j)); |
|
|
2735 } |
|
458
|
2736 os << "\n"; |
|
|
2737 } |
|
|
2738 return os; |
|
|
2739 } |
|
|
2740 |
|
3504
|
2741 std::istream& |
|
|
2742 operator >> (std::istream& is, ComplexMatrix& a) |
|
458
|
2743 { |
|
|
2744 int nr = a.rows (); |
|
|
2745 int nc = a.cols (); |
|
|
2746 |
|
|
2747 if (nr < 1 || nc < 1) |
|
3504
|
2748 is.clear (std::ios::badbit); |
|
458
|
2749 else |
|
|
2750 { |
|
|
2751 Complex tmp; |
|
|
2752 for (int i = 0; i < nr; i++) |
|
|
2753 for (int j = 0; j < nc; j++) |
|
|
2754 { |
|
4130
|
2755 tmp = octave_read_complex (is); |
|
458
|
2756 if (is) |
|
|
2757 a.elem (i, j) = tmp; |
|
|
2758 else |
|
2993
|
2759 goto done; |
|
458
|
2760 } |
|
|
2761 } |
|
|
2762 |
|
2993
|
2763 done: |
|
|
2764 |
|
458
|
2765 return is; |
|
|
2766 } |
|
|
2767 |
|
1819
|
2768 ComplexMatrix |
|
|
2769 Givens (const Complex& x, const Complex& y) |
|
|
2770 { |
|
|
2771 double cc; |
|
|
2772 Complex cs, temp_r; |
|
|
2773 |
|
3887
|
2774 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
1819
|
2775 |
|
|
2776 ComplexMatrix g (2, 2); |
|
|
2777 |
|
|
2778 g.elem (0, 0) = cc; |
|
|
2779 g.elem (1, 1) = cc; |
|
|
2780 g.elem (0, 1) = cs; |
|
|
2781 g.elem (1, 0) = -conj (cs); |
|
|
2782 |
|
|
2783 return g; |
|
|
2784 } |
|
|
2785 |
|
|
2786 ComplexMatrix |
|
|
2787 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
2788 const ComplexMatrix& c) |
|
|
2789 { |
|
|
2790 ComplexMatrix retval; |
|
|
2791 |
|
|
2792 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2793 // size. |
|
|
2794 |
|
|
2795 // Compute Schur decompositions |
|
|
2796 |
|
|
2797 ComplexSCHUR as (a, "U"); |
|
|
2798 ComplexSCHUR bs (b, "U"); |
|
|
2799 |
|
|
2800 // Transform c to new coordinates. |
|
|
2801 |
|
|
2802 ComplexMatrix ua = as.unitary_matrix (); |
|
|
2803 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
2804 |
|
|
2805 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
2806 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
2807 |
|
|
2808 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
2809 |
|
|
2810 // Solve the sylvester equation, back-transform, and return the |
|
|
2811 // solution. |
|
|
2812 |
|
|
2813 int a_nr = a.rows (); |
|
|
2814 int b_nr = b.rows (); |
|
|
2815 |
|
|
2816 double scale; |
|
|
2817 int info; |
|
1950
|
2818 |
|
|
2819 Complex *pa = sch_a.fortran_vec (); |
|
|
2820 Complex *pb = sch_b.fortran_vec (); |
|
|
2821 Complex *px = cx.fortran_vec (); |
|
1819
|
2822 |
|
1950
|
2823 F77_XFCN (ztrsyl, ZTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2824 b_nr, px, a_nr, scale, |
|
|
2825 info, 1L, 1L)); |
|
|
2826 |
|
|
2827 if (f77_exception_encountered) |
|
|
2828 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
2829 else |
|
|
2830 { |
|
|
2831 // XXX FIXME XXX -- check info? |
|
|
2832 |
|
|
2833 retval = -ua * cx * ub.hermitian (); |
|
|
2834 } |
|
1819
|
2835 |
|
|
2836 return retval; |
|
|
2837 } |
|
|
2838 |
|
2828
|
2839 ComplexMatrix |
|
|
2840 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
2841 { |
|
|
2842 ComplexMatrix tmp (a); |
|
|
2843 return m * tmp; |
|
|
2844 } |
|
|
2845 |
|
|
2846 ComplexMatrix |
|
|
2847 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
2848 { |
|
|
2849 ComplexMatrix tmp (m); |
|
|
2850 return tmp * a; |
|
|
2851 } |
|
|
2852 |
|
|
2853 ComplexMatrix |
|
|
2854 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
2855 { |
|
|
2856 ComplexMatrix retval; |
|
|
2857 |
|
|
2858 int nr = m.rows (); |
|
|
2859 int nc = m.cols (); |
|
|
2860 |
|
|
2861 int a_nr = a.rows (); |
|
|
2862 int a_nc = a.cols (); |
|
|
2863 |
|
|
2864 if (nc != a_nr) |
|
|
2865 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2866 else |
|
|
2867 { |
|
|
2868 if (nr == 0 || nc == 0 || a_nc == 0) |
|
3760
|
2869 retval.resize (nr, a_nc, 0.0); |
|
2828
|
2870 else |
|
|
2871 { |
|
|
2872 int ld = nr; |
|
|
2873 int lda = a.rows (); |
|
|
2874 |
|
|
2875 retval.resize (nr, a_nc); |
|
|
2876 Complex *c = retval.fortran_vec (); |
|
|
2877 |
|
|
2878 F77_XFCN (zgemm, ZGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
2879 m.data (), ld, a.data (), lda, 0.0, |
|
|
2880 c, nr, 1L, 1L)); |
|
|
2881 |
|
|
2882 if (f77_exception_encountered) |
|
|
2883 (*current_liboctave_error_handler) |
|
|
2884 ("unrecoverable error in zgemm"); |
|
|
2885 } |
|
|
2886 } |
|
|
2887 |
|
|
2888 return retval; |
|
|
2889 } |
|
|
2890 |
|
2870
|
2891 MS_CMP_OPS(ComplexMatrix, real, Complex, real) |
|
3504
|
2892 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
|
2870
|
2893 |
|
|
2894 SM_CMP_OPS(Complex, real, ComplexMatrix, real) |
|
3504
|
2895 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
|
2870
|
2896 |
|
|
2897 MM_CMP_OPS(ComplexMatrix, real, ComplexMatrix, real) |
|
3504
|
2898 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
|
2870
|
2899 |
|
458
|
2900 /* |
|
|
2901 ;;; Local Variables: *** |
|
|
2902 ;;; mode: C++ *** |
|
|
2903 ;;; End: *** |
|
|
2904 */ |
