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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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1296
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24 #if defined (__GNUG__) |
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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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458
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34 #include <iostream.h> |
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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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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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53 #include "mx-cm-s.h" |
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1367
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54 #include "mx-inlines.cc" |
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1650
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55 #include "oct-cmplx.h" |
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56 |
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57 // Fortran functions we call. |
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58 |
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59 extern "C" |
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60 { |
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1253
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61 int F77_FCN (zgemm, ZGEMM) (const char*, const char*, const int&, |
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62 const int&, const int&, const Complex&, |
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63 const Complex*, const int&, |
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64 const Complex*, const int&, |
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65 const Complex&, Complex*, const int&, |
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66 long, long); |
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67 |
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68 int F77_FCN (zgeco, ZGECO) (Complex*, const int&, const int&, int*, |
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69 double&, Complex*); |
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70 |
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71 int F77_FCN (zgedi, ZGEDI) (Complex*, const int&, const int&, int*, |
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72 Complex*, Complex*, const int&); |
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73 |
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74 int F77_FCN (zgesl, ZGESL) (Complex*, const int&, const int&, int*, |
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75 Complex*, const int&); |
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76 |
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77 int F77_FCN (zgelss, ZGELSS) (const int&, const int&, const int&, |
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78 Complex*, const int&, Complex*, |
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79 const int&, double*, double&, int&, |
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80 Complex*, const int&, double*, int&); |
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81 |
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1360
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82 // Note that the original complex fft routines were not written for |
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83 // double complex arguments. They have been modified by adding an |
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84 // implicit double precision (a-h,o-z) statement at the beginning of |
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85 // each subroutine. |
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86 |
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87 int F77_FCN (cffti, CFFTI) (const int&, Complex*); |
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88 |
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89 int F77_FCN (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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90 |
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91 int F77_FCN (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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92 |
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93 int F77_FCN (zlartg, ZLARTG) (const Complex&, const Complex&, |
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94 double&, Complex&, Complex&); |
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95 |
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96 int F77_FCN (ztrsyl, ZTRSYL) (const char*, const char*, const int&, |
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97 const int&, const int&, |
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98 const Complex*, const int&, |
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99 const Complex*, const int&, |
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100 const Complex*, const int&, double&, |
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101 int&, long, long); |
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102 |
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3130
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103 int F77_FCN (xzlange, XZLANGE) (const char*, const int&, |
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104 const int&, const Complex*, |
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105 const int&, double*, double&); |
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458
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106 } |
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107 |
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108 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
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109 |
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1360
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110 // Complex Matrix class |
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111 |
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112 ComplexMatrix::ComplexMatrix (const Matrix& a) |
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1214
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113 : MArray2<Complex> (a.rows (), a.cols ()) |
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114 { |
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115 for (int j = 0; j < cols (); j++) |
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116 for (int i = 0; i < rows (); i++) |
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117 elem (i, j) = a.elem (i, j); |
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118 } |
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119 |
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120 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
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121 : MArray2<Complex> (1, rv.length (), 0.0) |
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122 { |
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123 for (int i = 0; i < rv.length (); i++) |
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124 elem (0, i) = rv.elem (i); |
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125 } |
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126 |
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127 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) |
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128 : MArray2<Complex> (cv.length (), 1, 0.0) |
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129 { |
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130 for (int i = 0; i < cv.length (); i++) |
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131 elem (i, 0) = cv.elem (i); |
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132 } |
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133 |
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458
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134 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
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135 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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136 { |
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137 for (int i = 0; i < a.length (); i++) |
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138 elem (i, i) = a.elem (i, i); |
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139 } |
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140 |
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141 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
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142 : MArray2<Complex> (1, rv.length (), 0.0) |
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143 { |
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144 for (int i = 0; i < rv.length (); i++) |
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145 elem (0, i) = rv.elem (i); |
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146 } |
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147 |
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148 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) |
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149 : MArray2<Complex> (cv.length (), 1, 0.0) |
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150 { |
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151 for (int i = 0; i < cv.length (); i++) |
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152 elem (i, 0) = cv.elem (i); |
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153 } |
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154 |
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458
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155 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
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156 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
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458
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157 { |
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158 for (int i = 0; i < a.length (); i++) |
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159 elem (i, i) = a.elem (i, i); |
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160 } |
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161 |
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1574
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162 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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163 // here? |
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164 |
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2828
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165 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
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166 { |
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167 for (int i = 0; i < a.cols (); i++) |
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168 for (int j = 0; j < a.rows (); j++) |
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169 elem (i, j) = a.elem (i, j); |
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170 } |
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171 |
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1574
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172 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
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173 { |
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174 for (int i = 0; i < a.cols (); i++) |
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175 for (int j = 0; j < a.rows (); j++) |
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176 elem (i, j) = a.elem (i, j); |
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177 } |
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178 |
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2384
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179 bool |
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180 ComplexMatrix::operator == (const ComplexMatrix& a) const |
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181 { |
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182 if (rows () != a.rows () || cols () != a.cols ()) |
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183 return false; |
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184 |
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185 return equal (data (), a.data (), length ()); |
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186 } |
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187 |
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2384
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188 bool |
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458
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189 ComplexMatrix::operator != (const ComplexMatrix& a) const |
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190 { |
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191 return !(*this == a); |
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192 } |
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193 |
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2815
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194 bool |
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195 ComplexMatrix::is_hermitian (void) const |
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196 { |
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197 int nr = rows (); |
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198 int nc = cols (); |
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199 |
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200 if (is_square () && nr > 0) |
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201 { |
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202 for (int i = 0; i < nr; i++) |
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203 for (int j = i; j < nc; j++) |
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204 if (elem (i, j) != conj (elem (j, i))) |
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205 return false; |
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206 |
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207 return true; |
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208 } |
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209 |
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210 return false; |
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211 } |
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212 |
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458
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213 // destructive insert/delete/reorder operations |
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214 |
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215 ComplexMatrix& |
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216 ComplexMatrix::insert (const Matrix& a, int r, int c) |
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217 { |
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218 int a_nr = a.rows (); |
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219 int a_nc = a.cols (); |
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220 |
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221 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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222 { |
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223 (*current_liboctave_error_handler) ("range error for insert"); |
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224 return *this; |
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225 } |
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226 |
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227 for (int j = 0; j < a_nc; j++) |
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228 for (int i = 0; i < a_nr; i++) |
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229 elem (r+i, c+j) = a.elem (i, j); |
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230 |
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231 return *this; |
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232 } |
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233 |
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234 ComplexMatrix& |
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235 ComplexMatrix::insert (const RowVector& a, int r, int c) |
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236 { |
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237 int a_len = a.length (); |
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238 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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239 { |
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240 (*current_liboctave_error_handler) ("range error for insert"); |
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241 return *this; |
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242 } |
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243 |
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244 for (int i = 0; i < a_len; i++) |
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245 elem (r, c+i) = a.elem (i); |
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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 ColumnVector& 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 + a_len > rows () || c < 0 || c >= cols ()) |
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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+i, c) = 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 DiagMatrix& a, int r, int c) |
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268 { |
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269 int a_nr = a.rows (); |
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270 int a_nc = a.cols (); |
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271 |
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272 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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273 { |
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274 (*current_liboctave_error_handler) ("range error for insert"); |
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275 return *this; |
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276 } |
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277 |
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278 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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279 |
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458
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280 for (int i = 0; i < a.length (); i++) |
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281 elem (r+i, c+i) = a.elem (i, i); |
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282 |
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283 return *this; |
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284 } |
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285 |
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286 ComplexMatrix& |
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287 ComplexMatrix::insert (const ComplexMatrix& a, int r, int c) |
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288 { |
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289 Array2<Complex>::insert (a, r, c); |
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458
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290 return *this; |
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291 } |
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292 |
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293 ComplexMatrix& |
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294 ComplexMatrix::insert (const ComplexRowVector& a, int r, int c) |
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295 { |
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296 int a_len = a.length (); |
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297 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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298 { |
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299 (*current_liboctave_error_handler) ("range error for insert"); |
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300 return *this; |
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301 } |
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302 |
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303 for (int i = 0; i < a_len; i++) |
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304 elem (r, c+i) = a.elem (i); |
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305 |
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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 ComplexColumnVector& a, int r, int c) |
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311 { |
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312 int a_len = a.length (); |
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313 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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314 { |
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315 (*current_liboctave_error_handler) ("range error for insert"); |
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316 return *this; |
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317 } |
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318 |
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319 for (int i = 0; i < a_len; i++) |
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320 elem (r+i, c) = 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 ComplexDiagMatrix& a, int r, int c) |
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327 { |
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1699
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328 int a_nr = a.rows (); |
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329 int a_nc = a.cols (); |
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330 |
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331 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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332 { |
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333 (*current_liboctave_error_handler) ("range error for insert"); |
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334 return *this; |
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335 } |
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336 |
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337 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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338 |
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458
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339 for (int i = 0; i < a.length (); i++) |
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340 elem (r+i, c+i) = a.elem (i, i); |
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341 |
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342 return *this; |
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343 } |
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344 |
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345 ComplexMatrix& |
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346 ComplexMatrix::fill (double val) |
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347 { |
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348 int nr = rows (); |
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349 int nc = cols (); |
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350 if (nr > 0 && nc > 0) |
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351 for (int j = 0; j < nc; j++) |
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352 for (int i = 0; i < nr; i++) |
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353 elem (i, j) = val; |
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354 |
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355 return *this; |
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356 } |
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357 |
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358 ComplexMatrix& |
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359 ComplexMatrix::fill (const Complex& val) |
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360 { |
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361 int nr = rows (); |
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362 int nc = cols (); |
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363 if (nr > 0 && nc > 0) |
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364 for (int j = 0; j < nc; j++) |
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365 for (int i = 0; i < nr; i++) |
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366 elem (i, j) = val; |
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367 |
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368 return *this; |
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369 } |
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370 |
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371 ComplexMatrix& |
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372 ComplexMatrix::fill (double val, int r1, int c1, int r2, int c2) |
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373 { |
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374 int nr = rows (); |
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375 int nc = cols (); |
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376 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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377 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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378 { |
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379 (*current_liboctave_error_handler) ("range error for fill"); |
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380 return *this; |
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381 } |
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382 |
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383 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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384 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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385 |
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386 for (int j = c1; j <= c2; j++) |
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387 for (int i = r1; i <= r2; i++) |
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388 elem (i, j) = val; |
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389 |
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390 return *this; |
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391 } |
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392 |
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393 ComplexMatrix& |
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394 ComplexMatrix::fill (const Complex& val, int r1, int c1, int r2, int c2) |
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395 { |
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396 int nr = rows (); |
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397 int nc = cols (); |
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398 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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399 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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400 { |
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401 (*current_liboctave_error_handler) ("range error for fill"); |
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402 return *this; |
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403 } |
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404 |
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405 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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406 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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407 |
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408 for (int j = c1; j <= c2; j++) |
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409 for (int i = r1; i <= r2; i++) |
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410 elem (i, j) = val; |
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411 |
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412 return *this; |
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413 } |
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414 |
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415 ComplexMatrix |
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416 ComplexMatrix::append (const Matrix& a) const |
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417 { |
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418 int nr = rows (); |
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419 int nc = cols (); |
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420 if (nr != a.rows ()) |
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421 { |
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422 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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423 return *this; |
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424 } |
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425 |
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426 int nc_insert = nc; |
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427 ComplexMatrix retval (nr, nc + a.cols ()); |
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428 retval.insert (*this, 0, 0); |
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429 retval.insert (a, 0, nc_insert); |
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430 return retval; |
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431 } |
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432 |
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433 ComplexMatrix |
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434 ComplexMatrix::append (const RowVector& a) const |
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435 { |
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436 int nr = rows (); |
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437 int nc = cols (); |
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438 if (nr != 1) |
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439 { |
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440 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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441 return *this; |
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442 } |
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443 |
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444 int nc_insert = nc; |
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445 ComplexMatrix retval (nr, nc + a.length ()); |
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446 retval.insert (*this, 0, 0); |
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447 retval.insert (a, 0, nc_insert); |
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|
448 return retval; |
|
|
449 } |
|
|
450 |
|
|
451 ComplexMatrix |
|
|
452 ComplexMatrix::append (const ColumnVector& a) const |
|
|
453 { |
|
|
454 int nr = rows (); |
|
|
455 int nc = cols (); |
|
|
456 if (nr != a.length ()) |
|
|
457 { |
|
|
458 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
459 return *this; |
|
|
460 } |
|
|
461 |
|
|
462 int nc_insert = nc; |
|
|
463 ComplexMatrix retval (nr, nc + 1); |
|
|
464 retval.insert (*this, 0, 0); |
|
|
465 retval.insert (a, 0, nc_insert); |
|
|
466 return retval; |
|
|
467 } |
|
|
468 |
|
|
469 ComplexMatrix |
|
|
470 ComplexMatrix::append (const DiagMatrix& a) const |
|
|
471 { |
|
|
472 int nr = rows (); |
|
|
473 int nc = cols (); |
|
|
474 if (nr != a.rows ()) |
|
|
475 { |
|
|
476 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
477 return *this; |
|
|
478 } |
|
|
479 |
|
|
480 int nc_insert = nc; |
|
|
481 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
482 retval.insert (*this, 0, 0); |
|
|
483 retval.insert (a, 0, nc_insert); |
|
|
484 return retval; |
|
|
485 } |
|
|
486 |
|
|
487 ComplexMatrix |
|
|
488 ComplexMatrix::append (const ComplexMatrix& a) const |
|
|
489 { |
|
|
490 int nr = rows (); |
|
|
491 int nc = cols (); |
|
|
492 if (nr != a.rows ()) |
|
|
493 { |
|
|
494 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
495 return *this; |
|
|
496 } |
|
|
497 |
|
|
498 int nc_insert = nc; |
|
|
499 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
500 retval.insert (*this, 0, 0); |
|
|
501 retval.insert (a, 0, nc_insert); |
|
|
502 return retval; |
|
|
503 } |
|
|
504 |
|
|
505 ComplexMatrix |
|
|
506 ComplexMatrix::append (const ComplexRowVector& a) const |
|
|
507 { |
|
|
508 int nr = rows (); |
|
|
509 int nc = cols (); |
|
|
510 if (nr != 1) |
|
|
511 { |
|
|
512 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
513 return *this; |
|
|
514 } |
|
|
515 |
|
|
516 int nc_insert = nc; |
|
|
517 ComplexMatrix retval (nr, nc + a.length ()); |
|
|
518 retval.insert (*this, 0, 0); |
|
|
519 retval.insert (a, 0, nc_insert); |
|
|
520 return retval; |
|
|
521 } |
|
|
522 |
|
|
523 ComplexMatrix |
|
|
524 ComplexMatrix::append (const ComplexColumnVector& a) const |
|
|
525 { |
|
|
526 int nr = rows (); |
|
|
527 int nc = cols (); |
|
|
528 if (nr != a.length ()) |
|
|
529 { |
|
|
530 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
531 return *this; |
|
|
532 } |
|
|
533 |
|
|
534 int nc_insert = nc; |
|
|
535 ComplexMatrix retval (nr, nc + 1); |
|
|
536 retval.insert (*this, 0, 0); |
|
|
537 retval.insert (a, 0, nc_insert); |
|
|
538 return retval; |
|
|
539 } |
|
|
540 |
|
|
541 ComplexMatrix |
|
|
542 ComplexMatrix::append (const ComplexDiagMatrix& a) const |
|
|
543 { |
|
|
544 int nr = rows (); |
|
|
545 int nc = cols (); |
|
|
546 if (nr != a.rows ()) |
|
|
547 { |
|
|
548 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
549 return *this; |
|
|
550 } |
|
|
551 |
|
|
552 int nc_insert = nc; |
|
|
553 ComplexMatrix retval (nr, nc + a.cols ()); |
|
|
554 retval.insert (*this, 0, 0); |
|
|
555 retval.insert (a, 0, nc_insert); |
|
|
556 return retval; |
|
|
557 } |
|
|
558 |
|
|
559 ComplexMatrix |
|
|
560 ComplexMatrix::stack (const Matrix& a) const |
|
|
561 { |
|
|
562 int nr = rows (); |
|
|
563 int nc = cols (); |
|
|
564 if (nc != a.cols ()) |
|
|
565 { |
|
|
566 (*current_liboctave_error_handler) |
|
|
567 ("column dimension mismatch for stack"); |
|
|
568 return *this; |
|
|
569 } |
|
|
570 |
|
|
571 int nr_insert = nr; |
|
|
572 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
573 retval.insert (*this, 0, 0); |
|
|
574 retval.insert (a, nr_insert, 0); |
|
|
575 return retval; |
|
|
576 } |
|
|
577 |
|
|
578 ComplexMatrix |
|
|
579 ComplexMatrix::stack (const RowVector& a) const |
|
|
580 { |
|
|
581 int nr = rows (); |
|
|
582 int nc = cols (); |
|
|
583 if (nc != a.length ()) |
|
|
584 { |
|
|
585 (*current_liboctave_error_handler) |
|
|
586 ("column dimension mismatch for stack"); |
|
|
587 return *this; |
|
|
588 } |
|
|
589 |
|
|
590 int nr_insert = nr; |
|
|
591 ComplexMatrix retval (nr + 1, nc); |
|
|
592 retval.insert (*this, 0, 0); |
|
|
593 retval.insert (a, nr_insert, 0); |
|
|
594 return retval; |
|
|
595 } |
|
|
596 |
|
|
597 ComplexMatrix |
|
|
598 ComplexMatrix::stack (const ColumnVector& a) const |
|
|
599 { |
|
|
600 int nr = rows (); |
|
|
601 int nc = cols (); |
|
|
602 if (nc != 1) |
|
|
603 { |
|
|
604 (*current_liboctave_error_handler) |
|
|
605 ("column dimension mismatch for stack"); |
|
|
606 return *this; |
|
|
607 } |
|
|
608 |
|
|
609 int nr_insert = nr; |
|
|
610 ComplexMatrix retval (nr + a.length (), nc); |
|
|
611 retval.insert (*this, 0, 0); |
|
|
612 retval.insert (a, nr_insert, 0); |
|
|
613 return retval; |
|
|
614 } |
|
|
615 |
|
|
616 ComplexMatrix |
|
|
617 ComplexMatrix::stack (const DiagMatrix& a) const |
|
|
618 { |
|
|
619 int nr = rows (); |
|
|
620 int nc = cols (); |
|
|
621 if (nc != a.cols ()) |
|
|
622 { |
|
|
623 (*current_liboctave_error_handler) |
|
|
624 ("column dimension mismatch for stack"); |
|
|
625 return *this; |
|
|
626 } |
|
|
627 |
|
|
628 int nr_insert = nr; |
|
|
629 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
630 retval.insert (*this, 0, 0); |
|
|
631 retval.insert (a, nr_insert, 0); |
|
|
632 return retval; |
|
|
633 } |
|
|
634 |
|
|
635 ComplexMatrix |
|
|
636 ComplexMatrix::stack (const ComplexMatrix& a) const |
|
|
637 { |
|
|
638 int nr = rows (); |
|
|
639 int nc = cols (); |
|
|
640 if (nc != a.cols ()) |
|
|
641 { |
|
|
642 (*current_liboctave_error_handler) |
|
|
643 ("column dimension mismatch for stack"); |
|
|
644 return *this; |
|
|
645 } |
|
|
646 |
|
|
647 int nr_insert = nr; |
|
|
648 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
649 retval.insert (*this, 0, 0); |
|
|
650 retval.insert (a, nr_insert, 0); |
|
|
651 return retval; |
|
|
652 } |
|
|
653 |
|
|
654 ComplexMatrix |
|
|
655 ComplexMatrix::stack (const ComplexRowVector& a) const |
|
|
656 { |
|
|
657 int nr = rows (); |
|
|
658 int nc = cols (); |
|
|
659 if (nc != a.length ()) |
|
|
660 { |
|
|
661 (*current_liboctave_error_handler) |
|
|
662 ("column dimension mismatch for stack"); |
|
|
663 return *this; |
|
|
664 } |
|
|
665 |
|
|
666 int nr_insert = nr; |
|
|
667 ComplexMatrix retval (nr + 1, nc); |
|
|
668 retval.insert (*this, 0, 0); |
|
|
669 retval.insert (a, nr_insert, 0); |
|
|
670 return retval; |
|
|
671 } |
|
|
672 |
|
|
673 ComplexMatrix |
|
|
674 ComplexMatrix::stack (const ComplexColumnVector& a) const |
|
|
675 { |
|
|
676 int nr = rows (); |
|
|
677 int nc = cols (); |
|
|
678 if (nc != 1) |
|
|
679 { |
|
|
680 (*current_liboctave_error_handler) |
|
|
681 ("column dimension mismatch for stack"); |
|
|
682 return *this; |
|
|
683 } |
|
|
684 |
|
|
685 int nr_insert = nr; |
|
|
686 ComplexMatrix retval (nr + a.length (), nc); |
|
|
687 retval.insert (*this, 0, 0); |
|
|
688 retval.insert (a, nr_insert, 0); |
|
|
689 return retval; |
|
|
690 } |
|
|
691 |
|
|
692 ComplexMatrix |
|
|
693 ComplexMatrix::stack (const ComplexDiagMatrix& a) const |
|
|
694 { |
|
|
695 int nr = rows (); |
|
|
696 int nc = cols (); |
|
|
697 if (nc != a.cols ()) |
|
|
698 { |
|
|
699 (*current_liboctave_error_handler) |
|
|
700 ("column dimension mismatch for stack"); |
|
|
701 return *this; |
|
|
702 } |
|
|
703 |
|
|
704 int nr_insert = nr; |
|
|
705 ComplexMatrix retval (nr + a.rows (), nc); |
|
|
706 retval.insert (*this, 0, 0); |
|
|
707 retval.insert (a, nr_insert, 0); |
|
|
708 return retval; |
|
|
709 } |
|
|
710 |
|
|
711 ComplexMatrix |
|
|
712 ComplexMatrix::hermitian (void) const |
|
|
713 { |
|
|
714 int nr = rows (); |
|
|
715 int nc = cols (); |
|
|
716 ComplexMatrix result; |
|
|
717 if (length () > 0) |
|
|
718 { |
|
|
719 result.resize (nc, nr); |
|
|
720 for (int j = 0; j < nc; j++) |
|
|
721 for (int i = 0; i < nr; i++) |
|
|
722 result.elem (j, i) = conj (elem (i, j)); |
|
|
723 } |
|
|
724 return result; |
|
|
725 } |
|
|
726 |
|
|
727 ComplexMatrix |
|
|
728 ComplexMatrix::transpose (void) const |
|
|
729 { |
|
|
730 int nr = rows (); |
|
|
731 int nc = cols (); |
|
|
732 ComplexMatrix result (nc, nr); |
|
|
733 if (length () > 0) |
|
|
734 { |
|
|
735 for (int j = 0; j < nc; j++) |
|
|
736 for (int i = 0; i < nr; i++) |
|
|
737 result.elem (j, i) = elem (i, j); |
|
|
738 } |
|
|
739 return result; |
|
|
740 } |
|
|
741 |
|
|
742 ComplexMatrix |
|
|
743 conj (const ComplexMatrix& a) |
|
|
744 { |
|
|
745 int a_len = a.length (); |
|
|
746 ComplexMatrix retval; |
|
|
747 if (a_len > 0) |
|
|
748 retval = ComplexMatrix (conj_dup (a.data (), a_len), a.rows (), |
|
|
749 a.cols ()); |
|
|
750 return retval; |
|
|
751 } |
|
|
752 |
|
|
753 // resize is the destructive equivalent for this one |
|
|
754 |
|
|
755 ComplexMatrix |
|
|
756 ComplexMatrix::extract (int r1, int c1, int r2, int c2) const |
|
|
757 { |
|
|
758 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
759 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
760 |
|
|
761 int new_r = r2 - r1 + 1; |
|
|
762 int new_c = c2 - c1 + 1; |
|
|
763 |
|
|
764 ComplexMatrix result (new_r, new_c); |
|
|
765 |
|
|
766 for (int j = 0; j < new_c; j++) |
|
|
767 for (int i = 0; i < new_r; i++) |
|
|
768 result.elem (i, j) = elem (r1+i, c1+j); |
|
|
769 |
|
|
770 return result; |
|
|
771 } |
|
|
772 |
|
|
773 // extract row or column i. |
|
|
774 |
|
|
775 ComplexRowVector |
|
|
776 ComplexMatrix::row (int i) const |
|
|
777 { |
|
|
778 int nc = cols (); |
|
|
779 if (i < 0 || i >= rows ()) |
|
|
780 { |
|
|
781 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
782 return ComplexRowVector (); |
|
|
783 } |
|
|
784 |
|
|
785 ComplexRowVector retval (nc); |
|
|
786 for (int j = 0; j < cols (); j++) |
|
|
787 retval.elem (j) = elem (i, j); |
|
|
788 |
|
|
789 return retval; |
|
|
790 } |
|
|
791 |
|
|
792 ComplexRowVector |
|
|
793 ComplexMatrix::row (char *s) const |
|
|
794 { |
|
533
|
795 if (! s) |
|
458
|
796 { |
|
|
797 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
798 return ComplexRowVector (); |
|
|
799 } |
|
|
800 |
|
|
801 char c = *s; |
|
|
802 if (c == 'f' || c == 'F') |
|
|
803 return row (0); |
|
|
804 else if (c == 'l' || c == 'L') |
|
|
805 return row (rows () - 1); |
|
|
806 else |
|
|
807 { |
|
|
808 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
809 return ComplexRowVector (); |
|
|
810 } |
|
|
811 } |
|
|
812 |
|
|
813 ComplexColumnVector |
|
|
814 ComplexMatrix::column (int i) const |
|
|
815 { |
|
|
816 int nr = rows (); |
|
|
817 if (i < 0 || i >= cols ()) |
|
|
818 { |
|
|
819 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
820 return ComplexColumnVector (); |
|
|
821 } |
|
|
822 |
|
|
823 ComplexColumnVector retval (nr); |
|
|
824 for (int j = 0; j < nr; j++) |
|
|
825 retval.elem (j) = elem (j, i); |
|
|
826 |
|
|
827 return retval; |
|
|
828 } |
|
|
829 |
|
|
830 ComplexColumnVector |
|
|
831 ComplexMatrix::column (char *s) const |
|
|
832 { |
|
533
|
833 if (! s) |
|
458
|
834 { |
|
|
835 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
836 return ComplexColumnVector (); |
|
|
837 } |
|
|
838 |
|
|
839 char c = *s; |
|
|
840 if (c == 'f' || c == 'F') |
|
|
841 return column (0); |
|
|
842 else if (c == 'l' || c == 'L') |
|
|
843 return column (cols () - 1); |
|
|
844 else |
|
|
845 { |
|
|
846 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
847 return ComplexColumnVector (); |
|
|
848 } |
|
|
849 } |
|
|
850 |
|
|
851 ComplexMatrix |
|
|
852 ComplexMatrix::inverse (void) const |
|
|
853 { |
|
|
854 int info; |
|
479
|
855 double rcond; |
|
|
856 return inverse (info, rcond); |
|
458
|
857 } |
|
|
858 |
|
|
859 ComplexMatrix |
|
|
860 ComplexMatrix::inverse (int& info) const |
|
|
861 { |
|
|
862 double rcond; |
|
|
863 return inverse (info, rcond); |
|
|
864 } |
|
|
865 |
|
|
866 ComplexMatrix |
|
1656
|
867 ComplexMatrix::inverse (int& info, double& rcond, int force) const |
|
458
|
868 { |
|
1948
|
869 ComplexMatrix retval; |
|
|
870 |
|
458
|
871 int nr = rows (); |
|
|
872 int nc = cols (); |
|
1948
|
873 |
|
458
|
874 if (nr != nc) |
|
1948
|
875 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
876 else |
|
|
877 { |
|
1948
|
878 info = 0; |
|
|
879 |
|
|
880 Array<int> ipvt (nr); |
|
|
881 int *pipvt = ipvt.fortran_vec (); |
|
|
882 |
|
|
883 Array<Complex> z (nr); |
|
|
884 Complex *pz = z.fortran_vec (); |
|
|
885 |
|
|
886 retval = *this; |
|
|
887 Complex *tmp_data = retval.fortran_vec (); |
|
|
888 |
|
|
889 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nc, pipvt, rcond, pz)); |
|
|
890 |
|
|
891 if (f77_exception_encountered) |
|
|
892 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
893 else |
|
|
894 { |
|
|
895 volatile double rcond_plus_one = rcond + 1.0; |
|
|
896 |
|
|
897 if (rcond_plus_one == 1.0) |
|
|
898 info = -1; |
|
|
899 |
|
|
900 if (info == -1 && ! force) |
|
|
901 retval = *this; // Restore contents. |
|
|
902 else |
|
|
903 { |
|
|
904 Complex *dummy = 0; |
|
|
905 |
|
|
906 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nc, pipvt, dummy, |
|
|
907 pz, 1)); |
|
|
908 |
|
|
909 if (f77_exception_encountered) |
|
|
910 (*current_liboctave_error_handler) |
|
|
911 ("unrecoverable error in zgedi"); |
|
|
912 } |
|
|
913 } |
|
458
|
914 } |
|
|
915 |
|
1948
|
916 return retval; |
|
458
|
917 } |
|
|
918 |
|
|
919 ComplexMatrix |
|
740
|
920 ComplexMatrix::pseudo_inverse (double tol) |
|
|
921 { |
|
1549
|
922 ComplexMatrix retval; |
|
|
923 |
|
740
|
924 ComplexSVD result (*this); |
|
|
925 |
|
|
926 DiagMatrix S = result.singular_values (); |
|
|
927 ComplexMatrix U = result.left_singular_matrix (); |
|
|
928 ComplexMatrix V = result.right_singular_matrix (); |
|
|
929 |
|
|
930 ColumnVector sigma = S.diag (); |
|
|
931 |
|
|
932 int r = sigma.length () - 1; |
|
|
933 int nr = rows (); |
|
|
934 int nc = cols (); |
|
|
935 |
|
|
936 if (tol <= 0.0) |
|
|
937 { |
|
|
938 if (nr > nc) |
|
|
939 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
940 else |
|
|
941 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
942 } |
|
|
943 |
|
|
944 while (r >= 0 && sigma.elem (r) < tol) |
|
|
945 r--; |
|
|
946 |
|
|
947 if (r < 0) |
|
1549
|
948 retval = ComplexMatrix (nc, nr, 0.0); |
|
740
|
949 else |
|
|
950 { |
|
|
951 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); |
|
|
952 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
953 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); |
|
1549
|
954 retval = Vr * D * Ur.hermitian (); |
|
740
|
955 } |
|
1549
|
956 |
|
|
957 return retval; |
|
740
|
958 } |
|
|
959 |
|
|
960 ComplexMatrix |
|
458
|
961 ComplexMatrix::fourier (void) const |
|
|
962 { |
|
1948
|
963 ComplexMatrix retval; |
|
|
964 |
|
458
|
965 int nr = rows (); |
|
|
966 int nc = cols (); |
|
1948
|
967 |
|
458
|
968 int npts, nsamples; |
|
1948
|
969 |
|
458
|
970 if (nr == 1 || nc == 1) |
|
|
971 { |
|
|
972 npts = nr > nc ? nr : nc; |
|
|
973 nsamples = 1; |
|
|
974 } |
|
|
975 else |
|
|
976 { |
|
|
977 npts = nr; |
|
|
978 nsamples = nc; |
|
|
979 } |
|
|
980 |
|
|
981 int nn = 4*npts+15; |
|
1948
|
982 |
|
|
983 Array<Complex> wsave (nn); |
|
|
984 Complex *pwsave = wsave.fortran_vec (); |
|
|
985 |
|
|
986 retval = *this; |
|
|
987 Complex *tmp_data = retval.fortran_vec (); |
|
|
988 |
|
|
989 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
990 |
|
|
991 for (int j = 0; j < nsamples; j++) |
|
1948
|
992 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
993 |
|
|
994 return retval; |
|
458
|
995 } |
|
|
996 |
|
|
997 ComplexMatrix |
|
|
998 ComplexMatrix::ifourier (void) const |
|
|
999 { |
|
1948
|
1000 ComplexMatrix retval; |
|
|
1001 |
|
458
|
1002 int nr = rows (); |
|
|
1003 int nc = cols (); |
|
1948
|
1004 |
|
458
|
1005 int npts, nsamples; |
|
1948
|
1006 |
|
458
|
1007 if (nr == 1 || nc == 1) |
|
|
1008 { |
|
|
1009 npts = nr > nc ? nr : nc; |
|
|
1010 nsamples = 1; |
|
|
1011 } |
|
|
1012 else |
|
|
1013 { |
|
|
1014 npts = nr; |
|
|
1015 nsamples = nc; |
|
|
1016 } |
|
|
1017 |
|
|
1018 int nn = 4*npts+15; |
|
1948
|
1019 |
|
|
1020 Array<Complex> wsave (nn); |
|
|
1021 Complex *pwsave = wsave.fortran_vec (); |
|
|
1022 |
|
|
1023 retval = *this; |
|
|
1024 Complex *tmp_data = retval.fortran_vec (); |
|
|
1025 |
|
|
1026 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
1027 |
|
|
1028 for (int j = 0; j < nsamples; j++) |
|
1948
|
1029 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
458
|
1030 |
|
1321
|
1031 for (int j = 0; j < npts*nsamples; j++) |
|
2800
|
1032 tmp_data[j] = tmp_data[j] / npts; |
|
458
|
1033 |
|
1948
|
1034 return retval; |
|
458
|
1035 } |
|
|
1036 |
|
677
|
1037 ComplexMatrix |
|
|
1038 ComplexMatrix::fourier2d (void) const |
|
|
1039 { |
|
1948
|
1040 ComplexMatrix retval; |
|
|
1041 |
|
677
|
1042 int nr = rows (); |
|
|
1043 int nc = cols (); |
|
1948
|
1044 |
|
677
|
1045 int npts, nsamples; |
|
1948
|
1046 |
|
677
|
1047 if (nr == 1 || nc == 1) |
|
|
1048 { |
|
|
1049 npts = nr > nc ? nr : nc; |
|
|
1050 nsamples = 1; |
|
|
1051 } |
|
|
1052 else |
|
|
1053 { |
|
|
1054 npts = nr; |
|
|
1055 nsamples = nc; |
|
|
1056 } |
|
|
1057 |
|
|
1058 int nn = 4*npts+15; |
|
1948
|
1059 |
|
|
1060 Array<Complex> wsave (nn); |
|
|
1061 Complex *pwsave = wsave.fortran_vec (); |
|
|
1062 |
|
|
1063 retval = *this; |
|
|
1064 Complex *tmp_data = retval.fortran_vec (); |
|
|
1065 |
|
|
1066 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1067 |
|
|
1068 for (int j = 0; j < nsamples; j++) |
|
1948
|
1069 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1070 |
|
|
1071 npts = nc; |
|
|
1072 nsamples = nr; |
|
|
1073 nn = 4*npts+15; |
|
1948
|
1074 |
|
|
1075 wsave.resize (nn); |
|
|
1076 pwsave = wsave.fortran_vec (); |
|
|
1077 |
|
|
1078 Array<Complex> row (npts); |
|
|
1079 Complex *prow = row.fortran_vec (); |
|
|
1080 |
|
|
1081 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1082 |
|
1321
|
1083 for (int j = 0; j < nsamples; j++) |
|
677
|
1084 { |
|
|
1085 for (int i = 0; i < npts; i++) |
|
1948
|
1086 prow[i] = tmp_data[i*nr + j]; |
|
|
1087 |
|
|
1088 F77_FCN (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1089 |
|
1321
|
1090 for (int i = 0; i < npts; i++) |
|
1948
|
1091 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1092 } |
|
|
1093 |
|
1948
|
1094 return retval; |
|
677
|
1095 } |
|
|
1096 |
|
|
1097 ComplexMatrix |
|
|
1098 ComplexMatrix::ifourier2d (void) const |
|
|
1099 { |
|
1948
|
1100 ComplexMatrix retval; |
|
|
1101 |
|
677
|
1102 int nr = rows (); |
|
|
1103 int nc = cols (); |
|
1948
|
1104 |
|
677
|
1105 int npts, nsamples; |
|
1948
|
1106 |
|
677
|
1107 if (nr == 1 || nc == 1) |
|
|
1108 { |
|
|
1109 npts = nr > nc ? nr : nc; |
|
|
1110 nsamples = 1; |
|
|
1111 } |
|
|
1112 else |
|
|
1113 { |
|
|
1114 npts = nr; |
|
|
1115 nsamples = nc; |
|
|
1116 } |
|
|
1117 |
|
|
1118 int nn = 4*npts+15; |
|
1948
|
1119 |
|
|
1120 Array<Complex> wsave (nn); |
|
|
1121 Complex *pwsave = wsave.fortran_vec (); |
|
|
1122 |
|
|
1123 retval = *this; |
|
|
1124 Complex *tmp_data = retval.fortran_vec (); |
|
|
1125 |
|
|
1126 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1127 |
|
|
1128 for (int j = 0; j < nsamples; j++) |
|
1948
|
1129 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
1130 |
|
1321
|
1131 for (int j = 0; j < npts*nsamples; j++) |
|
2800
|
1132 tmp_data[j] = tmp_data[j] / npts; |
|
677
|
1133 |
|
|
1134 npts = nc; |
|
|
1135 nsamples = nr; |
|
|
1136 nn = 4*npts+15; |
|
1948
|
1137 |
|
|
1138 wsave.resize (nn); |
|
|
1139 pwsave = wsave.fortran_vec (); |
|
|
1140 |
|
|
1141 Array<Complex> row (npts); |
|
|
1142 Complex *prow = row.fortran_vec (); |
|
|
1143 |
|
|
1144 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
1145 |
|
1321
|
1146 for (int j = 0; j < nsamples; j++) |
|
677
|
1147 { |
|
|
1148 for (int i = 0; i < npts; i++) |
|
1948
|
1149 prow[i] = tmp_data[i*nr + j]; |
|
|
1150 |
|
|
1151 F77_FCN (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1152 |
|
1321
|
1153 for (int i = 0; i < npts; i++) |
|
2800
|
1154 tmp_data[i*nr + j] = prow[i] / npts; |
|
677
|
1155 } |
|
|
1156 |
|
1948
|
1157 return retval; |
|
677
|
1158 } |
|
|
1159 |
|
458
|
1160 ComplexDET |
|
|
1161 ComplexMatrix::determinant (void) const |
|
|
1162 { |
|
|
1163 int info; |
|
|
1164 double rcond; |
|
|
1165 return determinant (info, rcond); |
|
|
1166 } |
|
|
1167 |
|
|
1168 ComplexDET |
|
|
1169 ComplexMatrix::determinant (int& info) const |
|
|
1170 { |
|
|
1171 double rcond; |
|
|
1172 return determinant (info, rcond); |
|
|
1173 } |
|
|
1174 |
|
|
1175 ComplexDET |
|
532
|
1176 ComplexMatrix::determinant (int& info, double& rcond) const |
|
458
|
1177 { |
|
|
1178 ComplexDET retval; |
|
|
1179 |
|
|
1180 int nr = rows (); |
|
|
1181 int nc = cols (); |
|
|
1182 |
|
|
1183 if (nr == 0 || nc == 0) |
|
|
1184 { |
|
|
1185 Complex d[2]; |
|
|
1186 d[0] = 1.0; |
|
|
1187 d[1] = 0.0; |
|
|
1188 retval = ComplexDET (d); |
|
|
1189 } |
|
|
1190 else |
|
|
1191 { |
|
|
1192 info = 0; |
|
1948
|
1193 |
|
|
1194 Array<int> ipvt (nr); |
|
|
1195 int *pipvt = ipvt.fortran_vec (); |
|
|
1196 |
|
|
1197 Array<Complex> z (nr); |
|
|
1198 Complex *pz = z.fortran_vec (); |
|
|
1199 |
|
|
1200 ComplexMatrix atmp = *this; |
|
|
1201 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1202 |
|
|
1203 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1204 |
|
|
1205 if (f77_exception_encountered) |
|
|
1206 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
458
|
1207 else |
|
|
1208 { |
|
1948
|
1209 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1210 |
|
|
1211 if (rcond_plus_one == 1.0) |
|
|
1212 { |
|
|
1213 info = -1; |
|
|
1214 retval = ComplexDET (); |
|
|
1215 } |
|
|
1216 else |
|
|
1217 { |
|
|
1218 Complex d[2]; |
|
|
1219 |
|
|
1220 F77_XFCN (zgedi, ZGEDI, (tmp_data, nr, nr, pipvt, d, pz, 10)); |
|
|
1221 |
|
|
1222 if (f77_exception_encountered) |
|
|
1223 (*current_liboctave_error_handler) |
|
|
1224 ("unrecoverable error in dgedi"); |
|
|
1225 else |
|
|
1226 retval = ComplexDET (d); |
|
|
1227 } |
|
458
|
1228 } |
|
|
1229 } |
|
|
1230 |
|
|
1231 return retval; |
|
|
1232 } |
|
|
1233 |
|
|
1234 ComplexMatrix |
|
|
1235 ComplexMatrix::solve (const Matrix& b) const |
|
|
1236 { |
|
|
1237 int info; |
|
|
1238 double rcond; |
|
|
1239 return solve (b, info, rcond); |
|
|
1240 } |
|
|
1241 |
|
|
1242 ComplexMatrix |
|
|
1243 ComplexMatrix::solve (const Matrix& b, int& info) const |
|
|
1244 { |
|
|
1245 double rcond; |
|
|
1246 return solve (b, info, rcond); |
|
|
1247 } |
|
|
1248 |
|
|
1249 ComplexMatrix |
|
|
1250 ComplexMatrix::solve (const Matrix& b, int& info, double& rcond) const |
|
|
1251 { |
|
|
1252 ComplexMatrix tmp (b); |
|
|
1253 return solve (tmp, info, rcond); |
|
|
1254 } |
|
|
1255 |
|
|
1256 ComplexMatrix |
|
|
1257 ComplexMatrix::solve (const ComplexMatrix& b) const |
|
|
1258 { |
|
|
1259 int info; |
|
|
1260 double rcond; |
|
|
1261 return solve (b, info, rcond); |
|
|
1262 } |
|
|
1263 |
|
|
1264 ComplexMatrix |
|
|
1265 ComplexMatrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1266 { |
|
|
1267 double rcond; |
|
|
1268 return solve (b, info, rcond); |
|
|
1269 } |
|
|
1270 ComplexMatrix |
|
532
|
1271 ComplexMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
458
|
1272 { |
|
|
1273 ComplexMatrix retval; |
|
|
1274 |
|
|
1275 int nr = rows (); |
|
|
1276 int nc = cols (); |
|
1948
|
1277 |
|
|
1278 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1279 (*current_liboctave_error_handler) |
|
|
1280 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1281 else |
|
|
1282 { |
|
1948
|
1283 info = 0; |
|
|
1284 |
|
|
1285 Array<int> ipvt (nr); |
|
|
1286 int *pipvt = ipvt.fortran_vec (); |
|
|
1287 |
|
|
1288 Array<Complex> z (nr); |
|
|
1289 Complex *pz = z.fortran_vec (); |
|
|
1290 |
|
|
1291 ComplexMatrix atmp = *this; |
|
|
1292 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1293 |
|
|
1294 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1295 |
|
|
1296 if (f77_exception_encountered) |
|
|
1297 (*current_liboctave_error_handler) ("unrecoverable error in zgeco"); |
|
|
1298 else |
|
|
1299 { |
|
|
1300 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1301 |
|
|
1302 if (rcond_plus_one == 1.0) |
|
|
1303 { |
|
|
1304 info = -2; |
|
|
1305 } |
|
|
1306 else |
|
|
1307 { |
|
|
1308 retval = b; |
|
|
1309 Complex *result = retval.fortran_vec (); |
|
|
1310 |
|
|
1311 int b_nc = b.cols (); |
|
|
1312 |
|
|
1313 for (volatile int j = 0; j < b_nc; j++) |
|
|
1314 { |
|
|
1315 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, |
|
|
1316 &result[nr*j], 0)); |
|
|
1317 |
|
|
1318 if (f77_exception_encountered) |
|
|
1319 { |
|
|
1320 (*current_liboctave_error_handler) |
|
|
1321 ("unrecoverable error in dgesl"); |
|
|
1322 |
|
|
1323 break; |
|
|
1324 } |
|
|
1325 } |
|
|
1326 } |
|
|
1327 } |
|
458
|
1328 } |
|
|
1329 |
|
|
1330 return retval; |
|
|
1331 } |
|
|
1332 |
|
|
1333 ComplexColumnVector |
|
|
1334 ComplexMatrix::solve (const ComplexColumnVector& b) const |
|
|
1335 { |
|
|
1336 int info; |
|
|
1337 double rcond; |
|
|
1338 return solve (b, info, rcond); |
|
|
1339 } |
|
|
1340 |
|
|
1341 ComplexColumnVector |
|
|
1342 ComplexMatrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1343 { |
|
|
1344 double rcond; |
|
|
1345 return solve (b, info, rcond); |
|
|
1346 } |
|
|
1347 |
|
|
1348 ComplexColumnVector |
|
|
1349 ComplexMatrix::solve (const ComplexColumnVector& b, int& info, |
|
532
|
1350 double& rcond) const |
|
458
|
1351 { |
|
|
1352 ComplexColumnVector retval; |
|
|
1353 |
|
|
1354 int nr = rows (); |
|
|
1355 int nc = cols (); |
|
1948
|
1356 |
|
|
1357 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
1358 (*current_liboctave_error_handler) |
|
|
1359 ("matrix dimension mismatch in solution of linear equations"); |
|
458
|
1360 else |
|
|
1361 { |
|
1948
|
1362 info = 0; |
|
|
1363 |
|
|
1364 Array<int> ipvt (nr); |
|
|
1365 int *pipvt = ipvt.fortran_vec (); |
|
|
1366 |
|
|
1367 Array<Complex> z (nr); |
|
|
1368 Complex *pz = z.fortran_vec (); |
|
|
1369 |
|
|
1370 ComplexMatrix atmp = *this; |
|
|
1371 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1372 |
|
|
1373 F77_XFCN (zgeco, ZGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1374 |
|
|
1375 if (f77_exception_encountered) |
|
|
1376 (*current_liboctave_error_handler) |
|
|
1377 ("unrecoverable error in dgeco"); |
|
|
1378 else |
|
|
1379 { |
|
|
1380 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1381 |
|
|
1382 if (rcond_plus_one == 1.0) |
|
|
1383 { |
|
|
1384 info = -2; |
|
|
1385 } |
|
|
1386 else |
|
|
1387 { |
|
|
1388 retval = b; |
|
|
1389 Complex *result = retval.fortran_vec (); |
|
|
1390 |
|
|
1391 F77_XFCN (zgesl, ZGESL, (tmp_data, nr, nr, pipvt, result, 0)); |
|
|
1392 |
|
|
1393 if (f77_exception_encountered) |
|
|
1394 (*current_liboctave_error_handler) |
|
|
1395 ("unrecoverable error in dgesl"); |
|
|
1396 } |
|
|
1397 } |
|
458
|
1398 } |
|
|
1399 |
|
|
1400 return retval; |
|
|
1401 } |
|
|
1402 |
|
|
1403 ComplexMatrix |
|
|
1404 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
|
|
1405 { |
|
|
1406 int info; |
|
|
1407 int rank; |
|
|
1408 return lssolve (b, info, rank); |
|
|
1409 } |
|
|
1410 |
|
|
1411 ComplexMatrix |
|
|
1412 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1413 { |
|
|
1414 int rank; |
|
|
1415 return lssolve (b, info, rank); |
|
|
1416 } |
|
|
1417 |
|
|
1418 ComplexMatrix |
|
|
1419 ComplexMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1420 { |
|
1948
|
1421 ComplexMatrix retval; |
|
|
1422 |
|
458
|
1423 int nrhs = b.cols (); |
|
|
1424 |
|
|
1425 int m = rows (); |
|
|
1426 int n = cols (); |
|
|
1427 |
|
|
1428 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1429 (*current_liboctave_error_handler) |
|
|
1430 ("matrix dimension mismatch solution of linear equations"); |
|
|
1431 else |
|
458
|
1432 { |
|
1948
|
1433 ComplexMatrix atmp = *this; |
|
|
1434 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1435 |
|
|
1436 int nrr = m > n ? m : n; |
|
|
1437 ComplexMatrix result (nrr, nrhs); |
|
|
1438 |
|
|
1439 for (int j = 0; j < nrhs; j++) |
|
|
1440 for (int i = 0; i < m; i++) |
|
|
1441 result.elem (i, j) = b.elem (i, j); |
|
|
1442 |
|
|
1443 Complex *presult = result.fortran_vec (); |
|
|
1444 |
|
|
1445 int len_s = m < n ? m : n; |
|
|
1446 Array<double> s (len_s); |
|
|
1447 double *ps = s.fortran_vec (); |
|
2563
|
1448 |
|
1948
|
1449 double rcond = -1.0; |
|
2563
|
1450 |
|
1948
|
1451 int lwork; |
|
|
1452 if (m < n) |
|
|
1453 lwork = 2*m + (nrhs > n ? nrhs : n); |
|
|
1454 else |
|
|
1455 lwork = 2*n + (nrhs > m ? nrhs : m); |
|
|
1456 |
|
3075
|
1457 lwork *= 16; |
|
|
1458 |
|
1948
|
1459 Array<Complex> work (lwork); |
|
|
1460 Complex *pwork = work.fortran_vec (); |
|
|
1461 |
|
|
1462 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1463 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1464 Array<double> rwork (lrwork); |
|
|
1465 double *prwork = rwork.fortran_vec (); |
|
|
1466 |
|
|
1467 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1468 nrr, ps, rcond, rank, pwork, lwork, |
|
|
1469 prwork, info)); |
|
|
1470 |
|
|
1471 if (f77_exception_encountered) |
|
|
1472 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1473 else |
|
|
1474 { |
|
2563
|
1475 retval.resize (n, nrhs); |
|
1948
|
1476 for (int j = 0; j < nrhs; j++) |
|
|
1477 for (int i = 0; i < n; i++) |
|
|
1478 retval.elem (i, j) = result.elem (i, j); |
|
|
1479 } |
|
458
|
1480 } |
|
|
1481 |
|
|
1482 return retval; |
|
|
1483 } |
|
|
1484 |
|
|
1485 ComplexColumnVector |
|
|
1486 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
|
|
1487 { |
|
|
1488 int info; |
|
|
1489 int rank; |
|
|
1490 return lssolve (b, info, rank); |
|
|
1491 } |
|
|
1492 |
|
|
1493 ComplexColumnVector |
|
|
1494 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1495 { |
|
|
1496 int rank; |
|
|
1497 return lssolve (b, info, rank); |
|
|
1498 } |
|
|
1499 |
|
|
1500 ComplexColumnVector |
|
|
1501 ComplexMatrix::lssolve (const ComplexColumnVector& b, int& info, |
|
|
1502 int& rank) const |
|
|
1503 { |
|
1948
|
1504 ComplexColumnVector retval; |
|
|
1505 |
|
458
|
1506 int nrhs = 1; |
|
|
1507 |
|
|
1508 int m = rows (); |
|
|
1509 int n = cols (); |
|
|
1510 |
|
|
1511 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1512 (*current_liboctave_error_handler) |
|
|
1513 ("matrix dimension mismatch solution of least squares problem"); |
|
|
1514 else |
|
458
|
1515 { |
|
1948
|
1516 ComplexMatrix atmp = *this; |
|
|
1517 Complex *tmp_data = atmp.fortran_vec (); |
|
|
1518 |
|
|
1519 int nrr = m > n ? m : n; |
|
|
1520 ComplexColumnVector result (nrr); |
|
|
1521 |
|
|
1522 for (int i = 0; i < m; i++) |
|
|
1523 result.elem (i) = b.elem (i); |
|
|
1524 |
|
|
1525 Complex *presult = result.fortran_vec (); |
|
|
1526 |
|
|
1527 int len_s = m < n ? m : n; |
|
|
1528 Array<double> s (len_s); |
|
|
1529 double *ps = s.fortran_vec (); |
|
|
1530 |
|
|
1531 double rcond = -1.0; |
|
|
1532 |
|
|
1533 int lwork; |
|
|
1534 if (m < n) |
|
|
1535 lwork = 2*m + (nrhs > n ? nrhs : n); |
|
|
1536 else |
|
|
1537 lwork = 2*n + (nrhs > m ? nrhs : m); |
|
|
1538 |
|
3075
|
1539 lwork *= 16; |
|
|
1540 |
|
1948
|
1541 Array<Complex> work (lwork); |
|
|
1542 Complex *pwork = work.fortran_vec (); |
|
|
1543 |
|
|
1544 int lrwork = (5 * (m < n ? m : n)) - 4; |
|
|
1545 lrwork = lrwork > 1 ? lrwork : 1; |
|
|
1546 Array<double> rwork (lrwork); |
|
|
1547 double *prwork = rwork.fortran_vec (); |
|
|
1548 |
|
|
1549 F77_XFCN (zgelss, ZGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1550 nrr, ps, rcond, rank, pwork, lwork, |
|
|
1551 prwork, info)); |
|
|
1552 |
|
|
1553 if (f77_exception_encountered) |
|
|
1554 (*current_liboctave_error_handler) ("unrecoverable error in zgelss"); |
|
|
1555 else |
|
|
1556 { |
|
2563
|
1557 retval.resize (n); |
|
1948
|
1558 for (int i = 0; i < n; i++) |
|
|
1559 retval.elem (i) = result.elem (i); |
|
|
1560 } |
|
458
|
1561 } |
|
|
1562 |
|
|
1563 return retval; |
|
|
1564 } |
|
|
1565 |
|
1819
|
1566 // Constants for matrix exponential calculation. |
|
|
1567 |
|
|
1568 static double padec [] = |
|
|
1569 { |
|
|
1570 5.0000000000000000e-1, |
|
|
1571 1.1666666666666667e-1, |
|
|
1572 1.6666666666666667e-2, |
|
|
1573 1.6025641025641026e-3, |
|
|
1574 1.0683760683760684e-4, |
|
|
1575 4.8562548562548563e-6, |
|
|
1576 1.3875013875013875e-7, |
|
|
1577 1.9270852604185938e-9, |
|
|
1578 }; |
|
|
1579 |
|
|
1580 ComplexMatrix |
|
|
1581 ComplexMatrix::expm (void) const |
|
|
1582 { |
|
|
1583 ComplexMatrix retval; |
|
|
1584 |
|
|
1585 ComplexMatrix m = *this; |
|
|
1586 |
|
|
1587 int nc = columns (); |
|
|
1588 |
|
3130
|
1589 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1590 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1591 |
|
1819
|
1592 // trace shift value |
|
|
1593 Complex trshift = 0.0; |
|
|
1594 |
|
|
1595 for (int i = 0; i < nc; i++) |
|
|
1596 trshift += m.elem (i, i); |
|
|
1597 |
|
|
1598 trshift /= nc; |
|
|
1599 |
|
3130
|
1600 if (trshift.real () < 0.0) |
|
|
1601 trshift = trshift.imag (); |
|
|
1602 |
|
1819
|
1603 for (int i = 0; i < nc; i++) |
|
|
1604 m.elem (i, i) -= trshift; |
|
|
1605 |
|
|
1606 // Preconditioning step 2: eigenvalue balancing. |
|
|
1607 |
|
|
1608 ComplexAEPBALANCE mbal (m, "B"); |
|
|
1609 m = mbal.balanced_matrix (); |
|
|
1610 ComplexMatrix d = mbal.balancing_matrix (); |
|
|
1611 |
|
|
1612 // Preconditioning step 3: scaling. |
|
|
1613 |
|
|
1614 ColumnVector work (nc); |
|
3130
|
1615 double inf_norm; |
|
|
1616 |
|
|
1617 F77_FCN (xzlange, XZLANGE) ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1618 work.fortran_vec (), inf_norm); |
|
1819
|
1619 |
|
2800
|
1620 int sqpow = (inf_norm > 0.0 |
|
|
1621 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); |
|
1819
|
1622 |
|
|
1623 // Check whether we need to square at all. |
|
|
1624 |
|
|
1625 if (sqpow < 0) |
|
|
1626 sqpow = 0; |
|
|
1627 |
|
|
1628 if (sqpow > 0) |
|
|
1629 { |
|
|
1630 double scale_factor = 1.0; |
|
|
1631 for (int i = 0; i < sqpow; i++) |
|
|
1632 scale_factor *= 2.0; |
|
|
1633 |
|
|
1634 m = m / scale_factor; |
|
|
1635 } |
|
|
1636 |
|
|
1637 // npp, dpp: pade' approx polynomial matrices. |
|
|
1638 |
|
|
1639 ComplexMatrix npp (nc, nc, 0.0); |
|
|
1640 ComplexMatrix dpp = npp; |
|
|
1641 |
|
|
1642 // Now powers a^8 ... a^1. |
|
|
1643 |
|
|
1644 int minus_one_j = -1; |
|
|
1645 for (int j = 7; j >= 0; j--) |
|
|
1646 { |
|
|
1647 npp = m * npp + m * padec[j]; |
|
|
1648 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
1649 minus_one_j *= -1; |
|
|
1650 } |
|
|
1651 |
|
|
1652 // Zero power. |
|
|
1653 |
|
|
1654 dpp = -dpp; |
|
|
1655 for (int j = 0; j < nc; j++) |
|
|
1656 { |
|
|
1657 npp.elem (j, j) += 1.0; |
|
|
1658 dpp.elem (j, j) += 1.0; |
|
|
1659 } |
|
|
1660 |
|
|
1661 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1662 |
|
|
1663 retval = dpp.solve (npp); |
|
|
1664 |
|
|
1665 // Reverse preconditioning step 3: repeated squaring. |
|
|
1666 |
|
|
1667 while (sqpow) |
|
|
1668 { |
|
|
1669 retval = retval * retval; |
|
|
1670 sqpow--; |
|
|
1671 } |
|
|
1672 |
|
|
1673 // Reverse preconditioning step 2: inverse balancing. |
|
|
1674 // XXX FIXME XXX -- should probably do this with Lapack calls |
|
|
1675 // instead of a complete matrix inversion. |
|
|
1676 |
|
|
1677 retval = retval.transpose (); |
|
|
1678 d = d.transpose (); |
|
|
1679 retval = retval * d; |
|
|
1680 retval = d.solve (retval); |
|
|
1681 retval = retval.transpose (); |
|
|
1682 |
|
|
1683 // Reverse preconditioning step 1: fix trace normalization. |
|
|
1684 |
|
3130
|
1685 return exp (trshift) * retval; |
|
1819
|
1686 } |
|
|
1687 |
|
1205
|
1688 // column vector by row vector -> matrix operations |
|
|
1689 |
|
|
1690 ComplexMatrix |
|
|
1691 operator * (const ColumnVector& v, const ComplexRowVector& a) |
|
|
1692 { |
|
|
1693 ComplexColumnVector tmp (v); |
|
|
1694 return tmp * a; |
|
|
1695 } |
|
|
1696 |
|
|
1697 ComplexMatrix |
|
|
1698 operator * (const ComplexColumnVector& a, const RowVector& b) |
|
|
1699 { |
|
|
1700 ComplexRowVector tmp (b); |
|
|
1701 return a * tmp; |
|
|
1702 } |
|
|
1703 |
|
|
1704 ComplexMatrix |
|
|
1705 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) |
|
|
1706 { |
|
1948
|
1707 ComplexMatrix retval; |
|
|
1708 |
|
1205
|
1709 int len = v.length (); |
|
|
1710 int a_len = a.length (); |
|
1948
|
1711 |
|
1205
|
1712 if (len != a_len) |
|
2384
|
1713 gripe_nonconformant ("operator *", len, 1, 1, a_len); |
|
1948
|
1714 else |
|
1205
|
1715 { |
|
1948
|
1716 if (len != 0) |
|
|
1717 { |
|
|
1718 retval.resize (len, a_len); |
|
|
1719 Complex *c = retval.fortran_vec (); |
|
|
1720 |
|
|
1721 F77_XFCN (zgemm, ZGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
1722 v.data (), len, a.data (), 1, 0.0, |
|
|
1723 c, len, 1L, 1L)); |
|
|
1724 |
|
|
1725 if (f77_exception_encountered) |
|
|
1726 (*current_liboctave_error_handler) |
|
|
1727 ("unrecoverable error in zgemm"); |
|
|
1728 } |
|
1205
|
1729 } |
|
|
1730 |
|
1948
|
1731 return retval; |
|
1205
|
1732 } |
|
|
1733 |
|
458
|
1734 // matrix by diagonal matrix -> matrix operations |
|
|
1735 |
|
|
1736 ComplexMatrix& |
|
|
1737 ComplexMatrix::operator += (const DiagMatrix& a) |
|
|
1738 { |
|
|
1739 int nr = rows (); |
|
|
1740 int nc = cols (); |
|
2384
|
1741 |
|
|
1742 int a_nr = rows (); |
|
|
1743 int a_nc = cols (); |
|
|
1744 |
|
|
1745 if (nr != a_nr || nc != a_nc) |
|
458
|
1746 { |
|
2384
|
1747 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
1748 return *this; |
|
458
|
1749 } |
|
|
1750 |
|
|
1751 for (int i = 0; i < a.length (); i++) |
|
|
1752 elem (i, i) += a.elem (i, i); |
|
|
1753 |
|
|
1754 return *this; |
|
|
1755 } |
|
|
1756 |
|
|
1757 ComplexMatrix& |
|
|
1758 ComplexMatrix::operator -= (const DiagMatrix& a) |
|
|
1759 { |
|
|
1760 int nr = rows (); |
|
|
1761 int nc = cols (); |
|
2384
|
1762 |
|
|
1763 int a_nr = rows (); |
|
|
1764 int a_nc = cols (); |
|
|
1765 |
|
|
1766 if (nr != a_nr || nc != a_nc) |
|
458
|
1767 { |
|
2384
|
1768 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
1769 return *this; |
|
458
|
1770 } |
|
|
1771 |
|
|
1772 for (int i = 0; i < a.length (); i++) |
|
|
1773 elem (i, i) -= a.elem (i, i); |
|
|
1774 |
|
|
1775 return *this; |
|
|
1776 } |
|
|
1777 |
|
|
1778 ComplexMatrix& |
|
|
1779 ComplexMatrix::operator += (const ComplexDiagMatrix& a) |
|
|
1780 { |
|
|
1781 int nr = rows (); |
|
|
1782 int nc = cols (); |
|
2384
|
1783 |
|
|
1784 int a_nr = rows (); |
|
|
1785 int a_nc = cols (); |
|
|
1786 |
|
|
1787 if (nr != a_nr || nc != a_nc) |
|
458
|
1788 { |
|
2384
|
1789 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
889
|
1790 return *this; |
|
458
|
1791 } |
|
|
1792 |
|
|
1793 for (int i = 0; i < a.length (); i++) |
|
|
1794 elem (i, i) += a.elem (i, i); |
|
|
1795 |
|
|
1796 return *this; |
|
|
1797 } |
|
|
1798 |
|
|
1799 ComplexMatrix& |
|
|
1800 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) |
|
|
1801 { |
|
|
1802 int nr = rows (); |
|
|
1803 int nc = cols (); |
|
2384
|
1804 |
|
|
1805 int a_nr = rows (); |
|
|
1806 int a_nc = cols (); |
|
|
1807 |
|
|
1808 if (nr != a_nr || nc != a_nc) |
|
458
|
1809 { |
|
2384
|
1810 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
889
|
1811 return *this; |
|
458
|
1812 } |
|
|
1813 |
|
|
1814 for (int i = 0; i < a.length (); i++) |
|
|
1815 elem (i, i) -= a.elem (i, i); |
|
|
1816 |
|
|
1817 return *this; |
|
|
1818 } |
|
|
1819 |
|
|
1820 // matrix by matrix -> matrix operations |
|
|
1821 |
|
|
1822 ComplexMatrix& |
|
|
1823 ComplexMatrix::operator += (const Matrix& a) |
|
|
1824 { |
|
|
1825 int nr = rows (); |
|
|
1826 int nc = cols (); |
|
2384
|
1827 |
|
|
1828 int a_nr = a.rows (); |
|
|
1829 int a_nc = a.cols (); |
|
|
1830 |
|
|
1831 if (nr != a_nr || nc != a_nc) |
|
458
|
1832 { |
|
2384
|
1833 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1834 return *this; |
|
|
1835 } |
|
|
1836 |
|
|
1837 if (nr == 0 || nc == 0) |
|
|
1838 return *this; |
|
|
1839 |
|
|
1840 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1841 |
|
|
1842 add2 (d, a.data (), length ()); |
|
|
1843 return *this; |
|
|
1844 } |
|
|
1845 |
|
|
1846 ComplexMatrix& |
|
|
1847 ComplexMatrix::operator -= (const Matrix& a) |
|
|
1848 { |
|
|
1849 int nr = rows (); |
|
|
1850 int nc = cols (); |
|
2384
|
1851 |
|
|
1852 int a_nr = a.rows (); |
|
|
1853 int a_nc = a.cols (); |
|
|
1854 |
|
|
1855 if (nr != a_nr || nc != a_nc) |
|
458
|
1856 { |
|
2384
|
1857 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1858 return *this; |
|
|
1859 } |
|
|
1860 |
|
|
1861 if (nr == 0 || nc == 0) |
|
|
1862 return *this; |
|
|
1863 |
|
|
1864 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1865 |
|
|
1866 subtract2 (d, a.data (), length ()); |
|
|
1867 return *this; |
|
|
1868 } |
|
|
1869 |
|
|
1870 ComplexMatrix& |
|
|
1871 ComplexMatrix::operator += (const ComplexMatrix& a) |
|
|
1872 { |
|
|
1873 int nr = rows (); |
|
|
1874 int nc = cols (); |
|
2384
|
1875 |
|
|
1876 int a_nr = a.rows (); |
|
|
1877 int a_nc = a.cols (); |
|
|
1878 |
|
|
1879 if (nr != a_nr || nc != a_nc) |
|
458
|
1880 { |
|
2384
|
1881 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1882 return *this; |
|
|
1883 } |
|
|
1884 |
|
|
1885 if (nr == 0 || nc == 0) |
|
|
1886 return *this; |
|
|
1887 |
|
|
1888 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1889 |
|
|
1890 add2 (d, a.data (), length ()); |
|
|
1891 return *this; |
|
|
1892 } |
|
|
1893 |
|
|
1894 ComplexMatrix& |
|
|
1895 ComplexMatrix::operator -= (const ComplexMatrix& a) |
|
|
1896 { |
|
|
1897 int nr = rows (); |
|
|
1898 int nc = cols (); |
|
2384
|
1899 |
|
|
1900 int a_nr = a.rows (); |
|
|
1901 int a_nc = a.cols (); |
|
|
1902 |
|
|
1903 if (nr != a_nr || nc != a_nc) |
|
458
|
1904 { |
|
2384
|
1905 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1906 return *this; |
|
|
1907 } |
|
|
1908 |
|
|
1909 if (nr == 0 || nc == 0) |
|
|
1910 return *this; |
|
|
1911 |
|
|
1912 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1913 |
|
|
1914 subtract2 (d, a.data (), length ()); |
|
|
1915 return *this; |
|
|
1916 } |
|
|
1917 |
|
|
1918 // unary operations |
|
|
1919 |
|
2964
|
1920 boolMatrix |
|
458
|
1921 ComplexMatrix::operator ! (void) const |
|
|
1922 { |
|
2964
|
1923 int nr = rows (); |
|
|
1924 int nc = cols (); |
|
|
1925 |
|
|
1926 boolMatrix b (nr, nc); |
|
|
1927 |
|
|
1928 for (int j = 0; j < nc; j++) |
|
|
1929 for (int i = 0; i < nr; i++) |
|
|
1930 b.elem (i, j) = elem (i, j) != 0.0; |
|
|
1931 |
|
|
1932 return b; |
|
458
|
1933 } |
|
|
1934 |
|
|
1935 // other operations |
|
|
1936 |
|
|
1937 ComplexMatrix |
|
2676
|
1938 ComplexMatrix::map (c_c_Mapper f) const |
|
458
|
1939 { |
|
2676
|
1940 ComplexMatrix b (*this); |
|
|
1941 return b.apply (f); |
|
458
|
1942 } |
|
|
1943 |
|
2676
|
1944 Matrix |
|
|
1945 ComplexMatrix::map (d_c_Mapper f) const |
|
458
|
1946 { |
|
2676
|
1947 const Complex *d = data (); |
|
|
1948 |
|
|
1949 Matrix retval (rows (), columns ()); |
|
|
1950 |
|
|
1951 double *r = retval.fortran_vec (); |
|
|
1952 |
|
|
1953 for (int i = 0; i < length (); i++) |
|
|
1954 r[i] = f (d[i]); |
|
|
1955 |
|
|
1956 return retval; |
|
|
1957 } |
|
|
1958 |
|
|
1959 ComplexMatrix& |
|
|
1960 ComplexMatrix::apply (c_c_Mapper f) |
|
|
1961 { |
|
|
1962 Complex *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1963 |
|
|
1964 for (int i = 0; i < length (); i++) |
|
|
1965 d[i] = f (d[i]); |
|
|
1966 |
|
|
1967 return *this; |
|
458
|
1968 } |
|
|
1969 |
|
2384
|
1970 bool |
|
|
1971 ComplexMatrix::any_element_is_inf_or_nan (void) const |
|
|
1972 { |
|
|
1973 int nr = rows (); |
|
|
1974 int nc = cols (); |
|
|
1975 |
|
|
1976 for (int j = 0; j < nc; j++) |
|
|
1977 for (int i = 0; i < nr; i++) |
|
|
1978 { |
|
|
1979 Complex val = elem (i, j); |
|
|
1980 if (xisinf (val) || xisnan (val)) |
|
|
1981 return true; |
|
|
1982 } |
|
|
1983 |
|
|
1984 return false; |
|
|
1985 } |
|
|
1986 |
|
2408
|
1987 // Return true if no elements have imaginary components. |
|
|
1988 |
|
|
1989 bool |
|
|
1990 ComplexMatrix::all_elements_are_real (void) const |
|
|
1991 { |
|
|
1992 int nr = rows (); |
|
|
1993 int nc = cols (); |
|
|
1994 |
|
|
1995 for (int j = 0; j < nc; j++) |
|
|
1996 for (int i = 0; i < nr; i++) |
|
|
1997 if (imag (elem (i, j)) != 0.0) |
|
|
1998 return false; |
|
|
1999 |
|
|
2000 return true; |
|
|
2001 } |
|
|
2002 |
|
1968
|
2003 // Return nonzero if any element of CM has a non-integer real or |
|
|
2004 // imaginary part. Also extract the largest and smallest (real or |
|
|
2005 // imaginary) values and return them in MAX_VAL and MIN_VAL. |
|
|
2006 |
|
2384
|
2007 bool |
|
1968
|
2008 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
|
|
2009 { |
|
|
2010 int nr = rows (); |
|
2384
|
2011 int nc = cols (); |
|
1968
|
2012 |
|
|
2013 if (nr > 0 && nc > 0) |
|
|
2014 { |
|
|
2015 Complex val = elem (0, 0); |
|
|
2016 |
|
|
2017 double r_val = real (val); |
|
|
2018 double i_val = imag (val); |
|
|
2019 |
|
|
2020 max_val = r_val; |
|
|
2021 min_val = r_val; |
|
|
2022 |
|
|
2023 if (i_val > max_val) |
|
|
2024 max_val = i_val; |
|
|
2025 |
|
|
2026 if (i_val < max_val) |
|
|
2027 min_val = i_val; |
|
|
2028 } |
|
|
2029 else |
|
2384
|
2030 return false; |
|
1968
|
2031 |
|
|
2032 for (int j = 0; j < nc; j++) |
|
|
2033 for (int i = 0; i < nr; i++) |
|
|
2034 { |
|
|
2035 Complex val = elem (i, j); |
|
|
2036 |
|
|
2037 double r_val = real (val); |
|
|
2038 double i_val = imag (val); |
|
|
2039 |
|
|
2040 if (r_val > max_val) |
|
|
2041 max_val = r_val; |
|
|
2042 |
|
|
2043 if (i_val > max_val) |
|
|
2044 max_val = i_val; |
|
|
2045 |
|
|
2046 if (r_val < min_val) |
|
|
2047 min_val = r_val; |
|
|
2048 |
|
|
2049 if (i_val < min_val) |
|
|
2050 min_val = i_val; |
|
|
2051 |
|
|
2052 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) |
|
2384
|
2053 return false; |
|
1968
|
2054 } |
|
2384
|
2055 |
|
|
2056 return true; |
|
1968
|
2057 } |
|
|
2058 |
|
2384
|
2059 bool |
|
1968
|
2060 ComplexMatrix::too_large_for_float (void) const |
|
|
2061 { |
|
|
2062 int nr = rows (); |
|
2384
|
2063 int nc = cols (); |
|
1968
|
2064 |
|
|
2065 for (int j = 0; j < nc; j++) |
|
|
2066 for (int i = 0; i < nr; i++) |
|
|
2067 { |
|
|
2068 Complex val = elem (i, j); |
|
|
2069 |
|
|
2070 double r_val = real (val); |
|
|
2071 double i_val = imag (val); |
|
|
2072 |
|
|
2073 if (r_val > FLT_MAX |
|
|
2074 || i_val > FLT_MAX |
|
|
2075 || r_val < FLT_MIN |
|
|
2076 || i_val < FLT_MIN) |
|
2384
|
2077 return true; |
|
1968
|
2078 } |
|
|
2079 |
|
2384
|
2080 return false; |
|
1968
|
2081 } |
|
|
2082 |
|
2832
|
2083 boolMatrix |
|
458
|
2084 ComplexMatrix::all (void) const |
|
|
2085 { |
|
|
2086 int nr = rows (); |
|
|
2087 int nc = cols (); |
|
2832
|
2088 boolMatrix retval; |
|
458
|
2089 if (nr > 0 && nc > 0) |
|
|
2090 { |
|
|
2091 if (nr == 1) |
|
|
2092 { |
|
|
2093 retval.resize (1, 1); |
|
2832
|
2094 retval.elem (0, 0) = true; |
|
458
|
2095 for (int j = 0; j < nc; j++) |
|
|
2096 { |
|
|
2097 if (elem (0, j) == 0.0) |
|
|
2098 { |
|
2832
|
2099 retval.elem (0, 0) = false; |
|
458
|
2100 break; |
|
|
2101 } |
|
|
2102 } |
|
|
2103 } |
|
|
2104 else if (nc == 1) |
|
|
2105 { |
|
|
2106 retval.resize (1, 1); |
|
2832
|
2107 retval.elem (0, 0) = true; |
|
458
|
2108 for (int i = 0; i < nr; i++) |
|
|
2109 { |
|
|
2110 if (elem (i, 0) == 0.0) |
|
|
2111 { |
|
2832
|
2112 retval.elem (0, 0) = false; |
|
458
|
2113 break; |
|
|
2114 } |
|
|
2115 } |
|
|
2116 } |
|
|
2117 else |
|
|
2118 { |
|
|
2119 retval.resize (1, nc); |
|
|
2120 for (int j = 0; j < nc; j++) |
|
|
2121 { |
|
2832
|
2122 retval.elem (0, j) = true; |
|
458
|
2123 for (int i = 0; i < nr; i++) |
|
|
2124 { |
|
|
2125 if (elem (i, j) == 0.0) |
|
|
2126 { |
|
2832
|
2127 retval.elem (0, j) = false; |
|
458
|
2128 break; |
|
|
2129 } |
|
|
2130 } |
|
|
2131 } |
|
|
2132 } |
|
|
2133 } |
|
|
2134 return retval; |
|
|
2135 } |
|
|
2136 |
|
2832
|
2137 boolMatrix |
|
458
|
2138 ComplexMatrix::any (void) const |
|
|
2139 { |
|
|
2140 int nr = rows (); |
|
|
2141 int nc = cols (); |
|
2832
|
2142 boolMatrix retval; |
|
458
|
2143 if (nr > 0 && nc > 0) |
|
|
2144 { |
|
|
2145 if (nr == 1) |
|
|
2146 { |
|
|
2147 retval.resize (1, 1); |
|
2832
|
2148 retval.elem (0, 0) = false; |
|
458
|
2149 for (int j = 0; j < nc; j++) |
|
|
2150 { |
|
|
2151 if (elem (0, j) != 0.0) |
|
|
2152 { |
|
2832
|
2153 retval.elem (0, 0) = true; |
|
458
|
2154 break; |
|
|
2155 } |
|
|
2156 } |
|
|
2157 } |
|
|
2158 else if (nc == 1) |
|
|
2159 { |
|
|
2160 retval.resize (1, 1); |
|
2832
|
2161 retval.elem (0, 0) = false; |
|
458
|
2162 for (int i = 0; i < nr; i++) |
|
|
2163 { |
|
|
2164 if (elem (i, 0) != 0.0) |
|
|
2165 { |
|
2832
|
2166 retval.elem (0, 0) = true; |
|
458
|
2167 break; |
|
|
2168 } |
|
|
2169 } |
|
|
2170 } |
|
|
2171 else |
|
|
2172 { |
|
|
2173 retval.resize (1, nc); |
|
|
2174 for (int j = 0; j < nc; j++) |
|
|
2175 { |
|
2832
|
2176 retval.elem (0, j) = false; |
|
458
|
2177 for (int i = 0; i < nr; i++) |
|
|
2178 { |
|
|
2179 if (elem (i, j) != 0.0) |
|
|
2180 { |
|
2832
|
2181 retval.elem (0, j) = true; |
|
458
|
2182 break; |
|
|
2183 } |
|
|
2184 } |
|
|
2185 } |
|
|
2186 } |
|
|
2187 } |
|
|
2188 return retval; |
|
|
2189 } |
|
|
2190 |
|
|
2191 ComplexMatrix |
|
|
2192 ComplexMatrix::cumprod (void) const |
|
|
2193 { |
|
|
2194 int nr = rows (); |
|
|
2195 int nc = cols (); |
|
|
2196 ComplexMatrix retval; |
|
|
2197 if (nr > 0 && nc > 0) |
|
|
2198 { |
|
|
2199 if (nr == 1) |
|
|
2200 { |
|
|
2201 retval.resize (1, nc); |
|
|
2202 Complex prod = elem (0, 0); |
|
|
2203 for (int j = 0; j < nc; j++) |
|
|
2204 { |
|
|
2205 retval.elem (0, j) = prod; |
|
|
2206 if (j < nc - 1) |
|
|
2207 prod *= elem (0, j+1); |
|
|
2208 } |
|
|
2209 } |
|
|
2210 else if (nc == 1) |
|
|
2211 { |
|
|
2212 retval.resize (nr, 1); |
|
|
2213 Complex prod = elem (0, 0); |
|
|
2214 for (int i = 0; i < nr; i++) |
|
|
2215 { |
|
|
2216 retval.elem (i, 0) = prod; |
|
|
2217 if (i < nr - 1) |
|
|
2218 prod *= elem (i+1, 0); |
|
|
2219 } |
|
|
2220 } |
|
|
2221 else |
|
|
2222 { |
|
|
2223 retval.resize (nr, nc); |
|
|
2224 for (int j = 0; j < nc; j++) |
|
|
2225 { |
|
|
2226 Complex prod = elem (0, j); |
|
|
2227 for (int i = 0; i < nr; i++) |
|
|
2228 { |
|
|
2229 retval.elem (i, j) = prod; |
|
|
2230 if (i < nr - 1) |
|
|
2231 prod *= elem (i+1, j); |
|
|
2232 } |
|
|
2233 } |
|
|
2234 } |
|
|
2235 } |
|
|
2236 return retval; |
|
|
2237 } |
|
|
2238 |
|
|
2239 ComplexMatrix |
|
|
2240 ComplexMatrix::cumsum (void) const |
|
|
2241 { |
|
|
2242 int nr = rows (); |
|
|
2243 int nc = cols (); |
|
|
2244 ComplexMatrix retval; |
|
|
2245 if (nr > 0 && nc > 0) |
|
|
2246 { |
|
|
2247 if (nr == 1) |
|
|
2248 { |
|
|
2249 retval.resize (1, nc); |
|
|
2250 Complex sum = elem (0, 0); |
|
|
2251 for (int j = 0; j < nc; j++) |
|
|
2252 { |
|
|
2253 retval.elem (0, j) = sum; |
|
|
2254 if (j < nc - 1) |
|
|
2255 sum += elem (0, j+1); |
|
|
2256 } |
|
|
2257 } |
|
|
2258 else if (nc == 1) |
|
|
2259 { |
|
|
2260 retval.resize (nr, 1); |
|
|
2261 Complex sum = elem (0, 0); |
|
|
2262 for (int i = 0; i < nr; i++) |
|
|
2263 { |
|
|
2264 retval.elem (i, 0) = sum; |
|
|
2265 if (i < nr - 1) |
|
|
2266 sum += elem (i+1, 0); |
|
|
2267 } |
|
|
2268 } |
|
|
2269 else |
|
|
2270 { |
|
|
2271 retval.resize (nr, nc); |
|
|
2272 for (int j = 0; j < nc; j++) |
|
|
2273 { |
|
|
2274 Complex sum = elem (0, j); |
|
|
2275 for (int i = 0; i < nr; i++) |
|
|
2276 { |
|
|
2277 retval.elem (i, j) = sum; |
|
|
2278 if (i < nr - 1) |
|
|
2279 sum += elem (i+1, j); |
|
|
2280 } |
|
|
2281 } |
|
|
2282 } |
|
|
2283 } |
|
|
2284 return retval; |
|
|
2285 } |
|
|
2286 |
|
|
2287 ComplexMatrix |
|
|
2288 ComplexMatrix::prod (void) const |
|
|
2289 { |
|
|
2290 int nr = rows (); |
|
|
2291 int nc = cols (); |
|
|
2292 ComplexMatrix retval; |
|
|
2293 if (nr > 0 && nc > 0) |
|
|
2294 { |
|
|
2295 if (nr == 1) |
|
|
2296 { |
|
|
2297 retval.resize (1, 1); |
|
|
2298 retval.elem (0, 0) = 1.0; |
|
|
2299 for (int j = 0; j < nc; j++) |
|
|
2300 retval.elem (0, 0) *= elem (0, j); |
|
|
2301 } |
|
|
2302 else if (nc == 1) |
|
|
2303 { |
|
|
2304 retval.resize (1, 1); |
|
|
2305 retval.elem (0, 0) = 1.0; |
|
|
2306 for (int i = 0; i < nr; i++) |
|
|
2307 retval.elem (0, 0) *= elem (i, 0); |
|
|
2308 } |
|
|
2309 else |
|
|
2310 { |
|
|
2311 retval.resize (1, nc); |
|
|
2312 for (int j = 0; j < nc; j++) |
|
|
2313 { |
|
|
2314 retval.elem (0, j) = 1.0; |
|
|
2315 for (int i = 0; i < nr; i++) |
|
|
2316 retval.elem (0, j) *= elem (i, j); |
|
|
2317 } |
|
|
2318 } |
|
|
2319 } |
|
|
2320 return retval; |
|
|
2321 } |
|
|
2322 |
|
|
2323 ComplexMatrix |
|
|
2324 ComplexMatrix::sum (void) const |
|
|
2325 { |
|
|
2326 int nr = rows (); |
|
|
2327 int nc = cols (); |
|
|
2328 ComplexMatrix retval; |
|
|
2329 if (nr > 0 && nc > 0) |
|
|
2330 { |
|
|
2331 if (nr == 1) |
|
|
2332 { |
|
|
2333 retval.resize (1, 1); |
|
|
2334 retval.elem (0, 0) = 0.0; |
|
|
2335 for (int j = 0; j < nc; j++) |
|
|
2336 retval.elem (0, 0) += elem (0, j); |
|
|
2337 } |
|
|
2338 else if (nc == 1) |
|
|
2339 { |
|
|
2340 retval.resize (1, 1); |
|
|
2341 retval.elem (0, 0) = 0.0; |
|
|
2342 for (int i = 0; i < nr; i++) |
|
|
2343 retval.elem (0, 0) += elem (i, 0); |
|
|
2344 } |
|
|
2345 else |
|
|
2346 { |
|
|
2347 retval.resize (1, nc); |
|
|
2348 for (int j = 0; j < nc; j++) |
|
|
2349 { |
|
|
2350 retval.elem (0, j) = 0.0; |
|
|
2351 for (int i = 0; i < nr; i++) |
|
|
2352 retval.elem (0, j) += elem (i, j); |
|
|
2353 } |
|
|
2354 } |
|
|
2355 } |
|
|
2356 return retval; |
|
|
2357 } |
|
|
2358 |
|
|
2359 ComplexMatrix |
|
|
2360 ComplexMatrix::sumsq (void) const |
|
|
2361 { |
|
|
2362 int nr = rows (); |
|
|
2363 int nc = cols (); |
|
|
2364 ComplexMatrix retval; |
|
|
2365 if (nr > 0 && nc > 0) |
|
|
2366 { |
|
|
2367 if (nr == 1) |
|
|
2368 { |
|
|
2369 retval.resize (1, 1); |
|
|
2370 retval.elem (0, 0) = 0.0; |
|
|
2371 for (int j = 0; j < nc; j++) |
|
|
2372 { |
|
|
2373 Complex d = elem (0, j); |
|
3095
|
2374 retval.elem (0, 0) += d * conj (d); |
|
458
|
2375 } |
|
|
2376 } |
|
|
2377 else if (nc == 1) |
|
|
2378 { |
|
|
2379 retval.resize (1, 1); |
|
|
2380 retval.elem (0, 0) = 0.0; |
|
|
2381 for (int i = 0; i < nr; i++) |
|
|
2382 { |
|
|
2383 Complex d = elem (i, 0); |
|
3095
|
2384 retval.elem (0, 0) += d * conj (d); |
|
458
|
2385 } |
|
|
2386 } |
|
|
2387 else |
|
|
2388 { |
|
|
2389 retval.resize (1, nc); |
|
|
2390 for (int j = 0; j < nc; j++) |
|
|
2391 { |
|
|
2392 retval.elem (0, j) = 0.0; |
|
|
2393 for (int i = 0; i < nr; i++) |
|
|
2394 { |
|
|
2395 Complex d = elem (i, j); |
|
3095
|
2396 retval.elem (0, j) += d * conj (d); |
|
458
|
2397 } |
|
|
2398 } |
|
|
2399 } |
|
|
2400 } |
|
|
2401 return retval; |
|
|
2402 } |
|
|
2403 |
|
|
2404 ComplexColumnVector |
|
|
2405 ComplexMatrix::diag (void) const |
|
|
2406 { |
|
|
2407 return diag (0); |
|
|
2408 } |
|
|
2409 |
|
|
2410 ComplexColumnVector |
|
|
2411 ComplexMatrix::diag (int k) const |
|
|
2412 { |
|
|
2413 int nnr = rows (); |
|
|
2414 int nnc = cols (); |
|
|
2415 if (k > 0) |
|
|
2416 nnc -= k; |
|
|
2417 else if (k < 0) |
|
|
2418 nnr += k; |
|
|
2419 |
|
|
2420 ComplexColumnVector d; |
|
|
2421 |
|
|
2422 if (nnr > 0 && nnc > 0) |
|
|
2423 { |
|
|
2424 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2425 |
|
|
2426 d.resize (ndiag); |
|
|
2427 |
|
|
2428 if (k > 0) |
|
|
2429 { |
|
|
2430 for (int i = 0; i < ndiag; i++) |
|
|
2431 d.elem (i) = elem (i, i+k); |
|
|
2432 } |
|
|
2433 else if ( k < 0) |
|
|
2434 { |
|
|
2435 for (int i = 0; i < ndiag; i++) |
|
|
2436 d.elem (i) = elem (i-k, i); |
|
|
2437 } |
|
|
2438 else |
|
|
2439 { |
|
|
2440 for (int i = 0; i < ndiag; i++) |
|
|
2441 d.elem (i) = elem (i, i); |
|
|
2442 } |
|
|
2443 } |
|
|
2444 else |
|
|
2445 cerr << "diag: requested diagonal out of range\n"; |
|
|
2446 |
|
|
2447 return d; |
|
|
2448 } |
|
|
2449 |
|
2354
|
2450 bool |
|
|
2451 ComplexMatrix::row_is_real_only (int i) const |
|
|
2452 { |
|
|
2453 bool retval = true; |
|
|
2454 |
|
|
2455 int nc = columns (); |
|
|
2456 |
|
|
2457 for (int j = 0; j < nc; j++) |
|
|
2458 { |
|
|
2459 if (imag (elem (i, j)) != 0.0) |
|
|
2460 { |
|
|
2461 retval = false; |
|
|
2462 break; |
|
|
2463 } |
|
|
2464 } |
|
|
2465 |
|
|
2466 return retval; |
|
|
2467 } |
|
|
2468 |
|
|
2469 bool |
|
|
2470 ComplexMatrix::column_is_real_only (int j) const |
|
|
2471 { |
|
|
2472 bool retval = true; |
|
|
2473 |
|
|
2474 int nr = rows (); |
|
|
2475 |
|
|
2476 for (int i = 0; i < nr; i++) |
|
|
2477 { |
|
|
2478 if (imag (elem (i, j)) != 0.0) |
|
|
2479 { |
|
|
2480 retval = false; |
|
|
2481 break; |
|
|
2482 } |
|
|
2483 } |
|
|
2484 |
|
|
2485 return retval; |
|
|
2486 } |
|
891
|
2487 |
|
458
|
2488 ComplexColumnVector |
|
|
2489 ComplexMatrix::row_min (void) const |
|
|
2490 { |
|
2354
|
2491 Array<int> index; |
|
|
2492 return row_min (index); |
|
458
|
2493 } |
|
|
2494 |
|
|
2495 ComplexColumnVector |
|
2354
|
2496 ComplexMatrix::row_min (Array<int>& index) const |
|
458
|
2497 { |
|
|
2498 ComplexColumnVector result; |
|
|
2499 |
|
|
2500 int nr = rows (); |
|
|
2501 int nc = cols (); |
|
|
2502 |
|
|
2503 if (nr > 0 && nc > 0) |
|
|
2504 { |
|
|
2505 result.resize (nr); |
|
2354
|
2506 index.resize (nr); |
|
458
|
2507 |
|
|
2508 for (int i = 0; i < nr; i++) |
|
|
2509 { |
|
2354
|
2510 int idx = 0; |
|
|
2511 |
|
|
2512 Complex tmp_min = elem (i, idx); |
|
|
2513 |
|
|
2514 bool real_only = row_is_real_only (i); |
|
|
2515 |
|
|
2516 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2517 |
|
|
2518 if (xisnan (tmp_min)) |
|
|
2519 idx = -1; |
|
891
|
2520 else |
|
|
2521 { |
|
|
2522 for (int j = 1; j < nc; j++) |
|
2354
|
2523 { |
|
|
2524 Complex tmp = elem (i, j); |
|
|
2525 |
|
|
2526 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2527 |
|
|
2528 if (xisnan (tmp)) |
|
|
2529 { |
|
|
2530 idx = -1; |
|
|
2531 break; |
|
|
2532 } |
|
|
2533 else if (abs_tmp < abs_min) |
|
|
2534 { |
|
|
2535 idx = j; |
|
|
2536 tmp_min = tmp; |
|
|
2537 abs_min = abs_tmp; |
|
|
2538 } |
|
|
2539 } |
|
|
2540 |
|
|
2541 result.elem (i) = (idx < 0) ? Complex_NaN_result : tmp_min; |
|
|
2542 index.elem (i) = idx; |
|
891
|
2543 } |
|
458
|
2544 } |
|
|
2545 } |
|
|
2546 |
|
|
2547 return result; |
|
|
2548 } |
|
|
2549 |
|
|
2550 ComplexColumnVector |
|
|
2551 ComplexMatrix::row_max (void) const |
|
|
2552 { |
|
2354
|
2553 Array<int> index; |
|
|
2554 return row_max (index); |
|
458
|
2555 } |
|
|
2556 |
|
|
2557 ComplexColumnVector |
|
2354
|
2558 ComplexMatrix::row_max (Array<int>& index) const |
|
458
|
2559 { |
|
|
2560 ComplexColumnVector result; |
|
|
2561 |
|
|
2562 int nr = rows (); |
|
|
2563 int nc = cols (); |
|
|
2564 |
|
|
2565 if (nr > 0 && nc > 0) |
|
|
2566 { |
|
|
2567 result.resize (nr); |
|
2354
|
2568 index.resize (nr); |
|
458
|
2569 |
|
|
2570 for (int i = 0; i < nr; i++) |
|
|
2571 { |
|
2354
|
2572 int idx = 0; |
|
|
2573 |
|
|
2574 Complex tmp_max = elem (i, idx); |
|
|
2575 |
|
|
2576 bool real_only = row_is_real_only (i); |
|
|
2577 |
|
|
2578 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2579 |
|
|
2580 if (xisnan (tmp_max)) |
|
|
2581 idx = -1; |
|
891
|
2582 else |
|
|
2583 { |
|
|
2584 for (int j = 1; j < nc; j++) |
|
2354
|
2585 { |
|
|
2586 Complex tmp = elem (i, j); |
|
|
2587 |
|
|
2588 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2589 |
|
|
2590 if (xisnan (tmp)) |
|
|
2591 { |
|
|
2592 idx = -1; |
|
|
2593 break; |
|
|
2594 } |
|
|
2595 else if (abs_tmp > abs_max) |
|
|
2596 { |
|
|
2597 idx = j; |
|
|
2598 tmp_max = tmp; |
|
|
2599 abs_max = abs_tmp; |
|
|
2600 } |
|
|
2601 } |
|
|
2602 |
|
|
2603 result.elem (i) = (idx < 0) ? Complex_NaN_result : tmp_max; |
|
|
2604 index.elem (i) = idx; |
|
891
|
2605 } |
|
458
|
2606 } |
|
|
2607 } |
|
|
2608 |
|
|
2609 return result; |
|
|
2610 } |
|
|
2611 |
|
|
2612 ComplexRowVector |
|
|
2613 ComplexMatrix::column_min (void) const |
|
|
2614 { |
|
2354
|
2615 Array<int> index; |
|
|
2616 return column_min (index); |
|
458
|
2617 } |
|
|
2618 |
|
|
2619 ComplexRowVector |
|
2354
|
2620 ComplexMatrix::column_min (Array<int>& index) const |
|
458
|
2621 { |
|
|
2622 ComplexRowVector result; |
|
|
2623 |
|
|
2624 int nr = rows (); |
|
|
2625 int nc = cols (); |
|
|
2626 |
|
|
2627 if (nr > 0 && nc > 0) |
|
|
2628 { |
|
|
2629 result.resize (nc); |
|
2354
|
2630 index.resize (nc); |
|
458
|
2631 |
|
|
2632 for (int j = 0; j < nc; j++) |
|
|
2633 { |
|
2354
|
2634 int idx = 0; |
|
|
2635 |
|
|
2636 Complex tmp_min = elem (idx, j); |
|
|
2637 |
|
|
2638 bool real_only = column_is_real_only (j); |
|
|
2639 |
|
|
2640 double abs_min = real_only ? real (tmp_min) : abs (tmp_min); |
|
|
2641 |
|
|
2642 if (xisnan (tmp_min)) |
|
|
2643 idx = -1; |
|
891
|
2644 else |
|
|
2645 { |
|
|
2646 for (int i = 1; i < nr; i++) |
|
2354
|
2647 { |
|
|
2648 Complex tmp = elem (i, j); |
|
|
2649 |
|
|
2650 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2651 |
|
|
2652 if (xisnan (tmp)) |
|
|
2653 { |
|
|
2654 idx = -1; |
|
|
2655 break; |
|
|
2656 } |
|
|
2657 else if (abs_tmp < abs_min) |
|
|
2658 { |
|
|
2659 idx = i; |
|
|
2660 tmp_min = tmp; |
|
|
2661 abs_min = abs_tmp; |
|
|
2662 } |
|
|
2663 } |
|
|
2664 |
|
|
2665 result.elem (j) = (idx < 0) ? Complex_NaN_result : tmp_min; |
|
|
2666 index.elem (j) = idx; |
|
891
|
2667 } |
|
458
|
2668 } |
|
|
2669 } |
|
|
2670 |
|
|
2671 return result; |
|
|
2672 } |
|
|
2673 |
|
|
2674 ComplexRowVector |
|
|
2675 ComplexMatrix::column_max (void) const |
|
|
2676 { |
|
2354
|
2677 Array<int> index; |
|
|
2678 return column_max (index); |
|
458
|
2679 } |
|
|
2680 |
|
|
2681 ComplexRowVector |
|
2354
|
2682 ComplexMatrix::column_max (Array<int>& index) const |
|
458
|
2683 { |
|
|
2684 ComplexRowVector result; |
|
|
2685 |
|
|
2686 int nr = rows (); |
|
|
2687 int nc = cols (); |
|
|
2688 |
|
|
2689 if (nr > 0 && nc > 0) |
|
|
2690 { |
|
|
2691 result.resize (nc); |
|
2354
|
2692 index.resize (nc); |
|
458
|
2693 |
|
|
2694 for (int j = 0; j < nc; j++) |
|
|
2695 { |
|
2354
|
2696 int idx = 0; |
|
|
2697 |
|
|
2698 Complex tmp_max = elem (idx, j); |
|
|
2699 |
|
|
2700 bool real_only = column_is_real_only (j); |
|
|
2701 |
|
|
2702 double abs_max = real_only ? real (tmp_max) : abs (tmp_max); |
|
|
2703 |
|
|
2704 if (xisnan (tmp_max)) |
|
|
2705 idx = -1; |
|
891
|
2706 else |
|
|
2707 { |
|
|
2708 for (int i = 1; i < nr; i++) |
|
2354
|
2709 { |
|
|
2710 Complex tmp = elem (i, j); |
|
|
2711 |
|
|
2712 double abs_tmp = real_only ? real (tmp) : abs (tmp); |
|
|
2713 |
|
|
2714 if (xisnan (tmp)) |
|
|
2715 { |
|
|
2716 idx = -1; |
|
|
2717 break; |
|
|
2718 } |
|
|
2719 else if (abs_tmp > abs_max) |
|
|
2720 { |
|
|
2721 idx = i; |
|
|
2722 tmp_max = tmp; |
|
|
2723 abs_max = abs_tmp; |
|
|
2724 } |
|
|
2725 } |
|
|
2726 |
|
|
2727 result.elem (j) = (idx < 0) ? Complex_NaN_result : tmp_max; |
|
|
2728 index.elem (j) = idx; |
|
891
|
2729 } |
|
458
|
2730 } |
|
|
2731 } |
|
|
2732 |
|
|
2733 return result; |
|
|
2734 } |
|
|
2735 |
|
|
2736 // i/o |
|
|
2737 |
|
|
2738 ostream& |
|
|
2739 operator << (ostream& os, const ComplexMatrix& a) |
|
|
2740 { |
|
|
2741 // int field_width = os.precision () + 7; |
|
|
2742 for (int i = 0; i < a.rows (); i++) |
|
|
2743 { |
|
|
2744 for (int j = 0; j < a.cols (); j++) |
|
|
2745 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2746 os << "\n"; |
|
|
2747 } |
|
|
2748 return os; |
|
|
2749 } |
|
|
2750 |
|
|
2751 istream& |
|
|
2752 operator >> (istream& is, ComplexMatrix& a) |
|
|
2753 { |
|
|
2754 int nr = a.rows (); |
|
|
2755 int nc = a.cols (); |
|
|
2756 |
|
|
2757 if (nr < 1 || nc < 1) |
|
|
2758 is.clear (ios::badbit); |
|
|
2759 else |
|
|
2760 { |
|
|
2761 Complex tmp; |
|
|
2762 for (int i = 0; i < nr; i++) |
|
|
2763 for (int j = 0; j < nc; j++) |
|
|
2764 { |
|
|
2765 is >> tmp; |
|
|
2766 if (is) |
|
|
2767 a.elem (i, j) = tmp; |
|
|
2768 else |
|
2993
|
2769 goto done; |
|
458
|
2770 } |
|
|
2771 } |
|
|
2772 |
|
2993
|
2773 done: |
|
|
2774 |
|
458
|
2775 return is; |
|
|
2776 } |
|
|
2777 |
|
1819
|
2778 ComplexMatrix |
|
|
2779 Givens (const Complex& x, const Complex& y) |
|
|
2780 { |
|
|
2781 double cc; |
|
|
2782 Complex cs, temp_r; |
|
|
2783 |
|
|
2784 F77_FCN (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
|
|
2785 |
|
|
2786 ComplexMatrix g (2, 2); |
|
|
2787 |
|
|
2788 g.elem (0, 0) = cc; |
|
|
2789 g.elem (1, 1) = cc; |
|
|
2790 g.elem (0, 1) = cs; |
|
|
2791 g.elem (1, 0) = -conj (cs); |
|
|
2792 |
|
|
2793 return g; |
|
|
2794 } |
|
|
2795 |
|
|
2796 ComplexMatrix |
|
|
2797 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, |
|
|
2798 const ComplexMatrix& c) |
|
|
2799 { |
|
|
2800 ComplexMatrix retval; |
|
|
2801 |
|
|
2802 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2803 // size. |
|
|
2804 |
|
|
2805 // Compute Schur decompositions |
|
|
2806 |
|
|
2807 ComplexSCHUR as (a, "U"); |
|
|
2808 ComplexSCHUR bs (b, "U"); |
|
|
2809 |
|
|
2810 // Transform c to new coordinates. |
|
|
2811 |
|
|
2812 ComplexMatrix ua = as.unitary_matrix (); |
|
|
2813 ComplexMatrix sch_a = as.schur_matrix (); |
|
|
2814 |
|
|
2815 ComplexMatrix ub = bs.unitary_matrix (); |
|
|
2816 ComplexMatrix sch_b = bs.schur_matrix (); |
|
|
2817 |
|
|
2818 ComplexMatrix cx = ua.hermitian () * c * ub; |
|
|
2819 |
|
|
2820 // Solve the sylvester equation, back-transform, and return the |
|
|
2821 // solution. |
|
|
2822 |
|
|
2823 int a_nr = a.rows (); |
|
|
2824 int b_nr = b.rows (); |
|
|
2825 |
|
|
2826 double scale; |
|
|
2827 int info; |
|
1950
|
2828 |
|
|
2829 Complex *pa = sch_a.fortran_vec (); |
|
|
2830 Complex *pb = sch_b.fortran_vec (); |
|
|
2831 Complex *px = cx.fortran_vec (); |
|
1819
|
2832 |
|
1950
|
2833 F77_XFCN (ztrsyl, ZTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2834 b_nr, px, a_nr, scale, |
|
|
2835 info, 1L, 1L)); |
|
|
2836 |
|
|
2837 if (f77_exception_encountered) |
|
|
2838 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); |
|
|
2839 else |
|
|
2840 { |
|
|
2841 // XXX FIXME XXX -- check info? |
|
|
2842 |
|
|
2843 retval = -ua * cx * ub.hermitian (); |
|
|
2844 } |
|
1819
|
2845 |
|
|
2846 return retval; |
|
|
2847 } |
|
|
2848 |
|
2828
|
2849 ComplexMatrix |
|
|
2850 operator * (const ComplexMatrix& m, const Matrix& a) |
|
|
2851 { |
|
|
2852 ComplexMatrix tmp (a); |
|
|
2853 return m * tmp; |
|
|
2854 } |
|
|
2855 |
|
|
2856 ComplexMatrix |
|
|
2857 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
2858 { |
|
|
2859 ComplexMatrix tmp (m); |
|
|
2860 return tmp * a; |
|
|
2861 } |
|
|
2862 |
|
|
2863 ComplexMatrix |
|
|
2864 operator * (const ComplexMatrix& m, const ComplexMatrix& a) |
|
|
2865 { |
|
|
2866 ComplexMatrix retval; |
|
|
2867 |
|
|
2868 int nr = m.rows (); |
|
|
2869 int nc = m.cols (); |
|
|
2870 |
|
|
2871 int a_nr = a.rows (); |
|
|
2872 int a_nc = a.cols (); |
|
|
2873 |
|
|
2874 if (nc != a_nr) |
|
|
2875 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2876 else |
|
|
2877 { |
|
|
2878 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2879 retval.resize (nr, nc, 0.0); |
|
|
2880 else |
|
|
2881 { |
|
|
2882 int ld = nr; |
|
|
2883 int lda = a.rows (); |
|
|
2884 |
|
|
2885 retval.resize (nr, a_nc); |
|
|
2886 Complex *c = retval.fortran_vec (); |
|
|
2887 |
|
|
2888 F77_XFCN (zgemm, ZGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
2889 m.data (), ld, a.data (), lda, 0.0, |
|
|
2890 c, nr, 1L, 1L)); |
|
|
2891 |
|
|
2892 if (f77_exception_encountered) |
|
|
2893 (*current_liboctave_error_handler) |
|
|
2894 ("unrecoverable error in zgemm"); |
|
|
2895 } |
|
|
2896 } |
|
|
2897 |
|
|
2898 return retval; |
|
|
2899 } |
|
|
2900 |
|
2870
|
2901 MS_CMP_OPS(ComplexMatrix, real, Complex, real) |
|
|
2902 MS_BOOL_OPS(ComplexMatrix, Complex) |
|
|
2903 |
|
|
2904 SM_CMP_OPS(Complex, real, ComplexMatrix, real) |
|
|
2905 SM_BOOL_OPS(Complex, ComplexMatrix) |
|
|
2906 |
|
|
2907 MM_CMP_OPS(ComplexMatrix, real, ComplexMatrix, real) |
|
|
2908 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix) |
|
|
2909 |
|
458
|
2910 /* |
|
|
2911 ;;; Local Variables: *** |
|
|
2912 ;;; mode: C++ *** |
|
|
2913 ;;; End: *** |
|
|
2914 */ |
