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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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3503
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34 #include <iostream> |
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1367
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35 |
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2317
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36 #include "byte-swap.h" |
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2828
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37 #include "dMatrix.h" |
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1819
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38 #include "dbleAEPBAL.h" |
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458
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39 #include "dbleDET.h" |
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1819
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40 #include "dbleSCHUR.h" |
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740
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41 #include "dbleSVD.h" |
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1847
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42 #include "f77-fcn.h" |
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458
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43 #include "lo-error.h" |
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2354
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44 #include "lo-ieee.h" |
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45 #include "lo-mappers.h" |
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1968
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46 #include "lo-utils.h" |
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1367
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47 #include "mx-base.h" |
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2828
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48 #include "mx-m-dm.h" |
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3176
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49 #include "mx-dm-m.h" |
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1367
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50 #include "mx-inlines.cc" |
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1650
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51 #include "oct-cmplx.h" |
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458
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52 |
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3827
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53 #ifdef HAVE_FFTW |
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54 #include "oct-fftw.h" |
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55 #endif |
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56 |
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458
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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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3331
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61 int F77_FCN (dgebal, DGEBAL) (const char*, const int&, double*, |
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62 const int&, int&, int&, double*, |
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63 int&, long, long); |
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64 |
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65 int F77_FCN (dgebak, DGEBAK) (const char*, const char*, const int&, |
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66 const int&, const int&, double*, |
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67 const int&, double*, const int&, |
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68 int&, long, long); |
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69 |
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1253
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70 int F77_FCN (dgemm, DGEMM) (const char*, const char*, const int&, |
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71 const int&, const int&, const double&, |
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72 const double*, const int&, |
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73 const double*, const int&, |
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74 const double&, double*, const int&, |
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75 long, long); |
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76 |
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1253
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77 int F77_FCN (dgeco, DGECO) (double*, const int&, const int&, int*, |
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78 double&, double*); |
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458
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79 |
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1253
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80 int F77_FCN (dgesl, DGESL) (const double*, const int&, const int&, |
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81 const int*, double*, const int&); |
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82 |
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1253
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83 int F77_FCN (dgedi, DGEDI) (double*, const int&, const int&, |
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84 const int*, double*, double*, |
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85 const int&); |
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86 |
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1253
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87 int F77_FCN (dgelss, DGELSS) (const int&, const int&, const int&, |
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88 double*, const int&, double*, |
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89 const int&, double*, double&, int&, |
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90 double*, const int&, int&); |
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91 |
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1360
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92 // Note that the original complex fft routines were not written for |
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93 // double complex arguments. They have been modified by adding an |
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94 // implicit double precision (a-h,o-z) statement at the beginning of |
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95 // each subroutine. |
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96 |
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1253
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97 int F77_FCN (cffti, CFFTI) (const int&, Complex*); |
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98 |
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1253
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99 int F77_FCN (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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458
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100 |
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1253
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101 int F77_FCN (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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1819
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102 |
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103 int F77_FCN (dlartg, DLARTG) (const double&, const double&, double&, |
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104 double&, double&); |
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105 |
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106 int F77_FCN (dtrsyl, DTRSYL) (const char*, const char*, const int&, |
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107 const int&, const int&, const double*, |
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108 const int&, const double*, const int&, |
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109 const double*, const int&, double&, |
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110 int&, long, long); |
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111 |
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3130
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112 int F77_FCN (xdlange, XDLANGE) (const char*, const int&, |
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113 const int&, const double*, |
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114 const int&, double*, double&); |
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458
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115 } |
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116 |
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1360
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117 // Matrix class. |
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458
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118 |
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2349
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119 Matrix::Matrix (const RowVector& rv) |
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120 : MArray2<double> (1, rv.length (), 0.0) |
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121 { |
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122 for (int i = 0; i < rv.length (); i++) |
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123 elem (0, i) = rv.elem (i); |
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124 } |
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125 |
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126 Matrix::Matrix (const ColumnVector& cv) |
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127 : MArray2<double> (cv.length (), 1, 0.0) |
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128 { |
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129 for (int i = 0; i < cv.length (); i++) |
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130 elem (i, 0) = cv.elem (i); |
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131 } |
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132 |
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458
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133 Matrix::Matrix (const DiagMatrix& a) |
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1214
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134 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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458
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135 { |
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136 for (int i = 0; i < a.length (); i++) |
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137 elem (i, i) = a.elem (i, i); |
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138 } |
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139 |
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1574
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140 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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141 // here? |
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142 |
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2828
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143 Matrix::Matrix (const boolMatrix& a) |
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144 : MArray2<double> (a.rows (), a.cols ()) |
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145 { |
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146 for (int i = 0; i < a.rows (); i++) |
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147 for (int j = 0; j < a.cols (); j++) |
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148 elem (i, j) = a.elem (i, j); |
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149 } |
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150 |
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1574
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151 Matrix::Matrix (const charMatrix& a) |
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152 : MArray2<double> (a.rows (), a.cols ()) |
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153 { |
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154 for (int i = 0; i < a.rows (); i++) |
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155 for (int j = 0; j < a.cols (); j++) |
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156 elem (i, j) = a.elem (i, j); |
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157 } |
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158 |
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2385
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159 bool |
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458
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160 Matrix::operator == (const Matrix& a) const |
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161 { |
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162 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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163 return false; |
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458
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164 |
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3769
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165 return mx_inline_equal (data (), a.data (), length ()); |
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458
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166 } |
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167 |
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2385
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168 bool |
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458
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169 Matrix::operator != (const Matrix& a) const |
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170 { |
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171 return !(*this == a); |
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172 } |
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173 |
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3354
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174 bool |
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175 Matrix::is_symmetric (void) const |
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176 { |
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177 if (is_square () && rows () > 0) |
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178 { |
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179 for (int i = 0; i < rows (); i++) |
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180 for (int j = i+1; j < cols (); j++) |
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181 if (elem (i, j) != elem (j, i)) |
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182 return false; |
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183 |
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184 return true; |
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185 } |
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186 |
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187 return false; |
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188 } |
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189 |
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458
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190 Matrix& |
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191 Matrix::insert (const Matrix& a, int r, int c) |
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192 { |
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1561
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193 Array2<double>::insert (a, r, c); |
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458
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194 return *this; |
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195 } |
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196 |
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197 Matrix& |
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198 Matrix::insert (const RowVector& a, int r, int c) |
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199 { |
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200 int a_len = a.length (); |
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1698
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201 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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202 { |
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203 (*current_liboctave_error_handler) ("range error for insert"); |
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204 return *this; |
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205 } |
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206 |
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207 for (int i = 0; i < a_len; i++) |
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208 elem (r, c+i) = a.elem (i); |
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209 |
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210 return *this; |
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211 } |
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212 |
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213 Matrix& |
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214 Matrix::insert (const ColumnVector& a, int r, int c) |
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215 { |
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216 int a_len = a.length (); |
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1698
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217 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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218 { |
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219 (*current_liboctave_error_handler) ("range error for insert"); |
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220 return *this; |
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221 } |
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222 |
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223 for (int i = 0; i < a_len; i++) |
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224 elem (r+i, c) = a.elem (i); |
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225 |
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226 return *this; |
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227 } |
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228 |
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229 Matrix& |
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230 Matrix::insert (const DiagMatrix& a, int r, int c) |
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231 { |
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1697
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232 int a_nr = a.rows (); |
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233 int a_nc = a.cols (); |
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234 |
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1698
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235 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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236 { |
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237 (*current_liboctave_error_handler) ("range error for insert"); |
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238 return *this; |
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239 } |
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240 |
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1697
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241 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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242 |
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458
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243 for (int i = 0; i < a.length (); i++) |
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244 elem (r+i, c+i) = a.elem (i, i); |
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245 |
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246 return *this; |
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247 } |
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248 |
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249 Matrix& |
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250 Matrix::fill (double val) |
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251 { |
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252 int nr = rows (); |
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253 int nc = cols (); |
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254 if (nr > 0 && nc > 0) |
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255 for (int j = 0; j < nc; j++) |
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256 for (int i = 0; i < nr; i++) |
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257 elem (i, j) = val; |
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258 |
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259 return *this; |
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260 } |
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261 |
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262 Matrix& |
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263 Matrix::fill (double val, int r1, int c1, int r2, int c2) |
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264 { |
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265 int nr = rows (); |
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266 int nc = cols (); |
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267 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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268 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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269 { |
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270 (*current_liboctave_error_handler) ("range error for fill"); |
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271 return *this; |
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272 } |
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273 |
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274 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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275 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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276 |
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277 for (int j = c1; j <= c2; j++) |
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278 for (int i = r1; i <= r2; i++) |
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279 elem (i, j) = val; |
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280 |
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281 return *this; |
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282 } |
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283 |
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284 Matrix |
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285 Matrix::append (const Matrix& a) const |
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286 { |
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287 int nr = rows (); |
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288 int nc = cols (); |
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289 if (nr != a.rows ()) |
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290 { |
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291 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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292 return Matrix (); |
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293 } |
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294 |
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295 int nc_insert = nc; |
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296 Matrix retval (nr, nc + a.cols ()); |
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297 retval.insert (*this, 0, 0); |
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298 retval.insert (a, 0, nc_insert); |
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299 return retval; |
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300 } |
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301 |
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302 Matrix |
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303 Matrix::append (const RowVector& a) const |
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304 { |
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305 int nr = rows (); |
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306 int nc = cols (); |
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307 if (nr != 1) |
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308 { |
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309 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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310 return Matrix (); |
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311 } |
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312 |
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313 int nc_insert = nc; |
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314 Matrix retval (nr, nc + a.length ()); |
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315 retval.insert (*this, 0, 0); |
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316 retval.insert (a, 0, nc_insert); |
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317 return retval; |
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318 } |
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319 |
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320 Matrix |
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321 Matrix::append (const ColumnVector& a) const |
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322 { |
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323 int nr = rows (); |
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324 int nc = cols (); |
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325 if (nr != a.length ()) |
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326 { |
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327 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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328 return Matrix (); |
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329 } |
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330 |
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331 int nc_insert = nc; |
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332 Matrix retval (nr, nc + 1); |
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333 retval.insert (*this, 0, 0); |
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334 retval.insert (a, 0, nc_insert); |
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335 return retval; |
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336 } |
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337 |
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338 Matrix |
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339 Matrix::append (const DiagMatrix& a) const |
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340 { |
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341 int nr = rows (); |
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342 int nc = cols (); |
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343 if (nr != a.rows ()) |
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344 { |
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345 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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346 return *this; |
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347 } |
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348 |
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349 int nc_insert = nc; |
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350 Matrix retval (nr, nc + a.cols ()); |
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351 retval.insert (*this, 0, 0); |
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352 retval.insert (a, 0, nc_insert); |
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353 return retval; |
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354 } |
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355 |
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356 Matrix |
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357 Matrix::stack (const Matrix& a) const |
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358 { |
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359 int nr = rows (); |
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360 int nc = cols (); |
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361 if (nc != a.cols ()) |
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362 { |
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363 (*current_liboctave_error_handler) |
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364 ("column dimension mismatch for stack"); |
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365 return Matrix (); |
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366 } |
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367 |
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368 int nr_insert = nr; |
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369 Matrix retval (nr + a.rows (), nc); |
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370 retval.insert (*this, 0, 0); |
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371 retval.insert (a, nr_insert, 0); |
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372 return retval; |
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373 } |
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374 |
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375 Matrix |
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376 Matrix::stack (const RowVector& a) const |
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377 { |
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378 int nr = rows (); |
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379 int nc = cols (); |
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380 if (nc != a.length ()) |
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381 { |
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382 (*current_liboctave_error_handler) |
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383 ("column dimension mismatch for stack"); |
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384 return Matrix (); |
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385 } |
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386 |
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387 int nr_insert = nr; |
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388 Matrix retval (nr + 1, nc); |
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389 retval.insert (*this, 0, 0); |
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390 retval.insert (a, nr_insert, 0); |
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391 return retval; |
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392 } |
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393 |
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394 Matrix |
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395 Matrix::stack (const ColumnVector& a) const |
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396 { |
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397 int nr = rows (); |
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398 int nc = cols (); |
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399 if (nc != 1) |
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400 { |
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401 (*current_liboctave_error_handler) |
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402 ("column dimension mismatch for stack"); |
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403 return Matrix (); |
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404 } |
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405 |
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406 int nr_insert = nr; |
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407 Matrix retval (nr + a.length (), nc); |
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408 retval.insert (*this, 0, 0); |
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409 retval.insert (a, nr_insert, 0); |
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410 return retval; |
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411 } |
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412 |
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413 Matrix |
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414 Matrix::stack (const DiagMatrix& a) const |
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415 { |
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416 int nr = rows (); |
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417 int nc = cols (); |
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418 if (nc != a.cols ()) |
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419 { |
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420 (*current_liboctave_error_handler) |
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421 ("column dimension mismatch for stack"); |
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422 return Matrix (); |
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423 } |
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424 |
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425 int nr_insert = nr; |
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426 Matrix retval (nr + a.rows (), nc); |
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427 retval.insert (*this, 0, 0); |
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428 retval.insert (a, nr_insert, 0); |
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429 return retval; |
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430 } |
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431 |
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432 Matrix |
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1205
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433 real (const ComplexMatrix& a) |
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434 { |
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435 int a_len = a.length (); |
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436 Matrix retval; |
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437 if (a_len > 0) |
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3769
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438 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
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439 a.rows (), a.cols ()); |
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1205
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440 return retval; |
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441 } |
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442 |
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443 Matrix |
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444 imag (const ComplexMatrix& a) |
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445 { |
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446 int a_len = a.length (); |
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447 Matrix retval; |
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448 if (a_len > 0) |
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3769
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449 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
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450 a.rows (), a.cols ()); |
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1205
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451 return retval; |
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452 } |
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453 |
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454 Matrix |
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458
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455 Matrix::extract (int r1, int c1, int r2, int c2) const |
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456 { |
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457 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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458 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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459 |
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460 int new_r = r2 - r1 + 1; |
|
|
461 int new_c = c2 - c1 + 1; |
|
|
462 |
|
|
463 Matrix result (new_r, new_c); |
|
|
464 |
|
|
465 for (int j = 0; j < new_c; j++) |
|
|
466 for (int i = 0; i < new_r; i++) |
|
|
467 result.elem (i, j) = elem (r1+i, c1+j); |
|
|
468 |
|
|
469 return result; |
|
|
470 } |
|
|
471 |
|
|
472 // extract row or column i. |
|
|
473 |
|
|
474 RowVector |
|
|
475 Matrix::row (int i) const |
|
|
476 { |
|
|
477 int nc = cols (); |
|
|
478 if (i < 0 || i >= rows ()) |
|
|
479 { |
|
|
480 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
481 return RowVector (); |
|
|
482 } |
|
|
483 |
|
|
484 RowVector retval (nc); |
|
|
485 for (int j = 0; j < nc; j++) |
|
|
486 retval.elem (j) = elem (i, j); |
|
|
487 |
|
|
488 return retval; |
|
|
489 } |
|
|
490 |
|
|
491 RowVector |
|
|
492 Matrix::row (char *s) const |
|
|
493 { |
|
533
|
494 if (! s) |
|
458
|
495 { |
|
|
496 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
497 return RowVector (); |
|
|
498 } |
|
|
499 |
|
|
500 char c = *s; |
|
|
501 if (c == 'f' || c == 'F') |
|
|
502 return row (0); |
|
|
503 else if (c == 'l' || c == 'L') |
|
|
504 return row (rows () - 1); |
|
|
505 else |
|
|
506 { |
|
|
507 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
508 return RowVector (); |
|
|
509 } |
|
|
510 } |
|
|
511 |
|
|
512 ColumnVector |
|
|
513 Matrix::column (int i) const |
|
|
514 { |
|
|
515 int nr = rows (); |
|
|
516 if (i < 0 || i >= cols ()) |
|
|
517 { |
|
|
518 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
519 return ColumnVector (); |
|
|
520 } |
|
|
521 |
|
|
522 ColumnVector retval (nr); |
|
|
523 for (int j = 0; j < nr; j++) |
|
|
524 retval.elem (j) = elem (j, i); |
|
|
525 |
|
|
526 return retval; |
|
|
527 } |
|
|
528 |
|
|
529 ColumnVector |
|
|
530 Matrix::column (char *s) const |
|
|
531 { |
|
533
|
532 if (! s) |
|
458
|
533 { |
|
|
534 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
535 return ColumnVector (); |
|
|
536 } |
|
|
537 |
|
|
538 char c = *s; |
|
|
539 if (c == 'f' || c == 'F') |
|
|
540 return column (0); |
|
|
541 else if (c == 'l' || c == 'L') |
|
|
542 return column (cols () - 1); |
|
|
543 else |
|
|
544 { |
|
|
545 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
546 return ColumnVector (); |
|
|
547 } |
|
|
548 } |
|
|
549 |
|
|
550 Matrix |
|
|
551 Matrix::inverse (void) const |
|
|
552 { |
|
|
553 int info; |
|
|
554 double rcond; |
|
|
555 return inverse (info, rcond); |
|
|
556 } |
|
|
557 |
|
|
558 Matrix |
|
|
559 Matrix::inverse (int& info) const |
|
|
560 { |
|
|
561 double rcond; |
|
|
562 return inverse (info, rcond); |
|
|
563 } |
|
|
564 |
|
|
565 Matrix |
|
1656
|
566 Matrix::inverse (int& info, double& rcond, int force) const |
|
458
|
567 { |
|
1948
|
568 Matrix retval; |
|
|
569 |
|
458
|
570 int nr = rows (); |
|
|
571 int nc = cols (); |
|
1948
|
572 |
|
458
|
573 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
574 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
575 else |
|
|
576 { |
|
1948
|
577 info = 0; |
|
|
578 |
|
|
579 Array<int> ipvt (nr); |
|
|
580 int *pipvt = ipvt.fortran_vec (); |
|
|
581 |
|
|
582 Array<double> z (nr); |
|
|
583 double *pz = z.fortran_vec (); |
|
|
584 |
|
|
585 retval = *this; |
|
|
586 double *tmp_data = retval.fortran_vec (); |
|
|
587 |
|
|
588 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nc, pipvt, rcond, pz)); |
|
|
589 |
|
|
590 if (f77_exception_encountered) |
|
|
591 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
|
592 else |
|
|
593 { |
|
|
594 volatile double rcond_plus_one = rcond + 1.0; |
|
|
595 |
|
3838
|
596 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
597 info = -1; |
|
|
598 |
|
|
599 if (info == -1 && ! force) |
|
|
600 retval = *this; // Restore matrix contents. |
|
|
601 else |
|
|
602 { |
|
|
603 double *dummy = 0; |
|
|
604 |
|
|
605 F77_XFCN (dgedi, DGEDI, (tmp_data, nr, nc, pipvt, dummy, |
|
|
606 pz, 1)); |
|
|
607 |
|
|
608 if (f77_exception_encountered) |
|
|
609 (*current_liboctave_error_handler) |
|
|
610 ("unrecoverable error in dgedi"); |
|
|
611 } |
|
|
612 } |
|
458
|
613 } |
|
|
614 |
|
1948
|
615 return retval; |
|
458
|
616 } |
|
|
617 |
|
740
|
618 Matrix |
|
|
619 Matrix::pseudo_inverse (double tol) |
|
|
620 { |
|
3480
|
621 SVD result (*this, SVD::economy); |
|
740
|
622 |
|
|
623 DiagMatrix S = result.singular_values (); |
|
|
624 Matrix U = result.left_singular_matrix (); |
|
|
625 Matrix V = result.right_singular_matrix (); |
|
|
626 |
|
|
627 ColumnVector sigma = S.diag (); |
|
|
628 |
|
|
629 int r = sigma.length () - 1; |
|
|
630 int nr = rows (); |
|
|
631 int nc = cols (); |
|
|
632 |
|
|
633 if (tol <= 0.0) |
|
|
634 { |
|
|
635 if (nr > nc) |
|
|
636 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
637 else |
|
|
638 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
639 } |
|
|
640 |
|
|
641 while (r >= 0 && sigma.elem (r) < tol) |
|
|
642 r--; |
|
|
643 |
|
|
644 if (r < 0) |
|
|
645 return Matrix (nc, nr, 0.0); |
|
|
646 else |
|
|
647 { |
|
|
648 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
649 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
650 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
651 return Vr * D * Ur.transpose (); |
|
|
652 } |
|
|
653 } |
|
|
654 |
|
3827
|
655 #ifdef HAVE_FFTW |
|
|
656 |
|
|
657 ComplexMatrix |
|
|
658 Matrix::fourier (void) const |
|
|
659 { |
|
|
660 size_t nr = rows (); |
|
|
661 size_t nc = cols (); |
|
|
662 |
|
|
663 ComplexMatrix retval (nr, nc); |
|
|
664 |
|
|
665 size_t npts, nsamples; |
|
|
666 |
|
|
667 if (nr == 1 || nc == 1) |
|
|
668 { |
|
|
669 npts = nr > nc ? nr : nc; |
|
|
670 nsamples = 1; |
|
|
671 } |
|
|
672 else |
|
|
673 { |
|
|
674 npts = nr; |
|
|
675 nsamples = nc; |
|
|
676 } |
|
|
677 |
|
|
678 ComplexMatrix tmp (*this); |
|
|
679 Complex *in (tmp.fortran_vec ()); |
|
|
680 Complex *out (retval.fortran_vec ()); |
|
|
681 |
|
|
682 for (size_t i = 0; i < nsamples; i++) |
|
|
683 { |
|
|
684 octave_fftw::fft (&in[npts * i], &out[npts * i], npts); |
|
|
685 } |
|
|
686 |
|
|
687 return retval; |
|
|
688 } |
|
|
689 |
|
|
690 ComplexMatrix |
|
|
691 Matrix::ifourier (void) const |
|
|
692 { |
|
|
693 size_t nr = rows (); |
|
|
694 size_t nc = cols (); |
|
|
695 |
|
|
696 ComplexMatrix retval (nr, nc); |
|
|
697 |
|
|
698 size_t npts, nsamples; |
|
|
699 |
|
|
700 if (nr == 1 || nc == 1) |
|
|
701 { |
|
|
702 npts = nr > nc ? nr : nc; |
|
|
703 nsamples = 1; |
|
|
704 } |
|
|
705 else |
|
|
706 { |
|
|
707 npts = nr; |
|
|
708 nsamples = nc; |
|
|
709 } |
|
|
710 |
|
|
711 ComplexMatrix tmp (*this); |
|
|
712 Complex *in (tmp.fortran_vec ()); |
|
|
713 Complex *out (retval.fortran_vec ()); |
|
|
714 |
|
|
715 for (size_t i = 0; i < nsamples; i++) |
|
|
716 { |
|
|
717 octave_fftw::ifft (&in[npts * i], &out[npts * i], npts); |
|
|
718 } |
|
|
719 |
|
|
720 return retval; |
|
|
721 } |
|
|
722 |
|
|
723 ComplexMatrix |
|
|
724 Matrix::fourier2d (void) const |
|
|
725 { |
|
|
726 int nr = rows (); |
|
|
727 int nc = cols (); |
|
|
728 |
|
|
729 ComplexMatrix retval (*this); |
|
|
730 // Note the order of passing the rows and columns to account for |
|
|
731 // column-major storage. |
|
|
732 octave_fftw::fft2d (retval.fortran_vec (), nc, nr); |
|
|
733 |
|
|
734 return retval; |
|
|
735 } |
|
|
736 |
|
|
737 ComplexMatrix |
|
|
738 Matrix::ifourier2d (void) const |
|
|
739 { |
|
|
740 int nr = rows (); |
|
|
741 int nc = cols (); |
|
|
742 |
|
|
743 ComplexMatrix retval (*this); |
|
|
744 // Note the order of passing the rows and columns to account for |
|
|
745 // column-major storage. |
|
|
746 octave_fftw::ifft2d (retval.fortran_vec (), nc, nr); |
|
|
747 |
|
|
748 return retval; |
|
|
749 } |
|
|
750 |
|
|
751 #else |
|
|
752 |
|
458
|
753 ComplexMatrix |
|
|
754 Matrix::fourier (void) const |
|
|
755 { |
|
1948
|
756 ComplexMatrix retval; |
|
|
757 |
|
458
|
758 int nr = rows (); |
|
|
759 int nc = cols (); |
|
1948
|
760 |
|
458
|
761 int npts, nsamples; |
|
1948
|
762 |
|
458
|
763 if (nr == 1 || nc == 1) |
|
|
764 { |
|
|
765 npts = nr > nc ? nr : nc; |
|
|
766 nsamples = 1; |
|
|
767 } |
|
|
768 else |
|
|
769 { |
|
|
770 npts = nr; |
|
|
771 nsamples = nc; |
|
|
772 } |
|
|
773 |
|
|
774 int nn = 4*npts+15; |
|
1948
|
775 |
|
|
776 Array<Complex> wsave (nn); |
|
|
777 Complex *pwsave = wsave.fortran_vec (); |
|
|
778 |
|
3585
|
779 retval = ComplexMatrix (*this); |
|
1948
|
780 Complex *tmp_data = retval.fortran_vec (); |
|
|
781 |
|
|
782 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
783 |
|
|
784 for (int j = 0; j < nsamples; j++) |
|
1948
|
785 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
786 |
|
|
787 return retval; |
|
458
|
788 } |
|
|
789 |
|
|
790 ComplexMatrix |
|
|
791 Matrix::ifourier (void) const |
|
|
792 { |
|
1948
|
793 ComplexMatrix retval; |
|
|
794 |
|
458
|
795 int nr = rows (); |
|
|
796 int nc = cols (); |
|
1948
|
797 |
|
458
|
798 int npts, nsamples; |
|
1948
|
799 |
|
458
|
800 if (nr == 1 || nc == 1) |
|
|
801 { |
|
|
802 npts = nr > nc ? nr : nc; |
|
|
803 nsamples = 1; |
|
|
804 } |
|
|
805 else |
|
|
806 { |
|
|
807 npts = nr; |
|
|
808 nsamples = nc; |
|
|
809 } |
|
|
810 |
|
|
811 int nn = 4*npts+15; |
|
1948
|
812 |
|
|
813 Array<Complex> wsave (nn); |
|
|
814 Complex *pwsave = wsave.fortran_vec (); |
|
|
815 |
|
3585
|
816 retval = ComplexMatrix (*this); |
|
1948
|
817 Complex *tmp_data = retval.fortran_vec (); |
|
|
818 |
|
|
819 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
820 |
|
|
821 for (int j = 0; j < nsamples; j++) |
|
1948
|
822 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
458
|
823 |
|
1321
|
824 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
825 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
826 |
|
1948
|
827 return retval; |
|
458
|
828 } |
|
|
829 |
|
677
|
830 ComplexMatrix |
|
|
831 Matrix::fourier2d (void) const |
|
|
832 { |
|
1948
|
833 ComplexMatrix retval; |
|
|
834 |
|
677
|
835 int nr = rows (); |
|
|
836 int nc = cols (); |
|
1948
|
837 |
|
677
|
838 int npts, nsamples; |
|
1948
|
839 |
|
677
|
840 if (nr == 1 || nc == 1) |
|
|
841 { |
|
|
842 npts = nr > nc ? nr : nc; |
|
|
843 nsamples = 1; |
|
|
844 } |
|
|
845 else |
|
|
846 { |
|
|
847 npts = nr; |
|
|
848 nsamples = nc; |
|
|
849 } |
|
|
850 |
|
|
851 int nn = 4*npts+15; |
|
1948
|
852 |
|
|
853 Array<Complex> wsave (nn); |
|
|
854 Complex *pwsave = wsave.fortran_vec (); |
|
|
855 |
|
3585
|
856 retval = ComplexMatrix (*this); |
|
1948
|
857 Complex *tmp_data = retval.fortran_vec (); |
|
|
858 |
|
|
859 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
860 |
|
|
861 for (int j = 0; j < nsamples; j++) |
|
1948
|
862 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
863 |
|
|
864 npts = nc; |
|
|
865 nsamples = nr; |
|
|
866 nn = 4*npts+15; |
|
1948
|
867 |
|
|
868 wsave.resize (nn); |
|
|
869 pwsave = wsave.fortran_vec (); |
|
|
870 |
|
|
871 Array<Complex> row (npts); |
|
|
872 Complex *prow = row.fortran_vec (); |
|
|
873 |
|
|
874 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
875 |
|
1321
|
876 for (int j = 0; j < nsamples; j++) |
|
677
|
877 { |
|
|
878 for (int i = 0; i < npts; i++) |
|
1948
|
879 prow[i] = tmp_data[i*nr + j]; |
|
|
880 |
|
|
881 F77_FCN (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
882 |
|
1321
|
883 for (int i = 0; i < npts; i++) |
|
1948
|
884 tmp_data[i*nr + j] = prow[i]; |
|
677
|
885 } |
|
|
886 |
|
1948
|
887 return retval; |
|
677
|
888 } |
|
|
889 |
|
|
890 ComplexMatrix |
|
|
891 Matrix::ifourier2d (void) const |
|
|
892 { |
|
1948
|
893 ComplexMatrix retval; |
|
|
894 |
|
677
|
895 int nr = rows (); |
|
|
896 int nc = cols (); |
|
1948
|
897 |
|
677
|
898 int npts, nsamples; |
|
1948
|
899 |
|
677
|
900 if (nr == 1 || nc == 1) |
|
|
901 { |
|
|
902 npts = nr > nc ? nr : nc; |
|
|
903 nsamples = 1; |
|
|
904 } |
|
|
905 else |
|
|
906 { |
|
|
907 npts = nr; |
|
|
908 nsamples = nc; |
|
|
909 } |
|
|
910 |
|
|
911 int nn = 4*npts+15; |
|
1948
|
912 |
|
|
913 Array<Complex> wsave (nn); |
|
|
914 Complex *pwsave = wsave.fortran_vec (); |
|
|
915 |
|
3585
|
916 retval = ComplexMatrix (*this); |
|
1948
|
917 Complex *tmp_data = retval.fortran_vec (); |
|
|
918 |
|
|
919 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
920 |
|
|
921 for (int j = 0; j < nsamples; j++) |
|
1948
|
922 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
923 |
|
1321
|
924 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
925 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
926 |
|
|
927 npts = nc; |
|
|
928 nsamples = nr; |
|
|
929 nn = 4*npts+15; |
|
1948
|
930 |
|
|
931 wsave.resize (nn); |
|
|
932 pwsave = wsave.fortran_vec (); |
|
|
933 |
|
|
934 Array<Complex> row (npts); |
|
|
935 Complex *prow = row.fortran_vec (); |
|
|
936 |
|
|
937 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
938 |
|
1321
|
939 for (int j = 0; j < nsamples; j++) |
|
677
|
940 { |
|
|
941 for (int i = 0; i < npts; i++) |
|
1948
|
942 prow[i] = tmp_data[i*nr + j]; |
|
|
943 |
|
|
944 F77_FCN (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
945 |
|
1321
|
946 for (int i = 0; i < npts; i++) |
|
3572
|
947 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
948 } |
|
|
949 |
|
1948
|
950 return retval; |
|
677
|
951 } |
|
|
952 |
|
3827
|
953 #endif |
|
|
954 |
|
458
|
955 DET |
|
|
956 Matrix::determinant (void) const |
|
|
957 { |
|
|
958 int info; |
|
|
959 double rcond; |
|
|
960 return determinant (info, rcond); |
|
|
961 } |
|
|
962 |
|
|
963 DET |
|
|
964 Matrix::determinant (int& info) const |
|
|
965 { |
|
|
966 double rcond; |
|
|
967 return determinant (info, rcond); |
|
|
968 } |
|
|
969 |
|
|
970 DET |
|
532
|
971 Matrix::determinant (int& info, double& rcond) const |
|
458
|
972 { |
|
|
973 DET retval; |
|
|
974 |
|
|
975 int nr = rows (); |
|
|
976 int nc = cols (); |
|
|
977 |
|
|
978 if (nr == 0 || nc == 0) |
|
|
979 { |
|
|
980 double d[2]; |
|
|
981 d[0] = 1.0; |
|
|
982 d[1] = 0.0; |
|
|
983 retval = DET (d); |
|
|
984 } |
|
|
985 else |
|
|
986 { |
|
|
987 info = 0; |
|
1948
|
988 |
|
|
989 Array<int> ipvt (nr); |
|
|
990 int *pipvt = ipvt.fortran_vec (); |
|
|
991 |
|
|
992 Array<double> z (nr); |
|
|
993 double *pz = z.fortran_vec (); |
|
|
994 |
|
|
995 Matrix atmp = *this; |
|
|
996 double *tmp_data = atmp.fortran_vec (); |
|
|
997 |
|
|
998 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
999 |
|
|
1000 if (f77_exception_encountered) |
|
|
1001 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
458
|
1002 else |
|
|
1003 { |
|
1948
|
1004 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1005 |
|
3838
|
1006 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1007 { |
|
|
1008 info = -1; |
|
|
1009 retval = DET (); |
|
|
1010 } |
|
|
1011 else |
|
|
1012 { |
|
|
1013 double d[2]; |
|
|
1014 |
|
|
1015 F77_XFCN (dgedi, DGEDI, (tmp_data, nr, nr, pipvt, d, pz, 10)); |
|
|
1016 |
|
|
1017 if (f77_exception_encountered) |
|
|
1018 (*current_liboctave_error_handler) |
|
|
1019 ("unrecoverable error in dgedi"); |
|
|
1020 else |
|
|
1021 retval = DET (d); |
|
|
1022 } |
|
458
|
1023 } |
|
|
1024 } |
|
|
1025 |
|
|
1026 return retval; |
|
|
1027 } |
|
|
1028 |
|
|
1029 Matrix |
|
|
1030 Matrix::solve (const Matrix& b) const |
|
|
1031 { |
|
|
1032 int info; |
|
|
1033 double rcond; |
|
|
1034 return solve (b, info, rcond); |
|
|
1035 } |
|
|
1036 |
|
|
1037 Matrix |
|
|
1038 Matrix::solve (const Matrix& b, int& info) const |
|
|
1039 { |
|
|
1040 double rcond; |
|
|
1041 return solve (b, info, rcond); |
|
|
1042 } |
|
|
1043 |
|
|
1044 Matrix |
|
532
|
1045 Matrix::solve (const Matrix& b, int& info, double& rcond) const |
|
458
|
1046 { |
|
3480
|
1047 return solve (b, info, rcond, 0); |
|
|
1048 } |
|
|
1049 |
|
|
1050 Matrix |
|
|
1051 Matrix::solve (const Matrix& b, int& info, double& rcond, |
|
|
1052 solve_singularity_handler sing_handler) const |
|
|
1053 { |
|
458
|
1054 Matrix retval; |
|
|
1055 |
|
|
1056 int nr = rows (); |
|
|
1057 int nc = cols (); |
|
1948
|
1058 |
|
458
|
1059 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
1948
|
1060 (*current_liboctave_error_handler) |
|
|
1061 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1062 else |
|
|
1063 { |
|
1948
|
1064 info = 0; |
|
|
1065 |
|
|
1066 Array<int> ipvt (nr); |
|
|
1067 int *pipvt = ipvt.fortran_vec (); |
|
|
1068 |
|
|
1069 Array<double> z (nr); |
|
|
1070 double *pz = z.fortran_vec (); |
|
|
1071 |
|
|
1072 Matrix atmp = *this; |
|
|
1073 double *tmp_data = atmp.fortran_vec (); |
|
|
1074 |
|
|
1075 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1076 |
|
|
1077 if (f77_exception_encountered) |
|
|
1078 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
|
1079 else |
|
|
1080 { |
|
|
1081 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1082 |
|
3838
|
1083 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1084 { |
|
|
1085 info = -2; |
|
3480
|
1086 |
|
|
1087 if (sing_handler) |
|
|
1088 sing_handler (rcond); |
|
|
1089 else |
|
|
1090 (*current_liboctave_error_handler) |
|
|
1091 ("matrix singular to machine precision, rcond = %g", |
|
|
1092 rcond); |
|
1948
|
1093 } |
|
|
1094 else |
|
|
1095 { |
|
|
1096 retval = b; |
|
|
1097 double *result = retval.fortran_vec (); |
|
|
1098 |
|
|
1099 int b_nc = b.cols (); |
|
|
1100 |
|
|
1101 for (volatile int j = 0; j < b_nc; j++) |
|
|
1102 { |
|
|
1103 F77_XFCN (dgesl, DGESL, (tmp_data, nr, nr, pipvt, |
|
|
1104 &result[nr*j], 0)); |
|
|
1105 |
|
|
1106 if (f77_exception_encountered) |
|
|
1107 { |
|
|
1108 (*current_liboctave_error_handler) |
|
|
1109 ("unrecoverable error in dgesl"); |
|
|
1110 |
|
|
1111 break; |
|
|
1112 } |
|
|
1113 } |
|
|
1114 } |
|
|
1115 } |
|
458
|
1116 } |
|
|
1117 |
|
|
1118 return retval; |
|
|
1119 } |
|
|
1120 |
|
|
1121 ComplexMatrix |
|
|
1122 Matrix::solve (const ComplexMatrix& b) const |
|
|
1123 { |
|
|
1124 ComplexMatrix tmp (*this); |
|
|
1125 return tmp.solve (b); |
|
|
1126 } |
|
|
1127 |
|
|
1128 ComplexMatrix |
|
|
1129 Matrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1130 { |
|
|
1131 ComplexMatrix tmp (*this); |
|
|
1132 return tmp.solve (b, info); |
|
|
1133 } |
|
|
1134 |
|
|
1135 ComplexMatrix |
|
|
1136 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
|
1137 { |
|
|
1138 ComplexMatrix tmp (*this); |
|
|
1139 return tmp.solve (b, info, rcond); |
|
|
1140 } |
|
|
1141 |
|
3480
|
1142 ComplexMatrix |
|
|
1143 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond, |
|
|
1144 solve_singularity_handler sing_handler) const |
|
|
1145 { |
|
|
1146 ComplexMatrix tmp (*this); |
|
|
1147 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1148 } |
|
|
1149 |
|
458
|
1150 ColumnVector |
|
|
1151 Matrix::solve (const ColumnVector& b) const |
|
|
1152 { |
|
|
1153 int info; double rcond; |
|
|
1154 return solve (b, info, rcond); |
|
|
1155 } |
|
|
1156 |
|
|
1157 ColumnVector |
|
|
1158 Matrix::solve (const ColumnVector& b, int& info) const |
|
|
1159 { |
|
|
1160 double rcond; |
|
|
1161 return solve (b, info, rcond); |
|
|
1162 } |
|
|
1163 |
|
|
1164 ColumnVector |
|
532
|
1165 Matrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
458
|
1166 { |
|
3480
|
1167 return solve (b, info, rcond, 0); |
|
|
1168 } |
|
|
1169 |
|
|
1170 ColumnVector |
|
|
1171 Matrix::solve (const ColumnVector& b, int& info, double& rcond, |
|
|
1172 solve_singularity_handler sing_handler) const |
|
|
1173 { |
|
458
|
1174 ColumnVector retval; |
|
|
1175 |
|
|
1176 int nr = rows (); |
|
|
1177 int nc = cols (); |
|
1948
|
1178 |
|
458
|
1179 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
1948
|
1180 (*current_liboctave_error_handler) |
|
|
1181 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1182 else |
|
|
1183 { |
|
1948
|
1184 info = 0; |
|
|
1185 |
|
|
1186 Array<int> ipvt (nr); |
|
|
1187 int *pipvt = ipvt.fortran_vec (); |
|
|
1188 |
|
|
1189 Array<double> z (nr); |
|
|
1190 double *pz = z.fortran_vec (); |
|
|
1191 |
|
|
1192 Matrix atmp = *this; |
|
|
1193 double *tmp_data = atmp.fortran_vec (); |
|
|
1194 |
|
|
1195 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1196 |
|
|
1197 if (f77_exception_encountered) |
|
|
1198 (*current_liboctave_error_handler) |
|
|
1199 ("unrecoverable error in dgeco"); |
|
|
1200 else |
|
|
1201 { |
|
|
1202 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1203 |
|
3838
|
1204 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1205 { |
|
|
1206 info = -2; |
|
3480
|
1207 |
|
|
1208 if (sing_handler) |
|
|
1209 sing_handler (rcond); |
|
|
1210 else |
|
|
1211 (*current_liboctave_error_handler) |
|
|
1212 ("matrix singular to machine precision, rcond = %g", |
|
|
1213 rcond); |
|
1948
|
1214 } |
|
|
1215 else |
|
|
1216 { |
|
|
1217 retval = b; |
|
|
1218 double *result = retval.fortran_vec (); |
|
|
1219 |
|
|
1220 F77_XFCN (dgesl, DGESL, (tmp_data, nr, nr, pipvt, result, 0)); |
|
|
1221 |
|
|
1222 if (f77_exception_encountered) |
|
|
1223 (*current_liboctave_error_handler) |
|
|
1224 ("unrecoverable error in dgesl"); |
|
|
1225 } |
|
|
1226 } |
|
458
|
1227 } |
|
|
1228 |
|
|
1229 return retval; |
|
|
1230 } |
|
|
1231 |
|
|
1232 ComplexColumnVector |
|
|
1233 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1234 { |
|
|
1235 ComplexMatrix tmp (*this); |
|
|
1236 return tmp.solve (b); |
|
|
1237 } |
|
|
1238 |
|
|
1239 ComplexColumnVector |
|
|
1240 Matrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1241 { |
|
|
1242 ComplexMatrix tmp (*this); |
|
|
1243 return tmp.solve (b, info); |
|
|
1244 } |
|
|
1245 |
|
|
1246 ComplexColumnVector |
|
|
1247 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const |
|
|
1248 { |
|
|
1249 ComplexMatrix tmp (*this); |
|
|
1250 return tmp.solve (b, info, rcond); |
|
|
1251 } |
|
|
1252 |
|
3480
|
1253 ComplexColumnVector |
|
|
1254 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond, |
|
|
1255 solve_singularity_handler sing_handler) const |
|
|
1256 { |
|
|
1257 ComplexMatrix tmp (*this); |
|
|
1258 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1259 } |
|
|
1260 |
|
458
|
1261 Matrix |
|
|
1262 Matrix::lssolve (const Matrix& b) const |
|
|
1263 { |
|
|
1264 int info; |
|
|
1265 int rank; |
|
|
1266 return lssolve (b, info, rank); |
|
|
1267 } |
|
|
1268 |
|
|
1269 Matrix |
|
|
1270 Matrix::lssolve (const Matrix& b, int& info) const |
|
|
1271 { |
|
|
1272 int rank; |
|
|
1273 return lssolve (b, info, rank); |
|
|
1274 } |
|
|
1275 |
|
|
1276 Matrix |
|
|
1277 Matrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1278 { |
|
1948
|
1279 Matrix retval; |
|
|
1280 |
|
458
|
1281 int nrhs = b.cols (); |
|
|
1282 |
|
|
1283 int m = rows (); |
|
|
1284 int n = cols (); |
|
|
1285 |
|
|
1286 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1287 (*current_liboctave_error_handler) |
|
|
1288 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1289 else |
|
458
|
1290 { |
|
1948
|
1291 Matrix atmp = *this; |
|
|
1292 double *tmp_data = atmp.fortran_vec (); |
|
|
1293 |
|
|
1294 int nrr = m > n ? m : n; |
|
3754
|
1295 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
1296 |
|
|
1297 for (int j = 0; j < nrhs; j++) |
|
|
1298 for (int i = 0; i < m; i++) |
|
|
1299 result.elem (i, j) = b.elem (i, j); |
|
|
1300 |
|
|
1301 double *presult = result.fortran_vec (); |
|
|
1302 |
|
|
1303 int len_s = m < n ? m : n; |
|
|
1304 Array<double> s (len_s); |
|
|
1305 double *ps = s.fortran_vec (); |
|
|
1306 |
|
|
1307 double rcond = -1.0; |
|
|
1308 |
|
3752
|
1309 // Ask DGELSS what the dimension of WORK should be. |
|
|
1310 |
|
|
1311 int lwork = -1; |
|
|
1312 |
|
|
1313 Array<double> work (1); |
|
1948
|
1314 |
|
|
1315 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
1316 rcond, rank, work.fortran_vec (), |
|
|
1317 lwork, info)); |
|
1948
|
1318 |
|
|
1319 if (f77_exception_encountered) |
|
|
1320 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1321 else |
|
|
1322 { |
|
3752
|
1323 lwork = static_cast<int> (work(0)); |
|
|
1324 work.resize (lwork); |
|
|
1325 |
|
|
1326 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1327 nrr, ps, rcond, rank, |
|
|
1328 work.fortran_vec (), lwork, info)); |
|
|
1329 |
|
|
1330 if (f77_exception_encountered) |
|
|
1331 (*current_liboctave_error_handler) |
|
|
1332 ("unrecoverable error in dgelss"); |
|
|
1333 else |
|
|
1334 { |
|
|
1335 retval.resize (n, nrhs); |
|
|
1336 for (int j = 0; j < nrhs; j++) |
|
|
1337 for (int i = 0; i < n; i++) |
|
|
1338 retval.elem (i, j) = result.elem (i, j); |
|
|
1339 } |
|
1948
|
1340 } |
|
458
|
1341 } |
|
|
1342 |
|
|
1343 return retval; |
|
|
1344 } |
|
|
1345 |
|
|
1346 ComplexMatrix |
|
|
1347 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1348 { |
|
|
1349 ComplexMatrix tmp (*this); |
|
1484
|
1350 int info; |
|
|
1351 int rank; |
|
|
1352 return tmp.lssolve (b, info, rank); |
|
458
|
1353 } |
|
|
1354 |
|
|
1355 ComplexMatrix |
|
|
1356 Matrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1357 { |
|
|
1358 ComplexMatrix tmp (*this); |
|
1484
|
1359 int rank; |
|
|
1360 return tmp.lssolve (b, info, rank); |
|
458
|
1361 } |
|
|
1362 |
|
|
1363 ComplexMatrix |
|
|
1364 Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1365 { |
|
|
1366 ComplexMatrix tmp (*this); |
|
1484
|
1367 return tmp.lssolve (b, info, rank); |
|
458
|
1368 } |
|
|
1369 |
|
|
1370 ColumnVector |
|
|
1371 Matrix::lssolve (const ColumnVector& b) const |
|
|
1372 { |
|
|
1373 int info; |
|
1484
|
1374 int rank; |
|
|
1375 return lssolve (b, info, rank); |
|
458
|
1376 } |
|
|
1377 |
|
|
1378 ColumnVector |
|
|
1379 Matrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1380 { |
|
|
1381 int rank; |
|
|
1382 return lssolve (b, info, rank); |
|
|
1383 } |
|
|
1384 |
|
|
1385 ColumnVector |
|
|
1386 Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1387 { |
|
1948
|
1388 ColumnVector retval; |
|
|
1389 |
|
458
|
1390 int nrhs = 1; |
|
|
1391 |
|
|
1392 int m = rows (); |
|
|
1393 int n = cols (); |
|
|
1394 |
|
|
1395 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1396 (*current_liboctave_error_handler) |
|
|
1397 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1398 else |
|
458
|
1399 { |
|
1948
|
1400 Matrix atmp = *this; |
|
|
1401 double *tmp_data = atmp.fortran_vec (); |
|
|
1402 |
|
|
1403 int nrr = m > n ? m : n; |
|
|
1404 ColumnVector result (nrr); |
|
|
1405 |
|
|
1406 for (int i = 0; i < m; i++) |
|
|
1407 result.elem (i) = b.elem (i); |
|
|
1408 |
|
|
1409 double *presult = result.fortran_vec (); |
|
|
1410 |
|
|
1411 int len_s = m < n ? m : n; |
|
|
1412 Array<double> s (len_s); |
|
|
1413 double *ps = s.fortran_vec (); |
|
|
1414 |
|
|
1415 double rcond = -1.0; |
|
|
1416 |
|
3752
|
1417 // Ask DGELSS what the dimension of WORK should be. |
|
|
1418 |
|
|
1419 int lwork = -1; |
|
|
1420 |
|
|
1421 Array<double> work (1); |
|
|
1422 |
|
|
1423 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
1424 rcond, rank, work.fortran_vec (), |
|
|
1425 lwork, info)); |
|
1948
|
1426 |
|
|
1427 if (f77_exception_encountered) |
|
|
1428 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1429 else |
|
|
1430 { |
|
3752
|
1431 lwork = static_cast<int> (work(0)); |
|
|
1432 work.resize (lwork); |
|
|
1433 |
|
|
1434 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1435 nrr, ps, rcond, rank, |
|
|
1436 work.fortran_vec (), lwork, info)); |
|
|
1437 |
|
|
1438 if (f77_exception_encountered) |
|
|
1439 (*current_liboctave_error_handler) |
|
|
1440 ("unrecoverable error in dgelss"); |
|
|
1441 else |
|
|
1442 { |
|
|
1443 retval.resize (n); |
|
|
1444 for (int i = 0; i < n; i++) |
|
|
1445 retval.elem (i) = result.elem (i); |
|
|
1446 } |
|
1948
|
1447 } |
|
458
|
1448 } |
|
|
1449 |
|
|
1450 return retval; |
|
|
1451 } |
|
|
1452 |
|
|
1453 ComplexColumnVector |
|
|
1454 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
1455 { |
|
|
1456 ComplexMatrix tmp (*this); |
|
|
1457 return tmp.lssolve (b); |
|
|
1458 } |
|
|
1459 |
|
|
1460 ComplexColumnVector |
|
|
1461 Matrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1462 { |
|
|
1463 ComplexMatrix tmp (*this); |
|
|
1464 return tmp.lssolve (b, info); |
|
|
1465 } |
|
|
1466 |
|
|
1467 ComplexColumnVector |
|
|
1468 Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const |
|
|
1469 { |
|
|
1470 ComplexMatrix tmp (*this); |
|
|
1471 return tmp.lssolve (b, info, rank); |
|
|
1472 } |
|
|
1473 |
|
1819
|
1474 // Constants for matrix exponential calculation. |
|
|
1475 |
|
|
1476 static double padec [] = |
|
|
1477 { |
|
|
1478 5.0000000000000000e-1, |
|
|
1479 1.1666666666666667e-1, |
|
|
1480 1.6666666666666667e-2, |
|
|
1481 1.6025641025641026e-3, |
|
|
1482 1.0683760683760684e-4, |
|
|
1483 4.8562548562548563e-6, |
|
|
1484 1.3875013875013875e-7, |
|
|
1485 1.9270852604185938e-9, |
|
|
1486 }; |
|
|
1487 |
|
|
1488 Matrix |
|
|
1489 Matrix::expm (void) const |
|
|
1490 { |
|
|
1491 Matrix retval; |
|
|
1492 |
|
|
1493 Matrix m = *this; |
|
|
1494 |
|
|
1495 int nc = columns (); |
|
|
1496 |
|
3130
|
1497 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1498 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1499 |
|
1819
|
1500 // trace shift value |
|
3331
|
1501 volatile double trshift = 0.0; |
|
1819
|
1502 |
|
|
1503 for (int i = 0; i < nc; i++) |
|
|
1504 trshift += m.elem (i, i); |
|
|
1505 |
|
|
1506 trshift /= nc; |
|
|
1507 |
|
3130
|
1508 if (trshift > 0.0) |
|
|
1509 { |
|
|
1510 for (int i = 0; i < nc; i++) |
|
|
1511 m.elem (i, i) -= trshift; |
|
|
1512 } |
|
1819
|
1513 |
|
3331
|
1514 // Preconditioning step 2: balancing; code follows development |
|
|
1515 // in AEPBAL |
|
|
1516 |
|
|
1517 double *p_m = m.fortran_vec (); |
|
|
1518 |
|
3468
|
1519 int info, ilo, ihi, ilos, ihis; |
|
|
1520 Array<double> dpermute (nc); |
|
|
1521 Array<double> dscale (nc); |
|
3466
|
1522 |
|
3468
|
1523 // permutation first |
|
|
1524 char job = 'P'; |
|
3469
|
1525 F77_XFCN (dgebal, DGEBAL, (&job, nc, p_m, nc, ilo, ihi, |
|
|
1526 dpermute.fortran_vec (), info, 1L, 1L)); |
|
3466
|
1527 |
|
3468
|
1528 // then scaling |
|
|
1529 job = 'S'; |
|
3469
|
1530 F77_XFCN (dgebal, DGEBAL, (&job, nc, p_m, nc, ilos, ihis, |
|
|
1531 dscale.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1532 |
|
|
1533 if (f77_exception_encountered) |
|
|
1534 { |
|
|
1535 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
1536 return retval; |
|
|
1537 } |
|
|
1538 |
|
1819
|
1539 // Preconditioning step 3: scaling. |
|
3331
|
1540 |
|
1819
|
1541 ColumnVector work(nc); |
|
3130
|
1542 double inf_norm; |
|
3331
|
1543 |
|
|
1544 F77_XFCN (xdlange, XDLANGE, ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1545 work.fortran_vec (), inf_norm)); |
|
|
1546 |
|
|
1547 if (f77_exception_encountered) |
|
|
1548 { |
|
|
1549 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
1550 return retval; |
|
|
1551 } |
|
1819
|
1552 |
|
|
1553 int sqpow = (int) (inf_norm > 0.0 |
|
|
1554 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
1555 : 0.0); |
|
3331
|
1556 |
|
1819
|
1557 // Check whether we need to square at all. |
|
3331
|
1558 |
|
1819
|
1559 if (sqpow < 0) |
|
|
1560 sqpow = 0; |
|
3331
|
1561 |
|
1819
|
1562 if (sqpow > 0) |
|
|
1563 { |
|
|
1564 double scale_factor = 1.0; |
|
|
1565 for (int i = 0; i < sqpow; i++) |
|
|
1566 scale_factor *= 2.0; |
|
3331
|
1567 |
|
1819
|
1568 m = m / scale_factor; |
|
|
1569 } |
|
3331
|
1570 |
|
1819
|
1571 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
1572 |
|
1819
|
1573 Matrix npp (nc, nc, 0.0); |
|
|
1574 Matrix dpp = npp; |
|
3331
|
1575 |
|
1819
|
1576 // Now powers a^8 ... a^1. |
|
3331
|
1577 |
|
1819
|
1578 int minus_one_j = -1; |
|
|
1579 for (int j = 7; j >= 0; j--) |
|
|
1580 { |
|
3573
|
1581 npp = m * npp + padec[j] * m; |
|
|
1582 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
1583 minus_one_j *= -1; |
|
|
1584 } |
|
3331
|
1585 |
|
1819
|
1586 // Zero power. |
|
3331
|
1587 |
|
1819
|
1588 dpp = -dpp; |
|
3130
|
1589 for (int j = 0; j < nc; j++) |
|
1819
|
1590 { |
|
|
1591 npp.elem (j, j) += 1.0; |
|
|
1592 dpp.elem (j, j) += 1.0; |
|
|
1593 } |
|
3331
|
1594 |
|
1819
|
1595 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1596 |
|
3331
|
1597 retval = dpp.solve (npp, info); |
|
|
1598 |
|
1819
|
1599 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
1600 |
|
1819
|
1601 while (sqpow) |
|
|
1602 { |
|
|
1603 retval = retval * retval; |
|
|
1604 sqpow--; |
|
|
1605 } |
|
3331
|
1606 |
|
1819
|
1607 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
1608 // apply inverse scaling to computed exponential |
|
3468
|
1609 for (int i = 0; i < nc; i++) |
|
|
1610 for (int j = 0; j < nc; j++) |
|
|
1611 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
1612 |
|
|
1613 // construct balancing permutation vector |
|
3468
|
1614 Array<int> ipermute (nc); |
|
|
1615 for (int i = 0; i < nc; i++) |
|
|
1616 ipermute(i) = i; // identity permutation |
|
3466
|
1617 |
|
|
1618 // leading permutations in forward order |
|
3468
|
1619 for (int i = 0; i < (ilo-1); i++) |
|
|
1620 { |
|
|
1621 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1622 int tmp = ipermute(i); |
|
|
1623 ipermute(i) = ipermute (swapidx); |
|
|
1624 ipermute(swapidx) = tmp; |
|
|
1625 } |
|
3466
|
1626 |
|
|
1627 // trailing permutations must be done in reverse order |
|
3468
|
1628 for (int i = nc - 1; i >= ihi; i--) |
|
|
1629 { |
|
|
1630 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1631 int tmp = ipermute(i); |
|
|
1632 ipermute(i) = ipermute(swapidx); |
|
|
1633 ipermute(swapidx) = tmp; |
|
|
1634 } |
|
3466
|
1635 |
|
|
1636 // construct inverse balancing permutation vector |
|
3468
|
1637 Array<int> invpvec (nc); |
|
|
1638 for (int i = 0; i < nc; i++) |
|
|
1639 invpvec(ipermute(i)) = i; // Thanks to R. A. Lippert for this method |
|
3466
|
1640 |
|
|
1641 Matrix tmpMat = retval; |
|
3468
|
1642 for (int i = 0; i < nc; i++) |
|
|
1643 for (int j = 0; j < nc; j++) |
|
|
1644 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
1645 |
|
1819
|
1646 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
1647 |
|
3130
|
1648 if (trshift > 0.0) |
|
|
1649 retval = exp (trshift) * retval; |
|
|
1650 |
|
|
1651 return retval; |
|
1819
|
1652 } |
|
|
1653 |
|
458
|
1654 Matrix& |
|
|
1655 Matrix::operator += (const DiagMatrix& a) |
|
|
1656 { |
|
2385
|
1657 int nr = rows (); |
|
|
1658 int nc = cols (); |
|
|
1659 |
|
|
1660 int a_nr = a.rows (); |
|
|
1661 int a_nc = a.cols (); |
|
|
1662 |
|
|
1663 if (nr != a_nr || nc != a_nc) |
|
458
|
1664 { |
|
2385
|
1665 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1666 return *this; |
|
|
1667 } |
|
|
1668 |
|
|
1669 for (int i = 0; i < a.length (); i++) |
|
|
1670 elem (i, i) += a.elem (i, i); |
|
|
1671 |
|
|
1672 return *this; |
|
|
1673 } |
|
|
1674 |
|
|
1675 Matrix& |
|
|
1676 Matrix::operator -= (const DiagMatrix& a) |
|
|
1677 { |
|
2385
|
1678 int nr = rows (); |
|
|
1679 int nc = cols (); |
|
|
1680 |
|
|
1681 int a_nr = a.rows (); |
|
|
1682 int a_nc = a.cols (); |
|
|
1683 |
|
|
1684 if (nr != a_nr || nc != a_nc) |
|
458
|
1685 { |
|
2385
|
1686 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1687 return *this; |
|
|
1688 } |
|
|
1689 |
|
|
1690 for (int i = 0; i < a.length (); i++) |
|
|
1691 elem (i, i) -= a.elem (i, i); |
|
|
1692 |
|
|
1693 return *this; |
|
|
1694 } |
|
|
1695 |
|
|
1696 // unary operations |
|
|
1697 |
|
2964
|
1698 boolMatrix |
|
458
|
1699 Matrix::operator ! (void) const |
|
|
1700 { |
|
|
1701 int nr = rows (); |
|
|
1702 int nc = cols (); |
|
|
1703 |
|
2964
|
1704 boolMatrix b (nr, nc); |
|
458
|
1705 |
|
|
1706 for (int j = 0; j < nc; j++) |
|
|
1707 for (int i = 0; i < nr; i++) |
|
|
1708 b.elem (i, j) = ! elem (i, j); |
|
|
1709 |
|
|
1710 return b; |
|
|
1711 } |
|
|
1712 |
|
1205
|
1713 // column vector by row vector -> matrix operations |
|
458
|
1714 |
|
1205
|
1715 Matrix |
|
|
1716 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
1717 { |
|
1948
|
1718 Matrix retval; |
|
|
1719 |
|
1205
|
1720 int len = v.length (); |
|
3233
|
1721 |
|
|
1722 if (len != 0) |
|
1205
|
1723 { |
|
3233
|
1724 int a_len = a.length (); |
|
|
1725 |
|
|
1726 retval.resize (len, a_len); |
|
|
1727 double *c = retval.fortran_vec (); |
|
|
1728 |
|
|
1729 F77_XFCN (dgemm, DGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
1730 v.data (), len, a.data (), 1, 0.0, |
|
|
1731 c, len, 1L, 1L)); |
|
|
1732 |
|
|
1733 if (f77_exception_encountered) |
|
|
1734 (*current_liboctave_error_handler) |
|
|
1735 ("unrecoverable error in dgemm"); |
|
1205
|
1736 } |
|
458
|
1737 |
|
1948
|
1738 return retval; |
|
458
|
1739 } |
|
|
1740 |
|
|
1741 // other operations. |
|
|
1742 |
|
|
1743 Matrix |
|
2676
|
1744 Matrix::map (d_d_Mapper f) const |
|
1205
|
1745 { |
|
2676
|
1746 Matrix b (*this); |
|
|
1747 return b.apply (f); |
|
1205
|
1748 } |
|
|
1749 |
|
3248
|
1750 boolMatrix |
|
|
1751 Matrix::map (b_d_Mapper f) const |
|
|
1752 { |
|
|
1753 int nr = rows (); |
|
|
1754 int nc = cols (); |
|
|
1755 |
|
|
1756 boolMatrix retval (nr, nc); |
|
|
1757 |
|
|
1758 for (int j = 0; j < nc; j++) |
|
|
1759 for (int i = 0; i < nr; i++) |
|
|
1760 retval(i,j) = f (elem(i,j)); |
|
|
1761 |
|
|
1762 return retval; |
|
|
1763 } |
|
|
1764 |
|
2676
|
1765 Matrix& |
|
|
1766 Matrix::apply (d_d_Mapper f) |
|
458
|
1767 { |
|
|
1768 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1769 |
|
|
1770 for (int i = 0; i < length (); i++) |
|
|
1771 d[i] = f (d[i]); |
|
2676
|
1772 |
|
|
1773 return *this; |
|
458
|
1774 } |
|
|
1775 |
|
2385
|
1776 bool |
|
|
1777 Matrix::any_element_is_negative (void) const |
|
|
1778 { |
|
|
1779 int nr = rows (); |
|
|
1780 int nc = cols (); |
|
|
1781 |
|
|
1782 for (int j = 0; j < nc; j++) |
|
|
1783 for (int i = 0; i < nr; i++) |
|
|
1784 if (elem (i, j) < 0.0) |
|
|
1785 return true; |
|
|
1786 |
|
|
1787 return false; |
|
|
1788 } |
|
|
1789 |
|
|
1790 |
|
|
1791 bool |
|
|
1792 Matrix::any_element_is_inf_or_nan (void) const |
|
|
1793 { |
|
|
1794 int nr = rows (); |
|
|
1795 int nc = cols (); |
|
|
1796 |
|
|
1797 for (int j = 0; j < nc; j++) |
|
|
1798 for (int i = 0; i < nr; i++) |
|
|
1799 { |
|
|
1800 double val = elem (i, j); |
|
|
1801 if (xisinf (val) || xisnan (val)) |
|
|
1802 return 1; |
|
|
1803 } |
|
|
1804 return 0; |
|
|
1805 } |
|
|
1806 |
|
|
1807 bool |
|
|
1808 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
1809 { |
|
|
1810 int nr = rows (); |
|
|
1811 int nc = cols (); |
|
|
1812 |
|
|
1813 for (int j = 0; j < nc; j++) |
|
|
1814 for (int i = 0; i < nr; i++) |
|
|
1815 { |
|
|
1816 double val = elem (i, j); |
|
|
1817 if (xisnan (val) || D_NINT (val) == val) |
|
|
1818 continue; |
|
|
1819 else |
|
|
1820 return false; |
|
|
1821 } |
|
|
1822 |
|
|
1823 return true; |
|
|
1824 } |
|
|
1825 |
|
1968
|
1826 // Return nonzero if any element of M is not an integer. Also extract |
|
|
1827 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
1828 |
|
2385
|
1829 bool |
|
1968
|
1830 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
1831 { |
|
|
1832 int nr = rows (); |
|
|
1833 int nc = cols (); |
|
|
1834 |
|
|
1835 if (nr > 0 && nc > 0) |
|
|
1836 { |
|
|
1837 max_val = elem (0, 0); |
|
|
1838 min_val = elem (0, 0); |
|
|
1839 } |
|
|
1840 else |
|
2385
|
1841 return false; |
|
1968
|
1842 |
|
|
1843 for (int j = 0; j < nc; j++) |
|
|
1844 for (int i = 0; i < nr; i++) |
|
|
1845 { |
|
|
1846 double val = elem (i, j); |
|
|
1847 |
|
|
1848 if (val > max_val) |
|
|
1849 max_val = val; |
|
|
1850 |
|
|
1851 if (val < min_val) |
|
|
1852 min_val = val; |
|
|
1853 |
|
|
1854 if (D_NINT (val) != val) |
|
2385
|
1855 return false; |
|
1968
|
1856 } |
|
2385
|
1857 |
|
|
1858 return true; |
|
1968
|
1859 } |
|
|
1860 |
|
2385
|
1861 bool |
|
1968
|
1862 Matrix::too_large_for_float (void) const |
|
|
1863 { |
|
|
1864 int nr = rows (); |
|
2385
|
1865 int nc = cols (); |
|
1968
|
1866 |
|
|
1867 for (int j = 0; j < nc; j++) |
|
|
1868 for (int i = 0; i < nr; i++) |
|
|
1869 { |
|
|
1870 double val = elem (i, j); |
|
|
1871 |
|
|
1872 if (val > FLT_MAX || val < FLT_MIN) |
|
2385
|
1873 return true; |
|
1968
|
1874 } |
|
|
1875 |
|
2385
|
1876 return false; |
|
1968
|
1877 } |
|
|
1878 |
|
458
|
1879 // XXX FIXME XXX Do these really belong here? They should maybe be |
|
|
1880 // cleaned up a bit, no? What about corresponding functions for the |
|
|
1881 // Vectors? |
|
|
1882 |
|
2832
|
1883 boolMatrix |
|
458
|
1884 Matrix::all (void) const |
|
|
1885 { |
|
|
1886 int nr = rows (); |
|
|
1887 int nc = cols (); |
|
2832
|
1888 boolMatrix retval; |
|
458
|
1889 if (nr > 0 && nc > 0) |
|
|
1890 { |
|
|
1891 if (nr == 1) |
|
|
1892 { |
|
|
1893 retval.resize (1, 1); |
|
2832
|
1894 retval.elem (0, 0) = true; |
|
458
|
1895 for (int j = 0; j < nc; j++) |
|
|
1896 { |
|
|
1897 if (elem (0, j) == 0.0) |
|
|
1898 { |
|
2832
|
1899 retval.elem (0, 0) = false; |
|
458
|
1900 break; |
|
|
1901 } |
|
|
1902 } |
|
|
1903 } |
|
|
1904 else if (nc == 1) |
|
|
1905 { |
|
|
1906 retval.resize (1, 1); |
|
2832
|
1907 retval.elem (0, 0) = true; |
|
458
|
1908 for (int i = 0; i < nr; i++) |
|
|
1909 { |
|
|
1910 if (elem (i, 0) == 0.0) |
|
|
1911 { |
|
2832
|
1912 retval.elem (0, 0) = false; |
|
458
|
1913 break; |
|
|
1914 } |
|
|
1915 } |
|
|
1916 } |
|
|
1917 else |
|
|
1918 { |
|
|
1919 retval.resize (1, nc); |
|
|
1920 for (int j = 0; j < nc; j++) |
|
|
1921 { |
|
2832
|
1922 retval.elem (0, j) = true; |
|
458
|
1923 for (int i = 0; i < nr; i++) |
|
|
1924 { |
|
|
1925 if (elem (i, j) == 0.0) |
|
|
1926 { |
|
2832
|
1927 retval.elem (0, j) = false; |
|
458
|
1928 break; |
|
|
1929 } |
|
|
1930 } |
|
|
1931 } |
|
|
1932 } |
|
|
1933 } |
|
|
1934 return retval; |
|
|
1935 } |
|
|
1936 |
|
2832
|
1937 boolMatrix |
|
458
|
1938 Matrix::any (void) const |
|
|
1939 { |
|
|
1940 int nr = rows (); |
|
|
1941 int nc = cols (); |
|
2832
|
1942 boolMatrix retval; |
|
458
|
1943 if (nr > 0 && nc > 0) |
|
|
1944 { |
|
|
1945 if (nr == 1) |
|
|
1946 { |
|
|
1947 retval.resize (1, 1); |
|
2832
|
1948 retval.elem (0, 0) = false; |
|
458
|
1949 for (int j = 0; j < nc; j++) |
|
|
1950 { |
|
|
1951 if (elem (0, j) != 0.0) |
|
|
1952 { |
|
2832
|
1953 retval.elem (0, 0) = true; |
|
458
|
1954 break; |
|
|
1955 } |
|
|
1956 } |
|
|
1957 } |
|
|
1958 else if (nc == 1) |
|
|
1959 { |
|
|
1960 retval.resize (1, 1); |
|
2832
|
1961 retval.elem (0, 0) = false; |
|
458
|
1962 for (int i = 0; i < nr; i++) |
|
|
1963 { |
|
|
1964 if (elem (i, 0) != 0.0) |
|
|
1965 { |
|
2832
|
1966 retval.elem (0, 0) = true; |
|
458
|
1967 break; |
|
|
1968 } |
|
|
1969 } |
|
|
1970 } |
|
|
1971 else |
|
|
1972 { |
|
|
1973 retval.resize (1, nc); |
|
|
1974 for (int j = 0; j < nc; j++) |
|
|
1975 { |
|
2832
|
1976 retval.elem (0, j) = false; |
|
458
|
1977 for (int i = 0; i < nr; i++) |
|
|
1978 { |
|
|
1979 if (elem (i, j) != 0.0) |
|
|
1980 { |
|
2832
|
1981 retval.elem (0, j) = true; |
|
458
|
1982 break; |
|
|
1983 } |
|
|
1984 } |
|
|
1985 } |
|
|
1986 } |
|
|
1987 } |
|
|
1988 return retval; |
|
|
1989 } |
|
|
1990 |
|
|
1991 Matrix |
|
3723
|
1992 Matrix::cumprod (int dim) const |
|
458
|
1993 { |
|
3864
|
1994 MX_CUMMULATIVE_OP (Matrix, double, *=); |
|
458
|
1995 } |
|
|
1996 |
|
|
1997 Matrix |
|
3723
|
1998 Matrix::cumsum (int dim) const |
|
458
|
1999 { |
|
3864
|
2000 MX_CUMMULATIVE_OP (Matrix, double, +=); |
|
458
|
2001 } |
|
|
2002 |
|
|
2003 Matrix |
|
3723
|
2004 Matrix::prod (int dim) const |
|
458
|
2005 { |
|
3864
|
2006 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2007 } |
|
|
2008 |
|
|
2009 Matrix |
|
3723
|
2010 Matrix::sum (int dim) const |
|
458
|
2011 { |
|
3864
|
2012 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2013 } |
|
|
2014 |
|
|
2015 Matrix |
|
3723
|
2016 Matrix::sumsq (int dim) const |
|
458
|
2017 { |
|
3864
|
2018 #define ROW_EXPR \ |
|
|
2019 double d = elem (i, j); \ |
|
|
2020 retval.elem (i, 0) += d * d |
|
|
2021 |
|
|
2022 #define COL_EXPR \ |
|
|
2023 double d = elem (i, j); \ |
|
|
2024 retval.elem (0, j) += d * d |
|
|
2025 |
|
|
2026 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2027 |
|
|
2028 #undef ROW_EXPR |
|
|
2029 #undef COL_EXPR |
|
458
|
2030 } |
|
|
2031 |
|
2385
|
2032 Matrix |
|
|
2033 Matrix::abs (void) const |
|
|
2034 { |
|
|
2035 int nr = rows (); |
|
|
2036 int nc = cols (); |
|
|
2037 |
|
|
2038 Matrix retval (nr, nc); |
|
|
2039 |
|
|
2040 for (int j = 0; j < nc; j++) |
|
|
2041 for (int i = 0; i < nr; i++) |
|
|
2042 retval (i, j) = fabs (elem (i, j)); |
|
|
2043 |
|
|
2044 return retval; |
|
|
2045 } |
|
|
2046 |
|
458
|
2047 ColumnVector |
|
|
2048 Matrix::diag (void) const |
|
|
2049 { |
|
|
2050 return diag (0); |
|
|
2051 } |
|
|
2052 |
|
|
2053 ColumnVector |
|
|
2054 Matrix::diag (int k) const |
|
|
2055 { |
|
|
2056 int nnr = rows (); |
|
|
2057 int nnc = cols (); |
|
|
2058 if (k > 0) |
|
|
2059 nnc -= k; |
|
|
2060 else if (k < 0) |
|
|
2061 nnr += k; |
|
|
2062 |
|
|
2063 ColumnVector d; |
|
|
2064 |
|
|
2065 if (nnr > 0 && nnc > 0) |
|
|
2066 { |
|
|
2067 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2068 |
|
|
2069 d.resize (ndiag); |
|
|
2070 |
|
|
2071 if (k > 0) |
|
|
2072 { |
|
|
2073 for (int i = 0; i < ndiag; i++) |
|
|
2074 d.elem (i) = elem (i, i+k); |
|
|
2075 } |
|
|
2076 else if ( k < 0) |
|
|
2077 { |
|
|
2078 for (int i = 0; i < ndiag; i++) |
|
|
2079 d.elem (i) = elem (i-k, i); |
|
|
2080 } |
|
|
2081 else |
|
|
2082 { |
|
|
2083 for (int i = 0; i < ndiag; i++) |
|
|
2084 d.elem (i) = elem (i, i); |
|
|
2085 } |
|
|
2086 } |
|
|
2087 else |
|
3504
|
2088 std::cerr << "diag: requested diagonal out of range\n"; |
|
458
|
2089 |
|
|
2090 return d; |
|
|
2091 } |
|
|
2092 |
|
|
2093 ColumnVector |
|
|
2094 Matrix::row_min (void) const |
|
|
2095 { |
|
2354
|
2096 Array<int> index; |
|
|
2097 return row_min (index); |
|
458
|
2098 } |
|
|
2099 |
|
|
2100 ColumnVector |
|
2354
|
2101 Matrix::row_min (Array<int>& index) const |
|
458
|
2102 { |
|
|
2103 ColumnVector result; |
|
|
2104 |
|
|
2105 int nr = rows (); |
|
|
2106 int nc = cols (); |
|
|
2107 |
|
|
2108 if (nr > 0 && nc > 0) |
|
|
2109 { |
|
|
2110 result.resize (nr); |
|
2354
|
2111 index.resize (nr); |
|
458
|
2112 |
|
|
2113 for (int i = 0; i < nr; i++) |
|
|
2114 { |
|
3504
|
2115 int idx_j = 0; |
|
|
2116 |
|
|
2117 double tmp_min = elem (i, idx_j); |
|
2354
|
2118 |
|
|
2119 if (xisnan (tmp_min)) |
|
3504
|
2120 idx_j = -1; |
|
2354
|
2121 else |
|
|
2122 { |
|
|
2123 for (int j = 1; j < nc; j++) |
|
|
2124 { |
|
|
2125 double tmp = elem (i, j); |
|
|
2126 |
|
|
2127 if (xisnan (tmp)) |
|
|
2128 { |
|
3504
|
2129 idx_j = -1; |
|
2354
|
2130 break; |
|
|
2131 } |
|
|
2132 else if (tmp < tmp_min) |
|
|
2133 { |
|
3504
|
2134 idx_j = j; |
|
2354
|
2135 tmp_min = tmp; |
|
|
2136 } |
|
|
2137 } |
|
|
2138 } |
|
|
2139 |
|
3504
|
2140 result.elem (i) = (idx_j < 0) ? octave_NaN : tmp_min; |
|
|
2141 index.elem (i) = idx_j; |
|
458
|
2142 } |
|
|
2143 } |
|
|
2144 |
|
|
2145 return result; |
|
|
2146 } |
|
|
2147 |
|
|
2148 ColumnVector |
|
|
2149 Matrix::row_max (void) const |
|
|
2150 { |
|
2354
|
2151 Array<int> index; |
|
|
2152 return row_max (index); |
|
458
|
2153 } |
|
|
2154 |
|
|
2155 ColumnVector |
|
2354
|
2156 Matrix::row_max (Array<int>& index) const |
|
458
|
2157 { |
|
|
2158 ColumnVector result; |
|
|
2159 |
|
|
2160 int nr = rows (); |
|
|
2161 int nc = cols (); |
|
|
2162 |
|
|
2163 if (nr > 0 && nc > 0) |
|
|
2164 { |
|
|
2165 result.resize (nr); |
|
2354
|
2166 index.resize (nr); |
|
458
|
2167 |
|
|
2168 for (int i = 0; i < nr; i++) |
|
|
2169 { |
|
3504
|
2170 int idx_j = 0; |
|
|
2171 |
|
|
2172 double tmp_max = elem (i, idx_j); |
|
2354
|
2173 |
|
|
2174 if (xisnan (tmp_max)) |
|
3504
|
2175 idx_j = -1; |
|
2354
|
2176 else |
|
|
2177 { |
|
|
2178 for (int j = 1; j < nc; j++) |
|
|
2179 { |
|
|
2180 double tmp = elem (i, j); |
|
|
2181 |
|
|
2182 if (xisnan (tmp)) |
|
|
2183 { |
|
3504
|
2184 idx_j = -1; |
|
2354
|
2185 break; |
|
|
2186 } |
|
|
2187 else if (tmp > tmp_max) |
|
|
2188 { |
|
3504
|
2189 idx_j = j; |
|
2354
|
2190 tmp_max = tmp; |
|
|
2191 } |
|
|
2192 } |
|
|
2193 } |
|
|
2194 |
|
3504
|
2195 result.elem (i) = (idx_j < 0) ? octave_NaN : tmp_max; |
|
|
2196 index.elem (i) = idx_j; |
|
458
|
2197 } |
|
|
2198 } |
|
|
2199 |
|
|
2200 return result; |
|
|
2201 } |
|
|
2202 |
|
|
2203 RowVector |
|
|
2204 Matrix::column_min (void) const |
|
|
2205 { |
|
2354
|
2206 Array<int> index; |
|
|
2207 return column_min (index); |
|
458
|
2208 } |
|
2354
|
2209 |
|
458
|
2210 RowVector |
|
2354
|
2211 Matrix::column_min (Array<int>& index) const |
|
458
|
2212 { |
|
|
2213 RowVector result; |
|
|
2214 |
|
|
2215 int nr = rows (); |
|
|
2216 int nc = cols (); |
|
|
2217 |
|
|
2218 if (nr > 0 && nc > 0) |
|
|
2219 { |
|
|
2220 result.resize (nc); |
|
2354
|
2221 index.resize (nc); |
|
458
|
2222 |
|
|
2223 for (int j = 0; j < nc; j++) |
|
|
2224 { |
|
3504
|
2225 int idx_i = 0; |
|
|
2226 |
|
|
2227 double tmp_min = elem (idx_i, j); |
|
2354
|
2228 |
|
|
2229 if (xisnan (tmp_min)) |
|
3504
|
2230 idx_i = -1; |
|
2354
|
2231 else |
|
|
2232 { |
|
|
2233 for (int i = 1; i < nr; i++) |
|
|
2234 { |
|
|
2235 double tmp = elem (i, j); |
|
|
2236 |
|
|
2237 if (xisnan (tmp)) |
|
|
2238 { |
|
3504
|
2239 idx_i = -1; |
|
2354
|
2240 break; |
|
|
2241 } |
|
|
2242 else if (tmp < tmp_min) |
|
|
2243 { |
|
3504
|
2244 idx_i = i; |
|
2354
|
2245 tmp_min = tmp; |
|
|
2246 } |
|
|
2247 } |
|
|
2248 } |
|
|
2249 |
|
3504
|
2250 result.elem (j) = (idx_i < 0) ? octave_NaN : tmp_min; |
|
|
2251 index.elem (j) = idx_i; |
|
458
|
2252 } |
|
|
2253 } |
|
|
2254 |
|
|
2255 return result; |
|
|
2256 } |
|
|
2257 |
|
2354
|
2258 RowVector |
|
|
2259 Matrix::column_max (void) const |
|
|
2260 { |
|
|
2261 Array<int> index; |
|
|
2262 return column_max (index); |
|
|
2263 } |
|
458
|
2264 |
|
|
2265 RowVector |
|
2354
|
2266 Matrix::column_max (Array<int>& index) const |
|
458
|
2267 { |
|
|
2268 RowVector result; |
|
|
2269 |
|
|
2270 int nr = rows (); |
|
|
2271 int nc = cols (); |
|
|
2272 |
|
|
2273 if (nr > 0 && nc > 0) |
|
|
2274 { |
|
|
2275 result.resize (nc); |
|
2354
|
2276 index.resize (nc); |
|
458
|
2277 |
|
|
2278 for (int j = 0; j < nc; j++) |
|
|
2279 { |
|
3504
|
2280 int idx_i = 0; |
|
|
2281 |
|
|
2282 double tmp_max = elem (idx_i, j); |
|
2354
|
2283 |
|
|
2284 if (xisnan (tmp_max)) |
|
3504
|
2285 idx_i = -1; |
|
2354
|
2286 else |
|
|
2287 { |
|
|
2288 for (int i = 1; i < nr; i++) |
|
|
2289 { |
|
|
2290 double tmp = elem (i, j); |
|
|
2291 |
|
|
2292 if (xisnan (tmp)) |
|
|
2293 { |
|
3504
|
2294 idx_i = -1; |
|
2354
|
2295 break; |
|
|
2296 } |
|
|
2297 else if (tmp > tmp_max) |
|
|
2298 { |
|
3504
|
2299 idx_i = i; |
|
2354
|
2300 tmp_max = tmp; |
|
|
2301 } |
|
|
2302 } |
|
|
2303 } |
|
|
2304 |
|
3504
|
2305 result.elem (j) = (idx_i < 0) ? octave_NaN : tmp_max; |
|
|
2306 index.elem (j) = idx_i; |
|
458
|
2307 } |
|
|
2308 } |
|
|
2309 |
|
|
2310 return result; |
|
|
2311 } |
|
|
2312 |
|
3504
|
2313 std::ostream& |
|
|
2314 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2315 { |
|
|
2316 // int field_width = os.precision () + 7; |
|
1360
|
2317 |
|
458
|
2318 for (int i = 0; i < a.rows (); i++) |
|
|
2319 { |
|
|
2320 for (int j = 0; j < a.cols (); j++) |
|
|
2321 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2322 os << "\n"; |
|
|
2323 } |
|
|
2324 return os; |
|
|
2325 } |
|
|
2326 |
|
3504
|
2327 std::istream& |
|
|
2328 operator >> (std::istream& is, Matrix& a) |
|
458
|
2329 { |
|
|
2330 int nr = a.rows (); |
|
|
2331 int nc = a.cols (); |
|
|
2332 |
|
|
2333 if (nr < 1 || nc < 1) |
|
3504
|
2334 is.clear (std::ios::badbit); |
|
458
|
2335 else |
|
|
2336 { |
|
|
2337 double tmp; |
|
|
2338 for (int i = 0; i < nr; i++) |
|
|
2339 for (int j = 0; j < nc; j++) |
|
|
2340 { |
|
|
2341 is >> tmp; |
|
|
2342 if (is) |
|
|
2343 a.elem (i, j) = tmp; |
|
|
2344 else |
|
2795
|
2345 goto done; |
|
458
|
2346 } |
|
|
2347 } |
|
|
2348 |
|
2795
|
2349 done: |
|
|
2350 |
|
458
|
2351 return is; |
|
|
2352 } |
|
|
2353 |
|
2317
|
2354 template <class T> |
|
3504
|
2355 void |
|
|
2356 read_int (std::istream& is, bool swap_bytes, T& val) |
|
2317
|
2357 { |
|
3145
|
2358 is.read (X_CAST (char *, &val), sizeof (T)); |
|
2317
|
2359 |
|
|
2360 if (swap_bytes) |
|
|
2361 { |
|
|
2362 switch (sizeof (T)) |
|
|
2363 { |
|
|
2364 case 1: |
|
|
2365 break; |
|
|
2366 |
|
|
2367 case 2: |
|
3145
|
2368 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2369 break; |
|
|
2370 |
|
|
2371 case 4: |
|
3145
|
2372 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2373 break; |
|
|
2374 |
|
|
2375 case 8: |
|
3145
|
2376 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2377 break; |
|
|
2378 |
|
|
2379 default: |
|
|
2380 (*current_liboctave_error_handler) |
|
|
2381 ("read_int: unrecognized data format!"); |
|
|
2382 } |
|
|
2383 } |
|
|
2384 } |
|
|
2385 |
|
3504
|
2386 template void read_int (std::istream&, bool, char&); |
|
|
2387 template void read_int (std::istream&, bool, signed char&); |
|
|
2388 template void read_int (std::istream&, bool, unsigned char&); |
|
|
2389 template void read_int (std::istream&, bool, short&); |
|
|
2390 template void read_int (std::istream&, bool, unsigned short&); |
|
|
2391 template void read_int (std::istream&, bool, int&); |
|
|
2392 template void read_int (std::istream&, bool, unsigned int&); |
|
|
2393 template void read_int (std::istream&, bool, long&); |
|
|
2394 template void read_int (std::istream&, bool, unsigned long&); |
|
2317
|
2395 |
|
|
2396 static inline bool |
|
3504
|
2397 do_read (std::istream& is, oct_data_conv::data_type dt, |
|
2317
|
2398 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2399 bool do_float_conversion, double& val) |
|
|
2400 { |
|
|
2401 bool retval = true; |
|
|
2402 |
|
|
2403 switch (dt) |
|
|
2404 { |
|
|
2405 case oct_data_conv::dt_char: |
|
|
2406 { |
|
|
2407 char tmp; |
|
|
2408 read_int (is, swap_bytes, tmp); |
|
|
2409 val = tmp; |
|
|
2410 } |
|
|
2411 break; |
|
|
2412 |
|
|
2413 case oct_data_conv::dt_schar: |
|
|
2414 { |
|
|
2415 signed char tmp; |
|
|
2416 read_int (is, swap_bytes, tmp); |
|
|
2417 val = tmp; |
|
|
2418 } |
|
|
2419 break; |
|
|
2420 |
|
|
2421 case oct_data_conv::dt_uchar: |
|
|
2422 { |
|
|
2423 unsigned char tmp; |
|
|
2424 read_int (is, swap_bytes, tmp); |
|
|
2425 val = tmp; |
|
|
2426 } |
|
|
2427 break; |
|
|
2428 |
|
|
2429 case oct_data_conv::dt_short: |
|
|
2430 { |
|
|
2431 short tmp; |
|
|
2432 read_int (is, swap_bytes, tmp); |
|
|
2433 val = tmp; |
|
|
2434 } |
|
|
2435 break; |
|
|
2436 |
|
|
2437 case oct_data_conv::dt_ushort: |
|
|
2438 { |
|
|
2439 unsigned short tmp; |
|
|
2440 read_int (is, swap_bytes, tmp); |
|
|
2441 val = tmp; |
|
|
2442 } |
|
|
2443 break; |
|
|
2444 |
|
|
2445 case oct_data_conv::dt_int: |
|
|
2446 { |
|
|
2447 int tmp; |
|
|
2448 read_int (is, swap_bytes, tmp); |
|
|
2449 val = tmp; |
|
|
2450 } |
|
|
2451 break; |
|
|
2452 |
|
|
2453 case oct_data_conv::dt_uint: |
|
|
2454 { |
|
|
2455 unsigned int tmp; |
|
|
2456 read_int (is, swap_bytes, tmp); |
|
|
2457 val = tmp; |
|
|
2458 } |
|
|
2459 break; |
|
|
2460 |
|
|
2461 case oct_data_conv::dt_long: |
|
|
2462 { |
|
|
2463 long tmp; |
|
|
2464 read_int (is, swap_bytes, tmp); |
|
|
2465 val = tmp; |
|
|
2466 } |
|
|
2467 break; |
|
|
2468 |
|
|
2469 case oct_data_conv::dt_ulong: |
|
|
2470 { |
|
|
2471 unsigned long tmp; |
|
|
2472 read_int (is, swap_bytes, tmp); |
|
|
2473 val = tmp; |
|
|
2474 } |
|
|
2475 break; |
|
|
2476 |
|
|
2477 case oct_data_conv::dt_float: |
|
|
2478 { |
|
|
2479 float f; |
|
|
2480 |
|
3145
|
2481 is.read (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2482 |
|
|
2483 if (do_float_conversion) |
|
|
2484 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2485 |
|
|
2486 val = f; |
|
|
2487 } |
|
|
2488 break; |
|
|
2489 |
|
|
2490 case oct_data_conv::dt_double: |
|
|
2491 { |
|
3145
|
2492 is.read (X_CAST (char *, &val), sizeof (double)); |
|
2317
|
2493 |
|
|
2494 if (do_float_conversion) |
|
|
2495 do_double_format_conversion (&val, 1, flt_fmt); |
|
|
2496 } |
|
|
2497 break; |
|
|
2498 |
|
|
2499 default: |
|
|
2500 retval = false; |
|
|
2501 (*current_liboctave_error_handler) |
|
|
2502 ("read: invalid type specification"); |
|
|
2503 break; |
|
|
2504 } |
|
|
2505 |
|
|
2506 return retval; |
|
|
2507 } |
|
1360
|
2508 |
|
458
|
2509 int |
|
3504
|
2510 Matrix::read (std::istream& is, int nr, int nc, |
|
2317
|
2511 oct_data_conv::data_type dt, int skip, |
|
|
2512 oct_mach_info::float_format flt_fmt) |
|
458
|
2513 { |
|
2317
|
2514 int retval = -1; |
|
|
2515 |
|
|
2516 bool ok = true; |
|
|
2517 |
|
|
2518 int count = 0; |
|
|
2519 |
|
|
2520 double *data = 0; |
|
|
2521 int max_size = 0; |
|
|
2522 |
|
|
2523 int final_nr = 0; |
|
|
2524 int final_nc = 0; |
|
|
2525 |
|
|
2526 if (nr > 0) |
|
458
|
2527 { |
|
2317
|
2528 if (nc > 0) |
|
|
2529 { |
|
|
2530 resize (nr, nc, 0.0); |
|
|
2531 data = fortran_vec (); |
|
|
2532 max_size = nr * nc; |
|
|
2533 } |
|
|
2534 else |
|
|
2535 { |
|
|
2536 resize (nr, 32, 0.0); |
|
|
2537 data = fortran_vec (); |
|
|
2538 max_size = nr * 32; |
|
|
2539 } |
|
|
2540 } |
|
471
|
2541 else |
|
|
2542 { |
|
2317
|
2543 resize (32, 1, 0.0); |
|
|
2544 data = fortran_vec (); |
|
|
2545 max_size = 32; |
|
|
2546 } |
|
|
2547 |
|
|
2548 oct_mach_info::float_format native_flt_fmt |
|
|
2549 = oct_mach_info::float_format (); |
|
|
2550 |
|
|
2551 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2552 |
|
|
2553 // XXX FIXME XXX -- byte order for Cray? |
|
|
2554 |
|
|
2555 bool swap_bytes = false; |
|
|
2556 |
|
|
2557 if (oct_mach_info::words_big_endian ()) |
|
|
2558 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2559 || flt_fmt == oct_mach_info::vax_g |
|
|
2560 || flt_fmt == oct_mach_info::vax_g); |
|
|
2561 else |
|
|
2562 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2563 |
|
|
2564 for (;;) |
|
|
2565 { |
|
|
2566 // XXX FIXME XXX -- maybe there should be a special case for |
|
|
2567 // skip == 0. |
|
|
2568 |
|
|
2569 if (is) |
|
|
2570 { |
|
|
2571 if (nr > 0 && nc > 0 && count == max_size) |
|
|
2572 { |
|
|
2573 final_nr = nr; |
|
|
2574 final_nc = nc; |
|
|
2575 |
|
|
2576 break; |
|
|
2577 } |
|
|
2578 |
|
|
2579 if (is) |
|
|
2580 { |
|
|
2581 double tmp = 0.0; |
|
|
2582 |
|
|
2583 ok = do_read (is, dt, flt_fmt, swap_bytes, |
|
|
2584 do_float_conversion, tmp); |
|
|
2585 |
|
|
2586 if (ok) |
|
|
2587 { |
|
|
2588 if (is) |
|
|
2589 { |
|
|
2590 if (count == max_size) |
|
|
2591 { |
|
|
2592 max_size *= 2; |
|
|
2593 |
|
|
2594 if (nr > 0) |
|
2601
|
2595 resize (nr, max_size / nr, 0.0); |
|
2317
|
2596 else |
|
|
2597 resize (max_size, 1, 0.0); |
|
|
2598 |
|
|
2599 data = fortran_vec (); |
|
|
2600 } |
|
|
2601 |
|
|
2602 data[count++] = tmp; |
|
|
2603 } |
|
3180
|
2604 |
|
|
2605 if (ok && skip != 0) |
|
3504
|
2606 is.seekg (skip, std::ios::cur); |
|
3180
|
2607 |
|
3219
|
2608 if (! ok || is.eof ()) |
|
2317
|
2609 { |
|
|
2610 if (is.eof ()) |
|
|
2611 { |
|
|
2612 if (nr > 0) |
|
|
2613 { |
|
|
2614 if (count > nr) |
|
|
2615 { |
|
|
2616 final_nr = nr; |
|
|
2617 final_nc = (count - 1) / nr + 1; |
|
|
2618 } |
|
|
2619 else |
|
|
2620 { |
|
|
2621 final_nr = count; |
|
|
2622 final_nc = 1; |
|
|
2623 } |
|
|
2624 } |
|
|
2625 else |
|
|
2626 { |
|
|
2627 final_nr = count; |
|
|
2628 final_nc = 1; |
|
|
2629 } |
|
|
2630 } |
|
|
2631 |
|
|
2632 break; |
|
|
2633 } |
|
|
2634 } |
|
|
2635 else |
|
|
2636 break; |
|
|
2637 } |
|
|
2638 else |
|
|
2639 { |
|
|
2640 ok = false; |
|
|
2641 break; |
|
|
2642 } |
|
|
2643 } |
|
|
2644 else |
|
|
2645 { |
|
|
2646 ok = false; |
|
|
2647 break; |
|
|
2648 } |
|
|
2649 } |
|
|
2650 |
|
|
2651 if (ok) |
|
|
2652 { |
|
|
2653 resize (final_nr, final_nc, 0.0); |
|
|
2654 |
|
|
2655 retval = count; |
|
458
|
2656 } |
|
|
2657 |
|
2317
|
2658 return retval; |
|
|
2659 } |
|
|
2660 |
|
|
2661 template <class T> |
|
3504
|
2662 void |
|
|
2663 write_int (std::ostream& os, bool swap_bytes, T val) |
|
2317
|
2664 { |
|
|
2665 if (swap_bytes) |
|
|
2666 { |
|
|
2667 switch (sizeof (T)) |
|
|
2668 { |
|
|
2669 case 1: |
|
|
2670 break; |
|
|
2671 |
|
|
2672 case 2: |
|
3145
|
2673 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2674 break; |
|
|
2675 |
|
|
2676 case 4: |
|
3145
|
2677 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2678 break; |
|
|
2679 |
|
|
2680 case 8: |
|
3145
|
2681 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2682 break; |
|
|
2683 |
|
|
2684 default: |
|
|
2685 (*current_liboctave_error_handler) |
|
|
2686 ("write_int: unrecognized data format!"); |
|
|
2687 } |
|
|
2688 } |
|
|
2689 |
|
3145
|
2690 os.write (X_CAST (char *, &val), sizeof (T)); |
|
458
|
2691 } |
|
|
2692 |
|
3504
|
2693 template void write_int (std::ostream&, bool, char); |
|
|
2694 template void write_int (std::ostream&, bool, signed char); |
|
|
2695 template void write_int (std::ostream&, bool, unsigned char); |
|
|
2696 template void write_int (std::ostream&, bool, short); |
|
|
2697 template void write_int (std::ostream&, bool, unsigned short); |
|
|
2698 template void write_int (std::ostream&, bool, int); |
|
|
2699 template void write_int (std::ostream&, bool, unsigned int); |
|
|
2700 template void write_int (std::ostream&, bool, long); |
|
|
2701 template void write_int (std::ostream&, bool, unsigned long); |
|
2317
|
2702 |
|
|
2703 static inline bool |
|
3504
|
2704 do_write (std::ostream& os, double d, oct_data_conv::data_type dt, |
|
2317
|
2705 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2706 bool do_float_conversion) |
|
|
2707 { |
|
|
2708 bool retval = true; |
|
|
2709 |
|
|
2710 switch (dt) |
|
|
2711 { |
|
|
2712 case oct_data_conv::dt_char: |
|
3145
|
2713 write_int (os, swap_bytes, X_CAST (char, d)); |
|
2317
|
2714 break; |
|
|
2715 |
|
|
2716 case oct_data_conv::dt_schar: |
|
3145
|
2717 write_int (os, swap_bytes, X_CAST (signed char, d)); |
|
2317
|
2718 break; |
|
|
2719 |
|
|
2720 case oct_data_conv::dt_uchar: |
|
3145
|
2721 write_int (os, swap_bytes, X_CAST (unsigned char, d)); |
|
2317
|
2722 break; |
|
|
2723 |
|
|
2724 case oct_data_conv::dt_short: |
|
3145
|
2725 write_int (os, swap_bytes, X_CAST (short, d)); |
|
2317
|
2726 break; |
|
|
2727 |
|
|
2728 case oct_data_conv::dt_ushort: |
|
3145
|
2729 write_int (os, swap_bytes, X_CAST (unsigned short, d)); |
|
2317
|
2730 break; |
|
|
2731 |
|
|
2732 case oct_data_conv::dt_int: |
|
3145
|
2733 write_int (os, swap_bytes, X_CAST (int, d)); |
|
2317
|
2734 break; |
|
|
2735 |
|
|
2736 case oct_data_conv::dt_uint: |
|
3145
|
2737 write_int (os, swap_bytes, X_CAST (unsigned int, d)); |
|
2317
|
2738 break; |
|
|
2739 |
|
|
2740 case oct_data_conv::dt_long: |
|
3145
|
2741 write_int (os, swap_bytes, X_CAST (long, d)); |
|
2317
|
2742 break; |
|
|
2743 |
|
|
2744 case oct_data_conv::dt_ulong: |
|
3145
|
2745 write_int (os, swap_bytes, X_CAST (unsigned long, d)); |
|
2317
|
2746 break; |
|
|
2747 |
|
|
2748 case oct_data_conv::dt_float: |
|
|
2749 { |
|
2800
|
2750 float f = d; |
|
2317
|
2751 |
|
|
2752 if (do_float_conversion) |
|
|
2753 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2754 |
|
3145
|
2755 os.write (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2756 } |
|
|
2757 break; |
|
|
2758 |
|
|
2759 case oct_data_conv::dt_double: |
|
|
2760 { |
|
|
2761 if (do_float_conversion) |
|
|
2762 do_double_format_conversion (&d, 1, flt_fmt); |
|
|
2763 |
|
3145
|
2764 os.write (X_CAST (char *, &d), sizeof (double)); |
|
2317
|
2765 } |
|
|
2766 break; |
|
|
2767 |
|
|
2768 default: |
|
|
2769 retval = false; |
|
|
2770 (*current_liboctave_error_handler) |
|
|
2771 ("write: invalid type specification"); |
|
|
2772 break; |
|
|
2773 } |
|
|
2774 |
|
|
2775 return retval; |
|
|
2776 } |
|
1360
|
2777 |
|
458
|
2778 int |
|
3504
|
2779 Matrix::write (std::ostream& os, oct_data_conv::data_type dt, int skip, |
|
2317
|
2780 oct_mach_info::float_format flt_fmt) |
|
458
|
2781 { |
|
2317
|
2782 int retval = -1; |
|
|
2783 |
|
|
2784 bool ok = true; |
|
|
2785 |
|
|
2786 int count = 0; |
|
|
2787 |
|
|
2788 const double *d = data (); |
|
|
2789 |
|
|
2790 int n = length (); |
|
|
2791 |
|
|
2792 oct_mach_info::float_format native_flt_fmt |
|
|
2793 = oct_mach_info::float_format (); |
|
|
2794 |
|
|
2795 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2796 |
|
|
2797 // XXX FIXME XXX -- byte order for Cray? |
|
|
2798 |
|
|
2799 bool swap_bytes = false; |
|
|
2800 |
|
|
2801 if (oct_mach_info::words_big_endian ()) |
|
|
2802 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2803 || flt_fmt == oct_mach_info::vax_g |
|
|
2804 || flt_fmt == oct_mach_info::vax_g); |
|
|
2805 else |
|
|
2806 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2807 |
|
|
2808 for (int i = 0; i < n; i++) |
|
458
|
2809 { |
|
2317
|
2810 if (os) |
|
|
2811 { |
|
|
2812 if (skip != 0) |
|
3504
|
2813 os.seekp (skip, std::ios::cur); |
|
2317
|
2814 |
|
|
2815 if (os) |
|
|
2816 { |
|
|
2817 ok = do_write (os, d[i], dt, flt_fmt, swap_bytes, |
|
|
2818 do_float_conversion); |
|
|
2819 |
|
|
2820 if (os && ok) |
|
|
2821 count++; |
|
|
2822 else |
|
|
2823 break; |
|
|
2824 } |
|
|
2825 else |
|
|
2826 { |
|
|
2827 ok = false; |
|
|
2828 break; |
|
|
2829 } |
|
|
2830 } |
|
|
2831 else |
|
|
2832 { |
|
|
2833 ok = false; |
|
|
2834 break; |
|
|
2835 } |
|
471
|
2836 } |
|
458
|
2837 |
|
2317
|
2838 if (ok) |
|
|
2839 retval = count; |
|
|
2840 |
|
|
2841 return retval; |
|
458
|
2842 } |
|
|
2843 |
|
2317
|
2844 |
|
|
2845 |
|
1819
|
2846 Matrix |
|
|
2847 Givens (double x, double y) |
|
|
2848 { |
|
|
2849 double cc, s, temp_r; |
|
|
2850 |
|
|
2851 F77_FCN (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
|
2852 |
|
|
2853 Matrix g (2, 2); |
|
|
2854 |
|
|
2855 g.elem (0, 0) = cc; |
|
|
2856 g.elem (1, 1) = cc; |
|
|
2857 g.elem (0, 1) = s; |
|
|
2858 g.elem (1, 0) = -s; |
|
|
2859 |
|
|
2860 return g; |
|
|
2861 } |
|
|
2862 |
|
|
2863 Matrix |
|
|
2864 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2865 { |
|
|
2866 Matrix retval; |
|
|
2867 |
|
|
2868 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2869 // size. |
|
|
2870 |
|
|
2871 // Compute Schur decompositions. |
|
|
2872 |
|
|
2873 SCHUR as (a, "U"); |
|
|
2874 SCHUR bs (b, "U"); |
|
|
2875 |
|
|
2876 // Transform c to new coordinates. |
|
|
2877 |
|
|
2878 Matrix ua = as.unitary_matrix (); |
|
|
2879 Matrix sch_a = as.schur_matrix (); |
|
|
2880 |
|
|
2881 Matrix ub = bs.unitary_matrix (); |
|
|
2882 Matrix sch_b = bs.schur_matrix (); |
|
|
2883 |
|
|
2884 Matrix cx = ua.transpose () * c * ub; |
|
|
2885 |
|
|
2886 // Solve the sylvester equation, back-transform, and return the |
|
|
2887 // solution. |
|
|
2888 |
|
|
2889 int a_nr = a.rows (); |
|
|
2890 int b_nr = b.rows (); |
|
|
2891 |
|
|
2892 double scale; |
|
|
2893 int info; |
|
|
2894 |
|
1950
|
2895 double *pa = sch_a.fortran_vec (); |
|
|
2896 double *pb = sch_b.fortran_vec (); |
|
|
2897 double *px = cx.fortran_vec (); |
|
|
2898 |
|
|
2899 F77_XFCN (dtrsyl, DTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2900 b_nr, px, a_nr, scale, info, 1L, 1L)); |
|
|
2901 |
|
|
2902 |
|
|
2903 if (f77_exception_encountered) |
|
|
2904 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
2905 else |
|
|
2906 { |
|
|
2907 // XXX FIXME XXX -- check info? |
|
1819
|
2908 |
|
1950
|
2909 retval = -ua*cx*ub.transpose (); |
|
|
2910 } |
|
1819
|
2911 |
|
|
2912 return retval; |
|
|
2913 } |
|
|
2914 |
|
2828
|
2915 // matrix by matrix -> matrix operations |
|
|
2916 |
|
|
2917 Matrix |
|
|
2918 operator * (const Matrix& m, const Matrix& a) |
|
|
2919 { |
|
|
2920 Matrix retval; |
|
|
2921 |
|
|
2922 int nr = m.rows (); |
|
|
2923 int nc = m.cols (); |
|
|
2924 |
|
|
2925 int a_nr = a.rows (); |
|
|
2926 int a_nc = a.cols (); |
|
|
2927 |
|
|
2928 if (nc != a_nr) |
|
|
2929 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2930 else |
|
|
2931 { |
|
|
2932 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2933 retval.resize (nr, a_nc, 0.0); |
|
|
2934 else |
|
|
2935 { |
|
|
2936 int ld = nr; |
|
|
2937 int lda = a_nr; |
|
|
2938 |
|
|
2939 retval.resize (nr, a_nc); |
|
|
2940 double *c = retval.fortran_vec (); |
|
|
2941 |
|
|
2942 F77_XFCN (dgemm, DGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
2943 m.data (), ld, a.data (), lda, 0.0, |
|
|
2944 c, nr, 1L, 1L)); |
|
|
2945 |
|
|
2946 if (f77_exception_encountered) |
|
|
2947 (*current_liboctave_error_handler) |
|
|
2948 ("unrecoverable error in dgemm"); |
|
|
2949 } |
|
|
2950 } |
|
|
2951 |
|
|
2952 return retval; |
|
|
2953 } |
|
|
2954 |
|
2870
|
2955 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
2956 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
2957 |
|
|
2958 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
2959 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
2960 |
|
|
2961 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
2962 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
2963 |
|
458
|
2964 /* |
|
|
2965 ;;; Local Variables: *** |
|
|
2966 ;;; mode: C++ *** |
|
|
2967 ;;; End: *** |
|
|
2968 */ |
