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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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4 Copyright (C) 1996, 1997 John W. Eaton |
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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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21 02110-1301, USA. |
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22 |
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23 */ |
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24 |
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25 #ifdef HAVE_CONFIG_H |
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1192
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26 #include <config.h> |
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458
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27 #endif |
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28 |
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29 #include <cfloat> |
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30 |
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3503
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31 #include <iostream> |
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32 |
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4669
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33 #include "Array-util.h" |
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2317
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34 #include "byte-swap.h" |
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2828
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35 #include "dMatrix.h" |
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1819
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36 #include "dbleAEPBAL.h" |
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458
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37 #include "dbleDET.h" |
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1819
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38 #include "dbleSCHUR.h" |
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740
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39 #include "dbleSVD.h" |
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1847
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40 #include "f77-fcn.h" |
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458
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41 #include "lo-error.h" |
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2354
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42 #include "lo-ieee.h" |
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43 #include "lo-mappers.h" |
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44 #include "lo-utils.h" |
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1367
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45 #include "mx-base.h" |
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2828
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46 #include "mx-m-dm.h" |
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3176
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47 #include "mx-dm-m.h" |
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1367
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48 #include "mx-inlines.cc" |
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1650
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49 #include "oct-cmplx.h" |
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4153
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50 #include "quit.h" |
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51 |
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4773
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52 #if defined (HAVE_FFTW3) |
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3827
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53 #include "oct-fftw.h" |
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54 #endif |
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55 |
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458
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56 // Fortran functions we call. |
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57 |
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58 extern "C" |
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59 { |
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4552
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60 F77_RET_T |
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61 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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5275
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62 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
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63 octave_idx_type&, double*, octave_idx_type& |
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64 F77_CHAR_ARG_LEN_DECL); |
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65 |
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66 F77_RET_T |
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67 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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68 F77_CONST_CHAR_ARG_DECL, |
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5275
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69 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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70 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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71 F77_CHAR_ARG_LEN_DECL |
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72 F77_CHAR_ARG_LEN_DECL); |
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73 |
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74 |
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75 F77_RET_T |
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76 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, |
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77 F77_CONST_CHAR_ARG_DECL, |
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78 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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79 const double&, const double*, const octave_idx_type&, |
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80 const double*, const octave_idx_type&, const double&, |
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81 double*, const octave_idx_type& |
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82 F77_CHAR_ARG_LEN_DECL |
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83 F77_CHAR_ARG_LEN_DECL); |
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84 |
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85 F77_RET_T |
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86 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
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87 octave_idx_type*, octave_idx_type&); |
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88 |
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89 F77_RET_T |
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90 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
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91 const double*, const octave_idx_type&, |
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92 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& |
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93 F77_CHAR_ARG_LEN_DECL); |
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94 |
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95 F77_RET_T |
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96 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
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97 double*, const octave_idx_type&, octave_idx_type&); |
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98 |
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99 F77_RET_T |
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100 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
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101 const octave_idx_type&, const double&, double&, |
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102 double*, octave_idx_type*, octave_idx_type& |
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103 F77_CHAR_ARG_LEN_DECL); |
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104 |
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105 F77_RET_T |
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106 F77_FUNC (dgelss, DGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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107 double*, const octave_idx_type&, double*, |
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108 const octave_idx_type&, double*, double&, octave_idx_type&, |
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109 double*, const octave_idx_type&, octave_idx_type&); |
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110 |
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5785
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111 F77_RET_T |
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112 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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113 double *, const octave_idx_type&, |
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114 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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115 |
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116 F77_RET_T |
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117 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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118 double*, const octave_idx_type&, const double&, |
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119 double&, double*, octave_idx_type*, |
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120 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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121 F77_RET_T |
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122 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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123 const octave_idx_type&, const double*, |
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124 const octave_idx_type&, double*, |
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125 const octave_idx_type&, octave_idx_type& |
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126 F77_CHAR_ARG_LEN_DECL); |
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127 |
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128 F77_RET_T |
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129 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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130 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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131 const double*, const octave_idx_type&, double&, |
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132 double*, octave_idx_type*, octave_idx_type& |
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133 F77_CHAR_ARG_LEN_DECL |
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134 F77_CHAR_ARG_LEN_DECL |
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135 F77_CHAR_ARG_LEN_DECL); |
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136 F77_RET_T |
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137 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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138 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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139 const octave_idx_type&, const double*, |
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140 const octave_idx_type&, double*, |
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141 const octave_idx_type&, octave_idx_type& |
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142 F77_CHAR_ARG_LEN_DECL |
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143 F77_CHAR_ARG_LEN_DECL |
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144 F77_CHAR_ARG_LEN_DECL); |
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145 |
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1360
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146 // Note that the original complex fft routines were not written for |
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147 // double complex arguments. They have been modified by adding an |
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148 // implicit double precision (a-h,o-z) statement at the beginning of |
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149 // each subroutine. |
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150 |
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4552
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151 F77_RET_T |
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152 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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153 |
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154 F77_RET_T |
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155 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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156 |
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157 F77_RET_T |
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158 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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159 |
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160 F77_RET_T |
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161 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, |
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162 double&, double&); |
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163 |
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164 F77_RET_T |
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165 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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166 F77_CONST_CHAR_ARG_DECL, |
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5275
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167 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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168 const double*, const octave_idx_type&, const double*, |
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169 const octave_idx_type&, const double*, const octave_idx_type&, |
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170 double&, octave_idx_type& |
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171 F77_CHAR_ARG_LEN_DECL |
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172 F77_CHAR_ARG_LEN_DECL); |
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173 |
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174 F77_RET_T |
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175 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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176 const octave_idx_type&, const double*, |
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177 const octave_idx_type&, double*, double& |
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178 F77_CHAR_ARG_LEN_DECL); |
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458
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179 } |
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180 |
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181 // Matrix class. |
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182 |
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183 Matrix::Matrix (const RowVector& rv) |
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184 : MArray2<double> (1, rv.length (), 0.0) |
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185 { |
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186 for (octave_idx_type i = 0; i < rv.length (); i++) |
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187 elem (0, i) = rv.elem (i); |
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188 } |
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189 |
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190 Matrix::Matrix (const ColumnVector& cv) |
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191 : MArray2<double> (cv.length (), 1, 0.0) |
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192 { |
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193 for (octave_idx_type i = 0; i < cv.length (); i++) |
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194 elem (i, 0) = cv.elem (i); |
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195 } |
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196 |
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197 Matrix::Matrix (const DiagMatrix& a) |
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198 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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199 { |
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200 for (octave_idx_type i = 0; i < a.length (); i++) |
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201 elem (i, i) = a.elem (i, i); |
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202 } |
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203 |
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5775
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204 // FIXME -- could we use a templated mixed-type copy function |
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205 // here? |
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206 |
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207 Matrix::Matrix (const boolMatrix& a) |
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208 : MArray2<double> (a.rows (), a.cols ()) |
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209 { |
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210 for (octave_idx_type i = 0; i < a.rows (); i++) |
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211 for (octave_idx_type j = 0; j < a.cols (); j++) |
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212 elem (i, j) = a.elem (i, j); |
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213 } |
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214 |
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215 Matrix::Matrix (const charMatrix& a) |
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216 : MArray2<double> (a.rows (), a.cols ()) |
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217 { |
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218 for (octave_idx_type i = 0; i < a.rows (); i++) |
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219 for (octave_idx_type j = 0; j < a.cols (); j++) |
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220 elem (i, j) = a.elem (i, j); |
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221 } |
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222 |
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2385
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223 bool |
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458
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224 Matrix::operator == (const Matrix& a) const |
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225 { |
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226 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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227 return false; |
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228 |
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229 return mx_inline_equal (data (), a.data (), length ()); |
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230 } |
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231 |
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2385
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232 bool |
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233 Matrix::operator != (const Matrix& a) const |
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234 { |
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235 return !(*this == a); |
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236 } |
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237 |
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238 bool |
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239 Matrix::is_symmetric (void) const |
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240 { |
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241 if (is_square () && rows () > 0) |
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242 { |
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243 for (octave_idx_type i = 0; i < rows (); i++) |
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244 for (octave_idx_type j = i+1; j < cols (); j++) |
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245 if (elem (i, j) != elem (j, i)) |
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246 return false; |
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247 |
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248 return true; |
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249 } |
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250 |
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251 return false; |
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252 } |
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253 |
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458
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254 Matrix& |
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255 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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256 { |
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1561
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257 Array2<double>::insert (a, r, c); |
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458
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258 return *this; |
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259 } |
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260 |
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261 Matrix& |
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262 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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263 { |
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264 octave_idx_type a_len = a.length (); |
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265 |
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266 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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267 { |
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268 (*current_liboctave_error_handler) ("range error for insert"); |
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269 return *this; |
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270 } |
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271 |
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4316
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272 if (a_len > 0) |
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273 { |
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274 make_unique (); |
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275 |
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276 for (octave_idx_type i = 0; i < a_len; i++) |
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277 xelem (r, c+i) = a.elem (i); |
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278 } |
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458
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279 |
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280 return *this; |
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281 } |
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282 |
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283 Matrix& |
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284 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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285 { |
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5275
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286 octave_idx_type a_len = a.length (); |
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287 |
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1698
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288 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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289 { |
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290 (*current_liboctave_error_handler) ("range error for insert"); |
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291 return *this; |
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292 } |
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293 |
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4316
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294 if (a_len > 0) |
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295 { |
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296 make_unique (); |
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297 |
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298 for (octave_idx_type i = 0; i < a_len; i++) |
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299 xelem (r+i, c) = a.elem (i); |
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300 } |
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458
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301 |
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302 return *this; |
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303 } |
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304 |
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305 Matrix& |
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5275
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306 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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307 { |
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5275
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308 octave_idx_type a_nr = a.rows (); |
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309 octave_idx_type a_nc = a.cols (); |
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310 |
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1698
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311 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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312 { |
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313 (*current_liboctave_error_handler) ("range error for insert"); |
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314 return *this; |
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315 } |
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316 |
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1697
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317 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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318 |
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319 octave_idx_type a_len = a.length (); |
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4316
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320 |
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321 if (a_len > 0) |
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322 { |
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323 make_unique (); |
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324 |
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325 for (octave_idx_type i = 0; i < a_len; i++) |
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326 xelem (r+i, c+i) = a.elem (i, i); |
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327 } |
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458
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328 |
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329 return *this; |
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330 } |
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331 |
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332 Matrix& |
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333 Matrix::fill (double val) |
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334 { |
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335 octave_idx_type nr = rows (); |
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336 octave_idx_type nc = cols (); |
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4316
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337 |
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458
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338 if (nr > 0 && nc > 0) |
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4316
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339 { |
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340 make_unique (); |
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341 |
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5275
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342 for (octave_idx_type j = 0; j < nc; j++) |
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343 for (octave_idx_type i = 0; i < nr; i++) |
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344 xelem (i, j) = val; |
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345 } |
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458
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346 |
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347 return *this; |
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348 } |
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349 |
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350 Matrix& |
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5275
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351 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
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458
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352 { |
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5275
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353 octave_idx_type nr = rows (); |
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354 octave_idx_type nc = cols (); |
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4316
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355 |
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458
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356 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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357 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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358 { |
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359 (*current_liboctave_error_handler) ("range error for fill"); |
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360 return *this; |
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361 } |
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362 |
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5275
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363 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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364 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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458
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365 |
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4316
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366 if (r2 >= r1 && c2 >= c1) |
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367 { |
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368 make_unique (); |
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369 |
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5275
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370 for (octave_idx_type j = c1; j <= c2; j++) |
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371 for (octave_idx_type i = r1; i <= r2; i++) |
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4316
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372 xelem (i, j) = val; |
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373 } |
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458
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374 |
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375 return *this; |
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376 } |
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377 |
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378 Matrix |
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379 Matrix::append (const Matrix& a) const |
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380 { |
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5275
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381 octave_idx_type nr = rows (); |
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382 octave_idx_type nc = cols (); |
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458
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383 if (nr != a.rows ()) |
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384 { |
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385 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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386 return Matrix (); |
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387 } |
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388 |
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5275
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389 octave_idx_type nc_insert = nc; |
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458
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390 Matrix retval (nr, nc + a.cols ()); |
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391 retval.insert (*this, 0, 0); |
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392 retval.insert (a, 0, nc_insert); |
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393 return retval; |
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394 } |
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395 |
|
|
396 Matrix |
|
|
397 Matrix::append (const RowVector& a) const |
|
|
398 { |
|
5275
|
399 octave_idx_type nr = rows (); |
|
|
400 octave_idx_type nc = cols (); |
|
458
|
401 if (nr != 1) |
|
|
402 { |
|
|
403 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
404 return Matrix (); |
|
|
405 } |
|
|
406 |
|
5275
|
407 octave_idx_type nc_insert = nc; |
|
458
|
408 Matrix retval (nr, nc + a.length ()); |
|
|
409 retval.insert (*this, 0, 0); |
|
|
410 retval.insert (a, 0, nc_insert); |
|
|
411 return retval; |
|
|
412 } |
|
|
413 |
|
|
414 Matrix |
|
|
415 Matrix::append (const ColumnVector& a) const |
|
|
416 { |
|
5275
|
417 octave_idx_type nr = rows (); |
|
|
418 octave_idx_type nc = cols (); |
|
458
|
419 if (nr != a.length ()) |
|
|
420 { |
|
|
421 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
422 return Matrix (); |
|
|
423 } |
|
|
424 |
|
5275
|
425 octave_idx_type nc_insert = nc; |
|
458
|
426 Matrix retval (nr, nc + 1); |
|
|
427 retval.insert (*this, 0, 0); |
|
|
428 retval.insert (a, 0, nc_insert); |
|
|
429 return retval; |
|
|
430 } |
|
|
431 |
|
|
432 Matrix |
|
|
433 Matrix::append (const DiagMatrix& a) const |
|
|
434 { |
|
5275
|
435 octave_idx_type nr = rows (); |
|
|
436 octave_idx_type nc = cols (); |
|
458
|
437 if (nr != a.rows ()) |
|
|
438 { |
|
|
439 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
440 return *this; |
|
|
441 } |
|
|
442 |
|
5275
|
443 octave_idx_type nc_insert = nc; |
|
458
|
444 Matrix retval (nr, nc + a.cols ()); |
|
|
445 retval.insert (*this, 0, 0); |
|
|
446 retval.insert (a, 0, nc_insert); |
|
|
447 return retval; |
|
|
448 } |
|
|
449 |
|
|
450 Matrix |
|
|
451 Matrix::stack (const Matrix& a) const |
|
|
452 { |
|
5275
|
453 octave_idx_type nr = rows (); |
|
|
454 octave_idx_type nc = cols (); |
|
458
|
455 if (nc != a.cols ()) |
|
|
456 { |
|
|
457 (*current_liboctave_error_handler) |
|
|
458 ("column dimension mismatch for stack"); |
|
|
459 return Matrix (); |
|
|
460 } |
|
|
461 |
|
5275
|
462 octave_idx_type nr_insert = nr; |
|
458
|
463 Matrix retval (nr + a.rows (), nc); |
|
|
464 retval.insert (*this, 0, 0); |
|
|
465 retval.insert (a, nr_insert, 0); |
|
|
466 return retval; |
|
|
467 } |
|
|
468 |
|
|
469 Matrix |
|
|
470 Matrix::stack (const RowVector& a) const |
|
|
471 { |
|
5275
|
472 octave_idx_type nr = rows (); |
|
|
473 octave_idx_type nc = cols (); |
|
458
|
474 if (nc != a.length ()) |
|
|
475 { |
|
|
476 (*current_liboctave_error_handler) |
|
|
477 ("column dimension mismatch for stack"); |
|
|
478 return Matrix (); |
|
|
479 } |
|
|
480 |
|
5275
|
481 octave_idx_type nr_insert = nr; |
|
458
|
482 Matrix retval (nr + 1, nc); |
|
|
483 retval.insert (*this, 0, 0); |
|
|
484 retval.insert (a, nr_insert, 0); |
|
|
485 return retval; |
|
|
486 } |
|
|
487 |
|
|
488 Matrix |
|
|
489 Matrix::stack (const ColumnVector& a) const |
|
|
490 { |
|
5275
|
491 octave_idx_type nr = rows (); |
|
|
492 octave_idx_type nc = cols (); |
|
458
|
493 if (nc != 1) |
|
|
494 { |
|
|
495 (*current_liboctave_error_handler) |
|
|
496 ("column dimension mismatch for stack"); |
|
|
497 return Matrix (); |
|
|
498 } |
|
|
499 |
|
5275
|
500 octave_idx_type nr_insert = nr; |
|
458
|
501 Matrix retval (nr + a.length (), nc); |
|
|
502 retval.insert (*this, 0, 0); |
|
|
503 retval.insert (a, nr_insert, 0); |
|
|
504 return retval; |
|
|
505 } |
|
|
506 |
|
|
507 Matrix |
|
|
508 Matrix::stack (const DiagMatrix& a) const |
|
|
509 { |
|
5275
|
510 octave_idx_type nr = rows (); |
|
|
511 octave_idx_type nc = cols (); |
|
458
|
512 if (nc != a.cols ()) |
|
|
513 { |
|
|
514 (*current_liboctave_error_handler) |
|
|
515 ("column dimension mismatch for stack"); |
|
|
516 return Matrix (); |
|
|
517 } |
|
|
518 |
|
5275
|
519 octave_idx_type nr_insert = nr; |
|
458
|
520 Matrix retval (nr + a.rows (), nc); |
|
|
521 retval.insert (*this, 0, 0); |
|
|
522 retval.insert (a, nr_insert, 0); |
|
|
523 return retval; |
|
|
524 } |
|
|
525 |
|
|
526 Matrix |
|
1205
|
527 real (const ComplexMatrix& a) |
|
|
528 { |
|
5275
|
529 octave_idx_type a_len = a.length (); |
|
1205
|
530 Matrix retval; |
|
|
531 if (a_len > 0) |
|
3769
|
532 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
|
|
533 a.rows (), a.cols ()); |
|
1205
|
534 return retval; |
|
|
535 } |
|
|
536 |
|
|
537 Matrix |
|
|
538 imag (const ComplexMatrix& a) |
|
|
539 { |
|
5275
|
540 octave_idx_type a_len = a.length (); |
|
1205
|
541 Matrix retval; |
|
|
542 if (a_len > 0) |
|
3769
|
543 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
|
|
544 a.rows (), a.cols ()); |
|
1205
|
545 return retval; |
|
|
546 } |
|
|
547 |
|
|
548 Matrix |
|
5275
|
549 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
550 { |
|
5275
|
551 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
552 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
553 |
|
|
554 octave_idx_type new_r = r2 - r1 + 1; |
|
|
555 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
556 |
|
|
557 Matrix result (new_r, new_c); |
|
|
558 |
|
5275
|
559 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
560 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
561 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
562 |
|
|
563 return result; |
|
|
564 } |
|
|
565 |
|
|
566 Matrix |
|
5275
|
567 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
568 { |
|
|
569 Matrix result (nr, nc); |
|
|
570 |
|
5275
|
571 for (octave_idx_type j = 0; j < nc; j++) |
|
|
572 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
573 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
574 |
|
|
575 return result; |
|
|
576 } |
|
|
577 |
|
|
578 // extract row or column i. |
|
|
579 |
|
|
580 RowVector |
|
5275
|
581 Matrix::row (octave_idx_type i) const |
|
458
|
582 { |
|
5275
|
583 octave_idx_type nc = cols (); |
|
458
|
584 if (i < 0 || i >= rows ()) |
|
|
585 { |
|
|
586 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
587 return RowVector (); |
|
|
588 } |
|
|
589 |
|
|
590 RowVector retval (nc); |
|
5275
|
591 for (octave_idx_type j = 0; j < nc; j++) |
|
4316
|
592 retval.xelem (j) = elem (i, j); |
|
458
|
593 |
|
|
594 return retval; |
|
|
595 } |
|
|
596 |
|
|
597 ColumnVector |
|
5275
|
598 Matrix::column (octave_idx_type i) const |
|
458
|
599 { |
|
5275
|
600 octave_idx_type nr = rows (); |
|
458
|
601 if (i < 0 || i >= cols ()) |
|
|
602 { |
|
|
603 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
604 return ColumnVector (); |
|
|
605 } |
|
|
606 |
|
|
607 ColumnVector retval (nr); |
|
5275
|
608 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
609 retval.xelem (j) = elem (j, i); |
|
458
|
610 |
|
|
611 return retval; |
|
|
612 } |
|
|
613 |
|
|
614 Matrix |
|
|
615 Matrix::inverse (void) const |
|
|
616 { |
|
5275
|
617 octave_idx_type info; |
|
458
|
618 double rcond; |
|
4329
|
619 return inverse (info, rcond, 0, 0); |
|
458
|
620 } |
|
|
621 |
|
|
622 Matrix |
|
5275
|
623 Matrix::inverse (octave_idx_type& info) const |
|
458
|
624 { |
|
|
625 double rcond; |
|
4329
|
626 return inverse (info, rcond, 0, 0); |
|
458
|
627 } |
|
|
628 |
|
|
629 Matrix |
|
5275
|
630 Matrix::inverse (octave_idx_type& info, double& rcond, int force, int calc_cond) const |
|
458
|
631 { |
|
1948
|
632 Matrix retval; |
|
|
633 |
|
5275
|
634 octave_idx_type nr = rows (); |
|
|
635 octave_idx_type nc = cols (); |
|
1948
|
636 |
|
458
|
637 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
638 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
639 else |
|
|
640 { |
|
5275
|
641 Array<octave_idx_type> ipvt (nr); |
|
|
642 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
643 |
|
|
644 retval = *this; |
|
|
645 double *tmp_data = retval.fortran_vec (); |
|
|
646 |
|
4329
|
647 Array<double> z(1); |
|
5275
|
648 octave_idx_type lwork = -1; |
|
4329
|
649 |
|
4330
|
650 // Query the optimum work array size. |
|
4329
|
651 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
652 z.fortran_vec (), lwork, info)); |
|
|
653 |
|
|
654 if (f77_exception_encountered) |
|
|
655 { |
|
|
656 (*current_liboctave_error_handler) |
|
|
657 ("unrecoverable error in dgetri"); |
|
|
658 return retval; |
|
|
659 } |
|
|
660 |
|
5275
|
661 lwork = static_cast<octave_idx_type> (z(0)); |
|
4329
|
662 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
663 z.resize (lwork); |
|
|
664 double *pz = z.fortran_vec (); |
|
|
665 |
|
|
666 info = 0; |
|
|
667 |
|
4330
|
668 // Calculate the norm of the matrix, for later use. |
|
4329
|
669 double anorm = 0; |
|
|
670 if (calc_cond) |
|
5275
|
671 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
672 |
|
|
673 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
674 |
|
|
675 if (f77_exception_encountered) |
|
4329
|
676 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
677 else |
|
|
678 { |
|
4330
|
679 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
680 rcond = 0.0; |
|
|
681 if (info != 0) |
|
1948
|
682 info = -1; |
|
4329
|
683 else if (calc_cond) |
|
|
684 { |
|
5275
|
685 octave_idx_type dgecon_info = 0; |
|
5061
|
686 |
|
4330
|
687 // Now calculate the condition number for non-singular matrix. |
|
4329
|
688 char job = '1'; |
|
5275
|
689 Array<octave_idx_type> iz (nc); |
|
|
690 octave_idx_type *piz = iz.fortran_vec (); |
|
4552
|
691 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
692 nc, tmp_data, nr, anorm, |
|
5061
|
693 rcond, pz, piz, dgecon_info |
|
4552
|
694 F77_CHAR_ARG_LEN (1))); |
|
4329
|
695 |
|
|
696 if (f77_exception_encountered) |
|
|
697 (*current_liboctave_error_handler) |
|
|
698 ("unrecoverable error in dgecon"); |
|
|
699 |
|
5061
|
700 if (dgecon_info != 0) |
|
4329
|
701 info = -1; |
|
|
702 } |
|
1948
|
703 |
|
|
704 if (info == -1 && ! force) |
|
|
705 retval = *this; // Restore matrix contents. |
|
|
706 else |
|
|
707 { |
|
5275
|
708 octave_idx_type dgetri_info = 0; |
|
5061
|
709 |
|
4329
|
710 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
711 pz, lwork, dgetri_info)); |
|
1948
|
712 |
|
|
713 if (f77_exception_encountered) |
|
|
714 (*current_liboctave_error_handler) |
|
4329
|
715 ("unrecoverable error in dgetri"); |
|
|
716 |
|
5061
|
717 if (dgetri_info != 0) |
|
4329
|
718 info = -1; |
|
1948
|
719 } |
|
|
720 } |
|
458
|
721 } |
|
|
722 |
|
1948
|
723 return retval; |
|
458
|
724 } |
|
|
725 |
|
740
|
726 Matrix |
|
4384
|
727 Matrix::pseudo_inverse (double tol) const |
|
740
|
728 { |
|
3480
|
729 SVD result (*this, SVD::economy); |
|
740
|
730 |
|
|
731 DiagMatrix S = result.singular_values (); |
|
|
732 Matrix U = result.left_singular_matrix (); |
|
|
733 Matrix V = result.right_singular_matrix (); |
|
|
734 |
|
|
735 ColumnVector sigma = S.diag (); |
|
|
736 |
|
5275
|
737 octave_idx_type r = sigma.length () - 1; |
|
|
738 octave_idx_type nr = rows (); |
|
|
739 octave_idx_type nc = cols (); |
|
740
|
740 |
|
|
741 if (tol <= 0.0) |
|
|
742 { |
|
|
743 if (nr > nc) |
|
|
744 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
745 else |
|
|
746 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
747 } |
|
|
748 |
|
|
749 while (r >= 0 && sigma.elem (r) < tol) |
|
|
750 r--; |
|
|
751 |
|
|
752 if (r < 0) |
|
|
753 return Matrix (nc, nr, 0.0); |
|
|
754 else |
|
|
755 { |
|
|
756 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
757 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
758 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
759 return Vr * D * Ur.transpose (); |
|
|
760 } |
|
|
761 } |
|
|
762 |
|
4773
|
763 #if defined (HAVE_FFTW3) |
|
3827
|
764 |
|
|
765 ComplexMatrix |
|
|
766 Matrix::fourier (void) const |
|
|
767 { |
|
|
768 size_t nr = rows (); |
|
|
769 size_t nc = cols (); |
|
|
770 |
|
|
771 ComplexMatrix retval (nr, nc); |
|
|
772 |
|
|
773 size_t npts, nsamples; |
|
|
774 |
|
|
775 if (nr == 1 || nc == 1) |
|
|
776 { |
|
|
777 npts = nr > nc ? nr : nc; |
|
|
778 nsamples = 1; |
|
|
779 } |
|
|
780 else |
|
|
781 { |
|
|
782 npts = nr; |
|
|
783 nsamples = nc; |
|
|
784 } |
|
|
785 |
|
4773
|
786 const double *in (fortran_vec ()); |
|
3827
|
787 Complex *out (retval.fortran_vec ()); |
|
|
788 |
|
4773
|
789 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
790 |
|
|
791 return retval; |
|
|
792 } |
|
|
793 |
|
|
794 ComplexMatrix |
|
|
795 Matrix::ifourier (void) const |
|
|
796 { |
|
|
797 size_t nr = rows (); |
|
|
798 size_t nc = cols (); |
|
|
799 |
|
|
800 ComplexMatrix retval (nr, nc); |
|
|
801 |
|
|
802 size_t npts, nsamples; |
|
|
803 |
|
|
804 if (nr == 1 || nc == 1) |
|
|
805 { |
|
|
806 npts = nr > nc ? nr : nc; |
|
|
807 nsamples = 1; |
|
|
808 } |
|
|
809 else |
|
|
810 { |
|
|
811 npts = nr; |
|
|
812 nsamples = nc; |
|
|
813 } |
|
|
814 |
|
|
815 ComplexMatrix tmp (*this); |
|
|
816 Complex *in (tmp.fortran_vec ()); |
|
|
817 Complex *out (retval.fortran_vec ()); |
|
|
818 |
|
4773
|
819 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
820 |
|
|
821 return retval; |
|
|
822 } |
|
|
823 |
|
|
824 ComplexMatrix |
|
|
825 Matrix::fourier2d (void) const |
|
|
826 { |
|
4773
|
827 dim_vector dv(rows (), cols ()); |
|
|
828 |
|
|
829 const double *in = fortran_vec (); |
|
|
830 ComplexMatrix retval (rows (), cols ()); |
|
|
831 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); |
|
3827
|
832 |
|
|
833 return retval; |
|
|
834 } |
|
|
835 |
|
|
836 ComplexMatrix |
|
|
837 Matrix::ifourier2d (void) const |
|
|
838 { |
|
4773
|
839 dim_vector dv(rows (), cols ()); |
|
3827
|
840 |
|
|
841 ComplexMatrix retval (*this); |
|
4773
|
842 Complex *out (retval.fortran_vec ()); |
|
|
843 |
|
|
844 octave_fftw::ifftNd (out, out, 2, dv); |
|
3827
|
845 |
|
|
846 return retval; |
|
|
847 } |
|
|
848 |
|
|
849 #else |
|
|
850 |
|
458
|
851 ComplexMatrix |
|
|
852 Matrix::fourier (void) const |
|
|
853 { |
|
1948
|
854 ComplexMatrix retval; |
|
|
855 |
|
5275
|
856 octave_idx_type nr = rows (); |
|
|
857 octave_idx_type nc = cols (); |
|
|
858 |
|
|
859 octave_idx_type npts, nsamples; |
|
1948
|
860 |
|
458
|
861 if (nr == 1 || nc == 1) |
|
|
862 { |
|
|
863 npts = nr > nc ? nr : nc; |
|
|
864 nsamples = 1; |
|
|
865 } |
|
|
866 else |
|
|
867 { |
|
|
868 npts = nr; |
|
|
869 nsamples = nc; |
|
|
870 } |
|
|
871 |
|
5275
|
872 octave_idx_type nn = 4*npts+15; |
|
1948
|
873 |
|
|
874 Array<Complex> wsave (nn); |
|
|
875 Complex *pwsave = wsave.fortran_vec (); |
|
|
876 |
|
3585
|
877 retval = ComplexMatrix (*this); |
|
1948
|
878 Complex *tmp_data = retval.fortran_vec (); |
|
|
879 |
|
3887
|
880 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
881 |
|
5275
|
882 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
883 { |
|
|
884 OCTAVE_QUIT; |
|
|
885 |
|
|
886 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
887 } |
|
1948
|
888 |
|
|
889 return retval; |
|
458
|
890 } |
|
|
891 |
|
|
892 ComplexMatrix |
|
|
893 Matrix::ifourier (void) const |
|
|
894 { |
|
1948
|
895 ComplexMatrix retval; |
|
|
896 |
|
5275
|
897 octave_idx_type nr = rows (); |
|
|
898 octave_idx_type nc = cols (); |
|
|
899 |
|
|
900 octave_idx_type npts, nsamples; |
|
1948
|
901 |
|
458
|
902 if (nr == 1 || nc == 1) |
|
|
903 { |
|
|
904 npts = nr > nc ? nr : nc; |
|
|
905 nsamples = 1; |
|
|
906 } |
|
|
907 else |
|
|
908 { |
|
|
909 npts = nr; |
|
|
910 nsamples = nc; |
|
|
911 } |
|
|
912 |
|
5275
|
913 octave_idx_type nn = 4*npts+15; |
|
1948
|
914 |
|
|
915 Array<Complex> wsave (nn); |
|
|
916 Complex *pwsave = wsave.fortran_vec (); |
|
|
917 |
|
3585
|
918 retval = ComplexMatrix (*this); |
|
1948
|
919 Complex *tmp_data = retval.fortran_vec (); |
|
|
920 |
|
3887
|
921 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
922 |
|
5275
|
923 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
924 { |
|
|
925 OCTAVE_QUIT; |
|
|
926 |
|
|
927 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
928 } |
|
458
|
929 |
|
5275
|
930 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
931 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
932 |
|
1948
|
933 return retval; |
|
458
|
934 } |
|
|
935 |
|
677
|
936 ComplexMatrix |
|
|
937 Matrix::fourier2d (void) const |
|
|
938 { |
|
1948
|
939 ComplexMatrix retval; |
|
|
940 |
|
5275
|
941 octave_idx_type nr = rows (); |
|
|
942 octave_idx_type nc = cols (); |
|
|
943 |
|
|
944 octave_idx_type npts, nsamples; |
|
1948
|
945 |
|
677
|
946 if (nr == 1 || nc == 1) |
|
|
947 { |
|
|
948 npts = nr > nc ? nr : nc; |
|
|
949 nsamples = 1; |
|
|
950 } |
|
|
951 else |
|
|
952 { |
|
|
953 npts = nr; |
|
|
954 nsamples = nc; |
|
|
955 } |
|
|
956 |
|
5275
|
957 octave_idx_type nn = 4*npts+15; |
|
1948
|
958 |
|
|
959 Array<Complex> wsave (nn); |
|
|
960 Complex *pwsave = wsave.fortran_vec (); |
|
|
961 |
|
3585
|
962 retval = ComplexMatrix (*this); |
|
1948
|
963 Complex *tmp_data = retval.fortran_vec (); |
|
|
964 |
|
3887
|
965 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
966 |
|
5275
|
967 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
968 { |
|
|
969 OCTAVE_QUIT; |
|
|
970 |
|
|
971 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
972 } |
|
677
|
973 |
|
|
974 npts = nc; |
|
|
975 nsamples = nr; |
|
|
976 nn = 4*npts+15; |
|
1948
|
977 |
|
|
978 wsave.resize (nn); |
|
|
979 pwsave = wsave.fortran_vec (); |
|
|
980 |
|
4773
|
981 Array<Complex> tmp (npts); |
|
|
982 Complex *prow = tmp.fortran_vec (); |
|
1948
|
983 |
|
3887
|
984 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
985 |
|
5275
|
986 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
987 { |
|
4153
|
988 OCTAVE_QUIT; |
|
|
989 |
|
5275
|
990 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
991 prow[i] = tmp_data[i*nr + j]; |
|
|
992 |
|
3887
|
993 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
994 |
|
5275
|
995 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
996 tmp_data[i*nr + j] = prow[i]; |
|
677
|
997 } |
|
|
998 |
|
1948
|
999 return retval; |
|
677
|
1000 } |
|
|
1001 |
|
|
1002 ComplexMatrix |
|
|
1003 Matrix::ifourier2d (void) const |
|
|
1004 { |
|
1948
|
1005 ComplexMatrix retval; |
|
|
1006 |
|
5275
|
1007 octave_idx_type nr = rows (); |
|
|
1008 octave_idx_type nc = cols (); |
|
|
1009 |
|
|
1010 octave_idx_type npts, nsamples; |
|
1948
|
1011 |
|
677
|
1012 if (nr == 1 || nc == 1) |
|
|
1013 { |
|
|
1014 npts = nr > nc ? nr : nc; |
|
|
1015 nsamples = 1; |
|
|
1016 } |
|
|
1017 else |
|
|
1018 { |
|
|
1019 npts = nr; |
|
|
1020 nsamples = nc; |
|
|
1021 } |
|
|
1022 |
|
5275
|
1023 octave_idx_type nn = 4*npts+15; |
|
1948
|
1024 |
|
|
1025 Array<Complex> wsave (nn); |
|
|
1026 Complex *pwsave = wsave.fortran_vec (); |
|
|
1027 |
|
3585
|
1028 retval = ComplexMatrix (*this); |
|
1948
|
1029 Complex *tmp_data = retval.fortran_vec (); |
|
|
1030 |
|
3887
|
1031 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1032 |
|
5275
|
1033 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1034 { |
|
|
1035 OCTAVE_QUIT; |
|
|
1036 |
|
|
1037 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1038 } |
|
677
|
1039 |
|
5275
|
1040 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1041 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1042 |
|
|
1043 npts = nc; |
|
|
1044 nsamples = nr; |
|
|
1045 nn = 4*npts+15; |
|
1948
|
1046 |
|
|
1047 wsave.resize (nn); |
|
|
1048 pwsave = wsave.fortran_vec (); |
|
|
1049 |
|
4773
|
1050 Array<Complex> tmp (npts); |
|
|
1051 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1052 |
|
3887
|
1053 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1054 |
|
5275
|
1055 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1056 { |
|
4153
|
1057 OCTAVE_QUIT; |
|
|
1058 |
|
5275
|
1059 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1060 prow[i] = tmp_data[i*nr + j]; |
|
|
1061 |
|
3887
|
1062 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1063 |
|
5275
|
1064 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1065 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1066 } |
|
|
1067 |
|
1948
|
1068 return retval; |
|
677
|
1069 } |
|
|
1070 |
|
3827
|
1071 #endif |
|
|
1072 |
|
458
|
1073 DET |
|
|
1074 Matrix::determinant (void) const |
|
|
1075 { |
|
5275
|
1076 octave_idx_type info; |
|
458
|
1077 double rcond; |
|
4329
|
1078 return determinant (info, rcond, 0); |
|
458
|
1079 } |
|
|
1080 |
|
|
1081 DET |
|
5275
|
1082 Matrix::determinant (octave_idx_type& info) const |
|
458
|
1083 { |
|
|
1084 double rcond; |
|
4329
|
1085 return determinant (info, rcond, 0); |
|
458
|
1086 } |
|
|
1087 |
|
|
1088 DET |
|
5275
|
1089 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1090 { |
|
|
1091 DET retval; |
|
|
1092 |
|
5275
|
1093 octave_idx_type nr = rows (); |
|
|
1094 octave_idx_type nc = cols (); |
|
458
|
1095 |
|
|
1096 if (nr == 0 || nc == 0) |
|
|
1097 { |
|
5634
|
1098 retval = DET (1.0, 0); |
|
458
|
1099 } |
|
|
1100 else |
|
|
1101 { |
|
5275
|
1102 Array<octave_idx_type> ipvt (nr); |
|
|
1103 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1104 |
|
|
1105 Matrix atmp = *this; |
|
|
1106 double *tmp_data = atmp.fortran_vec (); |
|
|
1107 |
|
4329
|
1108 info = 0; |
|
|
1109 |
|
4330
|
1110 // Calculate the norm of the matrix, for later use. |
|
4329
|
1111 double anorm = 0; |
|
|
1112 if (calc_cond) |
|
5275
|
1113 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1114 |
|
|
1115 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1116 |
|
|
1117 if (f77_exception_encountered) |
|
4329
|
1118 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
458
|
1119 else |
|
|
1120 { |
|
4330
|
1121 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1122 rcond = 0.0; |
|
|
1123 if (info != 0) |
|
1948
|
1124 { |
|
4509
|
1125 info = -1; |
|
|
1126 retval = DET (); |
|
4329
|
1127 } |
|
|
1128 else |
|
1948
|
1129 { |
|
4329
|
1130 if (calc_cond) |
|
|
1131 { |
|
4330
|
1132 // Now calc the condition number for non-singular matrix. |
|
4329
|
1133 char job = '1'; |
|
|
1134 Array<double> z (4 * nc); |
|
|
1135 double *pz = z.fortran_vec (); |
|
5275
|
1136 Array<octave_idx_type> iz (nc); |
|
|
1137 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1138 |
|
4552
|
1139 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1140 nc, tmp_data, nr, anorm, |
|
|
1141 rcond, pz, piz, info |
|
|
1142 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1143 |
|
|
1144 if (f77_exception_encountered) |
|
|
1145 (*current_liboctave_error_handler) |
|
|
1146 ("unrecoverable error in dgecon"); |
|
|
1147 } |
|
|
1148 |
|
4509
|
1149 if (info != 0) |
|
4329
|
1150 { |
|
|
1151 info = -1; |
|
|
1152 retval = DET (); |
|
|
1153 } |
|
|
1154 else |
|
|
1155 { |
|
5634
|
1156 double c = 1.0; |
|
|
1157 int e = 0; |
|
|
1158 |
|
|
1159 for (octave_idx_type i = 0; i < nc; i++) |
|
4329
|
1160 { |
|
5634
|
1161 if (ipvt(i) != (i+1)) |
|
|
1162 c = -c; |
|
|
1163 |
|
|
1164 c *= atmp(i,i); |
|
|
1165 |
|
|
1166 if (c == 0.0) |
|
|
1167 break; |
|
|
1168 |
|
|
1169 while (fabs (c) < 0.5) |
|
4329
|
1170 { |
|
5634
|
1171 c *= 2.0; |
|
|
1172 e--; |
|
4329
|
1173 } |
|
5634
|
1174 |
|
|
1175 while (fabs (c) >= 2.0) |
|
4329
|
1176 { |
|
5634
|
1177 c /= 2.0; |
|
|
1178 e++; |
|
4329
|
1179 } |
|
|
1180 } |
|
5634
|
1181 |
|
|
1182 retval = DET (c, e); |
|
4329
|
1183 } |
|
1948
|
1184 } |
|
458
|
1185 } |
|
|
1186 } |
|
|
1187 |
|
|
1188 return retval; |
|
|
1189 } |
|
|
1190 |
|
|
1191 Matrix |
|
5785
|
1192 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1193 double& rcond, solve_singularity_handler sing_handler, |
|
|
1194 bool calc_cond) const |
|
|
1195 { |
|
|
1196 Matrix retval; |
|
|
1197 |
|
|
1198 octave_idx_type nr = rows (); |
|
|
1199 octave_idx_type nc = cols (); |
|
|
1200 |
|
|
1201 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1202 (*current_liboctave_error_handler) |
|
|
1203 ("matrix dimension mismatch solution of linear equations"); |
|
|
1204 else |
|
|
1205 { |
|
|
1206 volatile int typ = mattype.type (); |
|
|
1207 |
|
|
1208 if (typ == MatrixType::Permuted_Upper || |
|
|
1209 typ == MatrixType::Upper) |
|
|
1210 { |
|
|
1211 octave_idx_type b_nc = b.cols (); |
|
|
1212 rcond = 1.; |
|
|
1213 info = 0; |
|
|
1214 |
|
|
1215 if (typ == MatrixType::Permuted_Upper) |
|
|
1216 { |
|
|
1217 (*current_liboctave_error_handler) |
|
|
1218 ("Permuted triangular matrix not implemented"); |
|
|
1219 } |
|
|
1220 else |
|
|
1221 { |
|
|
1222 const double *tmp_data = fortran_vec (); |
|
|
1223 |
|
|
1224 if (calc_cond) |
|
|
1225 { |
|
|
1226 char norm = '1'; |
|
|
1227 char uplo = 'U'; |
|
|
1228 char dia = 'N'; |
|
|
1229 |
|
|
1230 Array<double> z (3 * nc); |
|
|
1231 double *pz = z.fortran_vec (); |
|
|
1232 Array<octave_idx_type> iz (nc); |
|
|
1233 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1234 |
|
|
1235 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1236 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1237 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1238 nr, tmp_data, nr, rcond, |
|
|
1239 pz, piz, info |
|
|
1240 F77_CHAR_ARG_LEN (1) |
|
|
1241 F77_CHAR_ARG_LEN (1) |
|
|
1242 F77_CHAR_ARG_LEN (1))); |
|
|
1243 |
|
|
1244 if (f77_exception_encountered) |
|
|
1245 (*current_liboctave_error_handler) |
|
|
1246 ("unrecoverable error in dtrcon"); |
|
|
1247 |
|
|
1248 if (info != 0) |
|
|
1249 info = -2; |
|
|
1250 |
|
|
1251 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1252 |
|
|
1253 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1254 { |
|
|
1255 info = -2; |
|
|
1256 |
|
|
1257 if (sing_handler) |
|
|
1258 sing_handler (rcond); |
|
|
1259 else |
|
|
1260 (*current_liboctave_error_handler) |
|
|
1261 ("matrix singular to machine precision, rcond = %g", |
|
|
1262 rcond); |
|
|
1263 } |
|
|
1264 } |
|
|
1265 |
|
|
1266 if (info == 0) |
|
|
1267 { |
|
|
1268 retval = b; |
|
|
1269 double *result = retval.fortran_vec (); |
|
|
1270 |
|
|
1271 char uplo = 'U'; |
|
|
1272 char trans = 'N'; |
|
|
1273 char dia = 'N'; |
|
|
1274 |
|
|
1275 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1276 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1277 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1278 nr, b_nc, tmp_data, nr, |
|
|
1279 result, nr, info |
|
|
1280 F77_CHAR_ARG_LEN (1) |
|
|
1281 F77_CHAR_ARG_LEN (1) |
|
|
1282 F77_CHAR_ARG_LEN (1))); |
|
|
1283 |
|
|
1284 if (f77_exception_encountered) |
|
|
1285 (*current_liboctave_error_handler) |
|
|
1286 ("unrecoverable error in dtrtrs"); |
|
|
1287 } |
|
|
1288 } |
|
|
1289 } |
|
|
1290 else |
|
|
1291 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1292 } |
|
|
1293 |
|
|
1294 return retval; |
|
|
1295 } |
|
|
1296 |
|
|
1297 Matrix |
|
|
1298 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1299 double& rcond, solve_singularity_handler sing_handler, |
|
|
1300 bool calc_cond) const |
|
|
1301 { |
|
|
1302 Matrix retval; |
|
|
1303 |
|
|
1304 octave_idx_type nr = rows (); |
|
|
1305 octave_idx_type nc = cols (); |
|
|
1306 |
|
|
1307 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1308 (*current_liboctave_error_handler) |
|
|
1309 ("matrix dimension mismatch solution of linear equations"); |
|
|
1310 else |
|
|
1311 { |
|
|
1312 volatile int typ = mattype.type (); |
|
|
1313 |
|
|
1314 if (typ == MatrixType::Permuted_Lower || |
|
|
1315 typ == MatrixType::Lower) |
|
|
1316 { |
|
|
1317 octave_idx_type b_nc = b.cols (); |
|
|
1318 rcond = 1.; |
|
|
1319 info = 0; |
|
|
1320 |
|
|
1321 if (typ == MatrixType::Permuted_Lower) |
|
|
1322 { |
|
|
1323 (*current_liboctave_error_handler) |
|
|
1324 ("Permuted triangular matrix not implemented"); |
|
|
1325 } |
|
|
1326 else |
|
|
1327 { |
|
|
1328 const double *tmp_data = fortran_vec (); |
|
|
1329 |
|
|
1330 if (calc_cond) |
|
|
1331 { |
|
|
1332 char norm = '1'; |
|
|
1333 char uplo = 'L'; |
|
|
1334 char dia = 'N'; |
|
|
1335 |
|
|
1336 Array<double> z (3 * nc); |
|
|
1337 double *pz = z.fortran_vec (); |
|
|
1338 Array<octave_idx_type> iz (nc); |
|
|
1339 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1340 |
|
|
1341 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1342 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1343 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1344 nr, tmp_data, nr, rcond, |
|
|
1345 pz, piz, info |
|
|
1346 F77_CHAR_ARG_LEN (1) |
|
|
1347 F77_CHAR_ARG_LEN (1) |
|
|
1348 F77_CHAR_ARG_LEN (1))); |
|
|
1349 |
|
|
1350 if (f77_exception_encountered) |
|
|
1351 (*current_liboctave_error_handler) |
|
|
1352 ("unrecoverable error in dtrcon"); |
|
|
1353 |
|
|
1354 if (info != 0) |
|
|
1355 info = -2; |
|
|
1356 |
|
|
1357 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1358 |
|
|
1359 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1360 { |
|
|
1361 info = -2; |
|
|
1362 |
|
|
1363 if (sing_handler) |
|
|
1364 sing_handler (rcond); |
|
|
1365 else |
|
|
1366 (*current_liboctave_error_handler) |
|
|
1367 ("matrix singular to machine precision, rcond = %g", |
|
|
1368 rcond); |
|
|
1369 } |
|
|
1370 } |
|
|
1371 |
|
|
1372 if (info == 0) |
|
|
1373 { |
|
|
1374 retval = b; |
|
|
1375 double *result = retval.fortran_vec (); |
|
|
1376 |
|
|
1377 char uplo = 'L'; |
|
|
1378 char trans = 'N'; |
|
|
1379 char dia = 'N'; |
|
|
1380 |
|
|
1381 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1382 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1383 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1384 nr, b_nc, tmp_data, nr, |
|
|
1385 result, nr, info |
|
|
1386 F77_CHAR_ARG_LEN (1) |
|
|
1387 F77_CHAR_ARG_LEN (1) |
|
|
1388 F77_CHAR_ARG_LEN (1))); |
|
|
1389 |
|
|
1390 if (f77_exception_encountered) |
|
|
1391 (*current_liboctave_error_handler) |
|
|
1392 ("unrecoverable error in dtrtrs"); |
|
|
1393 } |
|
|
1394 } |
|
|
1395 } |
|
|
1396 else |
|
|
1397 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1398 } |
|
|
1399 |
|
|
1400 return retval; |
|
|
1401 } |
|
|
1402 |
|
|
1403 Matrix |
|
|
1404 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1405 double& rcond, solve_singularity_handler sing_handler, |
|
|
1406 bool calc_cond) const |
|
|
1407 { |
|
|
1408 Matrix retval; |
|
|
1409 |
|
|
1410 octave_idx_type nr = rows (); |
|
|
1411 octave_idx_type nc = cols (); |
|
|
1412 |
|
|
1413 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1414 (*current_liboctave_error_handler) |
|
|
1415 ("matrix dimension mismatch solution of linear equations"); |
|
|
1416 else |
|
|
1417 { |
|
|
1418 volatile int typ = mattype.type (); |
|
|
1419 |
|
|
1420 // Calculate the norm of the matrix, for later use. |
|
|
1421 double anorm = -1.; |
|
|
1422 |
|
|
1423 if (typ == MatrixType::Hermitian) |
|
|
1424 { |
|
|
1425 info = 0; |
|
|
1426 char job = 'L'; |
|
|
1427 Matrix atmp = *this; |
|
|
1428 double *tmp_data = atmp.fortran_vec (); |
|
|
1429 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1430 |
|
|
1431 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
|
1432 tmp_data, nr, info |
|
|
1433 F77_CHAR_ARG_LEN (1))); |
|
|
1434 |
|
|
1435 if (f77_exception_encountered) |
|
|
1436 (*current_liboctave_error_handler) |
|
|
1437 ("unrecoverable error in dpotrf"); |
|
|
1438 else |
|
|
1439 { |
|
|
1440 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1441 rcond = 0.0; |
|
|
1442 if (info != 0) |
|
|
1443 { |
|
|
1444 info = -2; |
|
|
1445 |
|
|
1446 mattype.mark_as_unsymmetric (); |
|
|
1447 typ = MatrixType::Full; |
|
|
1448 } |
|
|
1449 else |
|
|
1450 { |
|
|
1451 if (calc_cond) |
|
|
1452 { |
|
|
1453 Array<double> z (3 * nc); |
|
|
1454 double *pz = z.fortran_vec (); |
|
|
1455 Array<octave_idx_type> iz (nc); |
|
|
1456 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1457 |
|
|
1458 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1459 nr, tmp_data, nr, anorm, |
|
|
1460 rcond, pz, piz, info |
|
|
1461 F77_CHAR_ARG_LEN (1))); |
|
|
1462 |
|
|
1463 if (f77_exception_encountered) |
|
|
1464 (*current_liboctave_error_handler) |
|
|
1465 ("unrecoverable error in dpocon"); |
|
|
1466 |
|
|
1467 if (info != 0) |
|
|
1468 info = -2; |
|
|
1469 |
|
|
1470 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1471 |
|
|
1472 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1473 { |
|
|
1474 info = -2; |
|
|
1475 |
|
|
1476 if (sing_handler) |
|
|
1477 sing_handler (rcond); |
|
|
1478 else |
|
|
1479 (*current_liboctave_error_handler) |
|
|
1480 ("matrix singular to machine precision, rcond = %g", |
|
|
1481 rcond); |
|
|
1482 } |
|
|
1483 } |
|
|
1484 |
|
|
1485 if (info == 0) |
|
|
1486 { |
|
|
1487 retval = b; |
|
|
1488 double *result = retval.fortran_vec (); |
|
|
1489 |
|
|
1490 octave_idx_type b_nc = b.cols (); |
|
|
1491 |
|
|
1492 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1493 nr, b_nc, tmp_data, nr, |
|
|
1494 result, b.rows(), info |
|
|
1495 F77_CHAR_ARG_LEN (1))); |
|
|
1496 |
|
|
1497 if (f77_exception_encountered) |
|
|
1498 (*current_liboctave_error_handler) |
|
|
1499 ("unrecoverable error in dpotrs"); |
|
|
1500 } |
|
|
1501 else |
|
|
1502 { |
|
|
1503 mattype.mark_as_unsymmetric (); |
|
|
1504 typ = MatrixType::Full; |
|
|
1505 } |
|
|
1506 } |
|
|
1507 } |
|
|
1508 } |
|
|
1509 |
|
|
1510 if (typ == MatrixType::Full) |
|
|
1511 { |
|
|
1512 info = 0; |
|
|
1513 |
|
|
1514 Array<octave_idx_type> ipvt (nr); |
|
|
1515 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
|
1516 |
|
|
1517 Matrix atmp = *this; |
|
|
1518 double *tmp_data = atmp.fortran_vec (); |
|
|
1519 if(anorm < 0.) |
|
|
1520 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1521 |
|
|
1522 Array<double> z (4 * nc); |
|
|
1523 double *pz = z.fortran_vec (); |
|
|
1524 Array<octave_idx_type> iz (nc); |
|
|
1525 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1526 |
|
|
1527 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
|
1528 |
|
|
1529 if (f77_exception_encountered) |
|
|
1530 (*current_liboctave_error_handler) |
|
|
1531 ("unrecoverable error in dgetrf"); |
|
|
1532 else |
|
|
1533 { |
|
|
1534 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1535 rcond = 0.0; |
|
|
1536 if (info != 0) |
|
|
1537 { |
|
|
1538 info = -2; |
|
|
1539 |
|
|
1540 if (sing_handler) |
|
|
1541 sing_handler (rcond); |
|
|
1542 else |
|
|
1543 (*current_liboctave_error_handler) |
|
|
1544 ("matrix singular to machine precision"); |
|
|
1545 |
|
|
1546 mattype.mark_as_rectangular (); |
|
|
1547 } |
|
|
1548 else |
|
|
1549 { |
|
|
1550 if (calc_cond) |
|
|
1551 { |
|
|
1552 // Now calculate the condition number for |
|
|
1553 // non-singular matrix. |
|
|
1554 char job = '1'; |
|
|
1555 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1556 nc, tmp_data, nr, anorm, |
|
|
1557 rcond, pz, piz, info |
|
|
1558 F77_CHAR_ARG_LEN (1))); |
|
|
1559 |
|
|
1560 if (f77_exception_encountered) |
|
|
1561 (*current_liboctave_error_handler) |
|
|
1562 ("unrecoverable error in dgecon"); |
|
|
1563 |
|
|
1564 if (info != 0) |
|
|
1565 info = -2; |
|
|
1566 |
|
|
1567 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1568 |
|
|
1569 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1570 { |
|
|
1571 info = -2; |
|
|
1572 |
|
|
1573 if (sing_handler) |
|
|
1574 sing_handler (rcond); |
|
|
1575 else |
|
|
1576 (*current_liboctave_error_handler) |
|
|
1577 ("matrix singular to machine precision, rcond = %g", |
|
|
1578 rcond); |
|
|
1579 } |
|
|
1580 } |
|
|
1581 |
|
|
1582 if (info == 0) |
|
|
1583 { |
|
|
1584 retval = b; |
|
|
1585 double *result = retval.fortran_vec (); |
|
|
1586 |
|
|
1587 octave_idx_type b_nc = b.cols (); |
|
|
1588 |
|
|
1589 char job = 'N'; |
|
|
1590 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1591 nr, b_nc, tmp_data, nr, |
|
|
1592 pipvt, result, b.rows(), info |
|
|
1593 F77_CHAR_ARG_LEN (1))); |
|
|
1594 |
|
|
1595 if (f77_exception_encountered) |
|
|
1596 (*current_liboctave_error_handler) |
|
|
1597 ("unrecoverable error in dgetrs"); |
|
|
1598 } |
|
|
1599 else |
|
|
1600 mattype.mark_as_rectangular (); |
|
|
1601 } |
|
|
1602 } |
|
|
1603 } |
|
|
1604 else if (typ != MatrixType::Hermitian) |
|
|
1605 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1606 } |
|
|
1607 |
|
|
1608 return retval; |
|
|
1609 } |
|
|
1610 |
|
|
1611 Matrix |
|
|
1612 Matrix::solve (MatrixType &typ, const Matrix& b) const |
|
|
1613 { |
|
|
1614 octave_idx_type info; |
|
|
1615 double rcond; |
|
|
1616 return solve (typ, b, info, rcond, 0); |
|
|
1617 } |
|
|
1618 |
|
|
1619 Matrix |
|
|
1620 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
1621 double& rcond) const |
|
|
1622 { |
|
|
1623 return solve (typ, b, info, rcond, 0); |
|
|
1624 } |
|
|
1625 |
|
|
1626 Matrix |
|
|
1627 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1628 double& rcond, solve_singularity_handler sing_handler, |
|
|
1629 bool singular_fallback) const |
|
|
1630 { |
|
|
1631 Matrix retval; |
|
|
1632 int typ = mattype.type (); |
|
|
1633 |
|
|
1634 if (typ == MatrixType::Unknown) |
|
|
1635 typ = mattype.type (*this); |
|
|
1636 |
|
|
1637 // Only calculate the condition number for LU/Cholesky |
|
|
1638 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
|
1639 retval = utsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1640 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
|
1641 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1642 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
|
1643 retval = fsolve (mattype, b, info, rcond, sing_handler, true); |
|
|
1644 else if (typ != MatrixType::Rectangular) |
|
|
1645 { |
|
|
1646 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
|
1647 return Matrix (); |
|
|
1648 } |
|
|
1649 |
|
|
1650 // Rectangular or one of the above solvers flags a singular matrix |
|
|
1651 if (singular_fallback && mattype.type () == MatrixType::Rectangular) |
|
|
1652 { |
|
|
1653 octave_idx_type rank; |
|
|
1654 retval = lssolve (b, info, rank); |
|
|
1655 } |
|
|
1656 |
|
|
1657 return retval; |
|
|
1658 } |
|
|
1659 |
|
|
1660 ComplexMatrix |
|
|
1661 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const |
|
|
1662 { |
|
|
1663 ComplexMatrix tmp (*this); |
|
|
1664 return tmp.solve (typ, b); |
|
|
1665 } |
|
|
1666 |
|
|
1667 ComplexMatrix |
|
|
1668 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
1669 octave_idx_type& info) const |
|
|
1670 { |
|
|
1671 ComplexMatrix tmp (*this); |
|
|
1672 return tmp.solve (typ, b, info); |
|
|
1673 } |
|
|
1674 |
|
|
1675 ComplexMatrix |
|
|
1676 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1677 double& rcond) const |
|
|
1678 { |
|
|
1679 ComplexMatrix tmp (*this); |
|
|
1680 return tmp.solve (typ, b, info, rcond); |
|
|
1681 } |
|
|
1682 |
|
|
1683 ComplexMatrix |
|
|
1684 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1685 double& rcond, solve_singularity_handler sing_handler, |
|
|
1686 bool singular_fallback) const |
|
|
1687 { |
|
|
1688 ComplexMatrix tmp (*this); |
|
|
1689 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); |
|
|
1690 } |
|
|
1691 |
|
|
1692 ColumnVector |
|
|
1693 Matrix::solve (MatrixType &typ, const ColumnVector& b) const |
|
|
1694 { |
|
|
1695 octave_idx_type info; double rcond; |
|
|
1696 return solve (typ, b, info, rcond); |
|
|
1697 } |
|
|
1698 |
|
|
1699 ColumnVector |
|
|
1700 Matrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
1701 octave_idx_type& info) const |
|
|
1702 { |
|
|
1703 double rcond; |
|
|
1704 return solve (typ, b, info, rcond); |
|
|
1705 } |
|
|
1706 |
|
|
1707 ColumnVector |
|
|
1708 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1709 double& rcond) const |
|
|
1710 { |
|
|
1711 return solve (typ, b, info, rcond, 0); |
|
|
1712 } |
|
|
1713 |
|
|
1714 ColumnVector |
|
|
1715 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1716 double& rcond, solve_singularity_handler sing_handler) const |
|
|
1717 { |
|
|
1718 Matrix tmp (b); |
|
|
1719 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); |
|
|
1720 } |
|
|
1721 |
|
|
1722 ComplexColumnVector |
|
|
1723 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const |
|
|
1724 { |
|
|
1725 ComplexMatrix tmp (*this); |
|
|
1726 return tmp.solve (typ, b); |
|
|
1727 } |
|
|
1728 |
|
|
1729 ComplexColumnVector |
|
|
1730 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1731 octave_idx_type& info) const |
|
|
1732 { |
|
|
1733 ComplexMatrix tmp (*this); |
|
|
1734 return tmp.solve (typ, b, info); |
|
|
1735 } |
|
|
1736 |
|
|
1737 ComplexColumnVector |
|
|
1738 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1739 octave_idx_type& info, double& rcond) const |
|
|
1740 { |
|
|
1741 ComplexMatrix tmp (*this); |
|
|
1742 return tmp.solve (typ, b, info, rcond); |
|
|
1743 } |
|
|
1744 |
|
|
1745 ComplexColumnVector |
|
|
1746 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1747 octave_idx_type& info, double& rcond, |
|
|
1748 solve_singularity_handler sing_handler) const |
|
|
1749 { |
|
|
1750 ComplexMatrix tmp (*this); |
|
|
1751 return tmp.solve(typ, b, info, rcond, sing_handler); |
|
|
1752 } |
|
|
1753 |
|
|
1754 Matrix |
|
458
|
1755 Matrix::solve (const Matrix& b) const |
|
|
1756 { |
|
5275
|
1757 octave_idx_type info; |
|
458
|
1758 double rcond; |
|
4329
|
1759 return solve (b, info, rcond, 0); |
|
458
|
1760 } |
|
|
1761 |
|
|
1762 Matrix |
|
5275
|
1763 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1764 { |
|
|
1765 double rcond; |
|
4329
|
1766 return solve (b, info, rcond, 0); |
|
458
|
1767 } |
|
|
1768 |
|
|
1769 Matrix |
|
5275
|
1770 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1771 { |
|
3480
|
1772 return solve (b, info, rcond, 0); |
|
|
1773 } |
|
|
1774 |
|
|
1775 Matrix |
|
5785
|
1776 Matrix::solve (const Matrix& b, octave_idx_type& info, |
|
|
1777 double& rcond, solve_singularity_handler sing_handler) const |
|
3480
|
1778 { |
|
5785
|
1779 MatrixType mattype (*this); |
|
|
1780 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1781 } |
|
|
1782 |
|
|
1783 ComplexMatrix |
|
|
1784 Matrix::solve (const ComplexMatrix& b) const |
|
|
1785 { |
|
|
1786 ComplexMatrix tmp (*this); |
|
|
1787 return tmp.solve (b); |
|
|
1788 } |
|
|
1789 |
|
|
1790 ComplexMatrix |
|
5275
|
1791 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1792 { |
|
|
1793 ComplexMatrix tmp (*this); |
|
|
1794 return tmp.solve (b, info); |
|
|
1795 } |
|
|
1796 |
|
|
1797 ComplexMatrix |
|
5275
|
1798 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1799 { |
|
|
1800 ComplexMatrix tmp (*this); |
|
|
1801 return tmp.solve (b, info, rcond); |
|
|
1802 } |
|
|
1803 |
|
3480
|
1804 ComplexMatrix |
|
5275
|
1805 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1806 solve_singularity_handler sing_handler) const |
|
|
1807 { |
|
|
1808 ComplexMatrix tmp (*this); |
|
|
1809 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1810 } |
|
|
1811 |
|
458
|
1812 ColumnVector |
|
|
1813 Matrix::solve (const ColumnVector& b) const |
|
|
1814 { |
|
5275
|
1815 octave_idx_type info; double rcond; |
|
458
|
1816 return solve (b, info, rcond); |
|
|
1817 } |
|
|
1818 |
|
|
1819 ColumnVector |
|
5275
|
1820 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1821 { |
|
|
1822 double rcond; |
|
|
1823 return solve (b, info, rcond); |
|
|
1824 } |
|
|
1825 |
|
|
1826 ColumnVector |
|
5275
|
1827 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1828 { |
|
3480
|
1829 return solve (b, info, rcond, 0); |
|
|
1830 } |
|
|
1831 |
|
|
1832 ColumnVector |
|
5275
|
1833 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1834 solve_singularity_handler sing_handler) const |
|
|
1835 { |
|
5785
|
1836 MatrixType mattype (*this); |
|
|
1837 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1838 } |
|
|
1839 |
|
|
1840 ComplexColumnVector |
|
|
1841 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1842 { |
|
|
1843 ComplexMatrix tmp (*this); |
|
|
1844 return tmp.solve (b); |
|
|
1845 } |
|
|
1846 |
|
|
1847 ComplexColumnVector |
|
5275
|
1848 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1849 { |
|
|
1850 ComplexMatrix tmp (*this); |
|
|
1851 return tmp.solve (b, info); |
|
|
1852 } |
|
|
1853 |
|
|
1854 ComplexColumnVector |
|
5275
|
1855 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1856 { |
|
|
1857 ComplexMatrix tmp (*this); |
|
|
1858 return tmp.solve (b, info, rcond); |
|
|
1859 } |
|
|
1860 |
|
3480
|
1861 ComplexColumnVector |
|
5275
|
1862 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1863 solve_singularity_handler sing_handler) const |
|
|
1864 { |
|
|
1865 ComplexMatrix tmp (*this); |
|
|
1866 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1867 } |
|
|
1868 |
|
458
|
1869 Matrix |
|
|
1870 Matrix::lssolve (const Matrix& b) const |
|
|
1871 { |
|
5275
|
1872 octave_idx_type info; |
|
|
1873 octave_idx_type rank; |
|
458
|
1874 return lssolve (b, info, rank); |
|
|
1875 } |
|
|
1876 |
|
|
1877 Matrix |
|
5275
|
1878 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1879 { |
|
5275
|
1880 octave_idx_type rank; |
|
458
|
1881 return lssolve (b, info, rank); |
|
|
1882 } |
|
|
1883 |
|
|
1884 Matrix |
|
5275
|
1885 Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1886 { |
|
1948
|
1887 Matrix retval; |
|
|
1888 |
|
5275
|
1889 octave_idx_type nrhs = b.cols (); |
|
|
1890 |
|
|
1891 octave_idx_type m = rows (); |
|
|
1892 octave_idx_type n = cols (); |
|
458
|
1893 |
|
|
1894 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1895 (*current_liboctave_error_handler) |
|
|
1896 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1897 else |
|
458
|
1898 { |
|
1948
|
1899 Matrix atmp = *this; |
|
|
1900 double *tmp_data = atmp.fortran_vec (); |
|
|
1901 |
|
5275
|
1902 octave_idx_type nrr = m > n ? m : n; |
|
3754
|
1903 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
1904 |
|
5275
|
1905 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1906 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
1907 result.elem (i, j) = b.elem (i, j); |
|
|
1908 |
|
|
1909 double *presult = result.fortran_vec (); |
|
|
1910 |
|
5275
|
1911 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
1912 Array<double> s (len_s); |
|
|
1913 double *ps = s.fortran_vec (); |
|
|
1914 |
|
|
1915 double rcond = -1.0; |
|
|
1916 |
|
3752
|
1917 // Ask DGELSS what the dimension of WORK should be. |
|
|
1918 |
|
5275
|
1919 octave_idx_type lwork = -1; |
|
3752
|
1920 |
|
|
1921 Array<double> work (1); |
|
1948
|
1922 |
|
|
1923 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
1924 rcond, rank, work.fortran_vec (), |
|
|
1925 lwork, info)); |
|
1948
|
1926 |
|
|
1927 if (f77_exception_encountered) |
|
|
1928 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1929 else |
|
|
1930 { |
|
5275
|
1931 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
1932 work.resize (lwork); |
|
|
1933 |
|
|
1934 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1935 nrr, ps, rcond, rank, |
|
|
1936 work.fortran_vec (), lwork, info)); |
|
|
1937 |
|
|
1938 if (f77_exception_encountered) |
|
|
1939 (*current_liboctave_error_handler) |
|
|
1940 ("unrecoverable error in dgelss"); |
|
|
1941 else |
|
|
1942 { |
|
|
1943 retval.resize (n, nrhs); |
|
5275
|
1944 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1945 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
1946 retval.elem (i, j) = result.elem (i, j); |
|
|
1947 } |
|
1948
|
1948 } |
|
458
|
1949 } |
|
|
1950 |
|
|
1951 return retval; |
|
|
1952 } |
|
|
1953 |
|
|
1954 ComplexMatrix |
|
|
1955 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1956 { |
|
|
1957 ComplexMatrix tmp (*this); |
|
5275
|
1958 octave_idx_type info; |
|
|
1959 octave_idx_type rank; |
|
1484
|
1960 return tmp.lssolve (b, info, rank); |
|
458
|
1961 } |
|
|
1962 |
|
|
1963 ComplexMatrix |
|
5275
|
1964 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1965 { |
|
|
1966 ComplexMatrix tmp (*this); |
|
5275
|
1967 octave_idx_type rank; |
|
1484
|
1968 return tmp.lssolve (b, info, rank); |
|
458
|
1969 } |
|
|
1970 |
|
|
1971 ComplexMatrix |
|
5275
|
1972 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1973 { |
|
|
1974 ComplexMatrix tmp (*this); |
|
1484
|
1975 return tmp.lssolve (b, info, rank); |
|
458
|
1976 } |
|
|
1977 |
|
|
1978 ColumnVector |
|
|
1979 Matrix::lssolve (const ColumnVector& b) const |
|
|
1980 { |
|
5275
|
1981 octave_idx_type info; |
|
|
1982 octave_idx_type rank; |
|
1484
|
1983 return lssolve (b, info, rank); |
|
458
|
1984 } |
|
|
1985 |
|
|
1986 ColumnVector |
|
5275
|
1987 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1988 { |
|
5275
|
1989 octave_idx_type rank; |
|
458
|
1990 return lssolve (b, info, rank); |
|
|
1991 } |
|
|
1992 |
|
|
1993 ColumnVector |
|
5275
|
1994 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1995 { |
|
1948
|
1996 ColumnVector retval; |
|
|
1997 |
|
5275
|
1998 octave_idx_type nrhs = 1; |
|
|
1999 |
|
|
2000 octave_idx_type m = rows (); |
|
|
2001 octave_idx_type n = cols (); |
|
458
|
2002 |
|
|
2003 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
2004 (*current_liboctave_error_handler) |
|
|
2005 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
2006 else |
|
458
|
2007 { |
|
1948
|
2008 Matrix atmp = *this; |
|
|
2009 double *tmp_data = atmp.fortran_vec (); |
|
|
2010 |
|
5275
|
2011 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2012 ColumnVector result (nrr); |
|
|
2013 |
|
5275
|
2014 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2015 result.elem (i) = b.elem (i); |
|
|
2016 |
|
|
2017 double *presult = result.fortran_vec (); |
|
|
2018 |
|
5275
|
2019 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2020 Array<double> s (len_s); |
|
|
2021 double *ps = s.fortran_vec (); |
|
|
2022 |
|
|
2023 double rcond = -1.0; |
|
|
2024 |
|
3752
|
2025 // Ask DGELSS what the dimension of WORK should be. |
|
|
2026 |
|
5275
|
2027 octave_idx_type lwork = -1; |
|
3752
|
2028 |
|
|
2029 Array<double> work (1); |
|
|
2030 |
|
|
2031 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
2032 rcond, rank, work.fortran_vec (), |
|
|
2033 lwork, info)); |
|
1948
|
2034 |
|
|
2035 if (f77_exception_encountered) |
|
|
2036 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
2037 else |
|
|
2038 { |
|
5275
|
2039 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
2040 work.resize (lwork); |
|
|
2041 |
|
|
2042 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2043 nrr, ps, rcond, rank, |
|
|
2044 work.fortran_vec (), lwork, info)); |
|
|
2045 |
|
|
2046 if (f77_exception_encountered) |
|
|
2047 (*current_liboctave_error_handler) |
|
|
2048 ("unrecoverable error in dgelss"); |
|
|
2049 else |
|
|
2050 { |
|
|
2051 retval.resize (n); |
|
5275
|
2052 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2053 retval.elem (i) = result.elem (i); |
|
|
2054 } |
|
1948
|
2055 } |
|
458
|
2056 } |
|
|
2057 |
|
|
2058 return retval; |
|
|
2059 } |
|
|
2060 |
|
|
2061 ComplexColumnVector |
|
|
2062 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
2063 { |
|
|
2064 ComplexMatrix tmp (*this); |
|
|
2065 return tmp.lssolve (b); |
|
|
2066 } |
|
|
2067 |
|
|
2068 ComplexColumnVector |
|
5275
|
2069 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2070 { |
|
|
2071 ComplexMatrix tmp (*this); |
|
|
2072 return tmp.lssolve (b, info); |
|
|
2073 } |
|
|
2074 |
|
|
2075 ComplexColumnVector |
|
5275
|
2076 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2077 { |
|
|
2078 ComplexMatrix tmp (*this); |
|
|
2079 return tmp.lssolve (b, info, rank); |
|
|
2080 } |
|
|
2081 |
|
1819
|
2082 // Constants for matrix exponential calculation. |
|
|
2083 |
|
|
2084 static double padec [] = |
|
|
2085 { |
|
|
2086 5.0000000000000000e-1, |
|
|
2087 1.1666666666666667e-1, |
|
|
2088 1.6666666666666667e-2, |
|
|
2089 1.6025641025641026e-3, |
|
|
2090 1.0683760683760684e-4, |
|
|
2091 4.8562548562548563e-6, |
|
|
2092 1.3875013875013875e-7, |
|
|
2093 1.9270852604185938e-9, |
|
|
2094 }; |
|
|
2095 |
|
|
2096 Matrix |
|
|
2097 Matrix::expm (void) const |
|
|
2098 { |
|
|
2099 Matrix retval; |
|
|
2100 |
|
|
2101 Matrix m = *this; |
|
|
2102 |
|
5275
|
2103 octave_idx_type nc = columns (); |
|
1819
|
2104 |
|
3130
|
2105 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2106 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2107 |
|
1819
|
2108 // trace shift value |
|
3331
|
2109 volatile double trshift = 0.0; |
|
1819
|
2110 |
|
5275
|
2111 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2112 trshift += m.elem (i, i); |
|
|
2113 |
|
|
2114 trshift /= nc; |
|
|
2115 |
|
3130
|
2116 if (trshift > 0.0) |
|
|
2117 { |
|
5275
|
2118 for (octave_idx_type i = 0; i < nc; i++) |
|
3130
|
2119 m.elem (i, i) -= trshift; |
|
|
2120 } |
|
1819
|
2121 |
|
3331
|
2122 // Preconditioning step 2: balancing; code follows development |
|
|
2123 // in AEPBAL |
|
|
2124 |
|
|
2125 double *p_m = m.fortran_vec (); |
|
|
2126 |
|
5275
|
2127 octave_idx_type info, ilo, ihi, ilos, ihis; |
|
3468
|
2128 Array<double> dpermute (nc); |
|
|
2129 Array<double> dscale (nc); |
|
3466
|
2130 |
|
3468
|
2131 // permutation first |
|
|
2132 char job = 'P'; |
|
4552
|
2133 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2134 nc, p_m, nc, ilo, ihi, |
|
|
2135 dpermute.fortran_vec (), info |
|
|
2136 F77_CHAR_ARG_LEN (1))); |
|
3466
|
2137 |
|
3468
|
2138 // then scaling |
|
|
2139 job = 'S'; |
|
4552
|
2140 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2141 nc, p_m, nc, ilos, ihis, |
|
|
2142 dscale.fortran_vec (), info |
|
|
2143 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2144 |
|
|
2145 if (f77_exception_encountered) |
|
|
2146 { |
|
|
2147 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
2148 return retval; |
|
|
2149 } |
|
|
2150 |
|
1819
|
2151 // Preconditioning step 3: scaling. |
|
3331
|
2152 |
|
1819
|
2153 ColumnVector work(nc); |
|
3130
|
2154 double inf_norm; |
|
3331
|
2155 |
|
4552
|
2156 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2157 nc, nc, m.fortran_vec (), nc, |
|
|
2158 work.fortran_vec (), inf_norm |
|
|
2159 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2160 |
|
|
2161 if (f77_exception_encountered) |
|
|
2162 { |
|
|
2163 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
2164 return retval; |
|
|
2165 } |
|
1819
|
2166 |
|
5275
|
2167 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
|
1819
|
2168 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
2169 : 0.0); |
|
3331
|
2170 |
|
1819
|
2171 // Check whether we need to square at all. |
|
3331
|
2172 |
|
1819
|
2173 if (sqpow < 0) |
|
|
2174 sqpow = 0; |
|
3331
|
2175 |
|
1819
|
2176 if (sqpow > 0) |
|
|
2177 { |
|
|
2178 double scale_factor = 1.0; |
|
5275
|
2179 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2180 scale_factor *= 2.0; |
|
3331
|
2181 |
|
1819
|
2182 m = m / scale_factor; |
|
|
2183 } |
|
3331
|
2184 |
|
1819
|
2185 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
2186 |
|
1819
|
2187 Matrix npp (nc, nc, 0.0); |
|
|
2188 Matrix dpp = npp; |
|
3331
|
2189 |
|
1819
|
2190 // Now powers a^8 ... a^1. |
|
3331
|
2191 |
|
5275
|
2192 octave_idx_type minus_one_j = -1; |
|
|
2193 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2194 { |
|
3573
|
2195 npp = m * npp + padec[j] * m; |
|
|
2196 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
2197 minus_one_j *= -1; |
|
|
2198 } |
|
3331
|
2199 |
|
1819
|
2200 // Zero power. |
|
3331
|
2201 |
|
1819
|
2202 dpp = -dpp; |
|
5275
|
2203 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2204 { |
|
|
2205 npp.elem (j, j) += 1.0; |
|
|
2206 dpp.elem (j, j) += 1.0; |
|
|
2207 } |
|
3331
|
2208 |
|
1819
|
2209 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2210 |
|
3331
|
2211 retval = dpp.solve (npp, info); |
|
|
2212 |
|
1819
|
2213 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
2214 |
|
1819
|
2215 while (sqpow) |
|
|
2216 { |
|
|
2217 retval = retval * retval; |
|
|
2218 sqpow--; |
|
|
2219 } |
|
3331
|
2220 |
|
1819
|
2221 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
2222 // apply inverse scaling to computed exponential |
|
5275
|
2223 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2224 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2225 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
2226 |
|
4153
|
2227 OCTAVE_QUIT; |
|
|
2228 |
|
3466
|
2229 // construct balancing permutation vector |
|
5275
|
2230 Array<octave_idx_type> iperm (nc); |
|
|
2231 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2232 iperm(i) = i; // identity permutation |
|
3466
|
2233 |
|
|
2234 // leading permutations in forward order |
|
5275
|
2235 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2236 { |
|
5275
|
2237 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2238 octave_idx_type tmp = iperm(i); |
|
4593
|
2239 iperm(i) = iperm (swapidx); |
|
|
2240 iperm(swapidx) = tmp; |
|
3468
|
2241 } |
|
3466
|
2242 |
|
|
2243 // trailing permutations must be done in reverse order |
|
5275
|
2244 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2245 { |
|
5275
|
2246 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2247 octave_idx_type tmp = iperm(i); |
|
4593
|
2248 iperm(i) = iperm(swapidx); |
|
|
2249 iperm(swapidx) = tmp; |
|
3468
|
2250 } |
|
3466
|
2251 |
|
|
2252 // construct inverse balancing permutation vector |
|
5275
|
2253 Array<octave_idx_type> invpvec (nc); |
|
|
2254 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2255 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
4153
|
2256 |
|
|
2257 OCTAVE_QUIT; |
|
3466
|
2258 |
|
|
2259 Matrix tmpMat = retval; |
|
5275
|
2260 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2261 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2262 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
2263 |
|
1819
|
2264 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
2265 |
|
3130
|
2266 if (trshift > 0.0) |
|
|
2267 retval = exp (trshift) * retval; |
|
|
2268 |
|
|
2269 return retval; |
|
1819
|
2270 } |
|
|
2271 |
|
458
|
2272 Matrix& |
|
|
2273 Matrix::operator += (const DiagMatrix& a) |
|
|
2274 { |
|
5275
|
2275 octave_idx_type nr = rows (); |
|
|
2276 octave_idx_type nc = cols (); |
|
|
2277 |
|
|
2278 octave_idx_type a_nr = a.rows (); |
|
|
2279 octave_idx_type a_nc = a.cols (); |
|
2385
|
2280 |
|
|
2281 if (nr != a_nr || nc != a_nc) |
|
458
|
2282 { |
|
2385
|
2283 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2284 return *this; |
|
|
2285 } |
|
|
2286 |
|
5275
|
2287 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2288 elem (i, i) += a.elem (i, i); |
|
|
2289 |
|
|
2290 return *this; |
|
|
2291 } |
|
|
2292 |
|
|
2293 Matrix& |
|
|
2294 Matrix::operator -= (const DiagMatrix& a) |
|
|
2295 { |
|
5275
|
2296 octave_idx_type nr = rows (); |
|
|
2297 octave_idx_type nc = cols (); |
|
|
2298 |
|
|
2299 octave_idx_type a_nr = a.rows (); |
|
|
2300 octave_idx_type a_nc = a.cols (); |
|
2385
|
2301 |
|
|
2302 if (nr != a_nr || nc != a_nc) |
|
458
|
2303 { |
|
2385
|
2304 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2305 return *this; |
|
|
2306 } |
|
|
2307 |
|
5275
|
2308 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2309 elem (i, i) -= a.elem (i, i); |
|
|
2310 |
|
|
2311 return *this; |
|
|
2312 } |
|
|
2313 |
|
|
2314 // unary operations |
|
|
2315 |
|
2964
|
2316 boolMatrix |
|
458
|
2317 Matrix::operator ! (void) const |
|
|
2318 { |
|
5275
|
2319 octave_idx_type nr = rows (); |
|
|
2320 octave_idx_type nc = cols (); |
|
458
|
2321 |
|
2964
|
2322 boolMatrix b (nr, nc); |
|
458
|
2323 |
|
5275
|
2324 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2325 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2326 b.elem (i, j) = ! elem (i, j); |
|
|
2327 |
|
|
2328 return b; |
|
|
2329 } |
|
|
2330 |
|
1205
|
2331 // column vector by row vector -> matrix operations |
|
458
|
2332 |
|
1205
|
2333 Matrix |
|
|
2334 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
2335 { |
|
1948
|
2336 Matrix retval; |
|
|
2337 |
|
5275
|
2338 octave_idx_type len = v.length (); |
|
3233
|
2339 |
|
|
2340 if (len != 0) |
|
1205
|
2341 { |
|
5275
|
2342 octave_idx_type a_len = a.length (); |
|
3233
|
2343 |
|
|
2344 retval.resize (len, a_len); |
|
|
2345 double *c = retval.fortran_vec (); |
|
|
2346 |
|
4552
|
2347 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2348 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2349 len, a_len, 1, 1.0, v.data (), len, |
|
|
2350 a.data (), 1, 0.0, c, len |
|
|
2351 F77_CHAR_ARG_LEN (1) |
|
|
2352 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2353 |
|
|
2354 if (f77_exception_encountered) |
|
|
2355 (*current_liboctave_error_handler) |
|
|
2356 ("unrecoverable error in dgemm"); |
|
1205
|
2357 } |
|
458
|
2358 |
|
1948
|
2359 return retval; |
|
458
|
2360 } |
|
|
2361 |
|
|
2362 // other operations. |
|
|
2363 |
|
|
2364 Matrix |
|
2676
|
2365 Matrix::map (d_d_Mapper f) const |
|
1205
|
2366 { |
|
2676
|
2367 Matrix b (*this); |
|
|
2368 return b.apply (f); |
|
1205
|
2369 } |
|
|
2370 |
|
3248
|
2371 boolMatrix |
|
|
2372 Matrix::map (b_d_Mapper f) const |
|
|
2373 { |
|
5275
|
2374 octave_idx_type nr = rows (); |
|
|
2375 octave_idx_type nc = cols (); |
|
3248
|
2376 |
|
|
2377 boolMatrix retval (nr, nc); |
|
|
2378 |
|
5275
|
2379 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2380 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2381 retval(i,j) = f (elem(i,j)); |
|
|
2382 |
|
|
2383 return retval; |
|
|
2384 } |
|
|
2385 |
|
2676
|
2386 Matrix& |
|
|
2387 Matrix::apply (d_d_Mapper f) |
|
458
|
2388 { |
|
|
2389 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2390 |
|
5275
|
2391 for (octave_idx_type i = 0; i < length (); i++) |
|
458
|
2392 d[i] = f (d[i]); |
|
2676
|
2393 |
|
|
2394 return *this; |
|
458
|
2395 } |
|
|
2396 |
|
2385
|
2397 bool |
|
4431
|
2398 Matrix::any_element_is_negative (bool neg_zero) const |
|
2385
|
2399 { |
|
5275
|
2400 octave_idx_type nel = nelem (); |
|
2385
|
2401 |
|
4431
|
2402 if (neg_zero) |
|
|
2403 { |
|
5275
|
2404 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2405 if (lo_ieee_signbit (elem (i))) |
|
|
2406 return true; |
|
4431
|
2407 } |
|
|
2408 else |
|
|
2409 { |
|
5275
|
2410 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2411 if (elem (i) < 0) |
|
|
2412 return true; |
|
4431
|
2413 } |
|
2385
|
2414 |
|
|
2415 return false; |
|
|
2416 } |
|
|
2417 |
|
|
2418 |
|
|
2419 bool |
|
|
2420 Matrix::any_element_is_inf_or_nan (void) const |
|
|
2421 { |
|
5275
|
2422 octave_idx_type nel = nelem (); |
|
|
2423 |
|
|
2424 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2425 { |
|
|
2426 double val = elem (i); |
|
|
2427 if (xisinf (val) || xisnan (val)) |
|
|
2428 return true; |
|
|
2429 } |
|
|
2430 |
|
|
2431 return false; |
|
2385
|
2432 } |
|
|
2433 |
|
|
2434 bool |
|
|
2435 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
2436 { |
|
5275
|
2437 octave_idx_type nel = nelem (); |
|
|
2438 |
|
|
2439 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2440 { |
|
|
2441 double val = elem (i); |
|
|
2442 if (xisnan (val) || D_NINT (val) == val) |
|
|
2443 continue; |
|
|
2444 else |
|
|
2445 return false; |
|
|
2446 } |
|
2385
|
2447 |
|
|
2448 return true; |
|
|
2449 } |
|
|
2450 |
|
1968
|
2451 // Return nonzero if any element of M is not an integer. Also extract |
|
|
2452 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
2453 |
|
2385
|
2454 bool |
|
1968
|
2455 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
2456 { |
|
5275
|
2457 octave_idx_type nel = nelem (); |
|
4634
|
2458 |
|
|
2459 if (nel > 0) |
|
1968
|
2460 { |
|
4634
|
2461 max_val = elem (0); |
|
|
2462 min_val = elem (0); |
|
1968
|
2463 } |
|
|
2464 else |
|
2385
|
2465 return false; |
|
1968
|
2466 |
|
5275
|
2467 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2468 { |
|
|
2469 double val = elem (i); |
|
|
2470 |
|
|
2471 if (val > max_val) |
|
|
2472 max_val = val; |
|
|
2473 |
|
|
2474 if (val < min_val) |
|
|
2475 min_val = val; |
|
|
2476 |
|
|
2477 if (D_NINT (val) != val) |
|
|
2478 return false; |
|
|
2479 } |
|
2385
|
2480 |
|
|
2481 return true; |
|
1968
|
2482 } |
|
|
2483 |
|
2385
|
2484 bool |
|
1968
|
2485 Matrix::too_large_for_float (void) const |
|
|
2486 { |
|
5275
|
2487 octave_idx_type nel = nelem (); |
|
|
2488 |
|
|
2489 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2490 { |
|
|
2491 double val = elem (i); |
|
|
2492 |
|
5389
|
2493 if (! (xisnan (val) || xisinf (val)) |
|
5387
|
2494 && fabs (val) > FLT_MAX) |
|
4634
|
2495 return true; |
|
|
2496 } |
|
1968
|
2497 |
|
2385
|
2498 return false; |
|
1968
|
2499 } |
|
|
2500 |
|
5775
|
2501 // FIXME Do these really belong here? Maybe they should be |
|
4015
|
2502 // in a base class? |
|
458
|
2503 |
|
2832
|
2504 boolMatrix |
|
4015
|
2505 Matrix::all (int dim) const |
|
458
|
2506 { |
|
4015
|
2507 MX_ALL_OP (dim); |
|
458
|
2508 } |
|
|
2509 |
|
2832
|
2510 boolMatrix |
|
4015
|
2511 Matrix::any (int dim) const |
|
458
|
2512 { |
|
4015
|
2513 MX_ANY_OP (dim); |
|
458
|
2514 } |
|
|
2515 |
|
|
2516 Matrix |
|
3723
|
2517 Matrix::cumprod (int dim) const |
|
458
|
2518 { |
|
4015
|
2519 MX_CUMULATIVE_OP (Matrix, double, *=); |
|
458
|
2520 } |
|
|
2521 |
|
|
2522 Matrix |
|
3723
|
2523 Matrix::cumsum (int dim) const |
|
458
|
2524 { |
|
4015
|
2525 MX_CUMULATIVE_OP (Matrix, double, +=); |
|
458
|
2526 } |
|
|
2527 |
|
|
2528 Matrix |
|
3723
|
2529 Matrix::prod (int dim) const |
|
458
|
2530 { |
|
3864
|
2531 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2532 } |
|
|
2533 |
|
|
2534 Matrix |
|
3723
|
2535 Matrix::sum (int dim) const |
|
458
|
2536 { |
|
3864
|
2537 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2538 } |
|
|
2539 |
|
|
2540 Matrix |
|
3723
|
2541 Matrix::sumsq (int dim) const |
|
458
|
2542 { |
|
3864
|
2543 #define ROW_EXPR \ |
|
|
2544 double d = elem (i, j); \ |
|
|
2545 retval.elem (i, 0) += d * d |
|
|
2546 |
|
|
2547 #define COL_EXPR \ |
|
|
2548 double d = elem (i, j); \ |
|
|
2549 retval.elem (0, j) += d * d |
|
|
2550 |
|
|
2551 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2552 |
|
|
2553 #undef ROW_EXPR |
|
|
2554 #undef COL_EXPR |
|
458
|
2555 } |
|
|
2556 |
|
2385
|
2557 Matrix |
|
|
2558 Matrix::abs (void) const |
|
|
2559 { |
|
5275
|
2560 octave_idx_type nr = rows (); |
|
|
2561 octave_idx_type nc = cols (); |
|
2385
|
2562 |
|
|
2563 Matrix retval (nr, nc); |
|
|
2564 |
|
5275
|
2565 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2566 for (octave_idx_type i = 0; i < nr; i++) |
|
2385
|
2567 retval (i, j) = fabs (elem (i, j)); |
|
|
2568 |
|
|
2569 return retval; |
|
|
2570 } |
|
|
2571 |
|
458
|
2572 ColumnVector |
|
|
2573 Matrix::diag (void) const |
|
|
2574 { |
|
|
2575 return diag (0); |
|
|
2576 } |
|
|
2577 |
|
|
2578 ColumnVector |
|
5275
|
2579 Matrix::diag (octave_idx_type k) const |
|
458
|
2580 { |
|
5275
|
2581 octave_idx_type nnr = rows (); |
|
|
2582 octave_idx_type nnc = cols (); |
|
458
|
2583 if (k > 0) |
|
|
2584 nnc -= k; |
|
|
2585 else if (k < 0) |
|
|
2586 nnr += k; |
|
|
2587 |
|
|
2588 ColumnVector d; |
|
|
2589 |
|
|
2590 if (nnr > 0 && nnc > 0) |
|
|
2591 { |
|
5275
|
2592 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
2593 |
|
|
2594 d.resize (ndiag); |
|
|
2595 |
|
|
2596 if (k > 0) |
|
|
2597 { |
|
5275
|
2598 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2599 d.elem (i) = elem (i, i+k); |
|
|
2600 } |
|
4509
|
2601 else if (k < 0) |
|
458
|
2602 { |
|
5275
|
2603 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2604 d.elem (i) = elem (i-k, i); |
|
|
2605 } |
|
|
2606 else |
|
|
2607 { |
|
5275
|
2608 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2609 d.elem (i) = elem (i, i); |
|
|
2610 } |
|
|
2611 } |
|
|
2612 else |
|
4513
|
2613 (*current_liboctave_error_handler) |
|
|
2614 ("diag: requested diagonal out of range"); |
|
458
|
2615 |
|
|
2616 return d; |
|
|
2617 } |
|
|
2618 |
|
|
2619 ColumnVector |
|
|
2620 Matrix::row_min (void) const |
|
|
2621 { |
|
5275
|
2622 Array<octave_idx_type> dummy_idx; |
|
4587
|
2623 return row_min (dummy_idx); |
|
458
|
2624 } |
|
|
2625 |
|
|
2626 ColumnVector |
|
5275
|
2627 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2628 { |
|
|
2629 ColumnVector result; |
|
|
2630 |
|
5275
|
2631 octave_idx_type nr = rows (); |
|
|
2632 octave_idx_type nc = cols (); |
|
458
|
2633 |
|
|
2634 if (nr > 0 && nc > 0) |
|
|
2635 { |
|
|
2636 result.resize (nr); |
|
4587
|
2637 idx_arg.resize (nr); |
|
458
|
2638 |
|
5275
|
2639 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2640 { |
|
5275
|
2641 octave_idx_type idx_j; |
|
4469
|
2642 |
|
|
2643 double tmp_min = octave_NaN; |
|
|
2644 |
|
|
2645 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2646 { |
|
4469
|
2647 tmp_min = elem (i, idx_j); |
|
|
2648 |
|
5389
|
2649 if (! xisnan (tmp_min)) |
|
4469
|
2650 break; |
|
|
2651 } |
|
|
2652 |
|
5275
|
2653 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2654 { |
|
|
2655 double tmp = elem (i, j); |
|
|
2656 |
|
5389
|
2657 if (xisnan (tmp)) |
|
4469
|
2658 continue; |
|
|
2659 else if (tmp < tmp_min) |
|
2354
|
2660 { |
|
4469
|
2661 idx_j = j; |
|
|
2662 tmp_min = tmp; |
|
2354
|
2663 } |
|
|
2664 } |
|
|
2665 |
|
4469
|
2666 result.elem (i) = tmp_min; |
|
5389
|
2667 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
|
458
|
2668 } |
|
|
2669 } |
|
|
2670 |
|
|
2671 return result; |
|
|
2672 } |
|
|
2673 |
|
|
2674 ColumnVector |
|
|
2675 Matrix::row_max (void) const |
|
|
2676 { |
|
5275
|
2677 Array<octave_idx_type> dummy_idx; |
|
4587
|
2678 return row_max (dummy_idx); |
|
458
|
2679 } |
|
|
2680 |
|
|
2681 ColumnVector |
|
5275
|
2682 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2683 { |
|
|
2684 ColumnVector result; |
|
|
2685 |
|
5275
|
2686 octave_idx_type nr = rows (); |
|
|
2687 octave_idx_type nc = cols (); |
|
458
|
2688 |
|
|
2689 if (nr > 0 && nc > 0) |
|
|
2690 { |
|
|
2691 result.resize (nr); |
|
4587
|
2692 idx_arg.resize (nr); |
|
458
|
2693 |
|
5275
|
2694 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2695 { |
|
5275
|
2696 octave_idx_type idx_j; |
|
4469
|
2697 |
|
|
2698 double tmp_max = octave_NaN; |
|
|
2699 |
|
|
2700 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2701 { |
|
4469
|
2702 tmp_max = elem (i, idx_j); |
|
|
2703 |
|
5389
|
2704 if (! xisnan (tmp_max)) |
|
4469
|
2705 break; |
|
|
2706 } |
|
|
2707 |
|
5275
|
2708 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2709 { |
|
|
2710 double tmp = elem (i, j); |
|
|
2711 |
|
5389
|
2712 if (xisnan (tmp)) |
|
4469
|
2713 continue; |
|
|
2714 else if (tmp > tmp_max) |
|
2354
|
2715 { |
|
4469
|
2716 idx_j = j; |
|
|
2717 tmp_max = tmp; |
|
2354
|
2718 } |
|
|
2719 } |
|
|
2720 |
|
4469
|
2721 result.elem (i) = tmp_max; |
|
5389
|
2722 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
|
458
|
2723 } |
|
|
2724 } |
|
|
2725 |
|
|
2726 return result; |
|
|
2727 } |
|
|
2728 |
|
|
2729 RowVector |
|
|
2730 Matrix::column_min (void) const |
|
|
2731 { |
|
5275
|
2732 Array<octave_idx_type> dummy_idx; |
|
4587
|
2733 return column_min (dummy_idx); |
|
458
|
2734 } |
|
2354
|
2735 |
|
458
|
2736 RowVector |
|
5275
|
2737 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2738 { |
|
|
2739 RowVector result; |
|
|
2740 |
|
5275
|
2741 octave_idx_type nr = rows (); |
|
|
2742 octave_idx_type nc = cols (); |
|
458
|
2743 |
|
|
2744 if (nr > 0 && nc > 0) |
|
|
2745 { |
|
|
2746 result.resize (nc); |
|
4587
|
2747 idx_arg.resize (nc); |
|
458
|
2748 |
|
5275
|
2749 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2750 { |
|
5275
|
2751 octave_idx_type idx_i; |
|
4469
|
2752 |
|
|
2753 double tmp_min = octave_NaN; |
|
|
2754 |
|
|
2755 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2756 { |
|
4469
|
2757 tmp_min = elem (idx_i, j); |
|
|
2758 |
|
5389
|
2759 if (! xisnan (tmp_min)) |
|
4469
|
2760 break; |
|
|
2761 } |
|
|
2762 |
|
5275
|
2763 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2764 { |
|
|
2765 double tmp = elem (i, j); |
|
|
2766 |
|
5389
|
2767 if (xisnan (tmp)) |
|
4469
|
2768 continue; |
|
|
2769 else if (tmp < tmp_min) |
|
2354
|
2770 { |
|
4469
|
2771 idx_i = i; |
|
|
2772 tmp_min = tmp; |
|
2354
|
2773 } |
|
|
2774 } |
|
|
2775 |
|
4469
|
2776 result.elem (j) = tmp_min; |
|
5389
|
2777 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
|
458
|
2778 } |
|
|
2779 } |
|
|
2780 |
|
|
2781 return result; |
|
|
2782 } |
|
|
2783 |
|
2354
|
2784 RowVector |
|
|
2785 Matrix::column_max (void) const |
|
|
2786 { |
|
5275
|
2787 Array<octave_idx_type> dummy_idx; |
|
4587
|
2788 return column_max (dummy_idx); |
|
2354
|
2789 } |
|
458
|
2790 |
|
|
2791 RowVector |
|
5275
|
2792 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2793 { |
|
|
2794 RowVector result; |
|
|
2795 |
|
5275
|
2796 octave_idx_type nr = rows (); |
|
|
2797 octave_idx_type nc = cols (); |
|
458
|
2798 |
|
|
2799 if (nr > 0 && nc > 0) |
|
|
2800 { |
|
|
2801 result.resize (nc); |
|
4587
|
2802 idx_arg.resize (nc); |
|
458
|
2803 |
|
5275
|
2804 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2805 { |
|
5275
|
2806 octave_idx_type idx_i; |
|
4469
|
2807 |
|
|
2808 double tmp_max = octave_NaN; |
|
|
2809 |
|
|
2810 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2811 { |
|
4469
|
2812 tmp_max = elem (idx_i, j); |
|
|
2813 |
|
5389
|
2814 if (! xisnan (tmp_max)) |
|
4469
|
2815 break; |
|
|
2816 } |
|
|
2817 |
|
5275
|
2818 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2819 { |
|
|
2820 double tmp = elem (i, j); |
|
|
2821 |
|
5389
|
2822 if (xisnan (tmp)) |
|
4469
|
2823 continue; |
|
|
2824 else if (tmp > tmp_max) |
|
2354
|
2825 { |
|
4469
|
2826 idx_i = i; |
|
|
2827 tmp_max = tmp; |
|
2354
|
2828 } |
|
|
2829 } |
|
|
2830 |
|
4469
|
2831 result.elem (j) = tmp_max; |
|
5389
|
2832 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
|
458
|
2833 } |
|
|
2834 } |
|
|
2835 |
|
|
2836 return result; |
|
|
2837 } |
|
|
2838 |
|
3504
|
2839 std::ostream& |
|
|
2840 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2841 { |
|
5275
|
2842 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
2843 { |
|
5275
|
2844 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
2845 { |
|
|
2846 os << " "; |
|
|
2847 octave_write_double (os, a.elem (i, j)); |
|
|
2848 } |
|
458
|
2849 os << "\n"; |
|
|
2850 } |
|
|
2851 return os; |
|
|
2852 } |
|
|
2853 |
|
3504
|
2854 std::istream& |
|
|
2855 operator >> (std::istream& is, Matrix& a) |
|
458
|
2856 { |
|
5275
|
2857 octave_idx_type nr = a.rows (); |
|
|
2858 octave_idx_type nc = a.cols (); |
|
458
|
2859 |
|
|
2860 if (nr < 1 || nc < 1) |
|
3504
|
2861 is.clear (std::ios::badbit); |
|
458
|
2862 else |
|
|
2863 { |
|
|
2864 double tmp; |
|
5275
|
2865 for (octave_idx_type i = 0; i < nr; i++) |
|
|
2866 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2867 { |
|
4130
|
2868 tmp = octave_read_double (is); |
|
458
|
2869 if (is) |
|
|
2870 a.elem (i, j) = tmp; |
|
|
2871 else |
|
2795
|
2872 goto done; |
|
458
|
2873 } |
|
|
2874 } |
|
|
2875 |
|
2795
|
2876 done: |
|
|
2877 |
|
458
|
2878 return is; |
|
|
2879 } |
|
|
2880 |
|
1819
|
2881 Matrix |
|
|
2882 Givens (double x, double y) |
|
|
2883 { |
|
|
2884 double cc, s, temp_r; |
|
|
2885 |
|
3887
|
2886 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
1819
|
2887 |
|
|
2888 Matrix g (2, 2); |
|
|
2889 |
|
|
2890 g.elem (0, 0) = cc; |
|
|
2891 g.elem (1, 1) = cc; |
|
|
2892 g.elem (0, 1) = s; |
|
|
2893 g.elem (1, 0) = -s; |
|
|
2894 |
|
|
2895 return g; |
|
|
2896 } |
|
|
2897 |
|
|
2898 Matrix |
|
|
2899 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2900 { |
|
|
2901 Matrix retval; |
|
|
2902 |
|
5775
|
2903 // FIXME -- need to check that a, b, and c are all the same |
|
1819
|
2904 // size. |
|
|
2905 |
|
|
2906 // Compute Schur decompositions. |
|
|
2907 |
|
|
2908 SCHUR as (a, "U"); |
|
|
2909 SCHUR bs (b, "U"); |
|
|
2910 |
|
|
2911 // Transform c to new coordinates. |
|
|
2912 |
|
|
2913 Matrix ua = as.unitary_matrix (); |
|
|
2914 Matrix sch_a = as.schur_matrix (); |
|
|
2915 |
|
|
2916 Matrix ub = bs.unitary_matrix (); |
|
|
2917 Matrix sch_b = bs.schur_matrix (); |
|
|
2918 |
|
|
2919 Matrix cx = ua.transpose () * c * ub; |
|
|
2920 |
|
|
2921 // Solve the sylvester equation, back-transform, and return the |
|
|
2922 // solution. |
|
|
2923 |
|
5275
|
2924 octave_idx_type a_nr = a.rows (); |
|
|
2925 octave_idx_type b_nr = b.rows (); |
|
1819
|
2926 |
|
|
2927 double scale; |
|
5275
|
2928 octave_idx_type info; |
|
1819
|
2929 |
|
1950
|
2930 double *pa = sch_a.fortran_vec (); |
|
|
2931 double *pb = sch_b.fortran_vec (); |
|
|
2932 double *px = cx.fortran_vec (); |
|
|
2933 |
|
4552
|
2934 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2935 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2936 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2937 b_nr, px, a_nr, scale, info |
|
|
2938 F77_CHAR_ARG_LEN (1) |
|
|
2939 F77_CHAR_ARG_LEN (1))); |
|
1950
|
2940 |
|
|
2941 |
|
|
2942 if (f77_exception_encountered) |
|
|
2943 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
2944 else |
|
|
2945 { |
|
5775
|
2946 // FIXME -- check info? |
|
1819
|
2947 |
|
1950
|
2948 retval = -ua*cx*ub.transpose (); |
|
|
2949 } |
|
1819
|
2950 |
|
|
2951 return retval; |
|
|
2952 } |
|
|
2953 |
|
2828
|
2954 // matrix by matrix -> matrix operations |
|
|
2955 |
|
|
2956 Matrix |
|
|
2957 operator * (const Matrix& m, const Matrix& a) |
|
|
2958 { |
|
|
2959 Matrix retval; |
|
|
2960 |
|
5275
|
2961 octave_idx_type nr = m.rows (); |
|
|
2962 octave_idx_type nc = m.cols (); |
|
|
2963 |
|
|
2964 octave_idx_type a_nr = a.rows (); |
|
|
2965 octave_idx_type a_nc = a.cols (); |
|
2828
|
2966 |
|
|
2967 if (nc != a_nr) |
|
|
2968 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2969 else |
|
|
2970 { |
|
|
2971 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2972 retval.resize (nr, a_nc, 0.0); |
|
|
2973 else |
|
|
2974 { |
|
5275
|
2975 octave_idx_type ld = nr; |
|
|
2976 octave_idx_type lda = a_nr; |
|
2828
|
2977 |
|
|
2978 retval.resize (nr, a_nc); |
|
|
2979 double *c = retval.fortran_vec (); |
|
|
2980 |
|
4552
|
2981 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2982 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2983 nr, a_nc, nc, 1.0, m.data (), |
|
|
2984 ld, a.data (), lda, 0.0, c, nr |
|
|
2985 F77_CHAR_ARG_LEN (1) |
|
|
2986 F77_CHAR_ARG_LEN (1))); |
|
2828
|
2987 |
|
|
2988 if (f77_exception_encountered) |
|
|
2989 (*current_liboctave_error_handler) |
|
|
2990 ("unrecoverable error in dgemm"); |
|
|
2991 } |
|
|
2992 } |
|
|
2993 |
|
|
2994 return retval; |
|
|
2995 } |
|
|
2996 |
|
5775
|
2997 // FIXME -- it would be nice to share code among the min/max |
|
4309
|
2998 // functions below. |
|
|
2999 |
|
|
3000 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3001 if (nr == 0 || nc == 0) \ |
|
|
3002 return T (nr, nc); |
|
|
3003 |
|
|
3004 Matrix |
|
|
3005 min (double d, const Matrix& m) |
|
|
3006 { |
|
5275
|
3007 octave_idx_type nr = m.rows (); |
|
|
3008 octave_idx_type nc = m.columns (); |
|
4309
|
3009 |
|
|
3010 EMPTY_RETURN_CHECK (Matrix); |
|
|
3011 |
|
|
3012 Matrix result (nr, nc); |
|
|
3013 |
|
5275
|
3014 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3015 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3016 { |
|
|
3017 OCTAVE_QUIT; |
|
|
3018 result (i, j) = xmin (d, m (i, j)); |
|
|
3019 } |
|
|
3020 |
|
|
3021 return result; |
|
|
3022 } |
|
|
3023 |
|
|
3024 Matrix |
|
|
3025 min (const Matrix& m, double d) |
|
|
3026 { |
|
5275
|
3027 octave_idx_type nr = m.rows (); |
|
|
3028 octave_idx_type nc = m.columns (); |
|
4309
|
3029 |
|
|
3030 EMPTY_RETURN_CHECK (Matrix); |
|
|
3031 |
|
|
3032 Matrix result (nr, nc); |
|
|
3033 |
|
5275
|
3034 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3035 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3036 { |
|
|
3037 OCTAVE_QUIT; |
|
|
3038 result (i, j) = xmin (m (i, j), d); |
|
|
3039 } |
|
|
3040 |
|
|
3041 return result; |
|
|
3042 } |
|
|
3043 |
|
|
3044 Matrix |
|
|
3045 min (const Matrix& a, const Matrix& b) |
|
|
3046 { |
|
5275
|
3047 octave_idx_type nr = a.rows (); |
|
|
3048 octave_idx_type nc = a.columns (); |
|
4309
|
3049 |
|
|
3050 if (nr != b.rows () || nc != b.columns ()) |
|
|
3051 { |
|
|
3052 (*current_liboctave_error_handler) |
|
|
3053 ("two-arg min expecting args of same size"); |
|
|
3054 return Matrix (); |
|
|
3055 } |
|
|
3056 |
|
|
3057 EMPTY_RETURN_CHECK (Matrix); |
|
|
3058 |
|
|
3059 Matrix result (nr, nc); |
|
|
3060 |
|
5275
|
3061 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3062 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3063 { |
|
|
3064 OCTAVE_QUIT; |
|
|
3065 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3066 } |
|
|
3067 |
|
|
3068 return result; |
|
|
3069 } |
|
|
3070 |
|
|
3071 Matrix |
|
|
3072 max (double d, const Matrix& m) |
|
|
3073 { |
|
5275
|
3074 octave_idx_type nr = m.rows (); |
|
|
3075 octave_idx_type nc = m.columns (); |
|
4309
|
3076 |
|
|
3077 EMPTY_RETURN_CHECK (Matrix); |
|
|
3078 |
|
|
3079 Matrix result (nr, nc); |
|
|
3080 |
|
5275
|
3081 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3082 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3083 { |
|
|
3084 OCTAVE_QUIT; |
|
|
3085 result (i, j) = xmax (d, m (i, j)); |
|
|
3086 } |
|
|
3087 |
|
|
3088 return result; |
|
|
3089 } |
|
|
3090 |
|
|
3091 Matrix |
|
|
3092 max (const Matrix& m, double d) |
|
|
3093 { |
|
5275
|
3094 octave_idx_type nr = m.rows (); |
|
|
3095 octave_idx_type nc = m.columns (); |
|
4309
|
3096 |
|
|
3097 EMPTY_RETURN_CHECK (Matrix); |
|
|
3098 |
|
|
3099 Matrix result (nr, nc); |
|
|
3100 |
|
5275
|
3101 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3102 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3103 { |
|
|
3104 OCTAVE_QUIT; |
|
|
3105 result (i, j) = xmax (m (i, j), d); |
|
|
3106 } |
|
|
3107 |
|
|
3108 return result; |
|
|
3109 } |
|
|
3110 |
|
|
3111 Matrix |
|
|
3112 max (const Matrix& a, const Matrix& b) |
|
|
3113 { |
|
5275
|
3114 octave_idx_type nr = a.rows (); |
|
|
3115 octave_idx_type nc = a.columns (); |
|
4309
|
3116 |
|
|
3117 if (nr != b.rows () || nc != b.columns ()) |
|
|
3118 { |
|
|
3119 (*current_liboctave_error_handler) |
|
|
3120 ("two-arg max expecting args of same size"); |
|
|
3121 return Matrix (); |
|
|
3122 } |
|
|
3123 |
|
|
3124 EMPTY_RETURN_CHECK (Matrix); |
|
|
3125 |
|
|
3126 Matrix result (nr, nc); |
|
|
3127 |
|
5275
|
3128 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3129 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3130 { |
|
|
3131 OCTAVE_QUIT; |
|
|
3132 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3133 } |
|
|
3134 |
|
|
3135 return result; |
|
|
3136 } |
|
|
3137 |
|
2870
|
3138 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
3139 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
3140 |
|
|
3141 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
3142 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
3143 |
|
|
3144 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
3145 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
3146 |
|
458
|
3147 /* |
|
|
3148 ;;; Local Variables: *** |
|
|
3149 ;;; mode: C++ *** |
|
|
3150 ;;; End: *** |
|
|
3151 */ |
