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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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1367
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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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6207
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40 #include "dbleCHOL.h" |
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1847
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41 #include "f77-fcn.h" |
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458
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42 #include "lo-error.h" |
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2354
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43 #include "lo-ieee.h" |
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44 #include "lo-mappers.h" |
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1968
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45 #include "lo-utils.h" |
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1367
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46 #include "mx-base.h" |
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2828
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47 #include "mx-m-dm.h" |
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3176
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48 #include "mx-dm-m.h" |
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1367
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49 #include "mx-inlines.cc" |
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1650
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50 #include "oct-cmplx.h" |
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4153
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51 #include "quit.h" |
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52 |
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4773
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53 #if defined (HAVE_FFTW3) |
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3827
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54 #include "oct-fftw.h" |
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55 #endif |
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56 |
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458
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57 // Fortran functions we call. |
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58 |
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59 extern "C" |
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60 { |
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4552
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61 F77_RET_T |
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62 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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63 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
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64 octave_idx_type&, double*, octave_idx_type& |
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65 F77_CHAR_ARG_LEN_DECL); |
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66 |
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67 F77_RET_T |
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68 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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69 F77_CONST_CHAR_ARG_DECL, |
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5275
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70 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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71 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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72 F77_CHAR_ARG_LEN_DECL |
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73 F77_CHAR_ARG_LEN_DECL); |
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74 |
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75 |
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76 F77_RET_T |
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77 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, |
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78 F77_CONST_CHAR_ARG_DECL, |
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5275
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79 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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80 const double&, const double*, const octave_idx_type&, |
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81 const double*, const octave_idx_type&, const double&, |
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82 double*, const octave_idx_type& |
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83 F77_CHAR_ARG_LEN_DECL |
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84 F77_CHAR_ARG_LEN_DECL); |
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85 |
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86 F77_RET_T |
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87 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
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88 const octave_idx_type&, const octave_idx_type&, const double&, |
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89 const double*, const octave_idx_type&, const double*, |
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90 const octave_idx_type&, const double&, double*, |
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91 const octave_idx_type& |
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92 F77_CHAR_ARG_LEN_DECL); |
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93 |
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94 F77_RET_T |
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95 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, |
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96 const double*, const octave_idx_type&, double&); |
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97 |
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98 F77_RET_T |
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99 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
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100 octave_idx_type*, octave_idx_type&); |
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101 |
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102 F77_RET_T |
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103 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
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104 const double*, const octave_idx_type&, |
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105 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& |
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106 F77_CHAR_ARG_LEN_DECL); |
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107 |
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108 F77_RET_T |
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109 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
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110 double*, const octave_idx_type&, octave_idx_type&); |
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111 |
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112 F77_RET_T |
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113 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
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114 const octave_idx_type&, const double&, double&, |
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115 double*, octave_idx_type*, octave_idx_type& |
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116 F77_CHAR_ARG_LEN_DECL); |
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117 |
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118 F77_RET_T |
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119 F77_FUNC (dgelss, DGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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120 double*, const octave_idx_type&, double*, |
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121 const octave_idx_type&, double*, double&, octave_idx_type&, |
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122 double*, const octave_idx_type&, octave_idx_type&); |
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123 |
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124 F77_RET_T |
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125 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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126 double *, const octave_idx_type&, |
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127 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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128 |
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129 F77_RET_T |
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130 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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131 double*, const octave_idx_type&, const double&, |
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132 double&, double*, octave_idx_type*, |
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133 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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134 F77_RET_T |
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135 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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136 const octave_idx_type&, const double*, |
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137 const octave_idx_type&, double*, |
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138 const octave_idx_type&, octave_idx_type& |
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139 F77_CHAR_ARG_LEN_DECL); |
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140 |
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141 F77_RET_T |
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6207
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142 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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143 const octave_idx_type&, const double*, |
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144 const octave_idx_type&, octave_idx_type& |
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145 F77_CHAR_ARG_LEN_DECL |
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146 F77_CHAR_ARG_LEN_DECL); |
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147 F77_RET_T |
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5785
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148 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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149 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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150 const double*, const octave_idx_type&, double&, |
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151 double*, octave_idx_type*, octave_idx_type& |
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152 F77_CHAR_ARG_LEN_DECL |
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153 F77_CHAR_ARG_LEN_DECL |
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154 F77_CHAR_ARG_LEN_DECL); |
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155 F77_RET_T |
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156 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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157 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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158 const octave_idx_type&, const double*, |
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159 const octave_idx_type&, double*, |
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160 const octave_idx_type&, octave_idx_type& |
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161 F77_CHAR_ARG_LEN_DECL |
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162 F77_CHAR_ARG_LEN_DECL |
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163 F77_CHAR_ARG_LEN_DECL); |
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164 |
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1360
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165 // Note that the original complex fft routines were not written for |
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166 // double complex arguments. They have been modified by adding an |
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167 // implicit double precision (a-h,o-z) statement at the beginning of |
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168 // each subroutine. |
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169 |
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170 F77_RET_T |
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171 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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172 |
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173 F77_RET_T |
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174 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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175 |
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176 F77_RET_T |
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177 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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178 |
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179 F77_RET_T |
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180 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, |
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181 double&, double&); |
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182 |
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183 F77_RET_T |
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184 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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185 F77_CONST_CHAR_ARG_DECL, |
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186 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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187 const double*, const octave_idx_type&, const double*, |
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188 const octave_idx_type&, const double*, const octave_idx_type&, |
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189 double&, octave_idx_type& |
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4552
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190 F77_CHAR_ARG_LEN_DECL |
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191 F77_CHAR_ARG_LEN_DECL); |
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192 |
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193 F77_RET_T |
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194 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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195 const octave_idx_type&, const double*, |
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196 const octave_idx_type&, double*, double& |
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197 F77_CHAR_ARG_LEN_DECL); |
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458
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198 } |
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199 |
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1360
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200 // Matrix class. |
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201 |
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2349
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202 Matrix::Matrix (const RowVector& rv) |
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203 : MArray2<double> (1, rv.length (), 0.0) |
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204 { |
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205 for (octave_idx_type i = 0; i < rv.length (); i++) |
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206 elem (0, i) = rv.elem (i); |
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207 } |
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208 |
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209 Matrix::Matrix (const ColumnVector& cv) |
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210 : MArray2<double> (cv.length (), 1, 0.0) |
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211 { |
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212 for (octave_idx_type i = 0; i < cv.length (); i++) |
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213 elem (i, 0) = cv.elem (i); |
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214 } |
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215 |
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458
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216 Matrix::Matrix (const DiagMatrix& a) |
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217 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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458
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218 { |
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219 for (octave_idx_type i = 0; i < a.length (); i++) |
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220 elem (i, i) = a.elem (i, i); |
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221 } |
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222 |
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5775
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223 // FIXME -- could we use a templated mixed-type copy function |
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224 // here? |
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225 |
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226 Matrix::Matrix (const boolMatrix& a) |
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227 : MArray2<double> (a.rows (), a.cols ()) |
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228 { |
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229 for (octave_idx_type i = 0; i < a.rows (); i++) |
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230 for (octave_idx_type j = 0; j < a.cols (); j++) |
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231 elem (i, j) = a.elem (i, j); |
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232 } |
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233 |
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234 Matrix::Matrix (const charMatrix& a) |
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235 : MArray2<double> (a.rows (), a.cols ()) |
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236 { |
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237 for (octave_idx_type i = 0; i < a.rows (); i++) |
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238 for (octave_idx_type j = 0; j < a.cols (); j++) |
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239 elem (i, j) = a.elem (i, j); |
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240 } |
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241 |
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2385
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242 bool |
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458
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243 Matrix::operator == (const Matrix& a) const |
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244 { |
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245 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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246 return false; |
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458
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247 |
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248 return mx_inline_equal (data (), a.data (), length ()); |
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458
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249 } |
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250 |
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2385
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251 bool |
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458
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252 Matrix::operator != (const Matrix& a) const |
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253 { |
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254 return !(*this == a); |
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255 } |
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256 |
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3354
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257 bool |
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258 Matrix::is_symmetric (void) const |
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259 { |
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260 if (is_square () && rows () > 0) |
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261 { |
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262 for (octave_idx_type i = 0; i < rows (); i++) |
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263 for (octave_idx_type j = i+1; j < cols (); j++) |
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3354
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264 if (elem (i, j) != elem (j, i)) |
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265 return false; |
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266 |
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267 return true; |
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268 } |
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269 |
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270 return false; |
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271 } |
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272 |
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458
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273 Matrix& |
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274 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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275 { |
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1561
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276 Array2<double>::insert (a, r, c); |
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458
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277 return *this; |
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278 } |
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279 |
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280 Matrix& |
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281 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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282 { |
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283 octave_idx_type a_len = a.length (); |
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4316
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284 |
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285 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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286 { |
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287 (*current_liboctave_error_handler) ("range error for insert"); |
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288 return *this; |
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289 } |
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290 |
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291 if (a_len > 0) |
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292 { |
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293 make_unique (); |
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294 |
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295 for (octave_idx_type i = 0; i < a_len; i++) |
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296 xelem (r, c+i) = a.elem (i); |
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297 } |
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458
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298 |
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299 return *this; |
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300 } |
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301 |
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302 Matrix& |
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303 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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304 { |
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5275
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305 octave_idx_type a_len = a.length (); |
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306 |
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1698
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307 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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308 { |
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309 (*current_liboctave_error_handler) ("range error for insert"); |
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310 return *this; |
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311 } |
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312 |
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4316
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313 if (a_len > 0) |
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314 { |
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315 make_unique (); |
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316 |
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317 for (octave_idx_type i = 0; i < a_len; i++) |
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318 xelem (r+i, c) = a.elem (i); |
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319 } |
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458
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320 |
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321 return *this; |
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322 } |
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323 |
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324 Matrix& |
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325 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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326 { |
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5275
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327 octave_idx_type a_nr = a.rows (); |
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328 octave_idx_type a_nc = a.cols (); |
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329 |
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1698
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330 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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331 { |
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332 (*current_liboctave_error_handler) ("range error for insert"); |
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333 return *this; |
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334 } |
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335 |
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336 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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337 |
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5275
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338 octave_idx_type a_len = a.length (); |
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4316
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339 |
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340 if (a_len > 0) |
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341 { |
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342 make_unique (); |
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343 |
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5275
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344 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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345 xelem (r+i, c+i) = a.elem (i, i); |
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346 } |
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458
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347 |
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348 return *this; |
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349 } |
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350 |
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351 Matrix& |
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352 Matrix::fill (double val) |
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353 { |
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5275
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354 octave_idx_type nr = rows (); |
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355 octave_idx_type nc = cols (); |
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4316
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356 |
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458
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357 if (nr > 0 && nc > 0) |
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4316
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358 { |
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359 make_unique (); |
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360 |
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5275
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361 for (octave_idx_type j = 0; j < nc; j++) |
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362 for (octave_idx_type i = 0; i < nr; i++) |
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4316
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363 xelem (i, j) = val; |
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364 } |
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458
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365 |
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366 return *this; |
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367 } |
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368 |
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369 Matrix& |
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5275
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370 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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371 { |
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5275
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372 octave_idx_type nr = rows (); |
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373 octave_idx_type nc = cols (); |
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4316
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374 |
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458
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375 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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376 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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377 { |
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378 (*current_liboctave_error_handler) ("range error for fill"); |
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379 return *this; |
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380 } |
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381 |
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5275
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382 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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383 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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458
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384 |
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4316
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385 if (r2 >= r1 && c2 >= c1) |
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386 { |
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387 make_unique (); |
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388 |
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5275
|
389 for (octave_idx_type j = c1; j <= c2; j++) |
|
|
390 for (octave_idx_type i = r1; i <= r2; i++) |
|
4316
|
391 xelem (i, j) = val; |
|
|
392 } |
|
458
|
393 |
|
|
394 return *this; |
|
|
395 } |
|
|
396 |
|
|
397 Matrix |
|
|
398 Matrix::append (const Matrix& a) const |
|
|
399 { |
|
5275
|
400 octave_idx_type nr = rows (); |
|
|
401 octave_idx_type nc = cols (); |
|
458
|
402 if (nr != a.rows ()) |
|
|
403 { |
|
|
404 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
405 return Matrix (); |
|
|
406 } |
|
|
407 |
|
5275
|
408 octave_idx_type nc_insert = nc; |
|
458
|
409 Matrix retval (nr, nc + a.cols ()); |
|
|
410 retval.insert (*this, 0, 0); |
|
|
411 retval.insert (a, 0, nc_insert); |
|
|
412 return retval; |
|
|
413 } |
|
|
414 |
|
|
415 Matrix |
|
|
416 Matrix::append (const RowVector& a) const |
|
|
417 { |
|
5275
|
418 octave_idx_type nr = rows (); |
|
|
419 octave_idx_type nc = cols (); |
|
458
|
420 if (nr != 1) |
|
|
421 { |
|
|
422 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
423 return Matrix (); |
|
|
424 } |
|
|
425 |
|
5275
|
426 octave_idx_type nc_insert = nc; |
|
458
|
427 Matrix retval (nr, nc + a.length ()); |
|
|
428 retval.insert (*this, 0, 0); |
|
|
429 retval.insert (a, 0, nc_insert); |
|
|
430 return retval; |
|
|
431 } |
|
|
432 |
|
|
433 Matrix |
|
|
434 Matrix::append (const ColumnVector& a) const |
|
|
435 { |
|
5275
|
436 octave_idx_type nr = rows (); |
|
|
437 octave_idx_type nc = cols (); |
|
458
|
438 if (nr != a.length ()) |
|
|
439 { |
|
|
440 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
441 return Matrix (); |
|
|
442 } |
|
|
443 |
|
5275
|
444 octave_idx_type nc_insert = nc; |
|
458
|
445 Matrix retval (nr, nc + 1); |
|
|
446 retval.insert (*this, 0, 0); |
|
|
447 retval.insert (a, 0, nc_insert); |
|
|
448 return retval; |
|
|
449 } |
|
|
450 |
|
|
451 Matrix |
|
|
452 Matrix::append (const DiagMatrix& a) const |
|
|
453 { |
|
5275
|
454 octave_idx_type nr = rows (); |
|
|
455 octave_idx_type nc = cols (); |
|
458
|
456 if (nr != a.rows ()) |
|
|
457 { |
|
|
458 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
459 return *this; |
|
|
460 } |
|
|
461 |
|
5275
|
462 octave_idx_type nc_insert = nc; |
|
458
|
463 Matrix retval (nr, nc + a.cols ()); |
|
|
464 retval.insert (*this, 0, 0); |
|
|
465 retval.insert (a, 0, nc_insert); |
|
|
466 return retval; |
|
|
467 } |
|
|
468 |
|
|
469 Matrix |
|
|
470 Matrix::stack (const Matrix& a) const |
|
|
471 { |
|
5275
|
472 octave_idx_type nr = rows (); |
|
|
473 octave_idx_type nc = cols (); |
|
458
|
474 if (nc != a.cols ()) |
|
|
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 + a.rows (), 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 RowVector& a) const |
|
|
490 { |
|
5275
|
491 octave_idx_type nr = rows (); |
|
|
492 octave_idx_type nc = cols (); |
|
458
|
493 if (nc != a.length ()) |
|
|
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 + 1, 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 ColumnVector& a) const |
|
|
509 { |
|
5275
|
510 octave_idx_type nr = rows (); |
|
|
511 octave_idx_type nc = cols (); |
|
458
|
512 if (nc != 1) |
|
|
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.length (), nc); |
|
|
521 retval.insert (*this, 0, 0); |
|
|
522 retval.insert (a, nr_insert, 0); |
|
|
523 return retval; |
|
|
524 } |
|
|
525 |
|
|
526 Matrix |
|
|
527 Matrix::stack (const DiagMatrix& a) const |
|
|
528 { |
|
5275
|
529 octave_idx_type nr = rows (); |
|
|
530 octave_idx_type nc = cols (); |
|
458
|
531 if (nc != a.cols ()) |
|
|
532 { |
|
|
533 (*current_liboctave_error_handler) |
|
|
534 ("column dimension mismatch for stack"); |
|
|
535 return Matrix (); |
|
|
536 } |
|
|
537 |
|
5275
|
538 octave_idx_type nr_insert = nr; |
|
458
|
539 Matrix retval (nr + a.rows (), nc); |
|
|
540 retval.insert (*this, 0, 0); |
|
|
541 retval.insert (a, nr_insert, 0); |
|
|
542 return retval; |
|
|
543 } |
|
|
544 |
|
|
545 Matrix |
|
1205
|
546 real (const ComplexMatrix& a) |
|
|
547 { |
|
5275
|
548 octave_idx_type a_len = a.length (); |
|
1205
|
549 Matrix retval; |
|
|
550 if (a_len > 0) |
|
3769
|
551 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
|
|
552 a.rows (), a.cols ()); |
|
1205
|
553 return retval; |
|
|
554 } |
|
|
555 |
|
|
556 Matrix |
|
|
557 imag (const ComplexMatrix& a) |
|
|
558 { |
|
5275
|
559 octave_idx_type a_len = a.length (); |
|
1205
|
560 Matrix retval; |
|
|
561 if (a_len > 0) |
|
3769
|
562 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
|
|
563 a.rows (), a.cols ()); |
|
1205
|
564 return retval; |
|
|
565 } |
|
|
566 |
|
|
567 Matrix |
|
5275
|
568 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
569 { |
|
5275
|
570 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
571 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
572 |
|
|
573 octave_idx_type new_r = r2 - r1 + 1; |
|
|
574 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
575 |
|
|
576 Matrix result (new_r, new_c); |
|
|
577 |
|
5275
|
578 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
579 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
580 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
581 |
|
|
582 return result; |
|
|
583 } |
|
|
584 |
|
|
585 Matrix |
|
5275
|
586 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
587 { |
|
|
588 Matrix result (nr, nc); |
|
|
589 |
|
5275
|
590 for (octave_idx_type j = 0; j < nc; j++) |
|
|
591 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
592 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
593 |
|
|
594 return result; |
|
|
595 } |
|
|
596 |
|
|
597 // extract row or column i. |
|
|
598 |
|
|
599 RowVector |
|
5275
|
600 Matrix::row (octave_idx_type i) const |
|
458
|
601 { |
|
5275
|
602 octave_idx_type nc = cols (); |
|
458
|
603 if (i < 0 || i >= rows ()) |
|
|
604 { |
|
|
605 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
606 return RowVector (); |
|
|
607 } |
|
|
608 |
|
|
609 RowVector retval (nc); |
|
5275
|
610 for (octave_idx_type j = 0; j < nc; j++) |
|
4316
|
611 retval.xelem (j) = elem (i, j); |
|
458
|
612 |
|
|
613 return retval; |
|
|
614 } |
|
|
615 |
|
|
616 ColumnVector |
|
5275
|
617 Matrix::column (octave_idx_type i) const |
|
458
|
618 { |
|
5275
|
619 octave_idx_type nr = rows (); |
|
458
|
620 if (i < 0 || i >= cols ()) |
|
|
621 { |
|
|
622 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
623 return ColumnVector (); |
|
|
624 } |
|
|
625 |
|
|
626 ColumnVector retval (nr); |
|
5275
|
627 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
628 retval.xelem (j) = elem (j, i); |
|
458
|
629 |
|
|
630 return retval; |
|
|
631 } |
|
|
632 |
|
|
633 Matrix |
|
|
634 Matrix::inverse (void) const |
|
|
635 { |
|
5275
|
636 octave_idx_type info; |
|
458
|
637 double rcond; |
|
6207
|
638 MatrixType mattype (*this); |
|
|
639 return inverse (mattype, info, rcond, 0, 0); |
|
|
640 } |
|
|
641 |
|
|
642 Matrix |
|
|
643 Matrix::inverse (MatrixType& mattype) const |
|
|
644 { |
|
|
645 octave_idx_type info; |
|
|
646 double rcond; |
|
|
647 return inverse (mattype, info, rcond, 0, 0); |
|
|
648 } |
|
|
649 |
|
|
650 Matrix |
|
|
651 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const |
|
|
652 { |
|
|
653 double rcond; |
|
|
654 return inverse (mattype, info, rcond, 0, 0); |
|
458
|
655 } |
|
|
656 |
|
|
657 Matrix |
|
6207
|
658 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
|
|
659 int force, int calc_cond) const |
|
458
|
660 { |
|
6207
|
661 Matrix retval; |
|
|
662 |
|
|
663 octave_idx_type nr = rows (); |
|
|
664 octave_idx_type nc = cols (); |
|
|
665 |
|
|
666 if (nr != nc || nr == 0 || nc == 0) |
|
|
667 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
668 else |
|
|
669 { |
|
|
670 int typ = mattype.type (); |
|
|
671 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); |
|
|
672 char udiag = 'N'; |
|
|
673 retval = *this; |
|
|
674 double *tmp_data = retval.fortran_vec (); |
|
|
675 |
|
|
676 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
677 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
678 nr, tmp_data, nr, info |
|
|
679 F77_CHAR_ARG_LEN (1) |
|
|
680 F77_CHAR_ARG_LEN (1))); |
|
|
681 |
|
|
682 if (f77_exception_encountered) |
|
|
683 (*current_liboctave_error_handler) ("unrecoverable error in dtrtri"); |
|
|
684 else |
|
|
685 { |
|
|
686 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
687 rcond = 0.0; |
|
|
688 if (info != 0) |
|
|
689 info = -1; |
|
|
690 else if (calc_cond) |
|
|
691 { |
|
|
692 octave_idx_type dtrcon_info = 0; |
|
|
693 char job = '1'; |
|
|
694 |
|
|
695 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
|
|
696 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
|
|
697 |
|
|
698 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
699 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
700 F77_CONST_CHAR_ARG2 (&udiag, 1), |
|
|
701 nr, tmp_data, nr, rcond, |
|
|
702 work, iwork, dtrcon_info |
|
|
703 F77_CHAR_ARG_LEN (1) |
|
|
704 F77_CHAR_ARG_LEN (1) |
|
|
705 F77_CHAR_ARG_LEN (1))); |
|
|
706 |
|
|
707 if (f77_exception_encountered) |
|
|
708 (*current_liboctave_error_handler) |
|
|
709 ("unrecoverable error in dtrcon"); |
|
|
710 |
|
|
711 if (dtrcon_info != 0) |
|
|
712 info = -1; |
|
|
713 } |
|
|
714 } |
|
|
715 |
|
|
716 if (info == -1 && ! force) |
|
|
717 retval = *this; // Restore matrix contents. |
|
|
718 } |
|
|
719 |
|
|
720 return retval; |
|
458
|
721 } |
|
|
722 |
|
6207
|
723 |
|
458
|
724 Matrix |
|
6207
|
725 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
|
|
726 int force, int calc_cond) const |
|
458
|
727 { |
|
1948
|
728 Matrix retval; |
|
|
729 |
|
5275
|
730 octave_idx_type nr = rows (); |
|
|
731 octave_idx_type nc = cols (); |
|
1948
|
732 |
|
458
|
733 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
734 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
735 else |
|
|
736 { |
|
5275
|
737 Array<octave_idx_type> ipvt (nr); |
|
|
738 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
739 |
|
|
740 retval = *this; |
|
|
741 double *tmp_data = retval.fortran_vec (); |
|
|
742 |
|
4329
|
743 Array<double> z(1); |
|
5275
|
744 octave_idx_type lwork = -1; |
|
4329
|
745 |
|
4330
|
746 // Query the optimum work array size. |
|
4329
|
747 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
748 z.fortran_vec (), lwork, info)); |
|
|
749 |
|
|
750 if (f77_exception_encountered) |
|
|
751 { |
|
|
752 (*current_liboctave_error_handler) |
|
|
753 ("unrecoverable error in dgetri"); |
|
|
754 return retval; |
|
|
755 } |
|
|
756 |
|
5275
|
757 lwork = static_cast<octave_idx_type> (z(0)); |
|
4329
|
758 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
759 z.resize (lwork); |
|
|
760 double *pz = z.fortran_vec (); |
|
|
761 |
|
|
762 info = 0; |
|
|
763 |
|
4330
|
764 // Calculate the norm of the matrix, for later use. |
|
4329
|
765 double anorm = 0; |
|
|
766 if (calc_cond) |
|
5275
|
767 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
768 |
|
|
769 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
770 |
|
|
771 if (f77_exception_encountered) |
|
4329
|
772 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
773 else |
|
|
774 { |
|
4330
|
775 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
776 rcond = 0.0; |
|
|
777 if (info != 0) |
|
1948
|
778 info = -1; |
|
4329
|
779 else if (calc_cond) |
|
|
780 { |
|
5275
|
781 octave_idx_type dgecon_info = 0; |
|
5061
|
782 |
|
4330
|
783 // Now calculate the condition number for non-singular matrix. |
|
4329
|
784 char job = '1'; |
|
5275
|
785 Array<octave_idx_type> iz (nc); |
|
|
786 octave_idx_type *piz = iz.fortran_vec (); |
|
4552
|
787 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
788 nc, tmp_data, nr, anorm, |
|
5061
|
789 rcond, pz, piz, dgecon_info |
|
4552
|
790 F77_CHAR_ARG_LEN (1))); |
|
4329
|
791 |
|
|
792 if (f77_exception_encountered) |
|
|
793 (*current_liboctave_error_handler) |
|
|
794 ("unrecoverable error in dgecon"); |
|
|
795 |
|
5061
|
796 if (dgecon_info != 0) |
|
4329
|
797 info = -1; |
|
|
798 } |
|
1948
|
799 |
|
|
800 if (info == -1 && ! force) |
|
|
801 retval = *this; // Restore matrix contents. |
|
|
802 else |
|
|
803 { |
|
5275
|
804 octave_idx_type dgetri_info = 0; |
|
5061
|
805 |
|
4329
|
806 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
807 pz, lwork, dgetri_info)); |
|
1948
|
808 |
|
|
809 if (f77_exception_encountered) |
|
|
810 (*current_liboctave_error_handler) |
|
4329
|
811 ("unrecoverable error in dgetri"); |
|
|
812 |
|
5061
|
813 if (dgetri_info != 0) |
|
4329
|
814 info = -1; |
|
1948
|
815 } |
|
|
816 } |
|
6207
|
817 |
|
|
818 if (info != 0) |
|
|
819 mattype.mark_as_rectangular(); |
|
458
|
820 } |
|
|
821 |
|
1948
|
822 return retval; |
|
458
|
823 } |
|
|
824 |
|
740
|
825 Matrix |
|
6207
|
826 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
|
|
827 int force, int calc_cond) const |
|
|
828 { |
|
|
829 int typ = mattype.type (false); |
|
|
830 Matrix ret; |
|
|
831 |
|
|
832 if (typ == MatrixType::Unknown) |
|
|
833 typ = mattype.type (*this); |
|
|
834 |
|
|
835 if (typ == MatrixType::Upper || typ == MatrixType::Lower) |
|
|
836 ret = tinverse (mattype, info, rcond, force, calc_cond); |
|
|
837 else if (typ != MatrixType::Rectangular) |
|
|
838 { |
|
|
839 if (mattype.is_hermitian ()) |
|
|
840 { |
|
|
841 CHOL chol (*this, info); |
|
|
842 if (info == 0) |
|
|
843 ret = chol.inverse (); |
|
|
844 else |
|
|
845 mattype.mark_as_unsymmetric (); |
|
|
846 } |
|
|
847 |
|
|
848 if (!mattype.is_hermitian ()) |
|
|
849 ret = finverse(mattype, info, rcond, force, calc_cond); |
|
|
850 } |
|
|
851 |
|
|
852 return ret; |
|
|
853 } |
|
|
854 |
|
|
855 Matrix |
|
4384
|
856 Matrix::pseudo_inverse (double tol) const |
|
740
|
857 { |
|
3480
|
858 SVD result (*this, SVD::economy); |
|
740
|
859 |
|
|
860 DiagMatrix S = result.singular_values (); |
|
|
861 Matrix U = result.left_singular_matrix (); |
|
|
862 Matrix V = result.right_singular_matrix (); |
|
|
863 |
|
|
864 ColumnVector sigma = S.diag (); |
|
|
865 |
|
5275
|
866 octave_idx_type r = sigma.length () - 1; |
|
|
867 octave_idx_type nr = rows (); |
|
|
868 octave_idx_type nc = cols (); |
|
740
|
869 |
|
|
870 if (tol <= 0.0) |
|
|
871 { |
|
|
872 if (nr > nc) |
|
|
873 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
874 else |
|
|
875 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
876 } |
|
|
877 |
|
|
878 while (r >= 0 && sigma.elem (r) < tol) |
|
|
879 r--; |
|
|
880 |
|
|
881 if (r < 0) |
|
|
882 return Matrix (nc, nr, 0.0); |
|
|
883 else |
|
|
884 { |
|
|
885 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
886 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
887 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
888 return Vr * D * Ur.transpose (); |
|
|
889 } |
|
|
890 } |
|
|
891 |
|
4773
|
892 #if defined (HAVE_FFTW3) |
|
3827
|
893 |
|
|
894 ComplexMatrix |
|
|
895 Matrix::fourier (void) const |
|
|
896 { |
|
|
897 size_t nr = rows (); |
|
|
898 size_t nc = cols (); |
|
|
899 |
|
|
900 ComplexMatrix retval (nr, nc); |
|
|
901 |
|
|
902 size_t npts, nsamples; |
|
|
903 |
|
|
904 if (nr == 1 || nc == 1) |
|
|
905 { |
|
|
906 npts = nr > nc ? nr : nc; |
|
|
907 nsamples = 1; |
|
|
908 } |
|
|
909 else |
|
|
910 { |
|
|
911 npts = nr; |
|
|
912 nsamples = nc; |
|
|
913 } |
|
|
914 |
|
4773
|
915 const double *in (fortran_vec ()); |
|
3827
|
916 Complex *out (retval.fortran_vec ()); |
|
|
917 |
|
4773
|
918 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
919 |
|
|
920 return retval; |
|
|
921 } |
|
|
922 |
|
|
923 ComplexMatrix |
|
|
924 Matrix::ifourier (void) const |
|
|
925 { |
|
|
926 size_t nr = rows (); |
|
|
927 size_t nc = cols (); |
|
|
928 |
|
|
929 ComplexMatrix retval (nr, nc); |
|
|
930 |
|
|
931 size_t npts, nsamples; |
|
|
932 |
|
|
933 if (nr == 1 || nc == 1) |
|
|
934 { |
|
|
935 npts = nr > nc ? nr : nc; |
|
|
936 nsamples = 1; |
|
|
937 } |
|
|
938 else |
|
|
939 { |
|
|
940 npts = nr; |
|
|
941 nsamples = nc; |
|
|
942 } |
|
|
943 |
|
|
944 ComplexMatrix tmp (*this); |
|
|
945 Complex *in (tmp.fortran_vec ()); |
|
|
946 Complex *out (retval.fortran_vec ()); |
|
|
947 |
|
4773
|
948 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
949 |
|
|
950 return retval; |
|
|
951 } |
|
|
952 |
|
|
953 ComplexMatrix |
|
|
954 Matrix::fourier2d (void) const |
|
|
955 { |
|
4773
|
956 dim_vector dv(rows (), cols ()); |
|
|
957 |
|
|
958 const double *in = fortran_vec (); |
|
|
959 ComplexMatrix retval (rows (), cols ()); |
|
|
960 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); |
|
3827
|
961 |
|
|
962 return retval; |
|
|
963 } |
|
|
964 |
|
|
965 ComplexMatrix |
|
|
966 Matrix::ifourier2d (void) const |
|
|
967 { |
|
4773
|
968 dim_vector dv(rows (), cols ()); |
|
3827
|
969 |
|
|
970 ComplexMatrix retval (*this); |
|
4773
|
971 Complex *out (retval.fortran_vec ()); |
|
|
972 |
|
|
973 octave_fftw::ifftNd (out, out, 2, dv); |
|
3827
|
974 |
|
|
975 return retval; |
|
|
976 } |
|
|
977 |
|
|
978 #else |
|
|
979 |
|
458
|
980 ComplexMatrix |
|
|
981 Matrix::fourier (void) const |
|
|
982 { |
|
1948
|
983 ComplexMatrix retval; |
|
|
984 |
|
5275
|
985 octave_idx_type nr = rows (); |
|
|
986 octave_idx_type nc = cols (); |
|
|
987 |
|
|
988 octave_idx_type npts, nsamples; |
|
1948
|
989 |
|
458
|
990 if (nr == 1 || nc == 1) |
|
|
991 { |
|
|
992 npts = nr > nc ? nr : nc; |
|
|
993 nsamples = 1; |
|
|
994 } |
|
|
995 else |
|
|
996 { |
|
|
997 npts = nr; |
|
|
998 nsamples = nc; |
|
|
999 } |
|
|
1000 |
|
5275
|
1001 octave_idx_type nn = 4*npts+15; |
|
1948
|
1002 |
|
|
1003 Array<Complex> wsave (nn); |
|
|
1004 Complex *pwsave = wsave.fortran_vec (); |
|
|
1005 |
|
3585
|
1006 retval = ComplexMatrix (*this); |
|
1948
|
1007 Complex *tmp_data = retval.fortran_vec (); |
|
|
1008 |
|
3887
|
1009 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1010 |
|
5275
|
1011 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1012 { |
|
|
1013 OCTAVE_QUIT; |
|
|
1014 |
|
|
1015 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1016 } |
|
1948
|
1017 |
|
|
1018 return retval; |
|
458
|
1019 } |
|
|
1020 |
|
|
1021 ComplexMatrix |
|
|
1022 Matrix::ifourier (void) const |
|
|
1023 { |
|
1948
|
1024 ComplexMatrix retval; |
|
|
1025 |
|
5275
|
1026 octave_idx_type nr = rows (); |
|
|
1027 octave_idx_type nc = cols (); |
|
|
1028 |
|
|
1029 octave_idx_type npts, nsamples; |
|
1948
|
1030 |
|
458
|
1031 if (nr == 1 || nc == 1) |
|
|
1032 { |
|
|
1033 npts = nr > nc ? nr : nc; |
|
|
1034 nsamples = 1; |
|
|
1035 } |
|
|
1036 else |
|
|
1037 { |
|
|
1038 npts = nr; |
|
|
1039 nsamples = nc; |
|
|
1040 } |
|
|
1041 |
|
5275
|
1042 octave_idx_type nn = 4*npts+15; |
|
1948
|
1043 |
|
|
1044 Array<Complex> wsave (nn); |
|
|
1045 Complex *pwsave = wsave.fortran_vec (); |
|
|
1046 |
|
3585
|
1047 retval = ComplexMatrix (*this); |
|
1948
|
1048 Complex *tmp_data = retval.fortran_vec (); |
|
|
1049 |
|
3887
|
1050 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
1051 |
|
5275
|
1052 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1053 { |
|
|
1054 OCTAVE_QUIT; |
|
|
1055 |
|
|
1056 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1057 } |
|
458
|
1058 |
|
5275
|
1059 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1060 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
1061 |
|
1948
|
1062 return retval; |
|
458
|
1063 } |
|
|
1064 |
|
677
|
1065 ComplexMatrix |
|
|
1066 Matrix::fourier2d (void) const |
|
|
1067 { |
|
1948
|
1068 ComplexMatrix retval; |
|
|
1069 |
|
5275
|
1070 octave_idx_type nr = rows (); |
|
|
1071 octave_idx_type nc = cols (); |
|
|
1072 |
|
|
1073 octave_idx_type npts, nsamples; |
|
1948
|
1074 |
|
677
|
1075 if (nr == 1 || nc == 1) |
|
|
1076 { |
|
|
1077 npts = nr > nc ? nr : nc; |
|
|
1078 nsamples = 1; |
|
|
1079 } |
|
|
1080 else |
|
|
1081 { |
|
|
1082 npts = nr; |
|
|
1083 nsamples = nc; |
|
|
1084 } |
|
|
1085 |
|
5275
|
1086 octave_idx_type nn = 4*npts+15; |
|
1948
|
1087 |
|
|
1088 Array<Complex> wsave (nn); |
|
|
1089 Complex *pwsave = wsave.fortran_vec (); |
|
|
1090 |
|
3585
|
1091 retval = ComplexMatrix (*this); |
|
1948
|
1092 Complex *tmp_data = retval.fortran_vec (); |
|
|
1093 |
|
3887
|
1094 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1095 |
|
5275
|
1096 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1097 { |
|
|
1098 OCTAVE_QUIT; |
|
|
1099 |
|
|
1100 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
1101 } |
|
677
|
1102 |
|
|
1103 npts = nc; |
|
|
1104 nsamples = nr; |
|
|
1105 nn = 4*npts+15; |
|
1948
|
1106 |
|
|
1107 wsave.resize (nn); |
|
|
1108 pwsave = wsave.fortran_vec (); |
|
|
1109 |
|
4773
|
1110 Array<Complex> tmp (npts); |
|
|
1111 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1112 |
|
3887
|
1113 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1114 |
|
5275
|
1115 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1116 { |
|
4153
|
1117 OCTAVE_QUIT; |
|
|
1118 |
|
5275
|
1119 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1120 prow[i] = tmp_data[i*nr + j]; |
|
|
1121 |
|
3887
|
1122 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1123 |
|
5275
|
1124 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1125 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1126 } |
|
|
1127 |
|
1948
|
1128 return retval; |
|
677
|
1129 } |
|
|
1130 |
|
|
1131 ComplexMatrix |
|
|
1132 Matrix::ifourier2d (void) const |
|
|
1133 { |
|
1948
|
1134 ComplexMatrix retval; |
|
|
1135 |
|
5275
|
1136 octave_idx_type nr = rows (); |
|
|
1137 octave_idx_type nc = cols (); |
|
|
1138 |
|
|
1139 octave_idx_type npts, nsamples; |
|
1948
|
1140 |
|
677
|
1141 if (nr == 1 || nc == 1) |
|
|
1142 { |
|
|
1143 npts = nr > nc ? nr : nc; |
|
|
1144 nsamples = 1; |
|
|
1145 } |
|
|
1146 else |
|
|
1147 { |
|
|
1148 npts = nr; |
|
|
1149 nsamples = nc; |
|
|
1150 } |
|
|
1151 |
|
5275
|
1152 octave_idx_type nn = 4*npts+15; |
|
1948
|
1153 |
|
|
1154 Array<Complex> wsave (nn); |
|
|
1155 Complex *pwsave = wsave.fortran_vec (); |
|
|
1156 |
|
3585
|
1157 retval = ComplexMatrix (*this); |
|
1948
|
1158 Complex *tmp_data = retval.fortran_vec (); |
|
|
1159 |
|
3887
|
1160 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1161 |
|
5275
|
1162 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1163 { |
|
|
1164 OCTAVE_QUIT; |
|
|
1165 |
|
|
1166 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1167 } |
|
677
|
1168 |
|
5275
|
1169 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1170 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1171 |
|
|
1172 npts = nc; |
|
|
1173 nsamples = nr; |
|
|
1174 nn = 4*npts+15; |
|
1948
|
1175 |
|
|
1176 wsave.resize (nn); |
|
|
1177 pwsave = wsave.fortran_vec (); |
|
|
1178 |
|
4773
|
1179 Array<Complex> tmp (npts); |
|
|
1180 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1181 |
|
3887
|
1182 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1183 |
|
5275
|
1184 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1185 { |
|
4153
|
1186 OCTAVE_QUIT; |
|
|
1187 |
|
5275
|
1188 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1189 prow[i] = tmp_data[i*nr + j]; |
|
|
1190 |
|
3887
|
1191 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1192 |
|
5275
|
1193 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1194 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1195 } |
|
|
1196 |
|
1948
|
1197 return retval; |
|
677
|
1198 } |
|
|
1199 |
|
3827
|
1200 #endif |
|
|
1201 |
|
458
|
1202 DET |
|
|
1203 Matrix::determinant (void) const |
|
|
1204 { |
|
5275
|
1205 octave_idx_type info; |
|
458
|
1206 double rcond; |
|
4329
|
1207 return determinant (info, rcond, 0); |
|
458
|
1208 } |
|
|
1209 |
|
|
1210 DET |
|
5275
|
1211 Matrix::determinant (octave_idx_type& info) const |
|
458
|
1212 { |
|
|
1213 double rcond; |
|
4329
|
1214 return determinant (info, rcond, 0); |
|
458
|
1215 } |
|
|
1216 |
|
|
1217 DET |
|
5275
|
1218 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1219 { |
|
|
1220 DET retval; |
|
|
1221 |
|
5275
|
1222 octave_idx_type nr = rows (); |
|
|
1223 octave_idx_type nc = cols (); |
|
458
|
1224 |
|
|
1225 if (nr == 0 || nc == 0) |
|
|
1226 { |
|
5634
|
1227 retval = DET (1.0, 0); |
|
458
|
1228 } |
|
|
1229 else |
|
|
1230 { |
|
5275
|
1231 Array<octave_idx_type> ipvt (nr); |
|
|
1232 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1233 |
|
|
1234 Matrix atmp = *this; |
|
|
1235 double *tmp_data = atmp.fortran_vec (); |
|
|
1236 |
|
4329
|
1237 info = 0; |
|
|
1238 |
|
4330
|
1239 // Calculate the norm of the matrix, for later use. |
|
4329
|
1240 double anorm = 0; |
|
|
1241 if (calc_cond) |
|
5275
|
1242 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1243 |
|
|
1244 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1245 |
|
|
1246 if (f77_exception_encountered) |
|
4329
|
1247 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
458
|
1248 else |
|
|
1249 { |
|
4330
|
1250 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1251 rcond = 0.0; |
|
|
1252 if (info != 0) |
|
1948
|
1253 { |
|
4509
|
1254 info = -1; |
|
|
1255 retval = DET (); |
|
4329
|
1256 } |
|
|
1257 else |
|
1948
|
1258 { |
|
4329
|
1259 if (calc_cond) |
|
|
1260 { |
|
4330
|
1261 // Now calc the condition number for non-singular matrix. |
|
4329
|
1262 char job = '1'; |
|
|
1263 Array<double> z (4 * nc); |
|
|
1264 double *pz = z.fortran_vec (); |
|
5275
|
1265 Array<octave_idx_type> iz (nc); |
|
|
1266 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1267 |
|
4552
|
1268 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1269 nc, tmp_data, nr, anorm, |
|
|
1270 rcond, pz, piz, info |
|
|
1271 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1272 |
|
|
1273 if (f77_exception_encountered) |
|
|
1274 (*current_liboctave_error_handler) |
|
|
1275 ("unrecoverable error in dgecon"); |
|
|
1276 } |
|
|
1277 |
|
4509
|
1278 if (info != 0) |
|
4329
|
1279 { |
|
|
1280 info = -1; |
|
|
1281 retval = DET (); |
|
|
1282 } |
|
|
1283 else |
|
|
1284 { |
|
5634
|
1285 double c = 1.0; |
|
|
1286 int e = 0; |
|
|
1287 |
|
|
1288 for (octave_idx_type i = 0; i < nc; i++) |
|
4329
|
1289 { |
|
5634
|
1290 if (ipvt(i) != (i+1)) |
|
|
1291 c = -c; |
|
|
1292 |
|
|
1293 c *= atmp(i,i); |
|
|
1294 |
|
|
1295 if (c == 0.0) |
|
|
1296 break; |
|
|
1297 |
|
|
1298 while (fabs (c) < 0.5) |
|
4329
|
1299 { |
|
5634
|
1300 c *= 2.0; |
|
|
1301 e--; |
|
4329
|
1302 } |
|
5634
|
1303 |
|
|
1304 while (fabs (c) >= 2.0) |
|
4329
|
1305 { |
|
5634
|
1306 c /= 2.0; |
|
|
1307 e++; |
|
4329
|
1308 } |
|
|
1309 } |
|
5634
|
1310 |
|
|
1311 retval = DET (c, e); |
|
4329
|
1312 } |
|
1948
|
1313 } |
|
458
|
1314 } |
|
|
1315 } |
|
|
1316 |
|
|
1317 return retval; |
|
|
1318 } |
|
|
1319 |
|
|
1320 Matrix |
|
5785
|
1321 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1322 double& rcond, solve_singularity_handler sing_handler, |
|
|
1323 bool calc_cond) const |
|
|
1324 { |
|
|
1325 Matrix retval; |
|
|
1326 |
|
|
1327 octave_idx_type nr = rows (); |
|
|
1328 octave_idx_type nc = cols (); |
|
|
1329 |
|
|
1330 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1331 (*current_liboctave_error_handler) |
|
|
1332 ("matrix dimension mismatch solution of linear equations"); |
|
|
1333 else |
|
|
1334 { |
|
|
1335 volatile int typ = mattype.type (); |
|
|
1336 |
|
|
1337 if (typ == MatrixType::Permuted_Upper || |
|
|
1338 typ == MatrixType::Upper) |
|
|
1339 { |
|
|
1340 octave_idx_type b_nc = b.cols (); |
|
|
1341 rcond = 1.; |
|
|
1342 info = 0; |
|
|
1343 |
|
|
1344 if (typ == MatrixType::Permuted_Upper) |
|
|
1345 { |
|
|
1346 (*current_liboctave_error_handler) |
|
|
1347 ("Permuted triangular matrix not implemented"); |
|
|
1348 } |
|
|
1349 else |
|
|
1350 { |
|
|
1351 const double *tmp_data = fortran_vec (); |
|
|
1352 |
|
|
1353 if (calc_cond) |
|
|
1354 { |
|
|
1355 char norm = '1'; |
|
|
1356 char uplo = 'U'; |
|
|
1357 char dia = 'N'; |
|
|
1358 |
|
|
1359 Array<double> z (3 * nc); |
|
|
1360 double *pz = z.fortran_vec (); |
|
|
1361 Array<octave_idx_type> iz (nc); |
|
|
1362 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1363 |
|
|
1364 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1365 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1366 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1367 nr, tmp_data, nr, rcond, |
|
|
1368 pz, piz, info |
|
|
1369 F77_CHAR_ARG_LEN (1) |
|
|
1370 F77_CHAR_ARG_LEN (1) |
|
|
1371 F77_CHAR_ARG_LEN (1))); |
|
|
1372 |
|
|
1373 if (f77_exception_encountered) |
|
|
1374 (*current_liboctave_error_handler) |
|
|
1375 ("unrecoverable error in dtrcon"); |
|
|
1376 |
|
|
1377 if (info != 0) |
|
|
1378 info = -2; |
|
|
1379 |
|
|
1380 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1381 |
|
|
1382 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1383 { |
|
|
1384 info = -2; |
|
|
1385 |
|
|
1386 if (sing_handler) |
|
|
1387 sing_handler (rcond); |
|
|
1388 else |
|
|
1389 (*current_liboctave_error_handler) |
|
|
1390 ("matrix singular to machine precision, rcond = %g", |
|
|
1391 rcond); |
|
|
1392 } |
|
|
1393 } |
|
|
1394 |
|
|
1395 if (info == 0) |
|
|
1396 { |
|
|
1397 retval = b; |
|
|
1398 double *result = retval.fortran_vec (); |
|
|
1399 |
|
|
1400 char uplo = 'U'; |
|
|
1401 char trans = 'N'; |
|
|
1402 char dia = 'N'; |
|
|
1403 |
|
|
1404 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1405 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1406 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1407 nr, b_nc, tmp_data, nr, |
|
|
1408 result, nr, info |
|
|
1409 F77_CHAR_ARG_LEN (1) |
|
|
1410 F77_CHAR_ARG_LEN (1) |
|
|
1411 F77_CHAR_ARG_LEN (1))); |
|
|
1412 |
|
|
1413 if (f77_exception_encountered) |
|
|
1414 (*current_liboctave_error_handler) |
|
|
1415 ("unrecoverable error in dtrtrs"); |
|
|
1416 } |
|
|
1417 } |
|
|
1418 } |
|
|
1419 else |
|
|
1420 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1421 } |
|
|
1422 |
|
|
1423 return retval; |
|
|
1424 } |
|
|
1425 |
|
|
1426 Matrix |
|
|
1427 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1428 double& rcond, solve_singularity_handler sing_handler, |
|
|
1429 bool calc_cond) const |
|
|
1430 { |
|
|
1431 Matrix retval; |
|
|
1432 |
|
|
1433 octave_idx_type nr = rows (); |
|
|
1434 octave_idx_type nc = cols (); |
|
|
1435 |
|
|
1436 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1437 (*current_liboctave_error_handler) |
|
|
1438 ("matrix dimension mismatch solution of linear equations"); |
|
|
1439 else |
|
|
1440 { |
|
|
1441 volatile int typ = mattype.type (); |
|
|
1442 |
|
|
1443 if (typ == MatrixType::Permuted_Lower || |
|
|
1444 typ == MatrixType::Lower) |
|
|
1445 { |
|
|
1446 octave_idx_type b_nc = b.cols (); |
|
|
1447 rcond = 1.; |
|
|
1448 info = 0; |
|
|
1449 |
|
|
1450 if (typ == MatrixType::Permuted_Lower) |
|
|
1451 { |
|
|
1452 (*current_liboctave_error_handler) |
|
|
1453 ("Permuted triangular matrix not implemented"); |
|
|
1454 } |
|
|
1455 else |
|
|
1456 { |
|
|
1457 const double *tmp_data = fortran_vec (); |
|
|
1458 |
|
|
1459 if (calc_cond) |
|
|
1460 { |
|
|
1461 char norm = '1'; |
|
|
1462 char uplo = 'L'; |
|
|
1463 char dia = 'N'; |
|
|
1464 |
|
|
1465 Array<double> z (3 * nc); |
|
|
1466 double *pz = z.fortran_vec (); |
|
|
1467 Array<octave_idx_type> iz (nc); |
|
|
1468 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1469 |
|
|
1470 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1471 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1472 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1473 nr, tmp_data, nr, rcond, |
|
|
1474 pz, piz, info |
|
|
1475 F77_CHAR_ARG_LEN (1) |
|
|
1476 F77_CHAR_ARG_LEN (1) |
|
|
1477 F77_CHAR_ARG_LEN (1))); |
|
|
1478 |
|
|
1479 if (f77_exception_encountered) |
|
|
1480 (*current_liboctave_error_handler) |
|
|
1481 ("unrecoverable error in dtrcon"); |
|
|
1482 |
|
|
1483 if (info != 0) |
|
|
1484 info = -2; |
|
|
1485 |
|
|
1486 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1487 |
|
|
1488 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1489 { |
|
|
1490 info = -2; |
|
|
1491 |
|
|
1492 if (sing_handler) |
|
|
1493 sing_handler (rcond); |
|
|
1494 else |
|
|
1495 (*current_liboctave_error_handler) |
|
|
1496 ("matrix singular to machine precision, rcond = %g", |
|
|
1497 rcond); |
|
|
1498 } |
|
|
1499 } |
|
|
1500 |
|
|
1501 if (info == 0) |
|
|
1502 { |
|
|
1503 retval = b; |
|
|
1504 double *result = retval.fortran_vec (); |
|
|
1505 |
|
|
1506 char uplo = 'L'; |
|
|
1507 char trans = 'N'; |
|
|
1508 char dia = 'N'; |
|
|
1509 |
|
|
1510 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1511 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1512 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1513 nr, b_nc, tmp_data, nr, |
|
|
1514 result, nr, info |
|
|
1515 F77_CHAR_ARG_LEN (1) |
|
|
1516 F77_CHAR_ARG_LEN (1) |
|
|
1517 F77_CHAR_ARG_LEN (1))); |
|
|
1518 |
|
|
1519 if (f77_exception_encountered) |
|
|
1520 (*current_liboctave_error_handler) |
|
|
1521 ("unrecoverable error in dtrtrs"); |
|
|
1522 } |
|
|
1523 } |
|
|
1524 } |
|
|
1525 else |
|
|
1526 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1527 } |
|
|
1528 |
|
|
1529 return retval; |
|
|
1530 } |
|
|
1531 |
|
|
1532 Matrix |
|
|
1533 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1534 double& rcond, solve_singularity_handler sing_handler, |
|
|
1535 bool calc_cond) const |
|
|
1536 { |
|
|
1537 Matrix retval; |
|
|
1538 |
|
|
1539 octave_idx_type nr = rows (); |
|
|
1540 octave_idx_type nc = cols (); |
|
|
1541 |
|
|
1542 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1543 (*current_liboctave_error_handler) |
|
|
1544 ("matrix dimension mismatch solution of linear equations"); |
|
|
1545 else |
|
|
1546 { |
|
|
1547 volatile int typ = mattype.type (); |
|
|
1548 |
|
|
1549 // Calculate the norm of the matrix, for later use. |
|
|
1550 double anorm = -1.; |
|
|
1551 |
|
|
1552 if (typ == MatrixType::Hermitian) |
|
|
1553 { |
|
|
1554 info = 0; |
|
|
1555 char job = 'L'; |
|
|
1556 Matrix atmp = *this; |
|
|
1557 double *tmp_data = atmp.fortran_vec (); |
|
|
1558 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1559 |
|
|
1560 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
|
1561 tmp_data, nr, info |
|
|
1562 F77_CHAR_ARG_LEN (1))); |
|
|
1563 |
|
|
1564 if (f77_exception_encountered) |
|
|
1565 (*current_liboctave_error_handler) |
|
|
1566 ("unrecoverable error in dpotrf"); |
|
|
1567 else |
|
|
1568 { |
|
|
1569 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1570 rcond = 0.0; |
|
|
1571 if (info != 0) |
|
|
1572 { |
|
|
1573 info = -2; |
|
|
1574 |
|
|
1575 mattype.mark_as_unsymmetric (); |
|
|
1576 typ = MatrixType::Full; |
|
|
1577 } |
|
|
1578 else |
|
|
1579 { |
|
|
1580 if (calc_cond) |
|
|
1581 { |
|
|
1582 Array<double> z (3 * nc); |
|
|
1583 double *pz = z.fortran_vec (); |
|
|
1584 Array<octave_idx_type> iz (nc); |
|
|
1585 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1586 |
|
|
1587 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1588 nr, tmp_data, nr, anorm, |
|
|
1589 rcond, pz, piz, info |
|
|
1590 F77_CHAR_ARG_LEN (1))); |
|
|
1591 |
|
|
1592 if (f77_exception_encountered) |
|
|
1593 (*current_liboctave_error_handler) |
|
|
1594 ("unrecoverable error in dpocon"); |
|
|
1595 |
|
|
1596 if (info != 0) |
|
|
1597 info = -2; |
|
|
1598 |
|
|
1599 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1600 |
|
|
1601 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1602 { |
|
|
1603 info = -2; |
|
|
1604 |
|
|
1605 if (sing_handler) |
|
|
1606 sing_handler (rcond); |
|
|
1607 else |
|
|
1608 (*current_liboctave_error_handler) |
|
|
1609 ("matrix singular to machine precision, rcond = %g", |
|
|
1610 rcond); |
|
|
1611 } |
|
|
1612 } |
|
|
1613 |
|
|
1614 if (info == 0) |
|
|
1615 { |
|
|
1616 retval = b; |
|
|
1617 double *result = retval.fortran_vec (); |
|
|
1618 |
|
|
1619 octave_idx_type b_nc = b.cols (); |
|
|
1620 |
|
|
1621 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1622 nr, b_nc, tmp_data, nr, |
|
|
1623 result, b.rows(), info |
|
|
1624 F77_CHAR_ARG_LEN (1))); |
|
|
1625 |
|
|
1626 if (f77_exception_encountered) |
|
|
1627 (*current_liboctave_error_handler) |
|
|
1628 ("unrecoverable error in dpotrs"); |
|
|
1629 } |
|
|
1630 else |
|
|
1631 { |
|
|
1632 mattype.mark_as_unsymmetric (); |
|
|
1633 typ = MatrixType::Full; |
|
|
1634 } |
|
|
1635 } |
|
|
1636 } |
|
|
1637 } |
|
|
1638 |
|
|
1639 if (typ == MatrixType::Full) |
|
|
1640 { |
|
|
1641 info = 0; |
|
|
1642 |
|
|
1643 Array<octave_idx_type> ipvt (nr); |
|
|
1644 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
|
1645 |
|
|
1646 Matrix atmp = *this; |
|
|
1647 double *tmp_data = atmp.fortran_vec (); |
|
|
1648 if(anorm < 0.) |
|
|
1649 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1650 |
|
|
1651 Array<double> z (4 * nc); |
|
|
1652 double *pz = z.fortran_vec (); |
|
|
1653 Array<octave_idx_type> iz (nc); |
|
|
1654 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1655 |
|
|
1656 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
|
1657 |
|
|
1658 if (f77_exception_encountered) |
|
|
1659 (*current_liboctave_error_handler) |
|
|
1660 ("unrecoverable error in dgetrf"); |
|
|
1661 else |
|
|
1662 { |
|
|
1663 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1664 rcond = 0.0; |
|
|
1665 if (info != 0) |
|
|
1666 { |
|
|
1667 info = -2; |
|
|
1668 |
|
|
1669 if (sing_handler) |
|
|
1670 sing_handler (rcond); |
|
|
1671 else |
|
|
1672 (*current_liboctave_error_handler) |
|
|
1673 ("matrix singular to machine precision"); |
|
|
1674 |
|
|
1675 mattype.mark_as_rectangular (); |
|
|
1676 } |
|
|
1677 else |
|
|
1678 { |
|
|
1679 if (calc_cond) |
|
|
1680 { |
|
|
1681 // Now calculate the condition number for |
|
|
1682 // non-singular matrix. |
|
|
1683 char job = '1'; |
|
|
1684 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1685 nc, tmp_data, nr, anorm, |
|
|
1686 rcond, pz, piz, info |
|
|
1687 F77_CHAR_ARG_LEN (1))); |
|
|
1688 |
|
|
1689 if (f77_exception_encountered) |
|
|
1690 (*current_liboctave_error_handler) |
|
|
1691 ("unrecoverable error in dgecon"); |
|
|
1692 |
|
|
1693 if (info != 0) |
|
|
1694 info = -2; |
|
|
1695 |
|
|
1696 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1697 |
|
|
1698 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1699 { |
|
|
1700 info = -2; |
|
|
1701 |
|
|
1702 if (sing_handler) |
|
|
1703 sing_handler (rcond); |
|
|
1704 else |
|
|
1705 (*current_liboctave_error_handler) |
|
|
1706 ("matrix singular to machine precision, rcond = %g", |
|
|
1707 rcond); |
|
|
1708 } |
|
|
1709 } |
|
|
1710 |
|
|
1711 if (info == 0) |
|
|
1712 { |
|
|
1713 retval = b; |
|
|
1714 double *result = retval.fortran_vec (); |
|
|
1715 |
|
|
1716 octave_idx_type b_nc = b.cols (); |
|
|
1717 |
|
|
1718 char job = 'N'; |
|
|
1719 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1720 nr, b_nc, tmp_data, nr, |
|
|
1721 pipvt, result, b.rows(), info |
|
|
1722 F77_CHAR_ARG_LEN (1))); |
|
|
1723 |
|
|
1724 if (f77_exception_encountered) |
|
|
1725 (*current_liboctave_error_handler) |
|
|
1726 ("unrecoverable error in dgetrs"); |
|
|
1727 } |
|
|
1728 else |
|
|
1729 mattype.mark_as_rectangular (); |
|
|
1730 } |
|
|
1731 } |
|
|
1732 } |
|
|
1733 else if (typ != MatrixType::Hermitian) |
|
|
1734 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1735 } |
|
|
1736 |
|
|
1737 return retval; |
|
|
1738 } |
|
|
1739 |
|
|
1740 Matrix |
|
|
1741 Matrix::solve (MatrixType &typ, const Matrix& b) const |
|
|
1742 { |
|
|
1743 octave_idx_type info; |
|
|
1744 double rcond; |
|
|
1745 return solve (typ, b, info, rcond, 0); |
|
|
1746 } |
|
|
1747 |
|
|
1748 Matrix |
|
|
1749 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
1750 double& rcond) const |
|
|
1751 { |
|
|
1752 return solve (typ, b, info, rcond, 0); |
|
|
1753 } |
|
|
1754 |
|
|
1755 Matrix |
|
|
1756 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1757 double& rcond, solve_singularity_handler sing_handler, |
|
|
1758 bool singular_fallback) const |
|
|
1759 { |
|
|
1760 Matrix retval; |
|
|
1761 int typ = mattype.type (); |
|
|
1762 |
|
|
1763 if (typ == MatrixType::Unknown) |
|
|
1764 typ = mattype.type (*this); |
|
|
1765 |
|
|
1766 // Only calculate the condition number for LU/Cholesky |
|
|
1767 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
|
1768 retval = utsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1769 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
|
1770 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1771 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
|
1772 retval = fsolve (mattype, b, info, rcond, sing_handler, true); |
|
|
1773 else if (typ != MatrixType::Rectangular) |
|
|
1774 { |
|
|
1775 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
|
1776 return Matrix (); |
|
|
1777 } |
|
|
1778 |
|
|
1779 // Rectangular or one of the above solvers flags a singular matrix |
|
|
1780 if (singular_fallback && mattype.type () == MatrixType::Rectangular) |
|
|
1781 { |
|
|
1782 octave_idx_type rank; |
|
|
1783 retval = lssolve (b, info, rank); |
|
|
1784 } |
|
|
1785 |
|
|
1786 return retval; |
|
|
1787 } |
|
|
1788 |
|
|
1789 ComplexMatrix |
|
|
1790 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const |
|
|
1791 { |
|
|
1792 ComplexMatrix tmp (*this); |
|
|
1793 return tmp.solve (typ, b); |
|
|
1794 } |
|
|
1795 |
|
|
1796 ComplexMatrix |
|
|
1797 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
1798 octave_idx_type& info) const |
|
|
1799 { |
|
|
1800 ComplexMatrix tmp (*this); |
|
|
1801 return tmp.solve (typ, b, info); |
|
|
1802 } |
|
|
1803 |
|
|
1804 ComplexMatrix |
|
|
1805 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1806 double& rcond) const |
|
|
1807 { |
|
|
1808 ComplexMatrix tmp (*this); |
|
|
1809 return tmp.solve (typ, b, info, rcond); |
|
|
1810 } |
|
|
1811 |
|
|
1812 ComplexMatrix |
|
|
1813 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1814 double& rcond, solve_singularity_handler sing_handler, |
|
|
1815 bool singular_fallback) const |
|
|
1816 { |
|
|
1817 ComplexMatrix tmp (*this); |
|
|
1818 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); |
|
|
1819 } |
|
|
1820 |
|
|
1821 ColumnVector |
|
|
1822 Matrix::solve (MatrixType &typ, const ColumnVector& b) const |
|
|
1823 { |
|
|
1824 octave_idx_type info; double rcond; |
|
|
1825 return solve (typ, b, info, rcond); |
|
|
1826 } |
|
|
1827 |
|
|
1828 ColumnVector |
|
|
1829 Matrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
1830 octave_idx_type& info) const |
|
|
1831 { |
|
|
1832 double rcond; |
|
|
1833 return solve (typ, b, info, rcond); |
|
|
1834 } |
|
|
1835 |
|
|
1836 ColumnVector |
|
|
1837 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1838 double& rcond) const |
|
|
1839 { |
|
|
1840 return solve (typ, b, info, rcond, 0); |
|
|
1841 } |
|
|
1842 |
|
|
1843 ColumnVector |
|
|
1844 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1845 double& rcond, solve_singularity_handler sing_handler) const |
|
|
1846 { |
|
|
1847 Matrix tmp (b); |
|
|
1848 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); |
|
|
1849 } |
|
|
1850 |
|
|
1851 ComplexColumnVector |
|
|
1852 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const |
|
|
1853 { |
|
|
1854 ComplexMatrix tmp (*this); |
|
|
1855 return tmp.solve (typ, b); |
|
|
1856 } |
|
|
1857 |
|
|
1858 ComplexColumnVector |
|
|
1859 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1860 octave_idx_type& info) const |
|
|
1861 { |
|
|
1862 ComplexMatrix tmp (*this); |
|
|
1863 return tmp.solve (typ, b, info); |
|
|
1864 } |
|
|
1865 |
|
|
1866 ComplexColumnVector |
|
|
1867 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1868 octave_idx_type& info, double& rcond) const |
|
|
1869 { |
|
|
1870 ComplexMatrix tmp (*this); |
|
|
1871 return tmp.solve (typ, b, info, rcond); |
|
|
1872 } |
|
|
1873 |
|
|
1874 ComplexColumnVector |
|
|
1875 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1876 octave_idx_type& info, double& rcond, |
|
|
1877 solve_singularity_handler sing_handler) const |
|
|
1878 { |
|
|
1879 ComplexMatrix tmp (*this); |
|
|
1880 return tmp.solve(typ, b, info, rcond, sing_handler); |
|
|
1881 } |
|
|
1882 |
|
|
1883 Matrix |
|
458
|
1884 Matrix::solve (const Matrix& b) const |
|
|
1885 { |
|
5275
|
1886 octave_idx_type info; |
|
458
|
1887 double rcond; |
|
4329
|
1888 return solve (b, info, rcond, 0); |
|
458
|
1889 } |
|
|
1890 |
|
|
1891 Matrix |
|
5275
|
1892 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1893 { |
|
|
1894 double rcond; |
|
4329
|
1895 return solve (b, info, rcond, 0); |
|
458
|
1896 } |
|
|
1897 |
|
|
1898 Matrix |
|
5275
|
1899 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1900 { |
|
3480
|
1901 return solve (b, info, rcond, 0); |
|
|
1902 } |
|
|
1903 |
|
|
1904 Matrix |
|
5785
|
1905 Matrix::solve (const Matrix& b, octave_idx_type& info, |
|
|
1906 double& rcond, solve_singularity_handler sing_handler) const |
|
3480
|
1907 { |
|
5785
|
1908 MatrixType mattype (*this); |
|
|
1909 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1910 } |
|
|
1911 |
|
|
1912 ComplexMatrix |
|
|
1913 Matrix::solve (const ComplexMatrix& b) const |
|
|
1914 { |
|
|
1915 ComplexMatrix tmp (*this); |
|
|
1916 return tmp.solve (b); |
|
|
1917 } |
|
|
1918 |
|
|
1919 ComplexMatrix |
|
5275
|
1920 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1921 { |
|
|
1922 ComplexMatrix tmp (*this); |
|
|
1923 return tmp.solve (b, info); |
|
|
1924 } |
|
|
1925 |
|
|
1926 ComplexMatrix |
|
5275
|
1927 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1928 { |
|
|
1929 ComplexMatrix tmp (*this); |
|
|
1930 return tmp.solve (b, info, rcond); |
|
|
1931 } |
|
|
1932 |
|
3480
|
1933 ComplexMatrix |
|
5275
|
1934 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1935 solve_singularity_handler sing_handler) const |
|
|
1936 { |
|
|
1937 ComplexMatrix tmp (*this); |
|
|
1938 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1939 } |
|
|
1940 |
|
458
|
1941 ColumnVector |
|
|
1942 Matrix::solve (const ColumnVector& b) const |
|
|
1943 { |
|
5275
|
1944 octave_idx_type info; double rcond; |
|
458
|
1945 return solve (b, info, rcond); |
|
|
1946 } |
|
|
1947 |
|
|
1948 ColumnVector |
|
5275
|
1949 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1950 { |
|
|
1951 double rcond; |
|
|
1952 return solve (b, info, rcond); |
|
|
1953 } |
|
|
1954 |
|
|
1955 ColumnVector |
|
5275
|
1956 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1957 { |
|
3480
|
1958 return solve (b, info, rcond, 0); |
|
|
1959 } |
|
|
1960 |
|
|
1961 ColumnVector |
|
5275
|
1962 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1963 solve_singularity_handler sing_handler) const |
|
|
1964 { |
|
5785
|
1965 MatrixType mattype (*this); |
|
|
1966 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1967 } |
|
|
1968 |
|
|
1969 ComplexColumnVector |
|
|
1970 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1971 { |
|
|
1972 ComplexMatrix tmp (*this); |
|
|
1973 return tmp.solve (b); |
|
|
1974 } |
|
|
1975 |
|
|
1976 ComplexColumnVector |
|
5275
|
1977 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1978 { |
|
|
1979 ComplexMatrix tmp (*this); |
|
|
1980 return tmp.solve (b, info); |
|
|
1981 } |
|
|
1982 |
|
|
1983 ComplexColumnVector |
|
5275
|
1984 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1985 { |
|
|
1986 ComplexMatrix tmp (*this); |
|
|
1987 return tmp.solve (b, info, rcond); |
|
|
1988 } |
|
|
1989 |
|
3480
|
1990 ComplexColumnVector |
|
5275
|
1991 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1992 solve_singularity_handler sing_handler) const |
|
|
1993 { |
|
|
1994 ComplexMatrix tmp (*this); |
|
|
1995 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1996 } |
|
|
1997 |
|
458
|
1998 Matrix |
|
|
1999 Matrix::lssolve (const Matrix& b) const |
|
|
2000 { |
|
5275
|
2001 octave_idx_type info; |
|
|
2002 octave_idx_type rank; |
|
458
|
2003 return lssolve (b, info, rank); |
|
|
2004 } |
|
|
2005 |
|
|
2006 Matrix |
|
5275
|
2007 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
458
|
2008 { |
|
5275
|
2009 octave_idx_type rank; |
|
458
|
2010 return lssolve (b, info, rank); |
|
|
2011 } |
|
|
2012 |
|
|
2013 Matrix |
|
5275
|
2014 Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2015 { |
|
1948
|
2016 Matrix retval; |
|
|
2017 |
|
5275
|
2018 octave_idx_type nrhs = b.cols (); |
|
|
2019 |
|
|
2020 octave_idx_type m = rows (); |
|
|
2021 octave_idx_type n = cols (); |
|
458
|
2022 |
|
|
2023 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
2024 (*current_liboctave_error_handler) |
|
|
2025 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
2026 else |
|
458
|
2027 { |
|
1948
|
2028 Matrix atmp = *this; |
|
|
2029 double *tmp_data = atmp.fortran_vec (); |
|
|
2030 |
|
5275
|
2031 octave_idx_type nrr = m > n ? m : n; |
|
3754
|
2032 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
2033 |
|
5275
|
2034 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
2035 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2036 result.elem (i, j) = b.elem (i, j); |
|
|
2037 |
|
|
2038 double *presult = result.fortran_vec (); |
|
|
2039 |
|
5275
|
2040 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2041 Array<double> s (len_s); |
|
|
2042 double *ps = s.fortran_vec (); |
|
|
2043 |
|
|
2044 double rcond = -1.0; |
|
|
2045 |
|
3752
|
2046 // Ask DGELSS what the dimension of WORK should be. |
|
|
2047 |
|
5275
|
2048 octave_idx_type lwork = -1; |
|
3752
|
2049 |
|
|
2050 Array<double> work (1); |
|
1948
|
2051 |
|
|
2052 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
2053 rcond, rank, work.fortran_vec (), |
|
|
2054 lwork, info)); |
|
1948
|
2055 |
|
|
2056 if (f77_exception_encountered) |
|
|
2057 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
2058 else |
|
|
2059 { |
|
5275
|
2060 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
2061 work.resize (lwork); |
|
|
2062 |
|
|
2063 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2064 nrr, ps, rcond, rank, |
|
|
2065 work.fortran_vec (), lwork, info)); |
|
|
2066 |
|
|
2067 if (f77_exception_encountered) |
|
|
2068 (*current_liboctave_error_handler) |
|
|
2069 ("unrecoverable error in dgelss"); |
|
|
2070 else |
|
|
2071 { |
|
|
2072 retval.resize (n, nrhs); |
|
5275
|
2073 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
2074 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2075 retval.elem (i, j) = result.elem (i, j); |
|
|
2076 } |
|
1948
|
2077 } |
|
458
|
2078 } |
|
|
2079 |
|
|
2080 return retval; |
|
|
2081 } |
|
|
2082 |
|
|
2083 ComplexMatrix |
|
|
2084 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
2085 { |
|
|
2086 ComplexMatrix tmp (*this); |
|
5275
|
2087 octave_idx_type info; |
|
|
2088 octave_idx_type rank; |
|
1484
|
2089 return tmp.lssolve (b, info, rank); |
|
458
|
2090 } |
|
|
2091 |
|
|
2092 ComplexMatrix |
|
5275
|
2093 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
2094 { |
|
|
2095 ComplexMatrix tmp (*this); |
|
5275
|
2096 octave_idx_type rank; |
|
1484
|
2097 return tmp.lssolve (b, info, rank); |
|
458
|
2098 } |
|
|
2099 |
|
|
2100 ComplexMatrix |
|
5275
|
2101 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2102 { |
|
|
2103 ComplexMatrix tmp (*this); |
|
1484
|
2104 return tmp.lssolve (b, info, rank); |
|
458
|
2105 } |
|
|
2106 |
|
|
2107 ColumnVector |
|
|
2108 Matrix::lssolve (const ColumnVector& b) const |
|
|
2109 { |
|
5275
|
2110 octave_idx_type info; |
|
|
2111 octave_idx_type rank; |
|
1484
|
2112 return lssolve (b, info, rank); |
|
458
|
2113 } |
|
|
2114 |
|
|
2115 ColumnVector |
|
5275
|
2116 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
2117 { |
|
5275
|
2118 octave_idx_type rank; |
|
458
|
2119 return lssolve (b, info, rank); |
|
|
2120 } |
|
|
2121 |
|
|
2122 ColumnVector |
|
5275
|
2123 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2124 { |
|
1948
|
2125 ColumnVector retval; |
|
|
2126 |
|
5275
|
2127 octave_idx_type nrhs = 1; |
|
|
2128 |
|
|
2129 octave_idx_type m = rows (); |
|
|
2130 octave_idx_type n = cols (); |
|
458
|
2131 |
|
|
2132 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
2133 (*current_liboctave_error_handler) |
|
|
2134 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
2135 else |
|
458
|
2136 { |
|
1948
|
2137 Matrix atmp = *this; |
|
|
2138 double *tmp_data = atmp.fortran_vec (); |
|
|
2139 |
|
5275
|
2140 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2141 ColumnVector result (nrr); |
|
|
2142 |
|
5275
|
2143 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2144 result.elem (i) = b.elem (i); |
|
|
2145 |
|
|
2146 double *presult = result.fortran_vec (); |
|
|
2147 |
|
5275
|
2148 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2149 Array<double> s (len_s); |
|
|
2150 double *ps = s.fortran_vec (); |
|
|
2151 |
|
|
2152 double rcond = -1.0; |
|
|
2153 |
|
3752
|
2154 // Ask DGELSS what the dimension of WORK should be. |
|
|
2155 |
|
5275
|
2156 octave_idx_type lwork = -1; |
|
3752
|
2157 |
|
|
2158 Array<double> work (1); |
|
|
2159 |
|
|
2160 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
2161 rcond, rank, work.fortran_vec (), |
|
|
2162 lwork, info)); |
|
1948
|
2163 |
|
|
2164 if (f77_exception_encountered) |
|
|
2165 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
2166 else |
|
|
2167 { |
|
5275
|
2168 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
2169 work.resize (lwork); |
|
|
2170 |
|
|
2171 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2172 nrr, ps, rcond, rank, |
|
|
2173 work.fortran_vec (), lwork, info)); |
|
|
2174 |
|
|
2175 if (f77_exception_encountered) |
|
|
2176 (*current_liboctave_error_handler) |
|
|
2177 ("unrecoverable error in dgelss"); |
|
|
2178 else |
|
|
2179 { |
|
|
2180 retval.resize (n); |
|
5275
|
2181 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2182 retval.elem (i) = result.elem (i); |
|
|
2183 } |
|
1948
|
2184 } |
|
458
|
2185 } |
|
|
2186 |
|
|
2187 return retval; |
|
|
2188 } |
|
|
2189 |
|
|
2190 ComplexColumnVector |
|
|
2191 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
2192 { |
|
|
2193 ComplexMatrix tmp (*this); |
|
|
2194 return tmp.lssolve (b); |
|
|
2195 } |
|
|
2196 |
|
|
2197 ComplexColumnVector |
|
5275
|
2198 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2199 { |
|
|
2200 ComplexMatrix tmp (*this); |
|
|
2201 return tmp.lssolve (b, info); |
|
|
2202 } |
|
|
2203 |
|
|
2204 ComplexColumnVector |
|
5275
|
2205 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2206 { |
|
|
2207 ComplexMatrix tmp (*this); |
|
|
2208 return tmp.lssolve (b, info, rank); |
|
|
2209 } |
|
|
2210 |
|
1819
|
2211 // Constants for matrix exponential calculation. |
|
|
2212 |
|
|
2213 static double padec [] = |
|
|
2214 { |
|
|
2215 5.0000000000000000e-1, |
|
|
2216 1.1666666666666667e-1, |
|
|
2217 1.6666666666666667e-2, |
|
|
2218 1.6025641025641026e-3, |
|
|
2219 1.0683760683760684e-4, |
|
|
2220 4.8562548562548563e-6, |
|
|
2221 1.3875013875013875e-7, |
|
|
2222 1.9270852604185938e-9, |
|
|
2223 }; |
|
|
2224 |
|
|
2225 Matrix |
|
|
2226 Matrix::expm (void) const |
|
|
2227 { |
|
|
2228 Matrix retval; |
|
|
2229 |
|
|
2230 Matrix m = *this; |
|
|
2231 |
|
5275
|
2232 octave_idx_type nc = columns (); |
|
1819
|
2233 |
|
3130
|
2234 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2235 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2236 |
|
1819
|
2237 // trace shift value |
|
3331
|
2238 volatile double trshift = 0.0; |
|
1819
|
2239 |
|
5275
|
2240 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2241 trshift += m.elem (i, i); |
|
|
2242 |
|
|
2243 trshift /= nc; |
|
|
2244 |
|
3130
|
2245 if (trshift > 0.0) |
|
|
2246 { |
|
5275
|
2247 for (octave_idx_type i = 0; i < nc; i++) |
|
3130
|
2248 m.elem (i, i) -= trshift; |
|
|
2249 } |
|
1819
|
2250 |
|
3331
|
2251 // Preconditioning step 2: balancing; code follows development |
|
|
2252 // in AEPBAL |
|
|
2253 |
|
|
2254 double *p_m = m.fortran_vec (); |
|
|
2255 |
|
5275
|
2256 octave_idx_type info, ilo, ihi, ilos, ihis; |
|
3468
|
2257 Array<double> dpermute (nc); |
|
|
2258 Array<double> dscale (nc); |
|
3466
|
2259 |
|
3468
|
2260 // permutation first |
|
|
2261 char job = 'P'; |
|
4552
|
2262 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2263 nc, p_m, nc, ilo, ihi, |
|
|
2264 dpermute.fortran_vec (), info |
|
|
2265 F77_CHAR_ARG_LEN (1))); |
|
3466
|
2266 |
|
3468
|
2267 // then scaling |
|
|
2268 job = 'S'; |
|
4552
|
2269 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2270 nc, p_m, nc, ilos, ihis, |
|
|
2271 dscale.fortran_vec (), info |
|
|
2272 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2273 |
|
|
2274 if (f77_exception_encountered) |
|
|
2275 { |
|
|
2276 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
2277 return retval; |
|
|
2278 } |
|
|
2279 |
|
1819
|
2280 // Preconditioning step 3: scaling. |
|
3331
|
2281 |
|
1819
|
2282 ColumnVector work(nc); |
|
3130
|
2283 double inf_norm; |
|
3331
|
2284 |
|
4552
|
2285 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2286 nc, nc, m.fortran_vec (), nc, |
|
|
2287 work.fortran_vec (), inf_norm |
|
|
2288 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2289 |
|
|
2290 if (f77_exception_encountered) |
|
|
2291 { |
|
|
2292 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
2293 return retval; |
|
|
2294 } |
|
1819
|
2295 |
|
5275
|
2296 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
|
1819
|
2297 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
2298 : 0.0); |
|
3331
|
2299 |
|
1819
|
2300 // Check whether we need to square at all. |
|
3331
|
2301 |
|
1819
|
2302 if (sqpow < 0) |
|
|
2303 sqpow = 0; |
|
3331
|
2304 |
|
1819
|
2305 if (sqpow > 0) |
|
|
2306 { |
|
|
2307 double scale_factor = 1.0; |
|
5275
|
2308 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2309 scale_factor *= 2.0; |
|
3331
|
2310 |
|
1819
|
2311 m = m / scale_factor; |
|
|
2312 } |
|
3331
|
2313 |
|
1819
|
2314 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
2315 |
|
1819
|
2316 Matrix npp (nc, nc, 0.0); |
|
|
2317 Matrix dpp = npp; |
|
3331
|
2318 |
|
1819
|
2319 // Now powers a^8 ... a^1. |
|
3331
|
2320 |
|
5275
|
2321 octave_idx_type minus_one_j = -1; |
|
|
2322 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2323 { |
|
3573
|
2324 npp = m * npp + padec[j] * m; |
|
|
2325 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
2326 minus_one_j *= -1; |
|
|
2327 } |
|
3331
|
2328 |
|
1819
|
2329 // Zero power. |
|
3331
|
2330 |
|
1819
|
2331 dpp = -dpp; |
|
5275
|
2332 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2333 { |
|
|
2334 npp.elem (j, j) += 1.0; |
|
|
2335 dpp.elem (j, j) += 1.0; |
|
|
2336 } |
|
3331
|
2337 |
|
1819
|
2338 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2339 |
|
3331
|
2340 retval = dpp.solve (npp, info); |
|
|
2341 |
|
1819
|
2342 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
2343 |
|
1819
|
2344 while (sqpow) |
|
|
2345 { |
|
|
2346 retval = retval * retval; |
|
|
2347 sqpow--; |
|
|
2348 } |
|
3331
|
2349 |
|
1819
|
2350 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
2351 // apply inverse scaling to computed exponential |
|
5275
|
2352 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2353 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2354 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
2355 |
|
4153
|
2356 OCTAVE_QUIT; |
|
|
2357 |
|
3466
|
2358 // construct balancing permutation vector |
|
5275
|
2359 Array<octave_idx_type> iperm (nc); |
|
|
2360 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2361 iperm(i) = i; // identity permutation |
|
3466
|
2362 |
|
|
2363 // leading permutations in forward order |
|
5275
|
2364 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2365 { |
|
5275
|
2366 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2367 octave_idx_type tmp = iperm(i); |
|
4593
|
2368 iperm(i) = iperm (swapidx); |
|
|
2369 iperm(swapidx) = tmp; |
|
3468
|
2370 } |
|
3466
|
2371 |
|
|
2372 // trailing permutations must be done in reverse order |
|
5275
|
2373 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2374 { |
|
5275
|
2375 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2376 octave_idx_type tmp = iperm(i); |
|
4593
|
2377 iperm(i) = iperm(swapidx); |
|
|
2378 iperm(swapidx) = tmp; |
|
3468
|
2379 } |
|
3466
|
2380 |
|
|
2381 // construct inverse balancing permutation vector |
|
5275
|
2382 Array<octave_idx_type> invpvec (nc); |
|
|
2383 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2384 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
4153
|
2385 |
|
|
2386 OCTAVE_QUIT; |
|
3466
|
2387 |
|
|
2388 Matrix tmpMat = retval; |
|
5275
|
2389 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2390 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2391 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
2392 |
|
1819
|
2393 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
2394 |
|
3130
|
2395 if (trshift > 0.0) |
|
|
2396 retval = exp (trshift) * retval; |
|
|
2397 |
|
|
2398 return retval; |
|
1819
|
2399 } |
|
|
2400 |
|
458
|
2401 Matrix& |
|
|
2402 Matrix::operator += (const DiagMatrix& a) |
|
|
2403 { |
|
5275
|
2404 octave_idx_type nr = rows (); |
|
|
2405 octave_idx_type nc = cols (); |
|
|
2406 |
|
|
2407 octave_idx_type a_nr = a.rows (); |
|
|
2408 octave_idx_type a_nc = a.cols (); |
|
2385
|
2409 |
|
|
2410 if (nr != a_nr || nc != a_nc) |
|
458
|
2411 { |
|
2385
|
2412 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2413 return *this; |
|
|
2414 } |
|
|
2415 |
|
5275
|
2416 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2417 elem (i, i) += a.elem (i, i); |
|
|
2418 |
|
|
2419 return *this; |
|
|
2420 } |
|
|
2421 |
|
|
2422 Matrix& |
|
|
2423 Matrix::operator -= (const DiagMatrix& a) |
|
|
2424 { |
|
5275
|
2425 octave_idx_type nr = rows (); |
|
|
2426 octave_idx_type nc = cols (); |
|
|
2427 |
|
|
2428 octave_idx_type a_nr = a.rows (); |
|
|
2429 octave_idx_type a_nc = a.cols (); |
|
2385
|
2430 |
|
|
2431 if (nr != a_nr || nc != a_nc) |
|
458
|
2432 { |
|
2385
|
2433 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2434 return *this; |
|
|
2435 } |
|
|
2436 |
|
5275
|
2437 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2438 elem (i, i) -= a.elem (i, i); |
|
|
2439 |
|
|
2440 return *this; |
|
|
2441 } |
|
|
2442 |
|
|
2443 // unary operations |
|
|
2444 |
|
2964
|
2445 boolMatrix |
|
458
|
2446 Matrix::operator ! (void) const |
|
|
2447 { |
|
5275
|
2448 octave_idx_type nr = rows (); |
|
|
2449 octave_idx_type nc = cols (); |
|
458
|
2450 |
|
2964
|
2451 boolMatrix b (nr, nc); |
|
458
|
2452 |
|
5275
|
2453 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2454 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2455 b.elem (i, j) = ! elem (i, j); |
|
|
2456 |
|
|
2457 return b; |
|
|
2458 } |
|
|
2459 |
|
1205
|
2460 // column vector by row vector -> matrix operations |
|
458
|
2461 |
|
1205
|
2462 Matrix |
|
|
2463 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
2464 { |
|
1948
|
2465 Matrix retval; |
|
|
2466 |
|
5275
|
2467 octave_idx_type len = v.length (); |
|
3233
|
2468 |
|
|
2469 if (len != 0) |
|
1205
|
2470 { |
|
5275
|
2471 octave_idx_type a_len = a.length (); |
|
3233
|
2472 |
|
|
2473 retval.resize (len, a_len); |
|
|
2474 double *c = retval.fortran_vec (); |
|
|
2475 |
|
4552
|
2476 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2477 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2478 len, a_len, 1, 1.0, v.data (), len, |
|
|
2479 a.data (), 1, 0.0, c, len |
|
|
2480 F77_CHAR_ARG_LEN (1) |
|
|
2481 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2482 |
|
|
2483 if (f77_exception_encountered) |
|
|
2484 (*current_liboctave_error_handler) |
|
|
2485 ("unrecoverable error in dgemm"); |
|
1205
|
2486 } |
|
458
|
2487 |
|
1948
|
2488 return retval; |
|
458
|
2489 } |
|
|
2490 |
|
|
2491 // other operations. |
|
|
2492 |
|
|
2493 Matrix |
|
2676
|
2494 Matrix::map (d_d_Mapper f) const |
|
1205
|
2495 { |
|
2676
|
2496 Matrix b (*this); |
|
|
2497 return b.apply (f); |
|
1205
|
2498 } |
|
|
2499 |
|
3248
|
2500 boolMatrix |
|
|
2501 Matrix::map (b_d_Mapper f) const |
|
|
2502 { |
|
5275
|
2503 octave_idx_type nr = rows (); |
|
|
2504 octave_idx_type nc = cols (); |
|
3248
|
2505 |
|
|
2506 boolMatrix retval (nr, nc); |
|
|
2507 |
|
5275
|
2508 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2509 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2510 retval(i,j) = f (elem(i,j)); |
|
|
2511 |
|
|
2512 return retval; |
|
|
2513 } |
|
|
2514 |
|
2676
|
2515 Matrix& |
|
|
2516 Matrix::apply (d_d_Mapper f) |
|
458
|
2517 { |
|
|
2518 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2519 |
|
5275
|
2520 for (octave_idx_type i = 0; i < length (); i++) |
|
458
|
2521 d[i] = f (d[i]); |
|
2676
|
2522 |
|
|
2523 return *this; |
|
458
|
2524 } |
|
|
2525 |
|
2385
|
2526 bool |
|
4431
|
2527 Matrix::any_element_is_negative (bool neg_zero) const |
|
2385
|
2528 { |
|
5275
|
2529 octave_idx_type nel = nelem (); |
|
2385
|
2530 |
|
4431
|
2531 if (neg_zero) |
|
|
2532 { |
|
5275
|
2533 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2534 if (lo_ieee_signbit (elem (i))) |
|
|
2535 return true; |
|
4431
|
2536 } |
|
|
2537 else |
|
|
2538 { |
|
5275
|
2539 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2540 if (elem (i) < 0) |
|
|
2541 return true; |
|
4431
|
2542 } |
|
2385
|
2543 |
|
|
2544 return false; |
|
|
2545 } |
|
|
2546 |
|
|
2547 |
|
|
2548 bool |
|
|
2549 Matrix::any_element_is_inf_or_nan (void) const |
|
|
2550 { |
|
5275
|
2551 octave_idx_type nel = nelem (); |
|
|
2552 |
|
|
2553 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2554 { |
|
|
2555 double val = elem (i); |
|
|
2556 if (xisinf (val) || xisnan (val)) |
|
|
2557 return true; |
|
|
2558 } |
|
|
2559 |
|
|
2560 return false; |
|
2385
|
2561 } |
|
|
2562 |
|
|
2563 bool |
|
5943
|
2564 Matrix::any_element_not_one_or_zero (void) const |
|
|
2565 { |
|
|
2566 octave_idx_type nel = nelem (); |
|
|
2567 |
|
|
2568 for (octave_idx_type i = 0; i < nel; i++) |
|
|
2569 { |
|
|
2570 double val = elem (i); |
|
|
2571 if (val != 0 && val != 1) |
|
|
2572 return true; |
|
|
2573 } |
|
|
2574 |
|
|
2575 return false; |
|
|
2576 } |
|
|
2577 |
|
|
2578 bool |
|
2385
|
2579 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
2580 { |
|
5275
|
2581 octave_idx_type nel = nelem (); |
|
|
2582 |
|
|
2583 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2584 { |
|
|
2585 double val = elem (i); |
|
|
2586 if (xisnan (val) || D_NINT (val) == val) |
|
|
2587 continue; |
|
|
2588 else |
|
|
2589 return false; |
|
|
2590 } |
|
2385
|
2591 |
|
|
2592 return true; |
|
|
2593 } |
|
|
2594 |
|
1968
|
2595 // Return nonzero if any element of M is not an integer. Also extract |
|
|
2596 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
2597 |
|
2385
|
2598 bool |
|
1968
|
2599 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
2600 { |
|
5275
|
2601 octave_idx_type nel = nelem (); |
|
4634
|
2602 |
|
|
2603 if (nel > 0) |
|
1968
|
2604 { |
|
4634
|
2605 max_val = elem (0); |
|
|
2606 min_val = elem (0); |
|
1968
|
2607 } |
|
|
2608 else |
|
2385
|
2609 return false; |
|
1968
|
2610 |
|
5275
|
2611 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2612 { |
|
|
2613 double val = elem (i); |
|
|
2614 |
|
|
2615 if (val > max_val) |
|
|
2616 max_val = val; |
|
|
2617 |
|
|
2618 if (val < min_val) |
|
|
2619 min_val = val; |
|
|
2620 |
|
|
2621 if (D_NINT (val) != val) |
|
|
2622 return false; |
|
|
2623 } |
|
2385
|
2624 |
|
|
2625 return true; |
|
1968
|
2626 } |
|
|
2627 |
|
2385
|
2628 bool |
|
1968
|
2629 Matrix::too_large_for_float (void) const |
|
|
2630 { |
|
5275
|
2631 octave_idx_type nel = nelem (); |
|
|
2632 |
|
|
2633 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2634 { |
|
|
2635 double val = elem (i); |
|
|
2636 |
|
5389
|
2637 if (! (xisnan (val) || xisinf (val)) |
|
5387
|
2638 && fabs (val) > FLT_MAX) |
|
4634
|
2639 return true; |
|
|
2640 } |
|
1968
|
2641 |
|
2385
|
2642 return false; |
|
1968
|
2643 } |
|
|
2644 |
|
5775
|
2645 // FIXME Do these really belong here? Maybe they should be |
|
4015
|
2646 // in a base class? |
|
458
|
2647 |
|
2832
|
2648 boolMatrix |
|
4015
|
2649 Matrix::all (int dim) const |
|
458
|
2650 { |
|
4015
|
2651 MX_ALL_OP (dim); |
|
458
|
2652 } |
|
|
2653 |
|
2832
|
2654 boolMatrix |
|
4015
|
2655 Matrix::any (int dim) const |
|
458
|
2656 { |
|
4015
|
2657 MX_ANY_OP (dim); |
|
458
|
2658 } |
|
|
2659 |
|
|
2660 Matrix |
|
3723
|
2661 Matrix::cumprod (int dim) const |
|
458
|
2662 { |
|
4015
|
2663 MX_CUMULATIVE_OP (Matrix, double, *=); |
|
458
|
2664 } |
|
|
2665 |
|
|
2666 Matrix |
|
3723
|
2667 Matrix::cumsum (int dim) const |
|
458
|
2668 { |
|
4015
|
2669 MX_CUMULATIVE_OP (Matrix, double, +=); |
|
458
|
2670 } |
|
|
2671 |
|
|
2672 Matrix |
|
3723
|
2673 Matrix::prod (int dim) const |
|
458
|
2674 { |
|
3864
|
2675 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2676 } |
|
|
2677 |
|
|
2678 Matrix |
|
3723
|
2679 Matrix::sum (int dim) const |
|
458
|
2680 { |
|
3864
|
2681 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2682 } |
|
|
2683 |
|
|
2684 Matrix |
|
3723
|
2685 Matrix::sumsq (int dim) const |
|
458
|
2686 { |
|
3864
|
2687 #define ROW_EXPR \ |
|
|
2688 double d = elem (i, j); \ |
|
|
2689 retval.elem (i, 0) += d * d |
|
|
2690 |
|
|
2691 #define COL_EXPR \ |
|
|
2692 double d = elem (i, j); \ |
|
|
2693 retval.elem (0, j) += d * d |
|
|
2694 |
|
|
2695 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2696 |
|
|
2697 #undef ROW_EXPR |
|
|
2698 #undef COL_EXPR |
|
458
|
2699 } |
|
|
2700 |
|
2385
|
2701 Matrix |
|
|
2702 Matrix::abs (void) const |
|
|
2703 { |
|
5275
|
2704 octave_idx_type nr = rows (); |
|
|
2705 octave_idx_type nc = cols (); |
|
2385
|
2706 |
|
|
2707 Matrix retval (nr, nc); |
|
|
2708 |
|
5275
|
2709 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2710 for (octave_idx_type i = 0; i < nr; i++) |
|
2385
|
2711 retval (i, j) = fabs (elem (i, j)); |
|
|
2712 |
|
|
2713 return retval; |
|
|
2714 } |
|
|
2715 |
|
458
|
2716 ColumnVector |
|
|
2717 Matrix::diag (void) const |
|
|
2718 { |
|
|
2719 return diag (0); |
|
|
2720 } |
|
|
2721 |
|
|
2722 ColumnVector |
|
5275
|
2723 Matrix::diag (octave_idx_type k) const |
|
458
|
2724 { |
|
5275
|
2725 octave_idx_type nnr = rows (); |
|
|
2726 octave_idx_type nnc = cols (); |
|
458
|
2727 if (k > 0) |
|
|
2728 nnc -= k; |
|
|
2729 else if (k < 0) |
|
|
2730 nnr += k; |
|
|
2731 |
|
|
2732 ColumnVector d; |
|
|
2733 |
|
|
2734 if (nnr > 0 && nnc > 0) |
|
|
2735 { |
|
5275
|
2736 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
2737 |
|
|
2738 d.resize (ndiag); |
|
|
2739 |
|
|
2740 if (k > 0) |
|
|
2741 { |
|
5275
|
2742 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2743 d.elem (i) = elem (i, i+k); |
|
|
2744 } |
|
4509
|
2745 else if (k < 0) |
|
458
|
2746 { |
|
5275
|
2747 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2748 d.elem (i) = elem (i-k, i); |
|
|
2749 } |
|
|
2750 else |
|
|
2751 { |
|
5275
|
2752 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2753 d.elem (i) = elem (i, i); |
|
|
2754 } |
|
|
2755 } |
|
|
2756 else |
|
4513
|
2757 (*current_liboctave_error_handler) |
|
|
2758 ("diag: requested diagonal out of range"); |
|
458
|
2759 |
|
|
2760 return d; |
|
|
2761 } |
|
|
2762 |
|
|
2763 ColumnVector |
|
|
2764 Matrix::row_min (void) const |
|
|
2765 { |
|
5275
|
2766 Array<octave_idx_type> dummy_idx; |
|
4587
|
2767 return row_min (dummy_idx); |
|
458
|
2768 } |
|
|
2769 |
|
|
2770 ColumnVector |
|
5275
|
2771 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2772 { |
|
|
2773 ColumnVector result; |
|
|
2774 |
|
5275
|
2775 octave_idx_type nr = rows (); |
|
|
2776 octave_idx_type nc = cols (); |
|
458
|
2777 |
|
|
2778 if (nr > 0 && nc > 0) |
|
|
2779 { |
|
|
2780 result.resize (nr); |
|
4587
|
2781 idx_arg.resize (nr); |
|
458
|
2782 |
|
5275
|
2783 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2784 { |
|
5275
|
2785 octave_idx_type idx_j; |
|
4469
|
2786 |
|
|
2787 double tmp_min = octave_NaN; |
|
|
2788 |
|
|
2789 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2790 { |
|
4469
|
2791 tmp_min = elem (i, idx_j); |
|
|
2792 |
|
5389
|
2793 if (! xisnan (tmp_min)) |
|
4469
|
2794 break; |
|
|
2795 } |
|
|
2796 |
|
5275
|
2797 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2798 { |
|
|
2799 double tmp = elem (i, j); |
|
|
2800 |
|
5389
|
2801 if (xisnan (tmp)) |
|
4469
|
2802 continue; |
|
|
2803 else if (tmp < tmp_min) |
|
2354
|
2804 { |
|
4469
|
2805 idx_j = j; |
|
|
2806 tmp_min = tmp; |
|
2354
|
2807 } |
|
|
2808 } |
|
|
2809 |
|
4469
|
2810 result.elem (i) = tmp_min; |
|
5389
|
2811 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
|
458
|
2812 } |
|
|
2813 } |
|
|
2814 |
|
|
2815 return result; |
|
|
2816 } |
|
|
2817 |
|
|
2818 ColumnVector |
|
|
2819 Matrix::row_max (void) const |
|
|
2820 { |
|
5275
|
2821 Array<octave_idx_type> dummy_idx; |
|
4587
|
2822 return row_max (dummy_idx); |
|
458
|
2823 } |
|
|
2824 |
|
|
2825 ColumnVector |
|
5275
|
2826 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2827 { |
|
|
2828 ColumnVector result; |
|
|
2829 |
|
5275
|
2830 octave_idx_type nr = rows (); |
|
|
2831 octave_idx_type nc = cols (); |
|
458
|
2832 |
|
|
2833 if (nr > 0 && nc > 0) |
|
|
2834 { |
|
|
2835 result.resize (nr); |
|
4587
|
2836 idx_arg.resize (nr); |
|
458
|
2837 |
|
5275
|
2838 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2839 { |
|
5275
|
2840 octave_idx_type idx_j; |
|
4469
|
2841 |
|
|
2842 double tmp_max = octave_NaN; |
|
|
2843 |
|
|
2844 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2845 { |
|
4469
|
2846 tmp_max = elem (i, idx_j); |
|
|
2847 |
|
5389
|
2848 if (! xisnan (tmp_max)) |
|
4469
|
2849 break; |
|
|
2850 } |
|
|
2851 |
|
5275
|
2852 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2853 { |
|
|
2854 double tmp = elem (i, j); |
|
|
2855 |
|
5389
|
2856 if (xisnan (tmp)) |
|
4469
|
2857 continue; |
|
|
2858 else if (tmp > tmp_max) |
|
2354
|
2859 { |
|
4469
|
2860 idx_j = j; |
|
|
2861 tmp_max = tmp; |
|
2354
|
2862 } |
|
|
2863 } |
|
|
2864 |
|
4469
|
2865 result.elem (i) = tmp_max; |
|
5389
|
2866 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
|
458
|
2867 } |
|
|
2868 } |
|
|
2869 |
|
|
2870 return result; |
|
|
2871 } |
|
|
2872 |
|
|
2873 RowVector |
|
|
2874 Matrix::column_min (void) const |
|
|
2875 { |
|
5275
|
2876 Array<octave_idx_type> dummy_idx; |
|
4587
|
2877 return column_min (dummy_idx); |
|
458
|
2878 } |
|
2354
|
2879 |
|
458
|
2880 RowVector |
|
5275
|
2881 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2882 { |
|
|
2883 RowVector result; |
|
|
2884 |
|
5275
|
2885 octave_idx_type nr = rows (); |
|
|
2886 octave_idx_type nc = cols (); |
|
458
|
2887 |
|
|
2888 if (nr > 0 && nc > 0) |
|
|
2889 { |
|
|
2890 result.resize (nc); |
|
4587
|
2891 idx_arg.resize (nc); |
|
458
|
2892 |
|
5275
|
2893 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2894 { |
|
5275
|
2895 octave_idx_type idx_i; |
|
4469
|
2896 |
|
|
2897 double tmp_min = octave_NaN; |
|
|
2898 |
|
|
2899 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2900 { |
|
4469
|
2901 tmp_min = elem (idx_i, j); |
|
|
2902 |
|
5389
|
2903 if (! xisnan (tmp_min)) |
|
4469
|
2904 break; |
|
|
2905 } |
|
|
2906 |
|
5275
|
2907 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2908 { |
|
|
2909 double tmp = elem (i, j); |
|
|
2910 |
|
5389
|
2911 if (xisnan (tmp)) |
|
4469
|
2912 continue; |
|
|
2913 else if (tmp < tmp_min) |
|
2354
|
2914 { |
|
4469
|
2915 idx_i = i; |
|
|
2916 tmp_min = tmp; |
|
2354
|
2917 } |
|
|
2918 } |
|
|
2919 |
|
4469
|
2920 result.elem (j) = tmp_min; |
|
5389
|
2921 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
|
458
|
2922 } |
|
|
2923 } |
|
|
2924 |
|
|
2925 return result; |
|
|
2926 } |
|
|
2927 |
|
2354
|
2928 RowVector |
|
|
2929 Matrix::column_max (void) const |
|
|
2930 { |
|
5275
|
2931 Array<octave_idx_type> dummy_idx; |
|
4587
|
2932 return column_max (dummy_idx); |
|
2354
|
2933 } |
|
458
|
2934 |
|
|
2935 RowVector |
|
5275
|
2936 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2937 { |
|
|
2938 RowVector result; |
|
|
2939 |
|
5275
|
2940 octave_idx_type nr = rows (); |
|
|
2941 octave_idx_type nc = cols (); |
|
458
|
2942 |
|
|
2943 if (nr > 0 && nc > 0) |
|
|
2944 { |
|
|
2945 result.resize (nc); |
|
4587
|
2946 idx_arg.resize (nc); |
|
458
|
2947 |
|
5275
|
2948 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2949 { |
|
5275
|
2950 octave_idx_type idx_i; |
|
4469
|
2951 |
|
|
2952 double tmp_max = octave_NaN; |
|
|
2953 |
|
|
2954 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2955 { |
|
4469
|
2956 tmp_max = elem (idx_i, j); |
|
|
2957 |
|
5389
|
2958 if (! xisnan (tmp_max)) |
|
4469
|
2959 break; |
|
|
2960 } |
|
|
2961 |
|
5275
|
2962 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2963 { |
|
|
2964 double tmp = elem (i, j); |
|
|
2965 |
|
5389
|
2966 if (xisnan (tmp)) |
|
4469
|
2967 continue; |
|
|
2968 else if (tmp > tmp_max) |
|
2354
|
2969 { |
|
4469
|
2970 idx_i = i; |
|
|
2971 tmp_max = tmp; |
|
2354
|
2972 } |
|
|
2973 } |
|
|
2974 |
|
4469
|
2975 result.elem (j) = tmp_max; |
|
5389
|
2976 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
|
458
|
2977 } |
|
|
2978 } |
|
|
2979 |
|
|
2980 return result; |
|
|
2981 } |
|
|
2982 |
|
3504
|
2983 std::ostream& |
|
|
2984 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2985 { |
|
5275
|
2986 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
2987 { |
|
5275
|
2988 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
2989 { |
|
|
2990 os << " "; |
|
|
2991 octave_write_double (os, a.elem (i, j)); |
|
|
2992 } |
|
458
|
2993 os << "\n"; |
|
|
2994 } |
|
|
2995 return os; |
|
|
2996 } |
|
|
2997 |
|
3504
|
2998 std::istream& |
|
|
2999 operator >> (std::istream& is, Matrix& a) |
|
458
|
3000 { |
|
5275
|
3001 octave_idx_type nr = a.rows (); |
|
|
3002 octave_idx_type nc = a.cols (); |
|
458
|
3003 |
|
|
3004 if (nr < 1 || nc < 1) |
|
3504
|
3005 is.clear (std::ios::badbit); |
|
458
|
3006 else |
|
|
3007 { |
|
|
3008 double tmp; |
|
5275
|
3009 for (octave_idx_type i = 0; i < nr; i++) |
|
|
3010 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
3011 { |
|
4130
|
3012 tmp = octave_read_double (is); |
|
458
|
3013 if (is) |
|
|
3014 a.elem (i, j) = tmp; |
|
|
3015 else |
|
2795
|
3016 goto done; |
|
458
|
3017 } |
|
|
3018 } |
|
|
3019 |
|
2795
|
3020 done: |
|
|
3021 |
|
458
|
3022 return is; |
|
|
3023 } |
|
|
3024 |
|
1819
|
3025 Matrix |
|
|
3026 Givens (double x, double y) |
|
|
3027 { |
|
|
3028 double cc, s, temp_r; |
|
|
3029 |
|
3887
|
3030 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
1819
|
3031 |
|
|
3032 Matrix g (2, 2); |
|
|
3033 |
|
|
3034 g.elem (0, 0) = cc; |
|
|
3035 g.elem (1, 1) = cc; |
|
|
3036 g.elem (0, 1) = s; |
|
|
3037 g.elem (1, 0) = -s; |
|
|
3038 |
|
|
3039 return g; |
|
|
3040 } |
|
|
3041 |
|
|
3042 Matrix |
|
|
3043 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
3044 { |
|
|
3045 Matrix retval; |
|
|
3046 |
|
5775
|
3047 // FIXME -- need to check that a, b, and c are all the same |
|
1819
|
3048 // size. |
|
|
3049 |
|
|
3050 // Compute Schur decompositions. |
|
|
3051 |
|
|
3052 SCHUR as (a, "U"); |
|
|
3053 SCHUR bs (b, "U"); |
|
|
3054 |
|
|
3055 // Transform c to new coordinates. |
|
|
3056 |
|
|
3057 Matrix ua = as.unitary_matrix (); |
|
|
3058 Matrix sch_a = as.schur_matrix (); |
|
|
3059 |
|
|
3060 Matrix ub = bs.unitary_matrix (); |
|
|
3061 Matrix sch_b = bs.schur_matrix (); |
|
|
3062 |
|
|
3063 Matrix cx = ua.transpose () * c * ub; |
|
|
3064 |
|
|
3065 // Solve the sylvester equation, back-transform, and return the |
|
|
3066 // solution. |
|
|
3067 |
|
5275
|
3068 octave_idx_type a_nr = a.rows (); |
|
|
3069 octave_idx_type b_nr = b.rows (); |
|
1819
|
3070 |
|
|
3071 double scale; |
|
5275
|
3072 octave_idx_type info; |
|
1819
|
3073 |
|
1950
|
3074 double *pa = sch_a.fortran_vec (); |
|
|
3075 double *pb = sch_b.fortran_vec (); |
|
|
3076 double *px = cx.fortran_vec (); |
|
|
3077 |
|
4552
|
3078 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3079 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3080 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3081 b_nr, px, a_nr, scale, info |
|
|
3082 F77_CHAR_ARG_LEN (1) |
|
|
3083 F77_CHAR_ARG_LEN (1))); |
|
1950
|
3084 |
|
|
3085 |
|
|
3086 if (f77_exception_encountered) |
|
|
3087 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
3088 else |
|
|
3089 { |
|
5775
|
3090 // FIXME -- check info? |
|
1819
|
3091 |
|
1950
|
3092 retval = -ua*cx*ub.transpose (); |
|
|
3093 } |
|
1819
|
3094 |
|
|
3095 return retval; |
|
|
3096 } |
|
|
3097 |
|
2828
|
3098 // matrix by matrix -> matrix operations |
|
|
3099 |
|
6162
|
3100 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
|
|
3101 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) |
|
|
3102 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) |
|
|
3103 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) |
|
|
3104 */ |
|
|
3105 |
|
|
3106 /* Test some simple identities |
|
|
3107 %!shared M, cv, rv |
|
|
3108 %! M = randn(10,10); |
|
|
3109 %! cv = randn(10,1); |
|
|
3110 %! rv = randn(1,10); |
|
|
3111 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) |
|
|
3112 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) |
|
|
3113 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) |
|
|
3114 */ |
|
|
3115 |
|
|
3116 |
|
2828
|
3117 Matrix |
|
|
3118 operator * (const Matrix& m, const Matrix& a) |
|
|
3119 { |
|
|
3120 Matrix retval; |
|
|
3121 |
|
5275
|
3122 octave_idx_type nr = m.rows (); |
|
|
3123 octave_idx_type nc = m.cols (); |
|
|
3124 |
|
|
3125 octave_idx_type a_nr = a.rows (); |
|
|
3126 octave_idx_type a_nc = a.cols (); |
|
2828
|
3127 |
|
|
3128 if (nc != a_nr) |
|
|
3129 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3130 else |
|
|
3131 { |
|
|
3132 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
3133 retval.resize (nr, a_nc, 0.0); |
|
|
3134 else |
|
|
3135 { |
|
5275
|
3136 octave_idx_type ld = nr; |
|
|
3137 octave_idx_type lda = a_nr; |
|
2828
|
3138 |
|
|
3139 retval.resize (nr, a_nc); |
|
|
3140 double *c = retval.fortran_vec (); |
|
|
3141 |
|
5983
|
3142 if (a_nc == 1) |
|
|
3143 { |
|
|
3144 if (nr == 1) |
|
|
3145 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); |
|
|
3146 else |
|
|
3147 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3148 nr, nc, 1.0, m.data (), ld, |
|
|
3149 a.data (), 1, 0.0, c, 1 |
|
|
3150 F77_CHAR_ARG_LEN (1))); |
|
|
3151 } |
|
|
3152 else |
|
|
3153 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3154 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3155 nr, a_nc, nc, 1.0, m.data (), |
|
|
3156 ld, a.data (), lda, 0.0, c, nr |
|
|
3157 F77_CHAR_ARG_LEN (1) |
|
|
3158 F77_CHAR_ARG_LEN (1))); |
|
2828
|
3159 |
|
|
3160 if (f77_exception_encountered) |
|
|
3161 (*current_liboctave_error_handler) |
|
|
3162 ("unrecoverable error in dgemm"); |
|
|
3163 } |
|
|
3164 } |
|
|
3165 |
|
|
3166 return retval; |
|
|
3167 } |
|
|
3168 |
|
5775
|
3169 // FIXME -- it would be nice to share code among the min/max |
|
4309
|
3170 // functions below. |
|
|
3171 |
|
|
3172 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3173 if (nr == 0 || nc == 0) \ |
|
|
3174 return T (nr, nc); |
|
|
3175 |
|
|
3176 Matrix |
|
|
3177 min (double d, const Matrix& m) |
|
|
3178 { |
|
5275
|
3179 octave_idx_type nr = m.rows (); |
|
|
3180 octave_idx_type nc = m.columns (); |
|
4309
|
3181 |
|
|
3182 EMPTY_RETURN_CHECK (Matrix); |
|
|
3183 |
|
|
3184 Matrix result (nr, nc); |
|
|
3185 |
|
5275
|
3186 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3187 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3188 { |
|
|
3189 OCTAVE_QUIT; |
|
|
3190 result (i, j) = xmin (d, m (i, j)); |
|
|
3191 } |
|
|
3192 |
|
|
3193 return result; |
|
|
3194 } |
|
|
3195 |
|
|
3196 Matrix |
|
|
3197 min (const Matrix& m, double d) |
|
|
3198 { |
|
5275
|
3199 octave_idx_type nr = m.rows (); |
|
|
3200 octave_idx_type nc = m.columns (); |
|
4309
|
3201 |
|
|
3202 EMPTY_RETURN_CHECK (Matrix); |
|
|
3203 |
|
|
3204 Matrix result (nr, nc); |
|
|
3205 |
|
5275
|
3206 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3207 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3208 { |
|
|
3209 OCTAVE_QUIT; |
|
|
3210 result (i, j) = xmin (m (i, j), d); |
|
|
3211 } |
|
|
3212 |
|
|
3213 return result; |
|
|
3214 } |
|
|
3215 |
|
|
3216 Matrix |
|
|
3217 min (const Matrix& a, const Matrix& b) |
|
|
3218 { |
|
5275
|
3219 octave_idx_type nr = a.rows (); |
|
|
3220 octave_idx_type nc = a.columns (); |
|
4309
|
3221 |
|
|
3222 if (nr != b.rows () || nc != b.columns ()) |
|
|
3223 { |
|
|
3224 (*current_liboctave_error_handler) |
|
|
3225 ("two-arg min expecting args of same size"); |
|
|
3226 return Matrix (); |
|
|
3227 } |
|
|
3228 |
|
|
3229 EMPTY_RETURN_CHECK (Matrix); |
|
|
3230 |
|
|
3231 Matrix result (nr, nc); |
|
|
3232 |
|
5275
|
3233 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3234 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3235 { |
|
|
3236 OCTAVE_QUIT; |
|
|
3237 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3238 } |
|
|
3239 |
|
|
3240 return result; |
|
|
3241 } |
|
|
3242 |
|
|
3243 Matrix |
|
|
3244 max (double d, const Matrix& m) |
|
|
3245 { |
|
5275
|
3246 octave_idx_type nr = m.rows (); |
|
|
3247 octave_idx_type nc = m.columns (); |
|
4309
|
3248 |
|
|
3249 EMPTY_RETURN_CHECK (Matrix); |
|
|
3250 |
|
|
3251 Matrix result (nr, nc); |
|
|
3252 |
|
5275
|
3253 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3254 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3255 { |
|
|
3256 OCTAVE_QUIT; |
|
|
3257 result (i, j) = xmax (d, m (i, j)); |
|
|
3258 } |
|
|
3259 |
|
|
3260 return result; |
|
|
3261 } |
|
|
3262 |
|
|
3263 Matrix |
|
|
3264 max (const Matrix& m, double d) |
|
|
3265 { |
|
5275
|
3266 octave_idx_type nr = m.rows (); |
|
|
3267 octave_idx_type nc = m.columns (); |
|
4309
|
3268 |
|
|
3269 EMPTY_RETURN_CHECK (Matrix); |
|
|
3270 |
|
|
3271 Matrix result (nr, nc); |
|
|
3272 |
|
5275
|
3273 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3274 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3275 { |
|
|
3276 OCTAVE_QUIT; |
|
|
3277 result (i, j) = xmax (m (i, j), d); |
|
|
3278 } |
|
|
3279 |
|
|
3280 return result; |
|
|
3281 } |
|
|
3282 |
|
|
3283 Matrix |
|
|
3284 max (const Matrix& a, const Matrix& b) |
|
|
3285 { |
|
5275
|
3286 octave_idx_type nr = a.rows (); |
|
|
3287 octave_idx_type nc = a.columns (); |
|
4309
|
3288 |
|
|
3289 if (nr != b.rows () || nc != b.columns ()) |
|
|
3290 { |
|
|
3291 (*current_liboctave_error_handler) |
|
|
3292 ("two-arg max expecting args of same size"); |
|
|
3293 return Matrix (); |
|
|
3294 } |
|
|
3295 |
|
|
3296 EMPTY_RETURN_CHECK (Matrix); |
|
|
3297 |
|
|
3298 Matrix result (nr, nc); |
|
|
3299 |
|
5275
|
3300 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3301 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3302 { |
|
|
3303 OCTAVE_QUIT; |
|
|
3304 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3305 } |
|
|
3306 |
|
|
3307 return result; |
|
|
3308 } |
|
|
3309 |
|
2870
|
3310 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
3311 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
3312 |
|
|
3313 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
3314 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
3315 |
|
|
3316 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
3317 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
3318 |
|
458
|
3319 /* |
|
|
3320 ;;; Local Variables: *** |
|
|
3321 ;;; mode: C++ *** |
|
|
3322 ;;; End: *** |
|
|
3323 */ |
