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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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1367
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32 |
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4669
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33 #include "Array-util.h" |
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2317
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34 #include "byte-swap.h" |
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2828
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35 #include "dMatrix.h" |
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1819
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36 #include "dbleAEPBAL.h" |
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458
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37 #include "dbleDET.h" |
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1819
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38 #include "dbleSCHUR.h" |
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740
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39 #include "dbleSVD.h" |
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1847
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40 #include "f77-fcn.h" |
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458
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41 #include "lo-error.h" |
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2354
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42 #include "lo-ieee.h" |
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43 #include "lo-mappers.h" |
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1968
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44 #include "lo-utils.h" |
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1367
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45 #include "mx-base.h" |
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2828
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46 #include "mx-m-dm.h" |
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3176
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47 #include "mx-dm-m.h" |
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1367
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48 #include "mx-inlines.cc" |
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1650
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49 #include "oct-cmplx.h" |
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4153
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50 #include "quit.h" |
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458
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51 |
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4773
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52 #if defined (HAVE_FFTW3) |
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3827
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53 #include "oct-fftw.h" |
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54 #endif |
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55 |
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458
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56 // Fortran functions we call. |
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57 |
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58 extern "C" |
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59 { |
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4552
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60 F77_RET_T |
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61 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, |
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5275
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62 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
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63 octave_idx_type&, double*, octave_idx_type& |
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64 F77_CHAR_ARG_LEN_DECL); |
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65 |
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66 F77_RET_T |
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67 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, |
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68 F77_CONST_CHAR_ARG_DECL, |
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5275
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69 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
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70 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& |
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71 F77_CHAR_ARG_LEN_DECL |
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72 F77_CHAR_ARG_LEN_DECL); |
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73 |
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74 |
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75 F77_RET_T |
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76 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, |
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77 F77_CONST_CHAR_ARG_DECL, |
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5275
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78 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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79 const double&, const double*, const octave_idx_type&, |
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80 const double*, const octave_idx_type&, const double&, |
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81 double*, const octave_idx_type& |
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82 F77_CHAR_ARG_LEN_DECL |
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83 F77_CHAR_ARG_LEN_DECL); |
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84 |
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85 F77_RET_T |
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86 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
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87 octave_idx_type*, octave_idx_type&); |
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88 |
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89 F77_RET_T |
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90 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
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91 const double*, const octave_idx_type&, |
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92 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& |
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93 F77_CHAR_ARG_LEN_DECL); |
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94 |
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95 F77_RET_T |
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96 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
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97 double*, const octave_idx_type&, octave_idx_type&); |
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98 |
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99 F77_RET_T |
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100 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
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101 const octave_idx_type&, const double&, double&, |
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102 double*, octave_idx_type*, octave_idx_type& |
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103 F77_CHAR_ARG_LEN_DECL); |
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104 |
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105 F77_RET_T |
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5275
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106 F77_FUNC (dgelss, DGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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107 double*, const octave_idx_type&, double*, |
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108 const octave_idx_type&, double*, double&, octave_idx_type&, |
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109 double*, const octave_idx_type&, octave_idx_type&); |
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110 |
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1360
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111 // Note that the original complex fft routines were not written for |
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112 // double complex arguments. They have been modified by adding an |
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113 // implicit double precision (a-h,o-z) statement at the beginning of |
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114 // each subroutine. |
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115 |
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116 F77_RET_T |
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5275
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117 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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118 |
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119 F77_RET_T |
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5275
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120 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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121 |
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122 F77_RET_T |
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5275
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123 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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124 |
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125 F77_RET_T |
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126 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, |
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127 double&, double&); |
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128 |
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129 F77_RET_T |
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130 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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131 F77_CONST_CHAR_ARG_DECL, |
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5275
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132 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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133 const double*, const octave_idx_type&, const double*, |
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134 const octave_idx_type&, const double*, const octave_idx_type&, |
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135 double&, octave_idx_type& |
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4552
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136 F77_CHAR_ARG_LEN_DECL |
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137 F77_CHAR_ARG_LEN_DECL); |
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138 |
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139 F77_RET_T |
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5275
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140 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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141 const octave_idx_type&, const double*, |
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142 const octave_idx_type&, double*, double& |
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4552
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143 F77_CHAR_ARG_LEN_DECL); |
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458
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144 } |
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145 |
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1360
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146 // Matrix class. |
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458
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147 |
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2349
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148 Matrix::Matrix (const RowVector& rv) |
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149 : MArray2<double> (1, rv.length (), 0.0) |
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150 { |
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5275
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151 for (octave_idx_type i = 0; i < rv.length (); i++) |
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2349
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152 elem (0, i) = rv.elem (i); |
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153 } |
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154 |
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155 Matrix::Matrix (const ColumnVector& cv) |
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156 : MArray2<double> (cv.length (), 1, 0.0) |
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157 { |
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5275
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158 for (octave_idx_type i = 0; i < cv.length (); i++) |
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159 elem (i, 0) = cv.elem (i); |
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160 } |
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161 |
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458
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162 Matrix::Matrix (const DiagMatrix& a) |
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1214
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163 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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458
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164 { |
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165 for (octave_idx_type i = 0; i < a.length (); i++) |
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458
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166 elem (i, i) = a.elem (i, i); |
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167 } |
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168 |
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1574
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169 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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170 // here? |
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171 |
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172 Matrix::Matrix (const boolMatrix& a) |
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173 : MArray2<double> (a.rows (), a.cols ()) |
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174 { |
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175 for (octave_idx_type i = 0; i < a.rows (); i++) |
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176 for (octave_idx_type j = 0; j < a.cols (); j++) |
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177 elem (i, j) = a.elem (i, j); |
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178 } |
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179 |
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180 Matrix::Matrix (const charMatrix& a) |
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181 : MArray2<double> (a.rows (), a.cols ()) |
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182 { |
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183 for (octave_idx_type i = 0; i < a.rows (); i++) |
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184 for (octave_idx_type j = 0; j < a.cols (); j++) |
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185 elem (i, j) = a.elem (i, j); |
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186 } |
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187 |
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2385
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188 bool |
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189 Matrix::operator == (const Matrix& a) const |
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190 { |
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191 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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192 return false; |
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458
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193 |
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3769
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194 return mx_inline_equal (data (), a.data (), length ()); |
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458
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195 } |
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196 |
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2385
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197 bool |
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458
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198 Matrix::operator != (const Matrix& a) const |
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199 { |
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200 return !(*this == a); |
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201 } |
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202 |
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3354
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203 bool |
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204 Matrix::is_symmetric (void) const |
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205 { |
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206 if (is_square () && rows () > 0) |
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207 { |
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208 for (octave_idx_type i = 0; i < rows (); i++) |
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209 for (octave_idx_type j = i+1; j < cols (); j++) |
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3354
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210 if (elem (i, j) != elem (j, i)) |
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211 return false; |
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212 |
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213 return true; |
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214 } |
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215 |
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216 return false; |
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217 } |
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218 |
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458
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219 Matrix& |
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220 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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221 { |
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1561
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222 Array2<double>::insert (a, r, c); |
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223 return *this; |
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224 } |
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225 |
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226 Matrix& |
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227 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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228 { |
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5275
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229 octave_idx_type a_len = a.length (); |
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4316
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230 |
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1698
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231 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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232 { |
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233 (*current_liboctave_error_handler) ("range error for insert"); |
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234 return *this; |
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235 } |
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236 |
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4316
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237 if (a_len > 0) |
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238 { |
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239 make_unique (); |
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240 |
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5275
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241 for (octave_idx_type i = 0; i < a_len; i++) |
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242 xelem (r, c+i) = a.elem (i); |
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243 } |
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458
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244 |
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245 return *this; |
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246 } |
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247 |
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248 Matrix& |
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249 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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250 { |
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5275
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251 octave_idx_type a_len = a.length (); |
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4316
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252 |
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1698
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253 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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254 { |
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255 (*current_liboctave_error_handler) ("range error for insert"); |
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256 return *this; |
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257 } |
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258 |
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4316
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259 if (a_len > 0) |
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260 { |
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261 make_unique (); |
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262 |
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5275
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263 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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264 xelem (r+i, c) = a.elem (i); |
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265 } |
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458
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266 |
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267 return *this; |
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268 } |
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269 |
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270 Matrix& |
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5275
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271 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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272 { |
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5275
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273 octave_idx_type a_nr = a.rows (); |
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274 octave_idx_type a_nc = a.cols (); |
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1697
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275 |
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1698
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276 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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277 { |
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278 (*current_liboctave_error_handler) ("range error for insert"); |
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279 return *this; |
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280 } |
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281 |
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1697
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282 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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283 |
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5275
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284 octave_idx_type a_len = a.length (); |
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4316
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285 |
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286 if (a_len > 0) |
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287 { |
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288 make_unique (); |
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289 |
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5275
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290 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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291 xelem (r+i, c+i) = a.elem (i, i); |
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292 } |
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458
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293 |
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294 return *this; |
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295 } |
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296 |
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297 Matrix& |
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298 Matrix::fill (double val) |
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299 { |
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5275
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300 octave_idx_type nr = rows (); |
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301 octave_idx_type nc = cols (); |
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4316
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302 |
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458
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303 if (nr > 0 && nc > 0) |
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4316
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304 { |
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305 make_unique (); |
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306 |
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5275
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307 for (octave_idx_type j = 0; j < nc; j++) |
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308 for (octave_idx_type i = 0; i < nr; i++) |
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4316
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309 xelem (i, j) = val; |
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310 } |
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458
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311 |
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312 return *this; |
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313 } |
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314 |
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315 Matrix& |
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5275
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316 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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317 { |
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5275
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318 octave_idx_type nr = rows (); |
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319 octave_idx_type nc = cols (); |
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4316
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320 |
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458
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321 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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322 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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323 { |
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324 (*current_liboctave_error_handler) ("range error for fill"); |
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325 return *this; |
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326 } |
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327 |
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5275
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328 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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329 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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458
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330 |
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4316
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331 if (r2 >= r1 && c2 >= c1) |
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332 { |
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333 make_unique (); |
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334 |
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5275
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335 for (octave_idx_type j = c1; j <= c2; j++) |
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336 for (octave_idx_type i = r1; i <= r2; i++) |
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4316
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337 xelem (i, j) = val; |
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338 } |
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458
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339 |
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340 return *this; |
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341 } |
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342 |
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343 Matrix |
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344 Matrix::append (const Matrix& a) const |
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345 { |
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5275
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346 octave_idx_type nr = rows (); |
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347 octave_idx_type nc = cols (); |
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458
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348 if (nr != a.rows ()) |
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349 { |
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350 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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351 return Matrix (); |
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352 } |
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353 |
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5275
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354 octave_idx_type nc_insert = nc; |
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458
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355 Matrix retval (nr, nc + a.cols ()); |
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356 retval.insert (*this, 0, 0); |
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357 retval.insert (a, 0, nc_insert); |
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358 return retval; |
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359 } |
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360 |
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361 Matrix |
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362 Matrix::append (const RowVector& a) const |
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363 { |
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5275
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364 octave_idx_type nr = rows (); |
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365 octave_idx_type nc = cols (); |
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458
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366 if (nr != 1) |
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367 { |
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368 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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369 return Matrix (); |
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370 } |
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371 |
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5275
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372 octave_idx_type nc_insert = nc; |
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458
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373 Matrix retval (nr, nc + a.length ()); |
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374 retval.insert (*this, 0, 0); |
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375 retval.insert (a, 0, nc_insert); |
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376 return retval; |
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377 } |
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378 |
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379 Matrix |
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380 Matrix::append (const ColumnVector& a) const |
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381 { |
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5275
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382 octave_idx_type nr = rows (); |
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383 octave_idx_type nc = cols (); |
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458
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384 if (nr != a.length ()) |
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385 { |
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386 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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387 return Matrix (); |
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388 } |
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389 |
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5275
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390 octave_idx_type nc_insert = nc; |
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458
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391 Matrix retval (nr, nc + 1); |
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392 retval.insert (*this, 0, 0); |
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393 retval.insert (a, 0, nc_insert); |
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394 return retval; |
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395 } |
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396 |
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397 Matrix |
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398 Matrix::append (const DiagMatrix& a) const |
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399 { |
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5275
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400 octave_idx_type nr = rows (); |
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401 octave_idx_type nc = cols (); |
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458
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402 if (nr != a.rows ()) |
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403 { |
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404 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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405 return *this; |
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406 } |
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407 |
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5275
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408 octave_idx_type nc_insert = nc; |
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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::stack (const Matrix& a) const |
|
|
417 { |
|
5275
|
418 octave_idx_type nr = rows (); |
|
|
419 octave_idx_type nc = cols (); |
|
458
|
420 if (nc != a.cols ()) |
|
|
421 { |
|
|
422 (*current_liboctave_error_handler) |
|
|
423 ("column dimension mismatch for stack"); |
|
|
424 return Matrix (); |
|
|
425 } |
|
|
426 |
|
5275
|
427 octave_idx_type nr_insert = nr; |
|
458
|
428 Matrix retval (nr + a.rows (), nc); |
|
|
429 retval.insert (*this, 0, 0); |
|
|
430 retval.insert (a, nr_insert, 0); |
|
|
431 return retval; |
|
|
432 } |
|
|
433 |
|
|
434 Matrix |
|
|
435 Matrix::stack (const RowVector& a) const |
|
|
436 { |
|
5275
|
437 octave_idx_type nr = rows (); |
|
|
438 octave_idx_type nc = cols (); |
|
458
|
439 if (nc != a.length ()) |
|
|
440 { |
|
|
441 (*current_liboctave_error_handler) |
|
|
442 ("column dimension mismatch for stack"); |
|
|
443 return Matrix (); |
|
|
444 } |
|
|
445 |
|
5275
|
446 octave_idx_type nr_insert = nr; |
|
458
|
447 Matrix retval (nr + 1, nc); |
|
|
448 retval.insert (*this, 0, 0); |
|
|
449 retval.insert (a, nr_insert, 0); |
|
|
450 return retval; |
|
|
451 } |
|
|
452 |
|
|
453 Matrix |
|
|
454 Matrix::stack (const ColumnVector& a) const |
|
|
455 { |
|
5275
|
456 octave_idx_type nr = rows (); |
|
|
457 octave_idx_type nc = cols (); |
|
458
|
458 if (nc != 1) |
|
|
459 { |
|
|
460 (*current_liboctave_error_handler) |
|
|
461 ("column dimension mismatch for stack"); |
|
|
462 return Matrix (); |
|
|
463 } |
|
|
464 |
|
5275
|
465 octave_idx_type nr_insert = nr; |
|
458
|
466 Matrix retval (nr + a.length (), nc); |
|
|
467 retval.insert (*this, 0, 0); |
|
|
468 retval.insert (a, nr_insert, 0); |
|
|
469 return retval; |
|
|
470 } |
|
|
471 |
|
|
472 Matrix |
|
|
473 Matrix::stack (const DiagMatrix& a) const |
|
|
474 { |
|
5275
|
475 octave_idx_type nr = rows (); |
|
|
476 octave_idx_type nc = cols (); |
|
458
|
477 if (nc != a.cols ()) |
|
|
478 { |
|
|
479 (*current_liboctave_error_handler) |
|
|
480 ("column dimension mismatch for stack"); |
|
|
481 return Matrix (); |
|
|
482 } |
|
|
483 |
|
5275
|
484 octave_idx_type nr_insert = nr; |
|
458
|
485 Matrix retval (nr + a.rows (), nc); |
|
|
486 retval.insert (*this, 0, 0); |
|
|
487 retval.insert (a, nr_insert, 0); |
|
|
488 return retval; |
|
|
489 } |
|
|
490 |
|
|
491 Matrix |
|
1205
|
492 real (const ComplexMatrix& a) |
|
|
493 { |
|
5275
|
494 octave_idx_type a_len = a.length (); |
|
1205
|
495 Matrix retval; |
|
|
496 if (a_len > 0) |
|
3769
|
497 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
|
|
498 a.rows (), a.cols ()); |
|
1205
|
499 return retval; |
|
|
500 } |
|
|
501 |
|
|
502 Matrix |
|
|
503 imag (const ComplexMatrix& a) |
|
|
504 { |
|
5275
|
505 octave_idx_type a_len = a.length (); |
|
1205
|
506 Matrix retval; |
|
|
507 if (a_len > 0) |
|
3769
|
508 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
|
|
509 a.rows (), a.cols ()); |
|
1205
|
510 return retval; |
|
|
511 } |
|
|
512 |
|
|
513 Matrix |
|
5275
|
514 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
515 { |
|
5275
|
516 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
517 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
518 |
|
|
519 octave_idx_type new_r = r2 - r1 + 1; |
|
|
520 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
521 |
|
|
522 Matrix result (new_r, new_c); |
|
|
523 |
|
5275
|
524 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
525 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
526 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
527 |
|
|
528 return result; |
|
|
529 } |
|
|
530 |
|
|
531 Matrix |
|
5275
|
532 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
533 { |
|
|
534 Matrix result (nr, nc); |
|
|
535 |
|
5275
|
536 for (octave_idx_type j = 0; j < nc; j++) |
|
|
537 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
538 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
539 |
|
|
540 return result; |
|
|
541 } |
|
|
542 |
|
|
543 // extract row or column i. |
|
|
544 |
|
|
545 RowVector |
|
5275
|
546 Matrix::row (octave_idx_type i) const |
|
458
|
547 { |
|
5275
|
548 octave_idx_type nc = cols (); |
|
458
|
549 if (i < 0 || i >= rows ()) |
|
|
550 { |
|
|
551 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
552 return RowVector (); |
|
|
553 } |
|
|
554 |
|
|
555 RowVector retval (nc); |
|
5275
|
556 for (octave_idx_type j = 0; j < nc; j++) |
|
4316
|
557 retval.xelem (j) = elem (i, j); |
|
458
|
558 |
|
|
559 return retval; |
|
|
560 } |
|
|
561 |
|
|
562 RowVector |
|
|
563 Matrix::row (char *s) const |
|
|
564 { |
|
533
|
565 if (! s) |
|
458
|
566 { |
|
|
567 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
568 return RowVector (); |
|
|
569 } |
|
|
570 |
|
|
571 char c = *s; |
|
|
572 if (c == 'f' || c == 'F') |
|
5275
|
573 return row ( static_cast<octave_idx_type>(0) ); |
|
458
|
574 else if (c == 'l' || c == 'L') |
|
|
575 return row (rows () - 1); |
|
|
576 else |
|
|
577 { |
|
|
578 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
579 return RowVector (); |
|
|
580 } |
|
|
581 } |
|
|
582 |
|
|
583 ColumnVector |
|
5275
|
584 Matrix::column (octave_idx_type i) const |
|
458
|
585 { |
|
5275
|
586 octave_idx_type nr = rows (); |
|
458
|
587 if (i < 0 || i >= cols ()) |
|
|
588 { |
|
|
589 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
590 return ColumnVector (); |
|
|
591 } |
|
|
592 |
|
|
593 ColumnVector retval (nr); |
|
5275
|
594 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
595 retval.xelem (j) = elem (j, i); |
|
458
|
596 |
|
|
597 return retval; |
|
|
598 } |
|
|
599 |
|
|
600 ColumnVector |
|
|
601 Matrix::column (char *s) const |
|
|
602 { |
|
533
|
603 if (! s) |
|
458
|
604 { |
|
|
605 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
606 return ColumnVector (); |
|
|
607 } |
|
|
608 |
|
|
609 char c = *s; |
|
|
610 if (c == 'f' || c == 'F') |
|
5275
|
611 return column (static_cast<octave_idx_type> (0)); |
|
458
|
612 else if (c == 'l' || c == 'L') |
|
|
613 return column (cols () - 1); |
|
|
614 else |
|
|
615 { |
|
|
616 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
617 return ColumnVector (); |
|
|
618 } |
|
|
619 } |
|
|
620 |
|
|
621 Matrix |
|
|
622 Matrix::inverse (void) const |
|
|
623 { |
|
5275
|
624 octave_idx_type info; |
|
458
|
625 double rcond; |
|
4329
|
626 return inverse (info, rcond, 0, 0); |
|
458
|
627 } |
|
|
628 |
|
|
629 Matrix |
|
5275
|
630 Matrix::inverse (octave_idx_type& info) const |
|
458
|
631 { |
|
|
632 double rcond; |
|
4329
|
633 return inverse (info, rcond, 0, 0); |
|
458
|
634 } |
|
|
635 |
|
|
636 Matrix |
|
5275
|
637 Matrix::inverse (octave_idx_type& info, double& rcond, int force, int calc_cond) const |
|
458
|
638 { |
|
1948
|
639 Matrix retval; |
|
|
640 |
|
5275
|
641 octave_idx_type nr = rows (); |
|
|
642 octave_idx_type nc = cols (); |
|
1948
|
643 |
|
458
|
644 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
645 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
646 else |
|
|
647 { |
|
5275
|
648 Array<octave_idx_type> ipvt (nr); |
|
|
649 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
650 |
|
|
651 retval = *this; |
|
|
652 double *tmp_data = retval.fortran_vec (); |
|
|
653 |
|
4329
|
654 Array<double> z(1); |
|
5275
|
655 octave_idx_type lwork = -1; |
|
4329
|
656 |
|
4330
|
657 // Query the optimum work array size. |
|
4329
|
658 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
659 z.fortran_vec (), lwork, info)); |
|
|
660 |
|
|
661 if (f77_exception_encountered) |
|
|
662 { |
|
|
663 (*current_liboctave_error_handler) |
|
|
664 ("unrecoverable error in dgetri"); |
|
|
665 return retval; |
|
|
666 } |
|
|
667 |
|
5275
|
668 lwork = static_cast<octave_idx_type> (z(0)); |
|
4329
|
669 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
670 z.resize (lwork); |
|
|
671 double *pz = z.fortran_vec (); |
|
|
672 |
|
|
673 info = 0; |
|
|
674 |
|
4330
|
675 // Calculate the norm of the matrix, for later use. |
|
4329
|
676 double anorm = 0; |
|
|
677 if (calc_cond) |
|
5275
|
678 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
679 |
|
|
680 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
681 |
|
|
682 if (f77_exception_encountered) |
|
4329
|
683 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
684 else |
|
|
685 { |
|
4330
|
686 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
687 rcond = 0.0; |
|
|
688 if (info != 0) |
|
1948
|
689 info = -1; |
|
4329
|
690 else if (calc_cond) |
|
|
691 { |
|
5275
|
692 octave_idx_type dgecon_info = 0; |
|
5061
|
693 |
|
4330
|
694 // Now calculate the condition number for non-singular matrix. |
|
4329
|
695 char job = '1'; |
|
5275
|
696 Array<octave_idx_type> iz (nc); |
|
|
697 octave_idx_type *piz = iz.fortran_vec (); |
|
4552
|
698 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
699 nc, tmp_data, nr, anorm, |
|
5061
|
700 rcond, pz, piz, dgecon_info |
|
4552
|
701 F77_CHAR_ARG_LEN (1))); |
|
4329
|
702 |
|
|
703 if (f77_exception_encountered) |
|
|
704 (*current_liboctave_error_handler) |
|
|
705 ("unrecoverable error in dgecon"); |
|
|
706 |
|
5061
|
707 if (dgecon_info != 0) |
|
4329
|
708 info = -1; |
|
|
709 } |
|
1948
|
710 |
|
|
711 if (info == -1 && ! force) |
|
|
712 retval = *this; // Restore matrix contents. |
|
|
713 else |
|
|
714 { |
|
5275
|
715 octave_idx_type dgetri_info = 0; |
|
5061
|
716 |
|
4329
|
717 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
718 pz, lwork, dgetri_info)); |
|
1948
|
719 |
|
|
720 if (f77_exception_encountered) |
|
|
721 (*current_liboctave_error_handler) |
|
4329
|
722 ("unrecoverable error in dgetri"); |
|
|
723 |
|
5061
|
724 if (dgetri_info != 0) |
|
4329
|
725 info = -1; |
|
1948
|
726 } |
|
|
727 } |
|
458
|
728 } |
|
|
729 |
|
1948
|
730 return retval; |
|
458
|
731 } |
|
|
732 |
|
740
|
733 Matrix |
|
4384
|
734 Matrix::pseudo_inverse (double tol) const |
|
740
|
735 { |
|
3480
|
736 SVD result (*this, SVD::economy); |
|
740
|
737 |
|
|
738 DiagMatrix S = result.singular_values (); |
|
|
739 Matrix U = result.left_singular_matrix (); |
|
|
740 Matrix V = result.right_singular_matrix (); |
|
|
741 |
|
|
742 ColumnVector sigma = S.diag (); |
|
|
743 |
|
5275
|
744 octave_idx_type r = sigma.length () - 1; |
|
|
745 octave_idx_type nr = rows (); |
|
|
746 octave_idx_type nc = cols (); |
|
740
|
747 |
|
|
748 if (tol <= 0.0) |
|
|
749 { |
|
|
750 if (nr > nc) |
|
|
751 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
752 else |
|
|
753 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
754 } |
|
|
755 |
|
|
756 while (r >= 0 && sigma.elem (r) < tol) |
|
|
757 r--; |
|
|
758 |
|
|
759 if (r < 0) |
|
|
760 return Matrix (nc, nr, 0.0); |
|
|
761 else |
|
|
762 { |
|
|
763 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
764 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
765 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
766 return Vr * D * Ur.transpose (); |
|
|
767 } |
|
|
768 } |
|
|
769 |
|
4773
|
770 #if defined (HAVE_FFTW3) |
|
3827
|
771 |
|
|
772 ComplexMatrix |
|
|
773 Matrix::fourier (void) const |
|
|
774 { |
|
|
775 size_t nr = rows (); |
|
|
776 size_t nc = cols (); |
|
|
777 |
|
|
778 ComplexMatrix retval (nr, nc); |
|
|
779 |
|
|
780 size_t npts, nsamples; |
|
|
781 |
|
|
782 if (nr == 1 || nc == 1) |
|
|
783 { |
|
|
784 npts = nr > nc ? nr : nc; |
|
|
785 nsamples = 1; |
|
|
786 } |
|
|
787 else |
|
|
788 { |
|
|
789 npts = nr; |
|
|
790 nsamples = nc; |
|
|
791 } |
|
|
792 |
|
4773
|
793 const double *in (fortran_vec ()); |
|
3827
|
794 Complex *out (retval.fortran_vec ()); |
|
|
795 |
|
4773
|
796 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
797 |
|
|
798 return retval; |
|
|
799 } |
|
|
800 |
|
|
801 ComplexMatrix |
|
|
802 Matrix::ifourier (void) const |
|
|
803 { |
|
|
804 size_t nr = rows (); |
|
|
805 size_t nc = cols (); |
|
|
806 |
|
|
807 ComplexMatrix retval (nr, nc); |
|
|
808 |
|
|
809 size_t npts, nsamples; |
|
|
810 |
|
|
811 if (nr == 1 || nc == 1) |
|
|
812 { |
|
|
813 npts = nr > nc ? nr : nc; |
|
|
814 nsamples = 1; |
|
|
815 } |
|
|
816 else |
|
|
817 { |
|
|
818 npts = nr; |
|
|
819 nsamples = nc; |
|
|
820 } |
|
|
821 |
|
|
822 ComplexMatrix tmp (*this); |
|
|
823 Complex *in (tmp.fortran_vec ()); |
|
|
824 Complex *out (retval.fortran_vec ()); |
|
|
825 |
|
4773
|
826 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
827 |
|
|
828 return retval; |
|
|
829 } |
|
|
830 |
|
|
831 ComplexMatrix |
|
|
832 Matrix::fourier2d (void) const |
|
|
833 { |
|
4773
|
834 dim_vector dv(rows (), cols ()); |
|
|
835 |
|
|
836 const double *in = fortran_vec (); |
|
|
837 ComplexMatrix retval (rows (), cols ()); |
|
|
838 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); |
|
3827
|
839 |
|
|
840 return retval; |
|
|
841 } |
|
|
842 |
|
|
843 ComplexMatrix |
|
|
844 Matrix::ifourier2d (void) const |
|
|
845 { |
|
4773
|
846 dim_vector dv(rows (), cols ()); |
|
3827
|
847 |
|
|
848 ComplexMatrix retval (*this); |
|
4773
|
849 Complex *out (retval.fortran_vec ()); |
|
|
850 |
|
|
851 octave_fftw::ifftNd (out, out, 2, dv); |
|
3827
|
852 |
|
|
853 return retval; |
|
|
854 } |
|
|
855 |
|
|
856 #else |
|
|
857 |
|
458
|
858 ComplexMatrix |
|
|
859 Matrix::fourier (void) const |
|
|
860 { |
|
1948
|
861 ComplexMatrix retval; |
|
|
862 |
|
5275
|
863 octave_idx_type nr = rows (); |
|
|
864 octave_idx_type nc = cols (); |
|
|
865 |
|
|
866 octave_idx_type npts, nsamples; |
|
1948
|
867 |
|
458
|
868 if (nr == 1 || nc == 1) |
|
|
869 { |
|
|
870 npts = nr > nc ? nr : nc; |
|
|
871 nsamples = 1; |
|
|
872 } |
|
|
873 else |
|
|
874 { |
|
|
875 npts = nr; |
|
|
876 nsamples = nc; |
|
|
877 } |
|
|
878 |
|
5275
|
879 octave_idx_type nn = 4*npts+15; |
|
1948
|
880 |
|
|
881 Array<Complex> wsave (nn); |
|
|
882 Complex *pwsave = wsave.fortran_vec (); |
|
|
883 |
|
3585
|
884 retval = ComplexMatrix (*this); |
|
1948
|
885 Complex *tmp_data = retval.fortran_vec (); |
|
|
886 |
|
3887
|
887 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
888 |
|
5275
|
889 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
890 { |
|
|
891 OCTAVE_QUIT; |
|
|
892 |
|
|
893 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
894 } |
|
1948
|
895 |
|
|
896 return retval; |
|
458
|
897 } |
|
|
898 |
|
|
899 ComplexMatrix |
|
|
900 Matrix::ifourier (void) const |
|
|
901 { |
|
1948
|
902 ComplexMatrix retval; |
|
|
903 |
|
5275
|
904 octave_idx_type nr = rows (); |
|
|
905 octave_idx_type nc = cols (); |
|
|
906 |
|
|
907 octave_idx_type npts, nsamples; |
|
1948
|
908 |
|
458
|
909 if (nr == 1 || nc == 1) |
|
|
910 { |
|
|
911 npts = nr > nc ? nr : nc; |
|
|
912 nsamples = 1; |
|
|
913 } |
|
|
914 else |
|
|
915 { |
|
|
916 npts = nr; |
|
|
917 nsamples = nc; |
|
|
918 } |
|
|
919 |
|
5275
|
920 octave_idx_type nn = 4*npts+15; |
|
1948
|
921 |
|
|
922 Array<Complex> wsave (nn); |
|
|
923 Complex *pwsave = wsave.fortran_vec (); |
|
|
924 |
|
3585
|
925 retval = ComplexMatrix (*this); |
|
1948
|
926 Complex *tmp_data = retval.fortran_vec (); |
|
|
927 |
|
3887
|
928 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
929 |
|
5275
|
930 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
931 { |
|
|
932 OCTAVE_QUIT; |
|
|
933 |
|
|
934 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
935 } |
|
458
|
936 |
|
5275
|
937 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
938 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
939 |
|
1948
|
940 return retval; |
|
458
|
941 } |
|
|
942 |
|
677
|
943 ComplexMatrix |
|
|
944 Matrix::fourier2d (void) const |
|
|
945 { |
|
1948
|
946 ComplexMatrix retval; |
|
|
947 |
|
5275
|
948 octave_idx_type nr = rows (); |
|
|
949 octave_idx_type nc = cols (); |
|
|
950 |
|
|
951 octave_idx_type npts, nsamples; |
|
1948
|
952 |
|
677
|
953 if (nr == 1 || nc == 1) |
|
|
954 { |
|
|
955 npts = nr > nc ? nr : nc; |
|
|
956 nsamples = 1; |
|
|
957 } |
|
|
958 else |
|
|
959 { |
|
|
960 npts = nr; |
|
|
961 nsamples = nc; |
|
|
962 } |
|
|
963 |
|
5275
|
964 octave_idx_type nn = 4*npts+15; |
|
1948
|
965 |
|
|
966 Array<Complex> wsave (nn); |
|
|
967 Complex *pwsave = wsave.fortran_vec (); |
|
|
968 |
|
3585
|
969 retval = ComplexMatrix (*this); |
|
1948
|
970 Complex *tmp_data = retval.fortran_vec (); |
|
|
971 |
|
3887
|
972 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
973 |
|
5275
|
974 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
975 { |
|
|
976 OCTAVE_QUIT; |
|
|
977 |
|
|
978 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
979 } |
|
677
|
980 |
|
|
981 npts = nc; |
|
|
982 nsamples = nr; |
|
|
983 nn = 4*npts+15; |
|
1948
|
984 |
|
|
985 wsave.resize (nn); |
|
|
986 pwsave = wsave.fortran_vec (); |
|
|
987 |
|
4773
|
988 Array<Complex> tmp (npts); |
|
|
989 Complex *prow = tmp.fortran_vec (); |
|
1948
|
990 |
|
3887
|
991 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
992 |
|
5275
|
993 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
994 { |
|
4153
|
995 OCTAVE_QUIT; |
|
|
996 |
|
5275
|
997 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
998 prow[i] = tmp_data[i*nr + j]; |
|
|
999 |
|
3887
|
1000 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1001 |
|
5275
|
1002 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1003 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1004 } |
|
|
1005 |
|
1948
|
1006 return retval; |
|
677
|
1007 } |
|
|
1008 |
|
|
1009 ComplexMatrix |
|
|
1010 Matrix::ifourier2d (void) const |
|
|
1011 { |
|
1948
|
1012 ComplexMatrix retval; |
|
|
1013 |
|
5275
|
1014 octave_idx_type nr = rows (); |
|
|
1015 octave_idx_type nc = cols (); |
|
|
1016 |
|
|
1017 octave_idx_type npts, nsamples; |
|
1948
|
1018 |
|
677
|
1019 if (nr == 1 || nc == 1) |
|
|
1020 { |
|
|
1021 npts = nr > nc ? nr : nc; |
|
|
1022 nsamples = 1; |
|
|
1023 } |
|
|
1024 else |
|
|
1025 { |
|
|
1026 npts = nr; |
|
|
1027 nsamples = nc; |
|
|
1028 } |
|
|
1029 |
|
5275
|
1030 octave_idx_type nn = 4*npts+15; |
|
1948
|
1031 |
|
|
1032 Array<Complex> wsave (nn); |
|
|
1033 Complex *pwsave = wsave.fortran_vec (); |
|
|
1034 |
|
3585
|
1035 retval = ComplexMatrix (*this); |
|
1948
|
1036 Complex *tmp_data = retval.fortran_vec (); |
|
|
1037 |
|
3887
|
1038 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1039 |
|
5275
|
1040 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1041 { |
|
|
1042 OCTAVE_QUIT; |
|
|
1043 |
|
|
1044 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1045 } |
|
677
|
1046 |
|
5275
|
1047 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1048 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1049 |
|
|
1050 npts = nc; |
|
|
1051 nsamples = nr; |
|
|
1052 nn = 4*npts+15; |
|
1948
|
1053 |
|
|
1054 wsave.resize (nn); |
|
|
1055 pwsave = wsave.fortran_vec (); |
|
|
1056 |
|
4773
|
1057 Array<Complex> tmp (npts); |
|
|
1058 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1059 |
|
3887
|
1060 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1061 |
|
5275
|
1062 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1063 { |
|
4153
|
1064 OCTAVE_QUIT; |
|
|
1065 |
|
5275
|
1066 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1067 prow[i] = tmp_data[i*nr + j]; |
|
|
1068 |
|
3887
|
1069 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1070 |
|
5275
|
1071 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1072 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1073 } |
|
|
1074 |
|
1948
|
1075 return retval; |
|
677
|
1076 } |
|
|
1077 |
|
3827
|
1078 #endif |
|
|
1079 |
|
458
|
1080 DET |
|
|
1081 Matrix::determinant (void) const |
|
|
1082 { |
|
5275
|
1083 octave_idx_type info; |
|
458
|
1084 double rcond; |
|
4329
|
1085 return determinant (info, rcond, 0); |
|
458
|
1086 } |
|
|
1087 |
|
|
1088 DET |
|
5275
|
1089 Matrix::determinant (octave_idx_type& info) const |
|
458
|
1090 { |
|
|
1091 double rcond; |
|
4329
|
1092 return determinant (info, rcond, 0); |
|
458
|
1093 } |
|
|
1094 |
|
|
1095 DET |
|
5275
|
1096 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1097 { |
|
|
1098 DET retval; |
|
|
1099 |
|
5275
|
1100 octave_idx_type nr = rows (); |
|
|
1101 octave_idx_type nc = cols (); |
|
458
|
1102 |
|
|
1103 if (nr == 0 || nc == 0) |
|
|
1104 { |
|
|
1105 double d[2]; |
|
|
1106 d[0] = 1.0; |
|
|
1107 d[1] = 0.0; |
|
|
1108 retval = DET (d); |
|
|
1109 } |
|
|
1110 else |
|
|
1111 { |
|
5275
|
1112 Array<octave_idx_type> ipvt (nr); |
|
|
1113 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1114 |
|
|
1115 Matrix atmp = *this; |
|
|
1116 double *tmp_data = atmp.fortran_vec (); |
|
|
1117 |
|
4329
|
1118 info = 0; |
|
|
1119 |
|
4330
|
1120 // Calculate the norm of the matrix, for later use. |
|
4329
|
1121 double anorm = 0; |
|
|
1122 if (calc_cond) |
|
5275
|
1123 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1124 |
|
|
1125 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1126 |
|
|
1127 if (f77_exception_encountered) |
|
4329
|
1128 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
458
|
1129 else |
|
|
1130 { |
|
4330
|
1131 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1132 rcond = 0.0; |
|
|
1133 if (info != 0) |
|
1948
|
1134 { |
|
4509
|
1135 info = -1; |
|
|
1136 retval = DET (); |
|
4329
|
1137 } |
|
|
1138 else |
|
1948
|
1139 { |
|
4329
|
1140 if (calc_cond) |
|
|
1141 { |
|
4330
|
1142 // Now calc the condition number for non-singular matrix. |
|
4329
|
1143 char job = '1'; |
|
|
1144 Array<double> z (4 * nc); |
|
|
1145 double *pz = z.fortran_vec (); |
|
5275
|
1146 Array<octave_idx_type> iz (nc); |
|
|
1147 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1148 |
|
4552
|
1149 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1150 nc, tmp_data, nr, anorm, |
|
|
1151 rcond, pz, piz, info |
|
|
1152 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1153 |
|
|
1154 if (f77_exception_encountered) |
|
|
1155 (*current_liboctave_error_handler) |
|
|
1156 ("unrecoverable error in dgecon"); |
|
|
1157 } |
|
|
1158 |
|
4509
|
1159 if (info != 0) |
|
4329
|
1160 { |
|
|
1161 info = -1; |
|
|
1162 retval = DET (); |
|
|
1163 } |
|
|
1164 else |
|
|
1165 { |
|
|
1166 double d[2] = { 1., 0.}; |
|
5275
|
1167 for (octave_idx_type i=0; i<nc; i++) |
|
4329
|
1168 { |
|
|
1169 if (ipvt(i) != (i+1)) d[0] = -d[0]; |
|
|
1170 d[0] *= atmp(i,i); |
|
|
1171 if (d[0] == 0.) break; |
|
|
1172 while (fabs(d[0]) < 1.) |
|
|
1173 { |
|
|
1174 d[0] = 10. * d[0]; |
|
4509
|
1175 d[1] = d[1] - 1.0; |
|
4329
|
1176 } |
|
|
1177 while (fabs(d[0]) >= 10.) |
|
|
1178 { |
|
|
1179 d[0] = 0.1 * d[0]; |
|
4509
|
1180 d[1] = d[1] + 1.0; |
|
4329
|
1181 } |
|
|
1182 } |
|
|
1183 retval = DET (d); |
|
|
1184 } |
|
1948
|
1185 } |
|
458
|
1186 } |
|
|
1187 } |
|
|
1188 |
|
|
1189 return retval; |
|
|
1190 } |
|
|
1191 |
|
|
1192 Matrix |
|
|
1193 Matrix::solve (const Matrix& b) const |
|
|
1194 { |
|
5275
|
1195 octave_idx_type info; |
|
458
|
1196 double rcond; |
|
4329
|
1197 return solve (b, info, rcond, 0); |
|
458
|
1198 } |
|
|
1199 |
|
|
1200 Matrix |
|
5275
|
1201 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1202 { |
|
|
1203 double rcond; |
|
4329
|
1204 return solve (b, info, rcond, 0); |
|
458
|
1205 } |
|
|
1206 |
|
|
1207 Matrix |
|
5275
|
1208 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1209 { |
|
3480
|
1210 return solve (b, info, rcond, 0); |
|
|
1211 } |
|
|
1212 |
|
|
1213 Matrix |
|
5275
|
1214 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1215 solve_singularity_handler sing_handler) const |
|
|
1216 { |
|
458
|
1217 Matrix retval; |
|
|
1218 |
|
5275
|
1219 octave_idx_type nr = rows (); |
|
|
1220 octave_idx_type nc = cols (); |
|
1948
|
1221 |
|
458
|
1222 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
1948
|
1223 (*current_liboctave_error_handler) |
|
|
1224 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1225 else |
|
|
1226 { |
|
1948
|
1227 info = 0; |
|
|
1228 |
|
5275
|
1229 Array<octave_idx_type> ipvt (nr); |
|
|
1230 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1231 |
|
|
1232 Matrix atmp = *this; |
|
|
1233 double *tmp_data = atmp.fortran_vec (); |
|
|
1234 |
|
4329
|
1235 Array<double> z (4 * nc); |
|
|
1236 double *pz = z.fortran_vec (); |
|
5275
|
1237 Array<octave_idx_type> iz (nc); |
|
|
1238 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1239 |
|
4330
|
1240 // Calculate the norm of the matrix, for later use. |
|
5275
|
1241 double anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1242 |
|
|
1243 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1244 |
|
|
1245 if (f77_exception_encountered) |
|
4329
|
1246 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
1247 else |
|
|
1248 { |
|
4330
|
1249 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1250 rcond = 0.0; |
|
|
1251 if (info != 0) |
|
1948
|
1252 { |
|
|
1253 info = -2; |
|
3480
|
1254 |
|
|
1255 if (sing_handler) |
|
|
1256 sing_handler (rcond); |
|
|
1257 else |
|
|
1258 (*current_liboctave_error_handler) |
|
4329
|
1259 ("matrix singular to machine precision"); |
|
|
1260 |
|
|
1261 } |
|
|
1262 else |
|
1948
|
1263 { |
|
4330
|
1264 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1265 char job = '1'; |
|
4552
|
1266 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1267 nc, tmp_data, nr, anorm, |
|
|
1268 rcond, pz, piz, info |
|
|
1269 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1270 |
|
|
1271 if (f77_exception_encountered) |
|
|
1272 (*current_liboctave_error_handler) |
|
|
1273 ("unrecoverable error in dgecon"); |
|
|
1274 |
|
4509
|
1275 if (info != 0) |
|
4329
|
1276 info = -2; |
|
|
1277 |
|
|
1278 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1279 |
|
|
1280 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1281 { |
|
4329
|
1282 info = -2; |
|
|
1283 |
|
|
1284 if (sing_handler) |
|
|
1285 sing_handler (rcond); |
|
|
1286 else |
|
|
1287 (*current_liboctave_error_handler) |
|
|
1288 ("matrix singular to machine precision, rcond = %g", |
|
|
1289 rcond); |
|
|
1290 } |
|
|
1291 else |
|
|
1292 { |
|
|
1293 retval = b; |
|
|
1294 double *result = retval.fortran_vec (); |
|
|
1295 |
|
5275
|
1296 octave_idx_type b_nc = b.cols (); |
|
4329
|
1297 |
|
4587
|
1298 job = 'N'; |
|
4552
|
1299 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1300 nr, b_nc, tmp_data, nr, |
|
|
1301 pipvt, result, b.rows(), info |
|
|
1302 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1303 |
|
1948
|
1304 if (f77_exception_encountered) |
|
4329
|
1305 (*current_liboctave_error_handler) |
|
|
1306 ("unrecoverable error in dgetrs"); |
|
1948
|
1307 } |
|
|
1308 } |
|
|
1309 } |
|
458
|
1310 } |
|
|
1311 |
|
|
1312 return retval; |
|
|
1313 } |
|
|
1314 |
|
|
1315 ComplexMatrix |
|
|
1316 Matrix::solve (const ComplexMatrix& b) const |
|
|
1317 { |
|
|
1318 ComplexMatrix tmp (*this); |
|
|
1319 return tmp.solve (b); |
|
|
1320 } |
|
|
1321 |
|
|
1322 ComplexMatrix |
|
5275
|
1323 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1324 { |
|
|
1325 ComplexMatrix tmp (*this); |
|
|
1326 return tmp.solve (b, info); |
|
|
1327 } |
|
|
1328 |
|
|
1329 ComplexMatrix |
|
5275
|
1330 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1331 { |
|
|
1332 ComplexMatrix tmp (*this); |
|
|
1333 return tmp.solve (b, info, rcond); |
|
|
1334 } |
|
|
1335 |
|
3480
|
1336 ComplexMatrix |
|
5275
|
1337 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1338 solve_singularity_handler sing_handler) const |
|
|
1339 { |
|
|
1340 ComplexMatrix tmp (*this); |
|
|
1341 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1342 } |
|
|
1343 |
|
458
|
1344 ColumnVector |
|
|
1345 Matrix::solve (const ColumnVector& b) const |
|
|
1346 { |
|
5275
|
1347 octave_idx_type info; double rcond; |
|
458
|
1348 return solve (b, info, rcond); |
|
|
1349 } |
|
|
1350 |
|
|
1351 ColumnVector |
|
5275
|
1352 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1353 { |
|
|
1354 double rcond; |
|
|
1355 return solve (b, info, rcond); |
|
|
1356 } |
|
|
1357 |
|
|
1358 ColumnVector |
|
5275
|
1359 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1360 { |
|
3480
|
1361 return solve (b, info, rcond, 0); |
|
|
1362 } |
|
|
1363 |
|
|
1364 ColumnVector |
|
5275
|
1365 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1366 solve_singularity_handler sing_handler) const |
|
|
1367 { |
|
458
|
1368 ColumnVector retval; |
|
|
1369 |
|
5275
|
1370 octave_idx_type nr = rows (); |
|
|
1371 octave_idx_type nc = cols (); |
|
1948
|
1372 |
|
458
|
1373 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
1948
|
1374 (*current_liboctave_error_handler) |
|
|
1375 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1376 else |
|
|
1377 { |
|
1948
|
1378 info = 0; |
|
|
1379 |
|
5275
|
1380 Array<octave_idx_type> ipvt (nr); |
|
|
1381 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1382 |
|
|
1383 Matrix atmp = *this; |
|
|
1384 double *tmp_data = atmp.fortran_vec (); |
|
|
1385 |
|
4329
|
1386 Array<double> z (4 * nc); |
|
|
1387 double *pz = z.fortran_vec (); |
|
5275
|
1388 Array<octave_idx_type> iz (nc); |
|
|
1389 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1390 |
|
4330
|
1391 // Calculate the norm of the matrix, for later use. |
|
5275
|
1392 double anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1393 |
|
|
1394 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1395 |
|
|
1396 if (f77_exception_encountered) |
|
4329
|
1397 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
1398 else |
|
|
1399 { |
|
4330
|
1400 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1401 rcond = 0.0; |
|
|
1402 if (info > 0) |
|
1948
|
1403 { |
|
|
1404 info = -2; |
|
3480
|
1405 |
|
|
1406 if (sing_handler) |
|
|
1407 sing_handler (rcond); |
|
|
1408 else |
|
|
1409 (*current_liboctave_error_handler) |
|
4329
|
1410 ("matrix singular to machine precision"); |
|
|
1411 |
|
|
1412 } |
|
|
1413 else |
|
1948
|
1414 { |
|
4330
|
1415 // Now calculate the condition number for non-singular matrix. |
|
4329
|
1416 char job = '1'; |
|
4552
|
1417 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1418 nc, tmp_data, nr, anorm, |
|
|
1419 rcond, pz, piz, info |
|
|
1420 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1421 |
|
1948
|
1422 if (f77_exception_encountered) |
|
4329
|
1423 (*current_liboctave_error_handler) |
|
|
1424 ("unrecoverable error in dgecon"); |
|
|
1425 |
|
4509
|
1426 if (info != 0) |
|
4329
|
1427 info = -2; |
|
|
1428 |
|
|
1429 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1430 |
|
|
1431 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1432 { |
|
|
1433 info = -2; |
|
|
1434 |
|
|
1435 if (sing_handler) |
|
|
1436 sing_handler (rcond); |
|
|
1437 else |
|
|
1438 (*current_liboctave_error_handler) |
|
|
1439 ("matrix singular to machine precision, rcond = %g", |
|
|
1440 rcond); |
|
|
1441 } |
|
|
1442 else |
|
|
1443 { |
|
|
1444 retval = b; |
|
|
1445 double *result = retval.fortran_vec (); |
|
|
1446 |
|
4587
|
1447 job = 'N'; |
|
4552
|
1448 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1449 nr, 1, tmp_data, nr, pipvt, |
|
|
1450 result, b.length(), info |
|
|
1451 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1452 |
|
|
1453 if (f77_exception_encountered) |
|
|
1454 (*current_liboctave_error_handler) |
|
|
1455 ("unrecoverable error in dgetrs"); |
|
|
1456 } |
|
1948
|
1457 } |
|
|
1458 } |
|
458
|
1459 } |
|
4329
|
1460 |
|
458
|
1461 return retval; |
|
|
1462 } |
|
|
1463 |
|
|
1464 ComplexColumnVector |
|
|
1465 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1466 { |
|
|
1467 ComplexMatrix tmp (*this); |
|
|
1468 return tmp.solve (b); |
|
|
1469 } |
|
|
1470 |
|
|
1471 ComplexColumnVector |
|
5275
|
1472 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1473 { |
|
|
1474 ComplexMatrix tmp (*this); |
|
|
1475 return tmp.solve (b, info); |
|
|
1476 } |
|
|
1477 |
|
|
1478 ComplexColumnVector |
|
5275
|
1479 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1480 { |
|
|
1481 ComplexMatrix tmp (*this); |
|
|
1482 return tmp.solve (b, info, rcond); |
|
|
1483 } |
|
|
1484 |
|
3480
|
1485 ComplexColumnVector |
|
5275
|
1486 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1487 solve_singularity_handler sing_handler) const |
|
|
1488 { |
|
|
1489 ComplexMatrix tmp (*this); |
|
|
1490 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1491 } |
|
|
1492 |
|
458
|
1493 Matrix |
|
|
1494 Matrix::lssolve (const Matrix& b) const |
|
|
1495 { |
|
5275
|
1496 octave_idx_type info; |
|
|
1497 octave_idx_type rank; |
|
458
|
1498 return lssolve (b, info, rank); |
|
|
1499 } |
|
|
1500 |
|
|
1501 Matrix |
|
5275
|
1502 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1503 { |
|
5275
|
1504 octave_idx_type rank; |
|
458
|
1505 return lssolve (b, info, rank); |
|
|
1506 } |
|
|
1507 |
|
|
1508 Matrix |
|
5275
|
1509 Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1510 { |
|
1948
|
1511 Matrix retval; |
|
|
1512 |
|
5275
|
1513 octave_idx_type nrhs = b.cols (); |
|
|
1514 |
|
|
1515 octave_idx_type m = rows (); |
|
|
1516 octave_idx_type n = cols (); |
|
458
|
1517 |
|
|
1518 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1519 (*current_liboctave_error_handler) |
|
|
1520 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1521 else |
|
458
|
1522 { |
|
1948
|
1523 Matrix atmp = *this; |
|
|
1524 double *tmp_data = atmp.fortran_vec (); |
|
|
1525 |
|
5275
|
1526 octave_idx_type nrr = m > n ? m : n; |
|
3754
|
1527 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
1528 |
|
5275
|
1529 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1530 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
1531 result.elem (i, j) = b.elem (i, j); |
|
|
1532 |
|
|
1533 double *presult = result.fortran_vec (); |
|
|
1534 |
|
5275
|
1535 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
1536 Array<double> s (len_s); |
|
|
1537 double *ps = s.fortran_vec (); |
|
|
1538 |
|
|
1539 double rcond = -1.0; |
|
|
1540 |
|
3752
|
1541 // Ask DGELSS what the dimension of WORK should be. |
|
|
1542 |
|
5275
|
1543 octave_idx_type lwork = -1; |
|
3752
|
1544 |
|
|
1545 Array<double> work (1); |
|
1948
|
1546 |
|
|
1547 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
1548 rcond, rank, work.fortran_vec (), |
|
|
1549 lwork, info)); |
|
1948
|
1550 |
|
|
1551 if (f77_exception_encountered) |
|
|
1552 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1553 else |
|
|
1554 { |
|
5275
|
1555 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
1556 work.resize (lwork); |
|
|
1557 |
|
|
1558 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1559 nrr, ps, rcond, rank, |
|
|
1560 work.fortran_vec (), lwork, info)); |
|
|
1561 |
|
|
1562 if (f77_exception_encountered) |
|
|
1563 (*current_liboctave_error_handler) |
|
|
1564 ("unrecoverable error in dgelss"); |
|
|
1565 else |
|
|
1566 { |
|
|
1567 retval.resize (n, nrhs); |
|
5275
|
1568 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1569 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
1570 retval.elem (i, j) = result.elem (i, j); |
|
|
1571 } |
|
1948
|
1572 } |
|
458
|
1573 } |
|
|
1574 |
|
|
1575 return retval; |
|
|
1576 } |
|
|
1577 |
|
|
1578 ComplexMatrix |
|
|
1579 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1580 { |
|
|
1581 ComplexMatrix tmp (*this); |
|
5275
|
1582 octave_idx_type info; |
|
|
1583 octave_idx_type rank; |
|
1484
|
1584 return tmp.lssolve (b, info, rank); |
|
458
|
1585 } |
|
|
1586 |
|
|
1587 ComplexMatrix |
|
5275
|
1588 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1589 { |
|
|
1590 ComplexMatrix tmp (*this); |
|
5275
|
1591 octave_idx_type rank; |
|
1484
|
1592 return tmp.lssolve (b, info, rank); |
|
458
|
1593 } |
|
|
1594 |
|
|
1595 ComplexMatrix |
|
5275
|
1596 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1597 { |
|
|
1598 ComplexMatrix tmp (*this); |
|
1484
|
1599 return tmp.lssolve (b, info, rank); |
|
458
|
1600 } |
|
|
1601 |
|
|
1602 ColumnVector |
|
|
1603 Matrix::lssolve (const ColumnVector& b) const |
|
|
1604 { |
|
5275
|
1605 octave_idx_type info; |
|
|
1606 octave_idx_type rank; |
|
1484
|
1607 return lssolve (b, info, rank); |
|
458
|
1608 } |
|
|
1609 |
|
|
1610 ColumnVector |
|
5275
|
1611 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1612 { |
|
5275
|
1613 octave_idx_type rank; |
|
458
|
1614 return lssolve (b, info, rank); |
|
|
1615 } |
|
|
1616 |
|
|
1617 ColumnVector |
|
5275
|
1618 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1619 { |
|
1948
|
1620 ColumnVector retval; |
|
|
1621 |
|
5275
|
1622 octave_idx_type nrhs = 1; |
|
|
1623 |
|
|
1624 octave_idx_type m = rows (); |
|
|
1625 octave_idx_type n = cols (); |
|
458
|
1626 |
|
|
1627 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1628 (*current_liboctave_error_handler) |
|
|
1629 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1630 else |
|
458
|
1631 { |
|
1948
|
1632 Matrix atmp = *this; |
|
|
1633 double *tmp_data = atmp.fortran_vec (); |
|
|
1634 |
|
5275
|
1635 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
1636 ColumnVector result (nrr); |
|
|
1637 |
|
5275
|
1638 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
1639 result.elem (i) = b.elem (i); |
|
|
1640 |
|
|
1641 double *presult = result.fortran_vec (); |
|
|
1642 |
|
5275
|
1643 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
1644 Array<double> s (len_s); |
|
|
1645 double *ps = s.fortran_vec (); |
|
|
1646 |
|
|
1647 double rcond = -1.0; |
|
|
1648 |
|
3752
|
1649 // Ask DGELSS what the dimension of WORK should be. |
|
|
1650 |
|
5275
|
1651 octave_idx_type lwork = -1; |
|
3752
|
1652 |
|
|
1653 Array<double> work (1); |
|
|
1654 |
|
|
1655 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
1656 rcond, rank, work.fortran_vec (), |
|
|
1657 lwork, info)); |
|
1948
|
1658 |
|
|
1659 if (f77_exception_encountered) |
|
|
1660 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1661 else |
|
|
1662 { |
|
5275
|
1663 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
1664 work.resize (lwork); |
|
|
1665 |
|
|
1666 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1667 nrr, ps, rcond, rank, |
|
|
1668 work.fortran_vec (), lwork, info)); |
|
|
1669 |
|
|
1670 if (f77_exception_encountered) |
|
|
1671 (*current_liboctave_error_handler) |
|
|
1672 ("unrecoverable error in dgelss"); |
|
|
1673 else |
|
|
1674 { |
|
|
1675 retval.resize (n); |
|
5275
|
1676 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
1677 retval.elem (i) = result.elem (i); |
|
|
1678 } |
|
1948
|
1679 } |
|
458
|
1680 } |
|
|
1681 |
|
|
1682 return retval; |
|
|
1683 } |
|
|
1684 |
|
|
1685 ComplexColumnVector |
|
|
1686 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
1687 { |
|
|
1688 ComplexMatrix tmp (*this); |
|
|
1689 return tmp.lssolve (b); |
|
|
1690 } |
|
|
1691 |
|
|
1692 ComplexColumnVector |
|
5275
|
1693 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1694 { |
|
|
1695 ComplexMatrix tmp (*this); |
|
|
1696 return tmp.lssolve (b, info); |
|
|
1697 } |
|
|
1698 |
|
|
1699 ComplexColumnVector |
|
5275
|
1700 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1701 { |
|
|
1702 ComplexMatrix tmp (*this); |
|
|
1703 return tmp.lssolve (b, info, rank); |
|
|
1704 } |
|
|
1705 |
|
1819
|
1706 // Constants for matrix exponential calculation. |
|
|
1707 |
|
|
1708 static double padec [] = |
|
|
1709 { |
|
|
1710 5.0000000000000000e-1, |
|
|
1711 1.1666666666666667e-1, |
|
|
1712 1.6666666666666667e-2, |
|
|
1713 1.6025641025641026e-3, |
|
|
1714 1.0683760683760684e-4, |
|
|
1715 4.8562548562548563e-6, |
|
|
1716 1.3875013875013875e-7, |
|
|
1717 1.9270852604185938e-9, |
|
|
1718 }; |
|
|
1719 |
|
|
1720 Matrix |
|
|
1721 Matrix::expm (void) const |
|
|
1722 { |
|
|
1723 Matrix retval; |
|
|
1724 |
|
|
1725 Matrix m = *this; |
|
|
1726 |
|
5275
|
1727 octave_idx_type nc = columns (); |
|
1819
|
1728 |
|
3130
|
1729 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1730 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1731 |
|
1819
|
1732 // trace shift value |
|
3331
|
1733 volatile double trshift = 0.0; |
|
1819
|
1734 |
|
5275
|
1735 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
1736 trshift += m.elem (i, i); |
|
|
1737 |
|
|
1738 trshift /= nc; |
|
|
1739 |
|
3130
|
1740 if (trshift > 0.0) |
|
|
1741 { |
|
5275
|
1742 for (octave_idx_type i = 0; i < nc; i++) |
|
3130
|
1743 m.elem (i, i) -= trshift; |
|
|
1744 } |
|
1819
|
1745 |
|
3331
|
1746 // Preconditioning step 2: balancing; code follows development |
|
|
1747 // in AEPBAL |
|
|
1748 |
|
|
1749 double *p_m = m.fortran_vec (); |
|
|
1750 |
|
5275
|
1751 octave_idx_type info, ilo, ihi, ilos, ihis; |
|
3468
|
1752 Array<double> dpermute (nc); |
|
|
1753 Array<double> dscale (nc); |
|
3466
|
1754 |
|
3468
|
1755 // permutation first |
|
|
1756 char job = 'P'; |
|
4552
|
1757 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1758 nc, p_m, nc, ilo, ihi, |
|
|
1759 dpermute.fortran_vec (), info |
|
|
1760 F77_CHAR_ARG_LEN (1))); |
|
3466
|
1761 |
|
3468
|
1762 // then scaling |
|
|
1763 job = 'S'; |
|
4552
|
1764 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1765 nc, p_m, nc, ilos, ihis, |
|
|
1766 dscale.fortran_vec (), info |
|
|
1767 F77_CHAR_ARG_LEN (1))); |
|
3331
|
1768 |
|
|
1769 if (f77_exception_encountered) |
|
|
1770 { |
|
|
1771 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
1772 return retval; |
|
|
1773 } |
|
|
1774 |
|
1819
|
1775 // Preconditioning step 3: scaling. |
|
3331
|
1776 |
|
1819
|
1777 ColumnVector work(nc); |
|
3130
|
1778 double inf_norm; |
|
3331
|
1779 |
|
4552
|
1780 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
1781 nc, nc, m.fortran_vec (), nc, |
|
|
1782 work.fortran_vec (), inf_norm |
|
|
1783 F77_CHAR_ARG_LEN (1))); |
|
3331
|
1784 |
|
|
1785 if (f77_exception_encountered) |
|
|
1786 { |
|
|
1787 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
1788 return retval; |
|
|
1789 } |
|
1819
|
1790 |
|
5275
|
1791 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
|
1819
|
1792 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
1793 : 0.0); |
|
3331
|
1794 |
|
1819
|
1795 // Check whether we need to square at all. |
|
3331
|
1796 |
|
1819
|
1797 if (sqpow < 0) |
|
|
1798 sqpow = 0; |
|
3331
|
1799 |
|
1819
|
1800 if (sqpow > 0) |
|
|
1801 { |
|
|
1802 double scale_factor = 1.0; |
|
5275
|
1803 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
1804 scale_factor *= 2.0; |
|
3331
|
1805 |
|
1819
|
1806 m = m / scale_factor; |
|
|
1807 } |
|
3331
|
1808 |
|
1819
|
1809 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
1810 |
|
1819
|
1811 Matrix npp (nc, nc, 0.0); |
|
|
1812 Matrix dpp = npp; |
|
3331
|
1813 |
|
1819
|
1814 // Now powers a^8 ... a^1. |
|
3331
|
1815 |
|
5275
|
1816 octave_idx_type minus_one_j = -1; |
|
|
1817 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
1818 { |
|
3573
|
1819 npp = m * npp + padec[j] * m; |
|
|
1820 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
1821 minus_one_j *= -1; |
|
|
1822 } |
|
3331
|
1823 |
|
1819
|
1824 // Zero power. |
|
3331
|
1825 |
|
1819
|
1826 dpp = -dpp; |
|
5275
|
1827 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
1828 { |
|
|
1829 npp.elem (j, j) += 1.0; |
|
|
1830 dpp.elem (j, j) += 1.0; |
|
|
1831 } |
|
3331
|
1832 |
|
1819
|
1833 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1834 |
|
3331
|
1835 retval = dpp.solve (npp, info); |
|
|
1836 |
|
1819
|
1837 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
1838 |
|
1819
|
1839 while (sqpow) |
|
|
1840 { |
|
|
1841 retval = retval * retval; |
|
|
1842 sqpow--; |
|
|
1843 } |
|
3331
|
1844 |
|
1819
|
1845 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
1846 // apply inverse scaling to computed exponential |
|
5275
|
1847 for (octave_idx_type i = 0; i < nc; i++) |
|
|
1848 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
1849 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
1850 |
|
4153
|
1851 OCTAVE_QUIT; |
|
|
1852 |
|
3466
|
1853 // construct balancing permutation vector |
|
5275
|
1854 Array<octave_idx_type> iperm (nc); |
|
|
1855 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
1856 iperm(i) = i; // identity permutation |
|
3466
|
1857 |
|
|
1858 // leading permutations in forward order |
|
5275
|
1859 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
1860 { |
|
5275
|
1861 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
1862 octave_idx_type tmp = iperm(i); |
|
4593
|
1863 iperm(i) = iperm (swapidx); |
|
|
1864 iperm(swapidx) = tmp; |
|
3468
|
1865 } |
|
3466
|
1866 |
|
|
1867 // trailing permutations must be done in reverse order |
|
5275
|
1868 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
1869 { |
|
5275
|
1870 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
1871 octave_idx_type tmp = iperm(i); |
|
4593
|
1872 iperm(i) = iperm(swapidx); |
|
|
1873 iperm(swapidx) = tmp; |
|
3468
|
1874 } |
|
3466
|
1875 |
|
|
1876 // construct inverse balancing permutation vector |
|
5275
|
1877 Array<octave_idx_type> invpvec (nc); |
|
|
1878 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
1879 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
4153
|
1880 |
|
|
1881 OCTAVE_QUIT; |
|
3466
|
1882 |
|
|
1883 Matrix tmpMat = retval; |
|
5275
|
1884 for (octave_idx_type i = 0; i < nc; i++) |
|
|
1885 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
1886 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
1887 |
|
1819
|
1888 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
1889 |
|
3130
|
1890 if (trshift > 0.0) |
|
|
1891 retval = exp (trshift) * retval; |
|
|
1892 |
|
|
1893 return retval; |
|
1819
|
1894 } |
|
|
1895 |
|
458
|
1896 Matrix& |
|
|
1897 Matrix::operator += (const DiagMatrix& a) |
|
|
1898 { |
|
5275
|
1899 octave_idx_type nr = rows (); |
|
|
1900 octave_idx_type nc = cols (); |
|
|
1901 |
|
|
1902 octave_idx_type a_nr = a.rows (); |
|
|
1903 octave_idx_type a_nc = a.cols (); |
|
2385
|
1904 |
|
|
1905 if (nr != a_nr || nc != a_nc) |
|
458
|
1906 { |
|
2385
|
1907 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1908 return *this; |
|
|
1909 } |
|
|
1910 |
|
5275
|
1911 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
1912 elem (i, i) += a.elem (i, i); |
|
|
1913 |
|
|
1914 return *this; |
|
|
1915 } |
|
|
1916 |
|
|
1917 Matrix& |
|
|
1918 Matrix::operator -= (const DiagMatrix& a) |
|
|
1919 { |
|
5275
|
1920 octave_idx_type nr = rows (); |
|
|
1921 octave_idx_type nc = cols (); |
|
|
1922 |
|
|
1923 octave_idx_type a_nr = a.rows (); |
|
|
1924 octave_idx_type a_nc = a.cols (); |
|
2385
|
1925 |
|
|
1926 if (nr != a_nr || nc != a_nc) |
|
458
|
1927 { |
|
2385
|
1928 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1929 return *this; |
|
|
1930 } |
|
|
1931 |
|
5275
|
1932 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
1933 elem (i, i) -= a.elem (i, i); |
|
|
1934 |
|
|
1935 return *this; |
|
|
1936 } |
|
|
1937 |
|
|
1938 // unary operations |
|
|
1939 |
|
2964
|
1940 boolMatrix |
|
458
|
1941 Matrix::operator ! (void) const |
|
|
1942 { |
|
5275
|
1943 octave_idx_type nr = rows (); |
|
|
1944 octave_idx_type nc = cols (); |
|
458
|
1945 |
|
2964
|
1946 boolMatrix b (nr, nc); |
|
458
|
1947 |
|
5275
|
1948 for (octave_idx_type j = 0; j < nc; j++) |
|
|
1949 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
1950 b.elem (i, j) = ! elem (i, j); |
|
|
1951 |
|
|
1952 return b; |
|
|
1953 } |
|
|
1954 |
|
1205
|
1955 // column vector by row vector -> matrix operations |
|
458
|
1956 |
|
1205
|
1957 Matrix |
|
|
1958 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
1959 { |
|
1948
|
1960 Matrix retval; |
|
|
1961 |
|
5275
|
1962 octave_idx_type len = v.length (); |
|
3233
|
1963 |
|
|
1964 if (len != 0) |
|
1205
|
1965 { |
|
5275
|
1966 octave_idx_type a_len = a.length (); |
|
3233
|
1967 |
|
|
1968 retval.resize (len, a_len); |
|
|
1969 double *c = retval.fortran_vec (); |
|
|
1970 |
|
4552
|
1971 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
1972 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
1973 len, a_len, 1, 1.0, v.data (), len, |
|
|
1974 a.data (), 1, 0.0, c, len |
|
|
1975 F77_CHAR_ARG_LEN (1) |
|
|
1976 F77_CHAR_ARG_LEN (1))); |
|
3233
|
1977 |
|
|
1978 if (f77_exception_encountered) |
|
|
1979 (*current_liboctave_error_handler) |
|
|
1980 ("unrecoverable error in dgemm"); |
|
1205
|
1981 } |
|
458
|
1982 |
|
1948
|
1983 return retval; |
|
458
|
1984 } |
|
|
1985 |
|
|
1986 // other operations. |
|
|
1987 |
|
|
1988 Matrix |
|
2676
|
1989 Matrix::map (d_d_Mapper f) const |
|
1205
|
1990 { |
|
2676
|
1991 Matrix b (*this); |
|
|
1992 return b.apply (f); |
|
1205
|
1993 } |
|
|
1994 |
|
3248
|
1995 boolMatrix |
|
|
1996 Matrix::map (b_d_Mapper f) const |
|
|
1997 { |
|
5275
|
1998 octave_idx_type nr = rows (); |
|
|
1999 octave_idx_type nc = cols (); |
|
3248
|
2000 |
|
|
2001 boolMatrix retval (nr, nc); |
|
|
2002 |
|
5275
|
2003 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2004 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2005 retval(i,j) = f (elem(i,j)); |
|
|
2006 |
|
|
2007 return retval; |
|
|
2008 } |
|
|
2009 |
|
2676
|
2010 Matrix& |
|
|
2011 Matrix::apply (d_d_Mapper f) |
|
458
|
2012 { |
|
|
2013 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2014 |
|
5275
|
2015 for (octave_idx_type i = 0; i < length (); i++) |
|
458
|
2016 d[i] = f (d[i]); |
|
2676
|
2017 |
|
|
2018 return *this; |
|
458
|
2019 } |
|
|
2020 |
|
2385
|
2021 bool |
|
4431
|
2022 Matrix::any_element_is_negative (bool neg_zero) const |
|
2385
|
2023 { |
|
5275
|
2024 octave_idx_type nel = nelem (); |
|
2385
|
2025 |
|
4431
|
2026 if (neg_zero) |
|
|
2027 { |
|
5275
|
2028 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2029 if (lo_ieee_signbit (elem (i))) |
|
|
2030 return true; |
|
4431
|
2031 } |
|
|
2032 else |
|
|
2033 { |
|
5275
|
2034 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2035 if (elem (i) < 0) |
|
|
2036 return true; |
|
4431
|
2037 } |
|
2385
|
2038 |
|
|
2039 return false; |
|
|
2040 } |
|
|
2041 |
|
|
2042 |
|
|
2043 bool |
|
|
2044 Matrix::any_element_is_inf_or_nan (void) const |
|
|
2045 { |
|
5275
|
2046 octave_idx_type nel = nelem (); |
|
|
2047 |
|
|
2048 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2049 { |
|
|
2050 double val = elem (i); |
|
|
2051 if (xisinf (val) || xisnan (val)) |
|
|
2052 return true; |
|
|
2053 } |
|
|
2054 |
|
|
2055 return false; |
|
2385
|
2056 } |
|
|
2057 |
|
|
2058 bool |
|
|
2059 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
2060 { |
|
5275
|
2061 octave_idx_type nel = nelem (); |
|
|
2062 |
|
|
2063 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2064 { |
|
|
2065 double val = elem (i); |
|
|
2066 if (xisnan (val) || D_NINT (val) == val) |
|
|
2067 continue; |
|
|
2068 else |
|
|
2069 return false; |
|
|
2070 } |
|
2385
|
2071 |
|
|
2072 return true; |
|
|
2073 } |
|
|
2074 |
|
1968
|
2075 // Return nonzero if any element of M is not an integer. Also extract |
|
|
2076 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
2077 |
|
2385
|
2078 bool |
|
1968
|
2079 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
2080 { |
|
5275
|
2081 octave_idx_type nel = nelem (); |
|
4634
|
2082 |
|
|
2083 if (nel > 0) |
|
1968
|
2084 { |
|
4634
|
2085 max_val = elem (0); |
|
|
2086 min_val = elem (0); |
|
1968
|
2087 } |
|
|
2088 else |
|
2385
|
2089 return false; |
|
1968
|
2090 |
|
5275
|
2091 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2092 { |
|
|
2093 double val = elem (i); |
|
|
2094 |
|
|
2095 if (val > max_val) |
|
|
2096 max_val = val; |
|
|
2097 |
|
|
2098 if (val < min_val) |
|
|
2099 min_val = val; |
|
|
2100 |
|
|
2101 if (D_NINT (val) != val) |
|
|
2102 return false; |
|
|
2103 } |
|
2385
|
2104 |
|
|
2105 return true; |
|
1968
|
2106 } |
|
|
2107 |
|
2385
|
2108 bool |
|
1968
|
2109 Matrix::too_large_for_float (void) const |
|
|
2110 { |
|
5275
|
2111 octave_idx_type nel = nelem (); |
|
|
2112 |
|
|
2113 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2114 { |
|
|
2115 double val = elem (i); |
|
|
2116 |
|
|
2117 if (val > FLT_MAX || val < FLT_MIN) |
|
|
2118 return true; |
|
|
2119 } |
|
1968
|
2120 |
|
2385
|
2121 return false; |
|
1968
|
2122 } |
|
|
2123 |
|
4015
|
2124 // XXX FIXME XXX Do these really belong here? Maybe they should be |
|
|
2125 // in a base class? |
|
458
|
2126 |
|
2832
|
2127 boolMatrix |
|
4015
|
2128 Matrix::all (int dim) const |
|
458
|
2129 { |
|
4015
|
2130 MX_ALL_OP (dim); |
|
458
|
2131 } |
|
|
2132 |
|
2832
|
2133 boolMatrix |
|
4015
|
2134 Matrix::any (int dim) const |
|
458
|
2135 { |
|
4015
|
2136 MX_ANY_OP (dim); |
|
458
|
2137 } |
|
|
2138 |
|
|
2139 Matrix |
|
3723
|
2140 Matrix::cumprod (int dim) const |
|
458
|
2141 { |
|
4015
|
2142 MX_CUMULATIVE_OP (Matrix, double, *=); |
|
458
|
2143 } |
|
|
2144 |
|
|
2145 Matrix |
|
3723
|
2146 Matrix::cumsum (int dim) const |
|
458
|
2147 { |
|
4015
|
2148 MX_CUMULATIVE_OP (Matrix, double, +=); |
|
458
|
2149 } |
|
|
2150 |
|
|
2151 Matrix |
|
3723
|
2152 Matrix::prod (int dim) const |
|
458
|
2153 { |
|
3864
|
2154 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2155 } |
|
|
2156 |
|
|
2157 Matrix |
|
3723
|
2158 Matrix::sum (int dim) const |
|
458
|
2159 { |
|
3864
|
2160 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2161 } |
|
|
2162 |
|
|
2163 Matrix |
|
3723
|
2164 Matrix::sumsq (int dim) const |
|
458
|
2165 { |
|
3864
|
2166 #define ROW_EXPR \ |
|
|
2167 double d = elem (i, j); \ |
|
|
2168 retval.elem (i, 0) += d * d |
|
|
2169 |
|
|
2170 #define COL_EXPR \ |
|
|
2171 double d = elem (i, j); \ |
|
|
2172 retval.elem (0, j) += d * d |
|
|
2173 |
|
|
2174 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2175 |
|
|
2176 #undef ROW_EXPR |
|
|
2177 #undef COL_EXPR |
|
458
|
2178 } |
|
|
2179 |
|
2385
|
2180 Matrix |
|
|
2181 Matrix::abs (void) const |
|
|
2182 { |
|
5275
|
2183 octave_idx_type nr = rows (); |
|
|
2184 octave_idx_type nc = cols (); |
|
2385
|
2185 |
|
|
2186 Matrix retval (nr, nc); |
|
|
2187 |
|
5275
|
2188 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2189 for (octave_idx_type i = 0; i < nr; i++) |
|
2385
|
2190 retval (i, j) = fabs (elem (i, j)); |
|
|
2191 |
|
|
2192 return retval; |
|
|
2193 } |
|
|
2194 |
|
458
|
2195 ColumnVector |
|
|
2196 Matrix::diag (void) const |
|
|
2197 { |
|
|
2198 return diag (0); |
|
|
2199 } |
|
|
2200 |
|
|
2201 ColumnVector |
|
5275
|
2202 Matrix::diag (octave_idx_type k) const |
|
458
|
2203 { |
|
5275
|
2204 octave_idx_type nnr = rows (); |
|
|
2205 octave_idx_type nnc = cols (); |
|
458
|
2206 if (k > 0) |
|
|
2207 nnc -= k; |
|
|
2208 else if (k < 0) |
|
|
2209 nnr += k; |
|
|
2210 |
|
|
2211 ColumnVector d; |
|
|
2212 |
|
|
2213 if (nnr > 0 && nnc > 0) |
|
|
2214 { |
|
5275
|
2215 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
2216 |
|
|
2217 d.resize (ndiag); |
|
|
2218 |
|
|
2219 if (k > 0) |
|
|
2220 { |
|
5275
|
2221 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2222 d.elem (i) = elem (i, i+k); |
|
|
2223 } |
|
4509
|
2224 else if (k < 0) |
|
458
|
2225 { |
|
5275
|
2226 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2227 d.elem (i) = elem (i-k, i); |
|
|
2228 } |
|
|
2229 else |
|
|
2230 { |
|
5275
|
2231 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2232 d.elem (i) = elem (i, i); |
|
|
2233 } |
|
|
2234 } |
|
|
2235 else |
|
4513
|
2236 (*current_liboctave_error_handler) |
|
|
2237 ("diag: requested diagonal out of range"); |
|
458
|
2238 |
|
|
2239 return d; |
|
|
2240 } |
|
|
2241 |
|
|
2242 ColumnVector |
|
|
2243 Matrix::row_min (void) const |
|
|
2244 { |
|
5275
|
2245 Array<octave_idx_type> dummy_idx; |
|
4587
|
2246 return row_min (dummy_idx); |
|
458
|
2247 } |
|
|
2248 |
|
|
2249 ColumnVector |
|
5275
|
2250 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2251 { |
|
|
2252 ColumnVector result; |
|
|
2253 |
|
5275
|
2254 octave_idx_type nr = rows (); |
|
|
2255 octave_idx_type nc = cols (); |
|
458
|
2256 |
|
|
2257 if (nr > 0 && nc > 0) |
|
|
2258 { |
|
|
2259 result.resize (nr); |
|
4587
|
2260 idx_arg.resize (nr); |
|
458
|
2261 |
|
5275
|
2262 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2263 { |
|
5275
|
2264 octave_idx_type idx_j; |
|
4469
|
2265 |
|
|
2266 double tmp_min = octave_NaN; |
|
|
2267 |
|
|
2268 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2269 { |
|
4469
|
2270 tmp_min = elem (i, idx_j); |
|
|
2271 |
|
|
2272 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2273 break; |
|
|
2274 } |
|
|
2275 |
|
5275
|
2276 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2277 { |
|
|
2278 double tmp = elem (i, j); |
|
|
2279 |
|
|
2280 if (octave_is_NaN_or_NA (tmp)) |
|
|
2281 continue; |
|
|
2282 else if (tmp < tmp_min) |
|
2354
|
2283 { |
|
4469
|
2284 idx_j = j; |
|
|
2285 tmp_min = tmp; |
|
2354
|
2286 } |
|
|
2287 } |
|
|
2288 |
|
4469
|
2289 result.elem (i) = tmp_min; |
|
4587
|
2290 idx_arg.elem (i) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_j; |
|
458
|
2291 } |
|
|
2292 } |
|
|
2293 |
|
|
2294 return result; |
|
|
2295 } |
|
|
2296 |
|
|
2297 ColumnVector |
|
|
2298 Matrix::row_max (void) const |
|
|
2299 { |
|
5275
|
2300 Array<octave_idx_type> dummy_idx; |
|
4587
|
2301 return row_max (dummy_idx); |
|
458
|
2302 } |
|
|
2303 |
|
|
2304 ColumnVector |
|
5275
|
2305 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2306 { |
|
|
2307 ColumnVector result; |
|
|
2308 |
|
5275
|
2309 octave_idx_type nr = rows (); |
|
|
2310 octave_idx_type nc = cols (); |
|
458
|
2311 |
|
|
2312 if (nr > 0 && nc > 0) |
|
|
2313 { |
|
|
2314 result.resize (nr); |
|
4587
|
2315 idx_arg.resize (nr); |
|
458
|
2316 |
|
5275
|
2317 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2318 { |
|
5275
|
2319 octave_idx_type idx_j; |
|
4469
|
2320 |
|
|
2321 double tmp_max = octave_NaN; |
|
|
2322 |
|
|
2323 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2324 { |
|
4469
|
2325 tmp_max = elem (i, idx_j); |
|
|
2326 |
|
|
2327 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
2328 break; |
|
|
2329 } |
|
|
2330 |
|
5275
|
2331 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2332 { |
|
|
2333 double tmp = elem (i, j); |
|
|
2334 |
|
|
2335 if (octave_is_NaN_or_NA (tmp)) |
|
|
2336 continue; |
|
|
2337 else if (tmp > tmp_max) |
|
2354
|
2338 { |
|
4469
|
2339 idx_j = j; |
|
|
2340 tmp_max = tmp; |
|
2354
|
2341 } |
|
|
2342 } |
|
|
2343 |
|
4469
|
2344 result.elem (i) = tmp_max; |
|
4587
|
2345 idx_arg.elem (i) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_j; |
|
458
|
2346 } |
|
|
2347 } |
|
|
2348 |
|
|
2349 return result; |
|
|
2350 } |
|
|
2351 |
|
|
2352 RowVector |
|
|
2353 Matrix::column_min (void) const |
|
|
2354 { |
|
5275
|
2355 Array<octave_idx_type> dummy_idx; |
|
4587
|
2356 return column_min (dummy_idx); |
|
458
|
2357 } |
|
2354
|
2358 |
|
458
|
2359 RowVector |
|
5275
|
2360 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2361 { |
|
|
2362 RowVector result; |
|
|
2363 |
|
5275
|
2364 octave_idx_type nr = rows (); |
|
|
2365 octave_idx_type nc = cols (); |
|
458
|
2366 |
|
|
2367 if (nr > 0 && nc > 0) |
|
|
2368 { |
|
|
2369 result.resize (nc); |
|
4587
|
2370 idx_arg.resize (nc); |
|
458
|
2371 |
|
5275
|
2372 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2373 { |
|
5275
|
2374 octave_idx_type idx_i; |
|
4469
|
2375 |
|
|
2376 double tmp_min = octave_NaN; |
|
|
2377 |
|
|
2378 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2379 { |
|
4469
|
2380 tmp_min = elem (idx_i, j); |
|
|
2381 |
|
|
2382 if (! octave_is_NaN_or_NA (tmp_min)) |
|
|
2383 break; |
|
|
2384 } |
|
|
2385 |
|
5275
|
2386 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2387 { |
|
|
2388 double tmp = elem (i, j); |
|
|
2389 |
|
|
2390 if (octave_is_NaN_or_NA (tmp)) |
|
|
2391 continue; |
|
|
2392 else if (tmp < tmp_min) |
|
2354
|
2393 { |
|
4469
|
2394 idx_i = i; |
|
|
2395 tmp_min = tmp; |
|
2354
|
2396 } |
|
|
2397 } |
|
|
2398 |
|
4469
|
2399 result.elem (j) = tmp_min; |
|
4587
|
2400 idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_i; |
|
458
|
2401 } |
|
|
2402 } |
|
|
2403 |
|
|
2404 return result; |
|
|
2405 } |
|
|
2406 |
|
2354
|
2407 RowVector |
|
|
2408 Matrix::column_max (void) const |
|
|
2409 { |
|
5275
|
2410 Array<octave_idx_type> dummy_idx; |
|
4587
|
2411 return column_max (dummy_idx); |
|
2354
|
2412 } |
|
458
|
2413 |
|
|
2414 RowVector |
|
5275
|
2415 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2416 { |
|
|
2417 RowVector result; |
|
|
2418 |
|
5275
|
2419 octave_idx_type nr = rows (); |
|
|
2420 octave_idx_type nc = cols (); |
|
458
|
2421 |
|
|
2422 if (nr > 0 && nc > 0) |
|
|
2423 { |
|
|
2424 result.resize (nc); |
|
4587
|
2425 idx_arg.resize (nc); |
|
458
|
2426 |
|
5275
|
2427 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2428 { |
|
5275
|
2429 octave_idx_type idx_i; |
|
4469
|
2430 |
|
|
2431 double tmp_max = octave_NaN; |
|
|
2432 |
|
|
2433 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2434 { |
|
4469
|
2435 tmp_max = elem (idx_i, j); |
|
|
2436 |
|
|
2437 if (! octave_is_NaN_or_NA (tmp_max)) |
|
|
2438 break; |
|
|
2439 } |
|
|
2440 |
|
5275
|
2441 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2442 { |
|
|
2443 double tmp = elem (i, j); |
|
|
2444 |
|
|
2445 if (octave_is_NaN_or_NA (tmp)) |
|
|
2446 continue; |
|
|
2447 else if (tmp > tmp_max) |
|
2354
|
2448 { |
|
4469
|
2449 idx_i = i; |
|
|
2450 tmp_max = tmp; |
|
2354
|
2451 } |
|
|
2452 } |
|
|
2453 |
|
4469
|
2454 result.elem (j) = tmp_max; |
|
4587
|
2455 idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_i; |
|
458
|
2456 } |
|
|
2457 } |
|
|
2458 |
|
|
2459 return result; |
|
|
2460 } |
|
|
2461 |
|
3504
|
2462 std::ostream& |
|
|
2463 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2464 { |
|
5275
|
2465 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
2466 { |
|
5275
|
2467 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
2468 { |
|
|
2469 os << " "; |
|
|
2470 octave_write_double (os, a.elem (i, j)); |
|
|
2471 } |
|
458
|
2472 os << "\n"; |
|
|
2473 } |
|
|
2474 return os; |
|
|
2475 } |
|
|
2476 |
|
3504
|
2477 std::istream& |
|
|
2478 operator >> (std::istream& is, Matrix& a) |
|
458
|
2479 { |
|
5275
|
2480 octave_idx_type nr = a.rows (); |
|
|
2481 octave_idx_type nc = a.cols (); |
|
458
|
2482 |
|
|
2483 if (nr < 1 || nc < 1) |
|
3504
|
2484 is.clear (std::ios::badbit); |
|
458
|
2485 else |
|
|
2486 { |
|
|
2487 double tmp; |
|
5275
|
2488 for (octave_idx_type i = 0; i < nr; i++) |
|
|
2489 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2490 { |
|
4130
|
2491 tmp = octave_read_double (is); |
|
458
|
2492 if (is) |
|
|
2493 a.elem (i, j) = tmp; |
|
|
2494 else |
|
2795
|
2495 goto done; |
|
458
|
2496 } |
|
|
2497 } |
|
|
2498 |
|
2795
|
2499 done: |
|
|
2500 |
|
458
|
2501 return is; |
|
|
2502 } |
|
|
2503 |
|
1819
|
2504 Matrix |
|
|
2505 Givens (double x, double y) |
|
|
2506 { |
|
|
2507 double cc, s, temp_r; |
|
|
2508 |
|
3887
|
2509 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
1819
|
2510 |
|
|
2511 Matrix g (2, 2); |
|
|
2512 |
|
|
2513 g.elem (0, 0) = cc; |
|
|
2514 g.elem (1, 1) = cc; |
|
|
2515 g.elem (0, 1) = s; |
|
|
2516 g.elem (1, 0) = -s; |
|
|
2517 |
|
|
2518 return g; |
|
|
2519 } |
|
|
2520 |
|
|
2521 Matrix |
|
|
2522 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2523 { |
|
|
2524 Matrix retval; |
|
|
2525 |
|
|
2526 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2527 // size. |
|
|
2528 |
|
|
2529 // Compute Schur decompositions. |
|
|
2530 |
|
|
2531 SCHUR as (a, "U"); |
|
|
2532 SCHUR bs (b, "U"); |
|
|
2533 |
|
|
2534 // Transform c to new coordinates. |
|
|
2535 |
|
|
2536 Matrix ua = as.unitary_matrix (); |
|
|
2537 Matrix sch_a = as.schur_matrix (); |
|
|
2538 |
|
|
2539 Matrix ub = bs.unitary_matrix (); |
|
|
2540 Matrix sch_b = bs.schur_matrix (); |
|
|
2541 |
|
|
2542 Matrix cx = ua.transpose () * c * ub; |
|
|
2543 |
|
|
2544 // Solve the sylvester equation, back-transform, and return the |
|
|
2545 // solution. |
|
|
2546 |
|
5275
|
2547 octave_idx_type a_nr = a.rows (); |
|
|
2548 octave_idx_type b_nr = b.rows (); |
|
1819
|
2549 |
|
|
2550 double scale; |
|
5275
|
2551 octave_idx_type info; |
|
1819
|
2552 |
|
1950
|
2553 double *pa = sch_a.fortran_vec (); |
|
|
2554 double *pb = sch_b.fortran_vec (); |
|
|
2555 double *px = cx.fortran_vec (); |
|
|
2556 |
|
4552
|
2557 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2558 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2559 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2560 b_nr, px, a_nr, scale, info |
|
|
2561 F77_CHAR_ARG_LEN (1) |
|
|
2562 F77_CHAR_ARG_LEN (1))); |
|
1950
|
2563 |
|
|
2564 |
|
|
2565 if (f77_exception_encountered) |
|
|
2566 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
2567 else |
|
|
2568 { |
|
|
2569 // XXX FIXME XXX -- check info? |
|
1819
|
2570 |
|
1950
|
2571 retval = -ua*cx*ub.transpose (); |
|
|
2572 } |
|
1819
|
2573 |
|
|
2574 return retval; |
|
|
2575 } |
|
|
2576 |
|
2828
|
2577 // matrix by matrix -> matrix operations |
|
|
2578 |
|
|
2579 Matrix |
|
|
2580 operator * (const Matrix& m, const Matrix& a) |
|
|
2581 { |
|
|
2582 Matrix retval; |
|
|
2583 |
|
5275
|
2584 octave_idx_type nr = m.rows (); |
|
|
2585 octave_idx_type nc = m.cols (); |
|
|
2586 |
|
|
2587 octave_idx_type a_nr = a.rows (); |
|
|
2588 octave_idx_type a_nc = a.cols (); |
|
2828
|
2589 |
|
|
2590 if (nc != a_nr) |
|
|
2591 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2592 else |
|
|
2593 { |
|
|
2594 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2595 retval.resize (nr, a_nc, 0.0); |
|
|
2596 else |
|
|
2597 { |
|
5275
|
2598 octave_idx_type ld = nr; |
|
|
2599 octave_idx_type lda = a_nr; |
|
2828
|
2600 |
|
|
2601 retval.resize (nr, a_nc); |
|
|
2602 double *c = retval.fortran_vec (); |
|
|
2603 |
|
4552
|
2604 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2605 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2606 nr, a_nc, nc, 1.0, m.data (), |
|
|
2607 ld, a.data (), lda, 0.0, c, nr |
|
|
2608 F77_CHAR_ARG_LEN (1) |
|
|
2609 F77_CHAR_ARG_LEN (1))); |
|
2828
|
2610 |
|
|
2611 if (f77_exception_encountered) |
|
|
2612 (*current_liboctave_error_handler) |
|
|
2613 ("unrecoverable error in dgemm"); |
|
|
2614 } |
|
|
2615 } |
|
|
2616 |
|
|
2617 return retval; |
|
|
2618 } |
|
|
2619 |
|
4309
|
2620 // XXX FIXME XXX -- it would be nice to share code among the min/max |
|
|
2621 // functions below. |
|
|
2622 |
|
|
2623 #define EMPTY_RETURN_CHECK(T) \ |
|
|
2624 if (nr == 0 || nc == 0) \ |
|
|
2625 return T (nr, nc); |
|
|
2626 |
|
|
2627 Matrix |
|
|
2628 min (double d, const Matrix& m) |
|
|
2629 { |
|
5275
|
2630 octave_idx_type nr = m.rows (); |
|
|
2631 octave_idx_type nc = m.columns (); |
|
4309
|
2632 |
|
|
2633 EMPTY_RETURN_CHECK (Matrix); |
|
|
2634 |
|
|
2635 Matrix result (nr, nc); |
|
|
2636 |
|
5275
|
2637 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2638 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2639 { |
|
|
2640 OCTAVE_QUIT; |
|
|
2641 result (i, j) = xmin (d, m (i, j)); |
|
|
2642 } |
|
|
2643 |
|
|
2644 return result; |
|
|
2645 } |
|
|
2646 |
|
|
2647 Matrix |
|
|
2648 min (const Matrix& m, double d) |
|
|
2649 { |
|
5275
|
2650 octave_idx_type nr = m.rows (); |
|
|
2651 octave_idx_type nc = m.columns (); |
|
4309
|
2652 |
|
|
2653 EMPTY_RETURN_CHECK (Matrix); |
|
|
2654 |
|
|
2655 Matrix result (nr, nc); |
|
|
2656 |
|
5275
|
2657 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2658 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2659 { |
|
|
2660 OCTAVE_QUIT; |
|
|
2661 result (i, j) = xmin (m (i, j), d); |
|
|
2662 } |
|
|
2663 |
|
|
2664 return result; |
|
|
2665 } |
|
|
2666 |
|
|
2667 Matrix |
|
|
2668 min (const Matrix& a, const Matrix& b) |
|
|
2669 { |
|
5275
|
2670 octave_idx_type nr = a.rows (); |
|
|
2671 octave_idx_type nc = a.columns (); |
|
4309
|
2672 |
|
|
2673 if (nr != b.rows () || nc != b.columns ()) |
|
|
2674 { |
|
|
2675 (*current_liboctave_error_handler) |
|
|
2676 ("two-arg min expecting args of same size"); |
|
|
2677 return Matrix (); |
|
|
2678 } |
|
|
2679 |
|
|
2680 EMPTY_RETURN_CHECK (Matrix); |
|
|
2681 |
|
|
2682 Matrix result (nr, nc); |
|
|
2683 |
|
5275
|
2684 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2685 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2686 { |
|
|
2687 OCTAVE_QUIT; |
|
|
2688 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
2689 } |
|
|
2690 |
|
|
2691 return result; |
|
|
2692 } |
|
|
2693 |
|
|
2694 Matrix |
|
|
2695 max (double d, const Matrix& m) |
|
|
2696 { |
|
5275
|
2697 octave_idx_type nr = m.rows (); |
|
|
2698 octave_idx_type nc = m.columns (); |
|
4309
|
2699 |
|
|
2700 EMPTY_RETURN_CHECK (Matrix); |
|
|
2701 |
|
|
2702 Matrix result (nr, nc); |
|
|
2703 |
|
5275
|
2704 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2705 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2706 { |
|
|
2707 OCTAVE_QUIT; |
|
|
2708 result (i, j) = xmax (d, m (i, j)); |
|
|
2709 } |
|
|
2710 |
|
|
2711 return result; |
|
|
2712 } |
|
|
2713 |
|
|
2714 Matrix |
|
|
2715 max (const Matrix& m, double d) |
|
|
2716 { |
|
5275
|
2717 octave_idx_type nr = m.rows (); |
|
|
2718 octave_idx_type nc = m.columns (); |
|
4309
|
2719 |
|
|
2720 EMPTY_RETURN_CHECK (Matrix); |
|
|
2721 |
|
|
2722 Matrix result (nr, nc); |
|
|
2723 |
|
5275
|
2724 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2725 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2726 { |
|
|
2727 OCTAVE_QUIT; |
|
|
2728 result (i, j) = xmax (m (i, j), d); |
|
|
2729 } |
|
|
2730 |
|
|
2731 return result; |
|
|
2732 } |
|
|
2733 |
|
|
2734 Matrix |
|
|
2735 max (const Matrix& a, const Matrix& b) |
|
|
2736 { |
|
5275
|
2737 octave_idx_type nr = a.rows (); |
|
|
2738 octave_idx_type nc = a.columns (); |
|
4309
|
2739 |
|
|
2740 if (nr != b.rows () || nc != b.columns ()) |
|
|
2741 { |
|
|
2742 (*current_liboctave_error_handler) |
|
|
2743 ("two-arg max expecting args of same size"); |
|
|
2744 return Matrix (); |
|
|
2745 } |
|
|
2746 |
|
|
2747 EMPTY_RETURN_CHECK (Matrix); |
|
|
2748 |
|
|
2749 Matrix result (nr, nc); |
|
|
2750 |
|
5275
|
2751 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2752 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
2753 { |
|
|
2754 OCTAVE_QUIT; |
|
|
2755 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
2756 } |
|
|
2757 |
|
|
2758 return result; |
|
|
2759 } |
|
|
2760 |
|
2870
|
2761 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
2762 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
2763 |
|
|
2764 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
2765 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
2766 |
|
|
2767 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
2768 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
2769 |
|
458
|
2770 /* |
|
|
2771 ;;; Local Variables: *** |
|
|
2772 ;;; mode: C++ *** |
|
|
2773 ;;; End: *** |
|
|
2774 */ |
