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1993
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1 // Matrix manipulations. |
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458
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2 /* |
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3 |
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4 Copyright (C) 1996, 1997 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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21 02110-1301, USA. |
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22 |
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23 */ |
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24 |
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25 #ifdef HAVE_CONFIG_H |
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1192
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26 #include <config.h> |
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458
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27 #endif |
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28 |
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1367
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29 #include <cfloat> |
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30 |
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3503
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31 #include <iostream> |
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32 |
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4669
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33 #include "Array-util.h" |
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2317
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34 #include "byte-swap.h" |
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2828
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35 #include "dMatrix.h" |
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1819
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36 #include "dbleAEPBAL.h" |
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458
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37 #include "dbleDET.h" |
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1819
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38 #include "dbleSCHUR.h" |
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740
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39 #include "dbleSVD.h" |
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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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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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5983
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86 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
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87 const octave_idx_type&, const octave_idx_type&, const double&, |
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88 const double*, const octave_idx_type&, const double*, |
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89 const octave_idx_type&, const double&, double*, |
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90 const octave_idx_type& |
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91 F77_CHAR_ARG_LEN_DECL); |
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92 |
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93 F77_RET_T |
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94 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, |
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95 const double*, const octave_idx_type&, double&); |
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96 |
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97 F77_RET_T |
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98 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
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99 octave_idx_type*, octave_idx_type&); |
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100 |
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101 F77_RET_T |
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102 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
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103 const double*, const octave_idx_type&, |
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104 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& |
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105 F77_CHAR_ARG_LEN_DECL); |
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106 |
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107 F77_RET_T |
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108 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const 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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111 F77_RET_T |
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112 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
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113 const octave_idx_type&, const double&, double&, |
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114 double*, octave_idx_type*, octave_idx_type& |
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115 F77_CHAR_ARG_LEN_DECL); |
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116 |
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117 F77_RET_T |
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5275
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118 F77_FUNC (dgelss, DGELSS) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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119 double*, const octave_idx_type&, double*, |
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120 const octave_idx_type&, double*, double&, octave_idx_type&, |
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121 double*, const octave_idx_type&, octave_idx_type&); |
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122 |
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5785
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123 F77_RET_T |
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124 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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125 double *, const octave_idx_type&, |
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126 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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127 |
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128 F77_RET_T |
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129 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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130 double*, const octave_idx_type&, const double&, |
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131 double&, double*, octave_idx_type*, |
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132 octave_idx_type& F77_CHAR_ARG_LEN_DECL); |
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133 F77_RET_T |
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134 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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135 const octave_idx_type&, const double*, |
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136 const octave_idx_type&, double*, |
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137 const octave_idx_type&, octave_idx_type& |
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138 F77_CHAR_ARG_LEN_DECL); |
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139 |
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140 F77_RET_T |
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141 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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142 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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143 const double*, const octave_idx_type&, double&, |
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144 double*, octave_idx_type*, octave_idx_type& |
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145 F77_CHAR_ARG_LEN_DECL |
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146 F77_CHAR_ARG_LEN_DECL |
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147 F77_CHAR_ARG_LEN_DECL); |
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148 F77_RET_T |
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149 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
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150 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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151 const octave_idx_type&, const double*, |
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152 const octave_idx_type&, double*, |
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153 const octave_idx_type&, octave_idx_type& |
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154 F77_CHAR_ARG_LEN_DECL |
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155 F77_CHAR_ARG_LEN_DECL |
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156 F77_CHAR_ARG_LEN_DECL); |
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157 |
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1360
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158 // Note that the original complex fft routines were not written for |
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159 // double complex arguments. They have been modified by adding an |
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160 // implicit double precision (a-h,o-z) statement at the beginning of |
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161 // each subroutine. |
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162 |
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4552
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163 F77_RET_T |
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5275
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164 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
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165 |
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166 F77_RET_T |
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5275
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167 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
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4552
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168 |
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169 F77_RET_T |
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170 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
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171 |
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172 F77_RET_T |
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173 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, |
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174 double&, double&); |
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175 |
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176 F77_RET_T |
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177 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, |
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178 F77_CONST_CHAR_ARG_DECL, |
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179 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
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180 const double*, const octave_idx_type&, const double*, |
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181 const octave_idx_type&, const double*, const octave_idx_type&, |
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182 double&, octave_idx_type& |
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4552
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183 F77_CHAR_ARG_LEN_DECL |
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184 F77_CHAR_ARG_LEN_DECL); |
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185 |
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186 F77_RET_T |
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187 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
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188 const octave_idx_type&, const double*, |
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189 const octave_idx_type&, double*, double& |
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190 F77_CHAR_ARG_LEN_DECL); |
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458
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191 } |
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192 |
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1360
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193 // Matrix class. |
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458
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194 |
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2349
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195 Matrix::Matrix (const RowVector& rv) |
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196 : MArray2<double> (1, rv.length (), 0.0) |
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197 { |
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198 for (octave_idx_type i = 0; i < rv.length (); i++) |
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199 elem (0, i) = rv.elem (i); |
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200 } |
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201 |
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202 Matrix::Matrix (const ColumnVector& cv) |
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203 : MArray2<double> (cv.length (), 1, 0.0) |
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204 { |
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205 for (octave_idx_type i = 0; i < cv.length (); i++) |
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206 elem (i, 0) = cv.elem (i); |
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207 } |
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208 |
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458
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209 Matrix::Matrix (const DiagMatrix& a) |
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1214
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210 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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211 { |
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212 for (octave_idx_type i = 0; i < a.length (); i++) |
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213 elem (i, i) = a.elem (i, i); |
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214 } |
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215 |
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5775
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216 // FIXME -- could we use a templated mixed-type copy function |
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1574
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217 // here? |
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218 |
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219 Matrix::Matrix (const boolMatrix& a) |
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220 : MArray2<double> (a.rows (), a.cols ()) |
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221 { |
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222 for (octave_idx_type i = 0; i < a.rows (); i++) |
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223 for (octave_idx_type j = 0; j < a.cols (); j++) |
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224 elem (i, j) = a.elem (i, j); |
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225 } |
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226 |
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1574
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227 Matrix::Matrix (const charMatrix& a) |
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228 : MArray2<double> (a.rows (), a.cols ()) |
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229 { |
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230 for (octave_idx_type i = 0; i < a.rows (); i++) |
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231 for (octave_idx_type j = 0; j < a.cols (); j++) |
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232 elem (i, j) = a.elem (i, j); |
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233 } |
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234 |
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2385
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235 bool |
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458
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236 Matrix::operator == (const Matrix& a) const |
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237 { |
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238 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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239 return false; |
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458
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240 |
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3769
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241 return mx_inline_equal (data (), a.data (), length ()); |
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458
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242 } |
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243 |
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2385
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244 bool |
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458
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245 Matrix::operator != (const Matrix& a) const |
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246 { |
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247 return !(*this == a); |
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248 } |
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249 |
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3354
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250 bool |
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251 Matrix::is_symmetric (void) const |
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252 { |
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253 if (is_square () && rows () > 0) |
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254 { |
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5275
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255 for (octave_idx_type i = 0; i < rows (); i++) |
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256 for (octave_idx_type j = i+1; j < cols (); j++) |
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3354
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257 if (elem (i, j) != elem (j, i)) |
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258 return false; |
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259 |
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260 return true; |
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261 } |
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262 |
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263 return false; |
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264 } |
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265 |
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458
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266 Matrix& |
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267 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
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458
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268 { |
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1561
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269 Array2<double>::insert (a, r, c); |
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458
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270 return *this; |
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271 } |
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272 |
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273 Matrix& |
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5275
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274 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
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458
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275 { |
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5275
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276 octave_idx_type a_len = a.length (); |
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4316
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277 |
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1698
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278 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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458
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279 { |
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280 (*current_liboctave_error_handler) ("range error for insert"); |
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281 return *this; |
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282 } |
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283 |
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4316
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284 if (a_len > 0) |
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285 { |
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286 make_unique (); |
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287 |
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5275
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288 for (octave_idx_type i = 0; i < a_len; i++) |
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289 xelem (r, c+i) = a.elem (i); |
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290 } |
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458
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291 |
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292 return *this; |
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293 } |
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294 |
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295 Matrix& |
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296 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
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458
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297 { |
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5275
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298 octave_idx_type a_len = a.length (); |
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299 |
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1698
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300 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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458
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301 { |
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302 (*current_liboctave_error_handler) ("range error for insert"); |
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303 return *this; |
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304 } |
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305 |
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4316
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306 if (a_len > 0) |
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307 { |
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308 make_unique (); |
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309 |
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5275
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310 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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311 xelem (r+i, c) = a.elem (i); |
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312 } |
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458
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313 |
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314 return *this; |
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315 } |
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316 |
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317 Matrix& |
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5275
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318 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
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458
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319 { |
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5275
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320 octave_idx_type a_nr = a.rows (); |
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321 octave_idx_type a_nc = a.cols (); |
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1697
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322 |
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1698
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323 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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458
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324 { |
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325 (*current_liboctave_error_handler) ("range error for insert"); |
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326 return *this; |
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327 } |
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328 |
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1697
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329 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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330 |
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5275
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331 octave_idx_type a_len = a.length (); |
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4316
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332 |
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333 if (a_len > 0) |
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334 { |
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335 make_unique (); |
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336 |
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5275
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337 for (octave_idx_type i = 0; i < a_len; i++) |
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4316
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338 xelem (r+i, c+i) = a.elem (i, i); |
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339 } |
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458
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340 |
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341 return *this; |
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342 } |
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343 |
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344 Matrix& |
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345 Matrix::fill (double val) |
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346 { |
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5275
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347 octave_idx_type nr = rows (); |
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348 octave_idx_type nc = cols (); |
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4316
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349 |
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458
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350 if (nr > 0 && nc > 0) |
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4316
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351 { |
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352 make_unique (); |
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353 |
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5275
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354 for (octave_idx_type j = 0; j < nc; j++) |
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355 for (octave_idx_type i = 0; i < nr; i++) |
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4316
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356 xelem (i, j) = val; |
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357 } |
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458
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358 |
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359 return *this; |
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360 } |
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361 |
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362 Matrix& |
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5275
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363 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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364 { |
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5275
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365 octave_idx_type nr = rows (); |
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366 octave_idx_type nc = cols (); |
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4316
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367 |
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458
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368 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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369 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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370 { |
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371 (*current_liboctave_error_handler) ("range error for fill"); |
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372 return *this; |
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373 } |
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374 |
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5275
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375 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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376 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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458
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377 |
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4316
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378 if (r2 >= r1 && c2 >= c1) |
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379 { |
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380 make_unique (); |
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381 |
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5275
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382 for (octave_idx_type j = c1; j <= c2; j++) |
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383 for (octave_idx_type i = r1; i <= r2; i++) |
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4316
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384 xelem (i, j) = val; |
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385 } |
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458
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386 |
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387 return *this; |
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388 } |
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389 |
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390 Matrix |
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391 Matrix::append (const Matrix& a) const |
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392 { |
|
5275
|
393 octave_idx_type nr = rows (); |
|
|
394 octave_idx_type nc = cols (); |
|
458
|
395 if (nr != a.rows ()) |
|
|
396 { |
|
|
397 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
398 return Matrix (); |
|
|
399 } |
|
|
400 |
|
5275
|
401 octave_idx_type nc_insert = nc; |
|
458
|
402 Matrix retval (nr, nc + a.cols ()); |
|
|
403 retval.insert (*this, 0, 0); |
|
|
404 retval.insert (a, 0, nc_insert); |
|
|
405 return retval; |
|
|
406 } |
|
|
407 |
|
|
408 Matrix |
|
|
409 Matrix::append (const RowVector& a) const |
|
|
410 { |
|
5275
|
411 octave_idx_type nr = rows (); |
|
|
412 octave_idx_type nc = cols (); |
|
458
|
413 if (nr != 1) |
|
|
414 { |
|
|
415 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
416 return Matrix (); |
|
|
417 } |
|
|
418 |
|
5275
|
419 octave_idx_type nc_insert = nc; |
|
458
|
420 Matrix retval (nr, nc + a.length ()); |
|
|
421 retval.insert (*this, 0, 0); |
|
|
422 retval.insert (a, 0, nc_insert); |
|
|
423 return retval; |
|
|
424 } |
|
|
425 |
|
|
426 Matrix |
|
|
427 Matrix::append (const ColumnVector& a) const |
|
|
428 { |
|
5275
|
429 octave_idx_type nr = rows (); |
|
|
430 octave_idx_type nc = cols (); |
|
458
|
431 if (nr != a.length ()) |
|
|
432 { |
|
|
433 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
434 return Matrix (); |
|
|
435 } |
|
|
436 |
|
5275
|
437 octave_idx_type nc_insert = nc; |
|
458
|
438 Matrix retval (nr, nc + 1); |
|
|
439 retval.insert (*this, 0, 0); |
|
|
440 retval.insert (a, 0, nc_insert); |
|
|
441 return retval; |
|
|
442 } |
|
|
443 |
|
|
444 Matrix |
|
|
445 Matrix::append (const DiagMatrix& a) const |
|
|
446 { |
|
5275
|
447 octave_idx_type nr = rows (); |
|
|
448 octave_idx_type nc = cols (); |
|
458
|
449 if (nr != a.rows ()) |
|
|
450 { |
|
|
451 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
452 return *this; |
|
|
453 } |
|
|
454 |
|
5275
|
455 octave_idx_type nc_insert = nc; |
|
458
|
456 Matrix retval (nr, nc + a.cols ()); |
|
|
457 retval.insert (*this, 0, 0); |
|
|
458 retval.insert (a, 0, nc_insert); |
|
|
459 return retval; |
|
|
460 } |
|
|
461 |
|
|
462 Matrix |
|
|
463 Matrix::stack (const Matrix& a) const |
|
|
464 { |
|
5275
|
465 octave_idx_type nr = rows (); |
|
|
466 octave_idx_type nc = cols (); |
|
458
|
467 if (nc != a.cols ()) |
|
|
468 { |
|
|
469 (*current_liboctave_error_handler) |
|
|
470 ("column dimension mismatch for stack"); |
|
|
471 return Matrix (); |
|
|
472 } |
|
|
473 |
|
5275
|
474 octave_idx_type nr_insert = nr; |
|
458
|
475 Matrix retval (nr + a.rows (), nc); |
|
|
476 retval.insert (*this, 0, 0); |
|
|
477 retval.insert (a, nr_insert, 0); |
|
|
478 return retval; |
|
|
479 } |
|
|
480 |
|
|
481 Matrix |
|
|
482 Matrix::stack (const RowVector& a) const |
|
|
483 { |
|
5275
|
484 octave_idx_type nr = rows (); |
|
|
485 octave_idx_type nc = cols (); |
|
458
|
486 if (nc != a.length ()) |
|
|
487 { |
|
|
488 (*current_liboctave_error_handler) |
|
|
489 ("column dimension mismatch for stack"); |
|
|
490 return Matrix (); |
|
|
491 } |
|
|
492 |
|
5275
|
493 octave_idx_type nr_insert = nr; |
|
458
|
494 Matrix retval (nr + 1, nc); |
|
|
495 retval.insert (*this, 0, 0); |
|
|
496 retval.insert (a, nr_insert, 0); |
|
|
497 return retval; |
|
|
498 } |
|
|
499 |
|
|
500 Matrix |
|
|
501 Matrix::stack (const ColumnVector& a) const |
|
|
502 { |
|
5275
|
503 octave_idx_type nr = rows (); |
|
|
504 octave_idx_type nc = cols (); |
|
458
|
505 if (nc != 1) |
|
|
506 { |
|
|
507 (*current_liboctave_error_handler) |
|
|
508 ("column dimension mismatch for stack"); |
|
|
509 return Matrix (); |
|
|
510 } |
|
|
511 |
|
5275
|
512 octave_idx_type nr_insert = nr; |
|
458
|
513 Matrix retval (nr + a.length (), nc); |
|
|
514 retval.insert (*this, 0, 0); |
|
|
515 retval.insert (a, nr_insert, 0); |
|
|
516 return retval; |
|
|
517 } |
|
|
518 |
|
|
519 Matrix |
|
|
520 Matrix::stack (const DiagMatrix& a) const |
|
|
521 { |
|
5275
|
522 octave_idx_type nr = rows (); |
|
|
523 octave_idx_type nc = cols (); |
|
458
|
524 if (nc != a.cols ()) |
|
|
525 { |
|
|
526 (*current_liboctave_error_handler) |
|
|
527 ("column dimension mismatch for stack"); |
|
|
528 return Matrix (); |
|
|
529 } |
|
|
530 |
|
5275
|
531 octave_idx_type nr_insert = nr; |
|
458
|
532 Matrix retval (nr + a.rows (), nc); |
|
|
533 retval.insert (*this, 0, 0); |
|
|
534 retval.insert (a, nr_insert, 0); |
|
|
535 return retval; |
|
|
536 } |
|
|
537 |
|
|
538 Matrix |
|
1205
|
539 real (const ComplexMatrix& a) |
|
|
540 { |
|
5275
|
541 octave_idx_type a_len = a.length (); |
|
1205
|
542 Matrix retval; |
|
|
543 if (a_len > 0) |
|
3769
|
544 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
|
|
545 a.rows (), a.cols ()); |
|
1205
|
546 return retval; |
|
|
547 } |
|
|
548 |
|
|
549 Matrix |
|
|
550 imag (const ComplexMatrix& a) |
|
|
551 { |
|
5275
|
552 octave_idx_type a_len = a.length (); |
|
1205
|
553 Matrix retval; |
|
|
554 if (a_len > 0) |
|
3769
|
555 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
|
|
556 a.rows (), a.cols ()); |
|
1205
|
557 return retval; |
|
|
558 } |
|
|
559 |
|
|
560 Matrix |
|
5275
|
561 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
|
458
|
562 { |
|
5275
|
563 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
|
|
564 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
|
|
565 |
|
|
566 octave_idx_type new_r = r2 - r1 + 1; |
|
|
567 octave_idx_type new_c = c2 - c1 + 1; |
|
458
|
568 |
|
|
569 Matrix result (new_r, new_c); |
|
|
570 |
|
5275
|
571 for (octave_idx_type j = 0; j < new_c; j++) |
|
|
572 for (octave_idx_type i = 0; i < new_r; i++) |
|
4316
|
573 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
574 |
|
|
575 return result; |
|
|
576 } |
|
|
577 |
|
|
578 Matrix |
|
5275
|
579 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
|
4316
|
580 { |
|
|
581 Matrix result (nr, nc); |
|
|
582 |
|
5275
|
583 for (octave_idx_type j = 0; j < nc; j++) |
|
|
584 for (octave_idx_type i = 0; i < nr; i++) |
|
4316
|
585 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
586 |
|
|
587 return result; |
|
|
588 } |
|
|
589 |
|
|
590 // extract row or column i. |
|
|
591 |
|
|
592 RowVector |
|
5275
|
593 Matrix::row (octave_idx_type i) const |
|
458
|
594 { |
|
5275
|
595 octave_idx_type nc = cols (); |
|
458
|
596 if (i < 0 || i >= rows ()) |
|
|
597 { |
|
|
598 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
599 return RowVector (); |
|
|
600 } |
|
|
601 |
|
|
602 RowVector retval (nc); |
|
5275
|
603 for (octave_idx_type j = 0; j < nc; j++) |
|
4316
|
604 retval.xelem (j) = elem (i, j); |
|
458
|
605 |
|
|
606 return retval; |
|
|
607 } |
|
|
608 |
|
|
609 ColumnVector |
|
5275
|
610 Matrix::column (octave_idx_type i) const |
|
458
|
611 { |
|
5275
|
612 octave_idx_type nr = rows (); |
|
458
|
613 if (i < 0 || i >= cols ()) |
|
|
614 { |
|
|
615 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
616 return ColumnVector (); |
|
|
617 } |
|
|
618 |
|
|
619 ColumnVector retval (nr); |
|
5275
|
620 for (octave_idx_type j = 0; j < nr; j++) |
|
4316
|
621 retval.xelem (j) = elem (j, i); |
|
458
|
622 |
|
|
623 return retval; |
|
|
624 } |
|
|
625 |
|
|
626 Matrix |
|
|
627 Matrix::inverse (void) const |
|
|
628 { |
|
5275
|
629 octave_idx_type info; |
|
458
|
630 double rcond; |
|
4329
|
631 return inverse (info, rcond, 0, 0); |
|
458
|
632 } |
|
|
633 |
|
|
634 Matrix |
|
5275
|
635 Matrix::inverse (octave_idx_type& info) const |
|
458
|
636 { |
|
|
637 double rcond; |
|
4329
|
638 return inverse (info, rcond, 0, 0); |
|
458
|
639 } |
|
|
640 |
|
|
641 Matrix |
|
5275
|
642 Matrix::inverse (octave_idx_type& info, double& rcond, int force, int calc_cond) const |
|
458
|
643 { |
|
1948
|
644 Matrix retval; |
|
|
645 |
|
5275
|
646 octave_idx_type nr = rows (); |
|
|
647 octave_idx_type nc = cols (); |
|
1948
|
648 |
|
458
|
649 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
650 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
651 else |
|
|
652 { |
|
5275
|
653 Array<octave_idx_type> ipvt (nr); |
|
|
654 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
655 |
|
|
656 retval = *this; |
|
|
657 double *tmp_data = retval.fortran_vec (); |
|
|
658 |
|
4329
|
659 Array<double> z(1); |
|
5275
|
660 octave_idx_type lwork = -1; |
|
4329
|
661 |
|
4330
|
662 // Query the optimum work array size. |
|
4329
|
663 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
664 z.fortran_vec (), lwork, info)); |
|
|
665 |
|
|
666 if (f77_exception_encountered) |
|
|
667 { |
|
|
668 (*current_liboctave_error_handler) |
|
|
669 ("unrecoverable error in dgetri"); |
|
|
670 return retval; |
|
|
671 } |
|
|
672 |
|
5275
|
673 lwork = static_cast<octave_idx_type> (z(0)); |
|
4329
|
674 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
675 z.resize (lwork); |
|
|
676 double *pz = z.fortran_vec (); |
|
|
677 |
|
|
678 info = 0; |
|
|
679 |
|
4330
|
680 // Calculate the norm of the matrix, for later use. |
|
4329
|
681 double anorm = 0; |
|
|
682 if (calc_cond) |
|
5275
|
683 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
684 |
|
|
685 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
686 |
|
|
687 if (f77_exception_encountered) |
|
4329
|
688 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
689 else |
|
|
690 { |
|
4330
|
691 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
692 rcond = 0.0; |
|
|
693 if (info != 0) |
|
1948
|
694 info = -1; |
|
4329
|
695 else if (calc_cond) |
|
|
696 { |
|
5275
|
697 octave_idx_type dgecon_info = 0; |
|
5061
|
698 |
|
4330
|
699 // Now calculate the condition number for non-singular matrix. |
|
4329
|
700 char job = '1'; |
|
5275
|
701 Array<octave_idx_type> iz (nc); |
|
|
702 octave_idx_type *piz = iz.fortran_vec (); |
|
4552
|
703 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
704 nc, tmp_data, nr, anorm, |
|
5061
|
705 rcond, pz, piz, dgecon_info |
|
4552
|
706 F77_CHAR_ARG_LEN (1))); |
|
4329
|
707 |
|
|
708 if (f77_exception_encountered) |
|
|
709 (*current_liboctave_error_handler) |
|
|
710 ("unrecoverable error in dgecon"); |
|
|
711 |
|
5061
|
712 if (dgecon_info != 0) |
|
4329
|
713 info = -1; |
|
|
714 } |
|
1948
|
715 |
|
|
716 if (info == -1 && ! force) |
|
|
717 retval = *this; // Restore matrix contents. |
|
|
718 else |
|
|
719 { |
|
5275
|
720 octave_idx_type dgetri_info = 0; |
|
5061
|
721 |
|
4329
|
722 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
5061
|
723 pz, lwork, dgetri_info)); |
|
1948
|
724 |
|
|
725 if (f77_exception_encountered) |
|
|
726 (*current_liboctave_error_handler) |
|
4329
|
727 ("unrecoverable error in dgetri"); |
|
|
728 |
|
5061
|
729 if (dgetri_info != 0) |
|
4329
|
730 info = -1; |
|
1948
|
731 } |
|
|
732 } |
|
458
|
733 } |
|
|
734 |
|
1948
|
735 return retval; |
|
458
|
736 } |
|
|
737 |
|
740
|
738 Matrix |
|
4384
|
739 Matrix::pseudo_inverse (double tol) const |
|
740
|
740 { |
|
3480
|
741 SVD result (*this, SVD::economy); |
|
740
|
742 |
|
|
743 DiagMatrix S = result.singular_values (); |
|
|
744 Matrix U = result.left_singular_matrix (); |
|
|
745 Matrix V = result.right_singular_matrix (); |
|
|
746 |
|
|
747 ColumnVector sigma = S.diag (); |
|
|
748 |
|
5275
|
749 octave_idx_type r = sigma.length () - 1; |
|
|
750 octave_idx_type nr = rows (); |
|
|
751 octave_idx_type nc = cols (); |
|
740
|
752 |
|
|
753 if (tol <= 0.0) |
|
|
754 { |
|
|
755 if (nr > nc) |
|
|
756 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
757 else |
|
|
758 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
759 } |
|
|
760 |
|
|
761 while (r >= 0 && sigma.elem (r) < tol) |
|
|
762 r--; |
|
|
763 |
|
|
764 if (r < 0) |
|
|
765 return Matrix (nc, nr, 0.0); |
|
|
766 else |
|
|
767 { |
|
|
768 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
769 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
770 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
771 return Vr * D * Ur.transpose (); |
|
|
772 } |
|
|
773 } |
|
|
774 |
|
4773
|
775 #if defined (HAVE_FFTW3) |
|
3827
|
776 |
|
|
777 ComplexMatrix |
|
|
778 Matrix::fourier (void) const |
|
|
779 { |
|
|
780 size_t nr = rows (); |
|
|
781 size_t nc = cols (); |
|
|
782 |
|
|
783 ComplexMatrix retval (nr, nc); |
|
|
784 |
|
|
785 size_t npts, nsamples; |
|
|
786 |
|
|
787 if (nr == 1 || nc == 1) |
|
|
788 { |
|
|
789 npts = nr > nc ? nr : nc; |
|
|
790 nsamples = 1; |
|
|
791 } |
|
|
792 else |
|
|
793 { |
|
|
794 npts = nr; |
|
|
795 nsamples = nc; |
|
|
796 } |
|
|
797 |
|
4773
|
798 const double *in (fortran_vec ()); |
|
3827
|
799 Complex *out (retval.fortran_vec ()); |
|
|
800 |
|
4773
|
801 octave_fftw::fft (in, out, npts, nsamples); |
|
3827
|
802 |
|
|
803 return retval; |
|
|
804 } |
|
|
805 |
|
|
806 ComplexMatrix |
|
|
807 Matrix::ifourier (void) const |
|
|
808 { |
|
|
809 size_t nr = rows (); |
|
|
810 size_t nc = cols (); |
|
|
811 |
|
|
812 ComplexMatrix retval (nr, nc); |
|
|
813 |
|
|
814 size_t npts, nsamples; |
|
|
815 |
|
|
816 if (nr == 1 || nc == 1) |
|
|
817 { |
|
|
818 npts = nr > nc ? nr : nc; |
|
|
819 nsamples = 1; |
|
|
820 } |
|
|
821 else |
|
|
822 { |
|
|
823 npts = nr; |
|
|
824 nsamples = nc; |
|
|
825 } |
|
|
826 |
|
|
827 ComplexMatrix tmp (*this); |
|
|
828 Complex *in (tmp.fortran_vec ()); |
|
|
829 Complex *out (retval.fortran_vec ()); |
|
|
830 |
|
4773
|
831 octave_fftw::ifft (in, out, npts, nsamples); |
|
3827
|
832 |
|
|
833 return retval; |
|
|
834 } |
|
|
835 |
|
|
836 ComplexMatrix |
|
|
837 Matrix::fourier2d (void) const |
|
|
838 { |
|
4773
|
839 dim_vector dv(rows (), cols ()); |
|
|
840 |
|
|
841 const double *in = fortran_vec (); |
|
|
842 ComplexMatrix retval (rows (), cols ()); |
|
|
843 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); |
|
3827
|
844 |
|
|
845 return retval; |
|
|
846 } |
|
|
847 |
|
|
848 ComplexMatrix |
|
|
849 Matrix::ifourier2d (void) const |
|
|
850 { |
|
4773
|
851 dim_vector dv(rows (), cols ()); |
|
3827
|
852 |
|
|
853 ComplexMatrix retval (*this); |
|
4773
|
854 Complex *out (retval.fortran_vec ()); |
|
|
855 |
|
|
856 octave_fftw::ifftNd (out, out, 2, dv); |
|
3827
|
857 |
|
|
858 return retval; |
|
|
859 } |
|
|
860 |
|
|
861 #else |
|
|
862 |
|
458
|
863 ComplexMatrix |
|
|
864 Matrix::fourier (void) const |
|
|
865 { |
|
1948
|
866 ComplexMatrix retval; |
|
|
867 |
|
5275
|
868 octave_idx_type nr = rows (); |
|
|
869 octave_idx_type nc = cols (); |
|
|
870 |
|
|
871 octave_idx_type npts, nsamples; |
|
1948
|
872 |
|
458
|
873 if (nr == 1 || nc == 1) |
|
|
874 { |
|
|
875 npts = nr > nc ? nr : nc; |
|
|
876 nsamples = 1; |
|
|
877 } |
|
|
878 else |
|
|
879 { |
|
|
880 npts = nr; |
|
|
881 nsamples = nc; |
|
|
882 } |
|
|
883 |
|
5275
|
884 octave_idx_type nn = 4*npts+15; |
|
1948
|
885 |
|
|
886 Array<Complex> wsave (nn); |
|
|
887 Complex *pwsave = wsave.fortran_vec (); |
|
|
888 |
|
3585
|
889 retval = ComplexMatrix (*this); |
|
1948
|
890 Complex *tmp_data = retval.fortran_vec (); |
|
|
891 |
|
3887
|
892 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
893 |
|
5275
|
894 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
895 { |
|
|
896 OCTAVE_QUIT; |
|
|
897 |
|
|
898 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
899 } |
|
1948
|
900 |
|
|
901 return retval; |
|
458
|
902 } |
|
|
903 |
|
|
904 ComplexMatrix |
|
|
905 Matrix::ifourier (void) const |
|
|
906 { |
|
1948
|
907 ComplexMatrix retval; |
|
|
908 |
|
5275
|
909 octave_idx_type nr = rows (); |
|
|
910 octave_idx_type nc = cols (); |
|
|
911 |
|
|
912 octave_idx_type npts, nsamples; |
|
1948
|
913 |
|
458
|
914 if (nr == 1 || nc == 1) |
|
|
915 { |
|
|
916 npts = nr > nc ? nr : nc; |
|
|
917 nsamples = 1; |
|
|
918 } |
|
|
919 else |
|
|
920 { |
|
|
921 npts = nr; |
|
|
922 nsamples = nc; |
|
|
923 } |
|
|
924 |
|
5275
|
925 octave_idx_type nn = 4*npts+15; |
|
1948
|
926 |
|
|
927 Array<Complex> wsave (nn); |
|
|
928 Complex *pwsave = wsave.fortran_vec (); |
|
|
929 |
|
3585
|
930 retval = ComplexMatrix (*this); |
|
1948
|
931 Complex *tmp_data = retval.fortran_vec (); |
|
|
932 |
|
3887
|
933 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
934 |
|
5275
|
935 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
936 { |
|
|
937 OCTAVE_QUIT; |
|
|
938 |
|
|
939 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
940 } |
|
458
|
941 |
|
5275
|
942 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
943 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
944 |
|
1948
|
945 return retval; |
|
458
|
946 } |
|
|
947 |
|
677
|
948 ComplexMatrix |
|
|
949 Matrix::fourier2d (void) const |
|
|
950 { |
|
1948
|
951 ComplexMatrix retval; |
|
|
952 |
|
5275
|
953 octave_idx_type nr = rows (); |
|
|
954 octave_idx_type nc = cols (); |
|
|
955 |
|
|
956 octave_idx_type npts, nsamples; |
|
1948
|
957 |
|
677
|
958 if (nr == 1 || nc == 1) |
|
|
959 { |
|
|
960 npts = nr > nc ? nr : nc; |
|
|
961 nsamples = 1; |
|
|
962 } |
|
|
963 else |
|
|
964 { |
|
|
965 npts = nr; |
|
|
966 nsamples = nc; |
|
|
967 } |
|
|
968 |
|
5275
|
969 octave_idx_type nn = 4*npts+15; |
|
1948
|
970 |
|
|
971 Array<Complex> wsave (nn); |
|
|
972 Complex *pwsave = wsave.fortran_vec (); |
|
|
973 |
|
3585
|
974 retval = ComplexMatrix (*this); |
|
1948
|
975 Complex *tmp_data = retval.fortran_vec (); |
|
|
976 |
|
3887
|
977 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
978 |
|
5275
|
979 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
980 { |
|
|
981 OCTAVE_QUIT; |
|
|
982 |
|
|
983 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
984 } |
|
677
|
985 |
|
|
986 npts = nc; |
|
|
987 nsamples = nr; |
|
|
988 nn = 4*npts+15; |
|
1948
|
989 |
|
|
990 wsave.resize (nn); |
|
|
991 pwsave = wsave.fortran_vec (); |
|
|
992 |
|
4773
|
993 Array<Complex> tmp (npts); |
|
|
994 Complex *prow = tmp.fortran_vec (); |
|
1948
|
995 |
|
3887
|
996 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
997 |
|
5275
|
998 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
999 { |
|
4153
|
1000 OCTAVE_QUIT; |
|
|
1001 |
|
5275
|
1002 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1003 prow[i] = tmp_data[i*nr + j]; |
|
|
1004 |
|
3887
|
1005 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
1006 |
|
5275
|
1007 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1008 tmp_data[i*nr + j] = prow[i]; |
|
677
|
1009 } |
|
|
1010 |
|
1948
|
1011 return retval; |
|
677
|
1012 } |
|
|
1013 |
|
|
1014 ComplexMatrix |
|
|
1015 Matrix::ifourier2d (void) const |
|
|
1016 { |
|
1948
|
1017 ComplexMatrix retval; |
|
|
1018 |
|
5275
|
1019 octave_idx_type nr = rows (); |
|
|
1020 octave_idx_type nc = cols (); |
|
|
1021 |
|
|
1022 octave_idx_type npts, nsamples; |
|
1948
|
1023 |
|
677
|
1024 if (nr == 1 || nc == 1) |
|
|
1025 { |
|
|
1026 npts = nr > nc ? nr : nc; |
|
|
1027 nsamples = 1; |
|
|
1028 } |
|
|
1029 else |
|
|
1030 { |
|
|
1031 npts = nr; |
|
|
1032 nsamples = nc; |
|
|
1033 } |
|
|
1034 |
|
5275
|
1035 octave_idx_type nn = 4*npts+15; |
|
1948
|
1036 |
|
|
1037 Array<Complex> wsave (nn); |
|
|
1038 Complex *pwsave = wsave.fortran_vec (); |
|
|
1039 |
|
3585
|
1040 retval = ComplexMatrix (*this); |
|
1948
|
1041 Complex *tmp_data = retval.fortran_vec (); |
|
|
1042 |
|
3887
|
1043 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1044 |
|
5275
|
1045 for (octave_idx_type j = 0; j < nsamples; j++) |
|
4153
|
1046 { |
|
|
1047 OCTAVE_QUIT; |
|
|
1048 |
|
|
1049 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1050 } |
|
677
|
1051 |
|
5275
|
1052 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
|
3572
|
1053 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1054 |
|
|
1055 npts = nc; |
|
|
1056 nsamples = nr; |
|
|
1057 nn = 4*npts+15; |
|
1948
|
1058 |
|
|
1059 wsave.resize (nn); |
|
|
1060 pwsave = wsave.fortran_vec (); |
|
|
1061 |
|
4773
|
1062 Array<Complex> tmp (npts); |
|
|
1063 Complex *prow = tmp.fortran_vec (); |
|
1948
|
1064 |
|
3887
|
1065 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1066 |
|
5275
|
1067 for (octave_idx_type j = 0; j < nsamples; j++) |
|
677
|
1068 { |
|
4153
|
1069 OCTAVE_QUIT; |
|
|
1070 |
|
5275
|
1071 for (octave_idx_type i = 0; i < npts; i++) |
|
1948
|
1072 prow[i] = tmp_data[i*nr + j]; |
|
|
1073 |
|
3887
|
1074 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1075 |
|
5275
|
1076 for (octave_idx_type i = 0; i < npts; i++) |
|
3572
|
1077 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1078 } |
|
|
1079 |
|
1948
|
1080 return retval; |
|
677
|
1081 } |
|
|
1082 |
|
3827
|
1083 #endif |
|
|
1084 |
|
458
|
1085 DET |
|
|
1086 Matrix::determinant (void) const |
|
|
1087 { |
|
5275
|
1088 octave_idx_type info; |
|
458
|
1089 double rcond; |
|
4329
|
1090 return determinant (info, rcond, 0); |
|
458
|
1091 } |
|
|
1092 |
|
|
1093 DET |
|
5275
|
1094 Matrix::determinant (octave_idx_type& info) const |
|
458
|
1095 { |
|
|
1096 double rcond; |
|
4329
|
1097 return determinant (info, rcond, 0); |
|
458
|
1098 } |
|
|
1099 |
|
|
1100 DET |
|
5275
|
1101 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
|
458
|
1102 { |
|
|
1103 DET retval; |
|
|
1104 |
|
5275
|
1105 octave_idx_type nr = rows (); |
|
|
1106 octave_idx_type nc = cols (); |
|
458
|
1107 |
|
|
1108 if (nr == 0 || nc == 0) |
|
|
1109 { |
|
5634
|
1110 retval = DET (1.0, 0); |
|
458
|
1111 } |
|
|
1112 else |
|
|
1113 { |
|
5275
|
1114 Array<octave_idx_type> ipvt (nr); |
|
|
1115 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
1948
|
1116 |
|
|
1117 Matrix atmp = *this; |
|
|
1118 double *tmp_data = atmp.fortran_vec (); |
|
|
1119 |
|
4329
|
1120 info = 0; |
|
|
1121 |
|
4330
|
1122 // Calculate the norm of the matrix, for later use. |
|
4329
|
1123 double anorm = 0; |
|
|
1124 if (calc_cond) |
|
5275
|
1125 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
4329
|
1126 |
|
|
1127 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1128 |
|
|
1129 if (f77_exception_encountered) |
|
4329
|
1130 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
458
|
1131 else |
|
|
1132 { |
|
4330
|
1133 // Throw-away extra info LAPACK gives so as to not change output. |
|
4509
|
1134 rcond = 0.0; |
|
|
1135 if (info != 0) |
|
1948
|
1136 { |
|
4509
|
1137 info = -1; |
|
|
1138 retval = DET (); |
|
4329
|
1139 } |
|
|
1140 else |
|
1948
|
1141 { |
|
4329
|
1142 if (calc_cond) |
|
|
1143 { |
|
4330
|
1144 // Now calc the condition number for non-singular matrix. |
|
4329
|
1145 char job = '1'; |
|
|
1146 Array<double> z (4 * nc); |
|
|
1147 double *pz = z.fortran_vec (); |
|
5275
|
1148 Array<octave_idx_type> iz (nc); |
|
|
1149 octave_idx_type *piz = iz.fortran_vec (); |
|
4329
|
1150 |
|
4552
|
1151 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1152 nc, tmp_data, nr, anorm, |
|
|
1153 rcond, pz, piz, info |
|
|
1154 F77_CHAR_ARG_LEN (1))); |
|
4329
|
1155 |
|
|
1156 if (f77_exception_encountered) |
|
|
1157 (*current_liboctave_error_handler) |
|
|
1158 ("unrecoverable error in dgecon"); |
|
|
1159 } |
|
|
1160 |
|
4509
|
1161 if (info != 0) |
|
4329
|
1162 { |
|
|
1163 info = -1; |
|
|
1164 retval = DET (); |
|
|
1165 } |
|
|
1166 else |
|
|
1167 { |
|
5634
|
1168 double c = 1.0; |
|
|
1169 int e = 0; |
|
|
1170 |
|
|
1171 for (octave_idx_type i = 0; i < nc; i++) |
|
4329
|
1172 { |
|
5634
|
1173 if (ipvt(i) != (i+1)) |
|
|
1174 c = -c; |
|
|
1175 |
|
|
1176 c *= atmp(i,i); |
|
|
1177 |
|
|
1178 if (c == 0.0) |
|
|
1179 break; |
|
|
1180 |
|
|
1181 while (fabs (c) < 0.5) |
|
4329
|
1182 { |
|
5634
|
1183 c *= 2.0; |
|
|
1184 e--; |
|
4329
|
1185 } |
|
5634
|
1186 |
|
|
1187 while (fabs (c) >= 2.0) |
|
4329
|
1188 { |
|
5634
|
1189 c /= 2.0; |
|
|
1190 e++; |
|
4329
|
1191 } |
|
|
1192 } |
|
5634
|
1193 |
|
|
1194 retval = DET (c, e); |
|
4329
|
1195 } |
|
1948
|
1196 } |
|
458
|
1197 } |
|
|
1198 } |
|
|
1199 |
|
|
1200 return retval; |
|
|
1201 } |
|
|
1202 |
|
|
1203 Matrix |
|
5785
|
1204 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1205 double& rcond, solve_singularity_handler sing_handler, |
|
|
1206 bool calc_cond) const |
|
|
1207 { |
|
|
1208 Matrix retval; |
|
|
1209 |
|
|
1210 octave_idx_type nr = rows (); |
|
|
1211 octave_idx_type nc = cols (); |
|
|
1212 |
|
|
1213 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1214 (*current_liboctave_error_handler) |
|
|
1215 ("matrix dimension mismatch solution of linear equations"); |
|
|
1216 else |
|
|
1217 { |
|
|
1218 volatile int typ = mattype.type (); |
|
|
1219 |
|
|
1220 if (typ == MatrixType::Permuted_Upper || |
|
|
1221 typ == MatrixType::Upper) |
|
|
1222 { |
|
|
1223 octave_idx_type b_nc = b.cols (); |
|
|
1224 rcond = 1.; |
|
|
1225 info = 0; |
|
|
1226 |
|
|
1227 if (typ == MatrixType::Permuted_Upper) |
|
|
1228 { |
|
|
1229 (*current_liboctave_error_handler) |
|
|
1230 ("Permuted triangular matrix not implemented"); |
|
|
1231 } |
|
|
1232 else |
|
|
1233 { |
|
|
1234 const double *tmp_data = fortran_vec (); |
|
|
1235 |
|
|
1236 if (calc_cond) |
|
|
1237 { |
|
|
1238 char norm = '1'; |
|
|
1239 char uplo = 'U'; |
|
|
1240 char dia = 'N'; |
|
|
1241 |
|
|
1242 Array<double> z (3 * nc); |
|
|
1243 double *pz = z.fortran_vec (); |
|
|
1244 Array<octave_idx_type> iz (nc); |
|
|
1245 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1246 |
|
|
1247 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1248 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1249 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1250 nr, tmp_data, nr, rcond, |
|
|
1251 pz, piz, info |
|
|
1252 F77_CHAR_ARG_LEN (1) |
|
|
1253 F77_CHAR_ARG_LEN (1) |
|
|
1254 F77_CHAR_ARG_LEN (1))); |
|
|
1255 |
|
|
1256 if (f77_exception_encountered) |
|
|
1257 (*current_liboctave_error_handler) |
|
|
1258 ("unrecoverable error in dtrcon"); |
|
|
1259 |
|
|
1260 if (info != 0) |
|
|
1261 info = -2; |
|
|
1262 |
|
|
1263 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1264 |
|
|
1265 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1266 { |
|
|
1267 info = -2; |
|
|
1268 |
|
|
1269 if (sing_handler) |
|
|
1270 sing_handler (rcond); |
|
|
1271 else |
|
|
1272 (*current_liboctave_error_handler) |
|
|
1273 ("matrix singular to machine precision, rcond = %g", |
|
|
1274 rcond); |
|
|
1275 } |
|
|
1276 } |
|
|
1277 |
|
|
1278 if (info == 0) |
|
|
1279 { |
|
|
1280 retval = b; |
|
|
1281 double *result = retval.fortran_vec (); |
|
|
1282 |
|
|
1283 char uplo = 'U'; |
|
|
1284 char trans = 'N'; |
|
|
1285 char dia = 'N'; |
|
|
1286 |
|
|
1287 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1288 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1289 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1290 nr, b_nc, tmp_data, nr, |
|
|
1291 result, nr, info |
|
|
1292 F77_CHAR_ARG_LEN (1) |
|
|
1293 F77_CHAR_ARG_LEN (1) |
|
|
1294 F77_CHAR_ARG_LEN (1))); |
|
|
1295 |
|
|
1296 if (f77_exception_encountered) |
|
|
1297 (*current_liboctave_error_handler) |
|
|
1298 ("unrecoverable error in dtrtrs"); |
|
|
1299 } |
|
|
1300 } |
|
|
1301 } |
|
|
1302 else |
|
|
1303 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1304 } |
|
|
1305 |
|
|
1306 return retval; |
|
|
1307 } |
|
|
1308 |
|
|
1309 Matrix |
|
|
1310 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1311 double& rcond, solve_singularity_handler sing_handler, |
|
|
1312 bool calc_cond) const |
|
|
1313 { |
|
|
1314 Matrix retval; |
|
|
1315 |
|
|
1316 octave_idx_type nr = rows (); |
|
|
1317 octave_idx_type nc = cols (); |
|
|
1318 |
|
|
1319 if (nr == 0 || nc == 0 || nr != b.rows ()) |
|
|
1320 (*current_liboctave_error_handler) |
|
|
1321 ("matrix dimension mismatch solution of linear equations"); |
|
|
1322 else |
|
|
1323 { |
|
|
1324 volatile int typ = mattype.type (); |
|
|
1325 |
|
|
1326 if (typ == MatrixType::Permuted_Lower || |
|
|
1327 typ == MatrixType::Lower) |
|
|
1328 { |
|
|
1329 octave_idx_type b_nc = b.cols (); |
|
|
1330 rcond = 1.; |
|
|
1331 info = 0; |
|
|
1332 |
|
|
1333 if (typ == MatrixType::Permuted_Lower) |
|
|
1334 { |
|
|
1335 (*current_liboctave_error_handler) |
|
|
1336 ("Permuted triangular matrix not implemented"); |
|
|
1337 } |
|
|
1338 else |
|
|
1339 { |
|
|
1340 const double *tmp_data = fortran_vec (); |
|
|
1341 |
|
|
1342 if (calc_cond) |
|
|
1343 { |
|
|
1344 char norm = '1'; |
|
|
1345 char uplo = 'L'; |
|
|
1346 char dia = 'N'; |
|
|
1347 |
|
|
1348 Array<double> z (3 * nc); |
|
|
1349 double *pz = z.fortran_vec (); |
|
|
1350 Array<octave_idx_type> iz (nc); |
|
|
1351 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1352 |
|
|
1353 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), |
|
|
1354 F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1355 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1356 nr, tmp_data, nr, rcond, |
|
|
1357 pz, piz, info |
|
|
1358 F77_CHAR_ARG_LEN (1) |
|
|
1359 F77_CHAR_ARG_LEN (1) |
|
|
1360 F77_CHAR_ARG_LEN (1))); |
|
|
1361 |
|
|
1362 if (f77_exception_encountered) |
|
|
1363 (*current_liboctave_error_handler) |
|
|
1364 ("unrecoverable error in dtrcon"); |
|
|
1365 |
|
|
1366 if (info != 0) |
|
|
1367 info = -2; |
|
|
1368 |
|
|
1369 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1370 |
|
|
1371 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1372 { |
|
|
1373 info = -2; |
|
|
1374 |
|
|
1375 if (sing_handler) |
|
|
1376 sing_handler (rcond); |
|
|
1377 else |
|
|
1378 (*current_liboctave_error_handler) |
|
|
1379 ("matrix singular to machine precision, rcond = %g", |
|
|
1380 rcond); |
|
|
1381 } |
|
|
1382 } |
|
|
1383 |
|
|
1384 if (info == 0) |
|
|
1385 { |
|
|
1386 retval = b; |
|
|
1387 double *result = retval.fortran_vec (); |
|
|
1388 |
|
|
1389 char uplo = 'L'; |
|
|
1390 char trans = 'N'; |
|
|
1391 char dia = 'N'; |
|
|
1392 |
|
|
1393 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), |
|
|
1394 F77_CONST_CHAR_ARG2 (&trans, 1), |
|
|
1395 F77_CONST_CHAR_ARG2 (&dia, 1), |
|
|
1396 nr, b_nc, tmp_data, nr, |
|
|
1397 result, nr, info |
|
|
1398 F77_CHAR_ARG_LEN (1) |
|
|
1399 F77_CHAR_ARG_LEN (1) |
|
|
1400 F77_CHAR_ARG_LEN (1))); |
|
|
1401 |
|
|
1402 if (f77_exception_encountered) |
|
|
1403 (*current_liboctave_error_handler) |
|
|
1404 ("unrecoverable error in dtrtrs"); |
|
|
1405 } |
|
|
1406 } |
|
|
1407 } |
|
|
1408 else |
|
|
1409 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1410 } |
|
|
1411 |
|
|
1412 return retval; |
|
|
1413 } |
|
|
1414 |
|
|
1415 Matrix |
|
|
1416 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1417 double& rcond, solve_singularity_handler sing_handler, |
|
|
1418 bool calc_cond) const |
|
|
1419 { |
|
|
1420 Matrix retval; |
|
|
1421 |
|
|
1422 octave_idx_type nr = rows (); |
|
|
1423 octave_idx_type nc = cols (); |
|
|
1424 |
|
|
1425 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
1426 (*current_liboctave_error_handler) |
|
|
1427 ("matrix dimension mismatch solution of linear equations"); |
|
|
1428 else |
|
|
1429 { |
|
|
1430 volatile int typ = mattype.type (); |
|
|
1431 |
|
|
1432 // Calculate the norm of the matrix, for later use. |
|
|
1433 double anorm = -1.; |
|
|
1434 |
|
|
1435 if (typ == MatrixType::Hermitian) |
|
|
1436 { |
|
|
1437 info = 0; |
|
|
1438 char job = 'L'; |
|
|
1439 Matrix atmp = *this; |
|
|
1440 double *tmp_data = atmp.fortran_vec (); |
|
|
1441 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1442 |
|
|
1443 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
|
1444 tmp_data, nr, info |
|
|
1445 F77_CHAR_ARG_LEN (1))); |
|
|
1446 |
|
|
1447 if (f77_exception_encountered) |
|
|
1448 (*current_liboctave_error_handler) |
|
|
1449 ("unrecoverable error in dpotrf"); |
|
|
1450 else |
|
|
1451 { |
|
|
1452 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1453 rcond = 0.0; |
|
|
1454 if (info != 0) |
|
|
1455 { |
|
|
1456 info = -2; |
|
|
1457 |
|
|
1458 mattype.mark_as_unsymmetric (); |
|
|
1459 typ = MatrixType::Full; |
|
|
1460 } |
|
|
1461 else |
|
|
1462 { |
|
|
1463 if (calc_cond) |
|
|
1464 { |
|
|
1465 Array<double> z (3 * nc); |
|
|
1466 double *pz = z.fortran_vec (); |
|
|
1467 Array<octave_idx_type> iz (nc); |
|
|
1468 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1469 |
|
|
1470 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1471 nr, tmp_data, nr, anorm, |
|
|
1472 rcond, pz, piz, info |
|
|
1473 F77_CHAR_ARG_LEN (1))); |
|
|
1474 |
|
|
1475 if (f77_exception_encountered) |
|
|
1476 (*current_liboctave_error_handler) |
|
|
1477 ("unrecoverable error in dpocon"); |
|
|
1478 |
|
|
1479 if (info != 0) |
|
|
1480 info = -2; |
|
|
1481 |
|
|
1482 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1483 |
|
|
1484 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1485 { |
|
|
1486 info = -2; |
|
|
1487 |
|
|
1488 if (sing_handler) |
|
|
1489 sing_handler (rcond); |
|
|
1490 else |
|
|
1491 (*current_liboctave_error_handler) |
|
|
1492 ("matrix singular to machine precision, rcond = %g", |
|
|
1493 rcond); |
|
|
1494 } |
|
|
1495 } |
|
|
1496 |
|
|
1497 if (info == 0) |
|
|
1498 { |
|
|
1499 retval = b; |
|
|
1500 double *result = retval.fortran_vec (); |
|
|
1501 |
|
|
1502 octave_idx_type b_nc = b.cols (); |
|
|
1503 |
|
|
1504 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1505 nr, b_nc, tmp_data, nr, |
|
|
1506 result, b.rows(), info |
|
|
1507 F77_CHAR_ARG_LEN (1))); |
|
|
1508 |
|
|
1509 if (f77_exception_encountered) |
|
|
1510 (*current_liboctave_error_handler) |
|
|
1511 ("unrecoverable error in dpotrs"); |
|
|
1512 } |
|
|
1513 else |
|
|
1514 { |
|
|
1515 mattype.mark_as_unsymmetric (); |
|
|
1516 typ = MatrixType::Full; |
|
|
1517 } |
|
|
1518 } |
|
|
1519 } |
|
|
1520 } |
|
|
1521 |
|
|
1522 if (typ == MatrixType::Full) |
|
|
1523 { |
|
|
1524 info = 0; |
|
|
1525 |
|
|
1526 Array<octave_idx_type> ipvt (nr); |
|
|
1527 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
|
1528 |
|
|
1529 Matrix atmp = *this; |
|
|
1530 double *tmp_data = atmp.fortran_vec (); |
|
|
1531 if(anorm < 0.) |
|
|
1532 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
|
|
1533 |
|
|
1534 Array<double> z (4 * nc); |
|
|
1535 double *pz = z.fortran_vec (); |
|
|
1536 Array<octave_idx_type> iz (nc); |
|
|
1537 octave_idx_type *piz = iz.fortran_vec (); |
|
|
1538 |
|
|
1539 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
|
1540 |
|
|
1541 if (f77_exception_encountered) |
|
|
1542 (*current_liboctave_error_handler) |
|
|
1543 ("unrecoverable error in dgetrf"); |
|
|
1544 else |
|
|
1545 { |
|
|
1546 // Throw-away extra info LAPACK gives so as to not change output. |
|
|
1547 rcond = 0.0; |
|
|
1548 if (info != 0) |
|
|
1549 { |
|
|
1550 info = -2; |
|
|
1551 |
|
|
1552 if (sing_handler) |
|
|
1553 sing_handler (rcond); |
|
|
1554 else |
|
|
1555 (*current_liboctave_error_handler) |
|
|
1556 ("matrix singular to machine precision"); |
|
|
1557 |
|
|
1558 mattype.mark_as_rectangular (); |
|
|
1559 } |
|
|
1560 else |
|
|
1561 { |
|
|
1562 if (calc_cond) |
|
|
1563 { |
|
|
1564 // Now calculate the condition number for |
|
|
1565 // non-singular matrix. |
|
|
1566 char job = '1'; |
|
|
1567 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1568 nc, tmp_data, nr, anorm, |
|
|
1569 rcond, pz, piz, info |
|
|
1570 F77_CHAR_ARG_LEN (1))); |
|
|
1571 |
|
|
1572 if (f77_exception_encountered) |
|
|
1573 (*current_liboctave_error_handler) |
|
|
1574 ("unrecoverable error in dgecon"); |
|
|
1575 |
|
|
1576 if (info != 0) |
|
|
1577 info = -2; |
|
|
1578 |
|
|
1579 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1580 |
|
|
1581 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1582 { |
|
|
1583 info = -2; |
|
|
1584 |
|
|
1585 if (sing_handler) |
|
|
1586 sing_handler (rcond); |
|
|
1587 else |
|
|
1588 (*current_liboctave_error_handler) |
|
|
1589 ("matrix singular to machine precision, rcond = %g", |
|
|
1590 rcond); |
|
|
1591 } |
|
|
1592 } |
|
|
1593 |
|
|
1594 if (info == 0) |
|
|
1595 { |
|
|
1596 retval = b; |
|
|
1597 double *result = retval.fortran_vec (); |
|
|
1598 |
|
|
1599 octave_idx_type b_nc = b.cols (); |
|
|
1600 |
|
|
1601 char job = 'N'; |
|
|
1602 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
1603 nr, b_nc, tmp_data, nr, |
|
|
1604 pipvt, result, b.rows(), info |
|
|
1605 F77_CHAR_ARG_LEN (1))); |
|
|
1606 |
|
|
1607 if (f77_exception_encountered) |
|
|
1608 (*current_liboctave_error_handler) |
|
|
1609 ("unrecoverable error in dgetrs"); |
|
|
1610 } |
|
|
1611 else |
|
|
1612 mattype.mark_as_rectangular (); |
|
|
1613 } |
|
|
1614 } |
|
|
1615 } |
|
|
1616 else if (typ != MatrixType::Hermitian) |
|
|
1617 (*current_liboctave_error_handler) ("incorrect matrix type"); |
|
|
1618 } |
|
|
1619 |
|
|
1620 return retval; |
|
|
1621 } |
|
|
1622 |
|
|
1623 Matrix |
|
|
1624 Matrix::solve (MatrixType &typ, const Matrix& b) const |
|
|
1625 { |
|
|
1626 octave_idx_type info; |
|
|
1627 double rcond; |
|
|
1628 return solve (typ, b, info, rcond, 0); |
|
|
1629 } |
|
|
1630 |
|
|
1631 Matrix |
|
|
1632 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, |
|
|
1633 double& rcond) const |
|
|
1634 { |
|
|
1635 return solve (typ, b, info, rcond, 0); |
|
|
1636 } |
|
|
1637 |
|
|
1638 Matrix |
|
|
1639 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
|
|
1640 double& rcond, solve_singularity_handler sing_handler, |
|
|
1641 bool singular_fallback) const |
|
|
1642 { |
|
|
1643 Matrix retval; |
|
|
1644 int typ = mattype.type (); |
|
|
1645 |
|
|
1646 if (typ == MatrixType::Unknown) |
|
|
1647 typ = mattype.type (*this); |
|
|
1648 |
|
|
1649 // Only calculate the condition number for LU/Cholesky |
|
|
1650 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) |
|
|
1651 retval = utsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1652 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
|
|
1653 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); |
|
|
1654 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
|
|
1655 retval = fsolve (mattype, b, info, rcond, sing_handler, true); |
|
|
1656 else if (typ != MatrixType::Rectangular) |
|
|
1657 { |
|
|
1658 (*current_liboctave_error_handler) ("unknown matrix type"); |
|
|
1659 return Matrix (); |
|
|
1660 } |
|
|
1661 |
|
|
1662 // Rectangular or one of the above solvers flags a singular matrix |
|
|
1663 if (singular_fallback && mattype.type () == MatrixType::Rectangular) |
|
|
1664 { |
|
|
1665 octave_idx_type rank; |
|
|
1666 retval = lssolve (b, info, rank); |
|
|
1667 } |
|
|
1668 |
|
|
1669 return retval; |
|
|
1670 } |
|
|
1671 |
|
|
1672 ComplexMatrix |
|
|
1673 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const |
|
|
1674 { |
|
|
1675 ComplexMatrix tmp (*this); |
|
|
1676 return tmp.solve (typ, b); |
|
|
1677 } |
|
|
1678 |
|
|
1679 ComplexMatrix |
|
|
1680 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, |
|
|
1681 octave_idx_type& info) const |
|
|
1682 { |
|
|
1683 ComplexMatrix tmp (*this); |
|
|
1684 return tmp.solve (typ, b, info); |
|
|
1685 } |
|
|
1686 |
|
|
1687 ComplexMatrix |
|
|
1688 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1689 double& rcond) const |
|
|
1690 { |
|
|
1691 ComplexMatrix tmp (*this); |
|
|
1692 return tmp.solve (typ, b, info, rcond); |
|
|
1693 } |
|
|
1694 |
|
|
1695 ComplexMatrix |
|
|
1696 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, |
|
|
1697 double& rcond, solve_singularity_handler sing_handler, |
|
|
1698 bool singular_fallback) const |
|
|
1699 { |
|
|
1700 ComplexMatrix tmp (*this); |
|
|
1701 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); |
|
|
1702 } |
|
|
1703 |
|
|
1704 ColumnVector |
|
|
1705 Matrix::solve (MatrixType &typ, const ColumnVector& b) const |
|
|
1706 { |
|
|
1707 octave_idx_type info; double rcond; |
|
|
1708 return solve (typ, b, info, rcond); |
|
|
1709 } |
|
|
1710 |
|
|
1711 ColumnVector |
|
|
1712 Matrix::solve (MatrixType &typ, const ColumnVector& b, |
|
|
1713 octave_idx_type& info) const |
|
|
1714 { |
|
|
1715 double rcond; |
|
|
1716 return solve (typ, b, info, rcond); |
|
|
1717 } |
|
|
1718 |
|
|
1719 ColumnVector |
|
|
1720 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1721 double& rcond) const |
|
|
1722 { |
|
|
1723 return solve (typ, b, info, rcond, 0); |
|
|
1724 } |
|
|
1725 |
|
|
1726 ColumnVector |
|
|
1727 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, |
|
|
1728 double& rcond, solve_singularity_handler sing_handler) const |
|
|
1729 { |
|
|
1730 Matrix tmp (b); |
|
|
1731 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); |
|
|
1732 } |
|
|
1733 |
|
|
1734 ComplexColumnVector |
|
|
1735 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const |
|
|
1736 { |
|
|
1737 ComplexMatrix tmp (*this); |
|
|
1738 return tmp.solve (typ, b); |
|
|
1739 } |
|
|
1740 |
|
|
1741 ComplexColumnVector |
|
|
1742 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1743 octave_idx_type& info) const |
|
|
1744 { |
|
|
1745 ComplexMatrix tmp (*this); |
|
|
1746 return tmp.solve (typ, b, info); |
|
|
1747 } |
|
|
1748 |
|
|
1749 ComplexColumnVector |
|
|
1750 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1751 octave_idx_type& info, double& rcond) const |
|
|
1752 { |
|
|
1753 ComplexMatrix tmp (*this); |
|
|
1754 return tmp.solve (typ, b, info, rcond); |
|
|
1755 } |
|
|
1756 |
|
|
1757 ComplexColumnVector |
|
|
1758 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, |
|
|
1759 octave_idx_type& info, double& rcond, |
|
|
1760 solve_singularity_handler sing_handler) const |
|
|
1761 { |
|
|
1762 ComplexMatrix tmp (*this); |
|
|
1763 return tmp.solve(typ, b, info, rcond, sing_handler); |
|
|
1764 } |
|
|
1765 |
|
|
1766 Matrix |
|
458
|
1767 Matrix::solve (const Matrix& b) const |
|
|
1768 { |
|
5275
|
1769 octave_idx_type info; |
|
458
|
1770 double rcond; |
|
4329
|
1771 return solve (b, info, rcond, 0); |
|
458
|
1772 } |
|
|
1773 |
|
|
1774 Matrix |
|
5275
|
1775 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1776 { |
|
|
1777 double rcond; |
|
4329
|
1778 return solve (b, info, rcond, 0); |
|
458
|
1779 } |
|
|
1780 |
|
|
1781 Matrix |
|
5275
|
1782 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1783 { |
|
3480
|
1784 return solve (b, info, rcond, 0); |
|
|
1785 } |
|
|
1786 |
|
|
1787 Matrix |
|
5785
|
1788 Matrix::solve (const Matrix& b, octave_idx_type& info, |
|
|
1789 double& rcond, solve_singularity_handler sing_handler) const |
|
3480
|
1790 { |
|
5785
|
1791 MatrixType mattype (*this); |
|
|
1792 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1793 } |
|
|
1794 |
|
|
1795 ComplexMatrix |
|
|
1796 Matrix::solve (const ComplexMatrix& b) const |
|
|
1797 { |
|
|
1798 ComplexMatrix tmp (*this); |
|
|
1799 return tmp.solve (b); |
|
|
1800 } |
|
|
1801 |
|
|
1802 ComplexMatrix |
|
5275
|
1803 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1804 { |
|
|
1805 ComplexMatrix tmp (*this); |
|
|
1806 return tmp.solve (b, info); |
|
|
1807 } |
|
|
1808 |
|
|
1809 ComplexMatrix |
|
5275
|
1810 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
|
458
|
1811 { |
|
|
1812 ComplexMatrix tmp (*this); |
|
|
1813 return tmp.solve (b, info, rcond); |
|
|
1814 } |
|
|
1815 |
|
3480
|
1816 ComplexMatrix |
|
5275
|
1817 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
|
3480
|
1818 solve_singularity_handler sing_handler) const |
|
|
1819 { |
|
|
1820 ComplexMatrix tmp (*this); |
|
|
1821 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1822 } |
|
|
1823 |
|
458
|
1824 ColumnVector |
|
|
1825 Matrix::solve (const ColumnVector& b) const |
|
|
1826 { |
|
5275
|
1827 octave_idx_type info; double rcond; |
|
458
|
1828 return solve (b, info, rcond); |
|
|
1829 } |
|
|
1830 |
|
|
1831 ColumnVector |
|
5275
|
1832 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
1833 { |
|
|
1834 double rcond; |
|
|
1835 return solve (b, info, rcond); |
|
|
1836 } |
|
|
1837 |
|
|
1838 ColumnVector |
|
5275
|
1839 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1840 { |
|
3480
|
1841 return solve (b, info, rcond, 0); |
|
|
1842 } |
|
|
1843 |
|
|
1844 ColumnVector |
|
5275
|
1845 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1846 solve_singularity_handler sing_handler) const |
|
|
1847 { |
|
5785
|
1848 MatrixType mattype (*this); |
|
|
1849 return solve (mattype, b, info, rcond, sing_handler); |
|
458
|
1850 } |
|
|
1851 |
|
|
1852 ComplexColumnVector |
|
|
1853 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1854 { |
|
|
1855 ComplexMatrix tmp (*this); |
|
|
1856 return tmp.solve (b); |
|
|
1857 } |
|
|
1858 |
|
|
1859 ComplexColumnVector |
|
5275
|
1860 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
1861 { |
|
|
1862 ComplexMatrix tmp (*this); |
|
|
1863 return tmp.solve (b, info); |
|
|
1864 } |
|
|
1865 |
|
|
1866 ComplexColumnVector |
|
5275
|
1867 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
|
458
|
1868 { |
|
|
1869 ComplexMatrix tmp (*this); |
|
|
1870 return tmp.solve (b, info, rcond); |
|
|
1871 } |
|
|
1872 |
|
3480
|
1873 ComplexColumnVector |
|
5275
|
1874 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
|
3480
|
1875 solve_singularity_handler sing_handler) const |
|
|
1876 { |
|
|
1877 ComplexMatrix tmp (*this); |
|
|
1878 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1879 } |
|
|
1880 |
|
458
|
1881 Matrix |
|
|
1882 Matrix::lssolve (const Matrix& b) const |
|
|
1883 { |
|
5275
|
1884 octave_idx_type info; |
|
|
1885 octave_idx_type rank; |
|
458
|
1886 return lssolve (b, info, rank); |
|
|
1887 } |
|
|
1888 |
|
|
1889 Matrix |
|
5275
|
1890 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
|
458
|
1891 { |
|
5275
|
1892 octave_idx_type rank; |
|
458
|
1893 return lssolve (b, info, rank); |
|
|
1894 } |
|
|
1895 |
|
|
1896 Matrix |
|
5275
|
1897 Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1898 { |
|
1948
|
1899 Matrix retval; |
|
|
1900 |
|
5275
|
1901 octave_idx_type nrhs = b.cols (); |
|
|
1902 |
|
|
1903 octave_idx_type m = rows (); |
|
|
1904 octave_idx_type n = cols (); |
|
458
|
1905 |
|
|
1906 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1907 (*current_liboctave_error_handler) |
|
|
1908 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1909 else |
|
458
|
1910 { |
|
1948
|
1911 Matrix atmp = *this; |
|
|
1912 double *tmp_data = atmp.fortran_vec (); |
|
|
1913 |
|
5275
|
1914 octave_idx_type nrr = m > n ? m : n; |
|
3754
|
1915 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
1916 |
|
5275
|
1917 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1918 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
1919 result.elem (i, j) = b.elem (i, j); |
|
|
1920 |
|
|
1921 double *presult = result.fortran_vec (); |
|
|
1922 |
|
5275
|
1923 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
1924 Array<double> s (len_s); |
|
|
1925 double *ps = s.fortran_vec (); |
|
|
1926 |
|
|
1927 double rcond = -1.0; |
|
|
1928 |
|
3752
|
1929 // Ask DGELSS what the dimension of WORK should be. |
|
|
1930 |
|
5275
|
1931 octave_idx_type lwork = -1; |
|
3752
|
1932 |
|
|
1933 Array<double> work (1); |
|
1948
|
1934 |
|
|
1935 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
1936 rcond, rank, work.fortran_vec (), |
|
|
1937 lwork, info)); |
|
1948
|
1938 |
|
|
1939 if (f77_exception_encountered) |
|
|
1940 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1941 else |
|
|
1942 { |
|
5275
|
1943 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
1944 work.resize (lwork); |
|
|
1945 |
|
|
1946 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1947 nrr, ps, rcond, rank, |
|
|
1948 work.fortran_vec (), lwork, info)); |
|
|
1949 |
|
|
1950 if (f77_exception_encountered) |
|
|
1951 (*current_liboctave_error_handler) |
|
|
1952 ("unrecoverable error in dgelss"); |
|
|
1953 else |
|
|
1954 { |
|
|
1955 retval.resize (n, nrhs); |
|
5275
|
1956 for (octave_idx_type j = 0; j < nrhs; j++) |
|
|
1957 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
1958 retval.elem (i, j) = result.elem (i, j); |
|
|
1959 } |
|
1948
|
1960 } |
|
458
|
1961 } |
|
|
1962 |
|
|
1963 return retval; |
|
|
1964 } |
|
|
1965 |
|
|
1966 ComplexMatrix |
|
|
1967 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1968 { |
|
|
1969 ComplexMatrix tmp (*this); |
|
5275
|
1970 octave_idx_type info; |
|
|
1971 octave_idx_type rank; |
|
1484
|
1972 return tmp.lssolve (b, info, rank); |
|
458
|
1973 } |
|
|
1974 |
|
|
1975 ComplexMatrix |
|
5275
|
1976 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
|
458
|
1977 { |
|
|
1978 ComplexMatrix tmp (*this); |
|
5275
|
1979 octave_idx_type rank; |
|
1484
|
1980 return tmp.lssolve (b, info, rank); |
|
458
|
1981 } |
|
|
1982 |
|
|
1983 ComplexMatrix |
|
5275
|
1984 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
1985 { |
|
|
1986 ComplexMatrix tmp (*this); |
|
1484
|
1987 return tmp.lssolve (b, info, rank); |
|
458
|
1988 } |
|
|
1989 |
|
|
1990 ColumnVector |
|
|
1991 Matrix::lssolve (const ColumnVector& b) const |
|
|
1992 { |
|
5275
|
1993 octave_idx_type info; |
|
|
1994 octave_idx_type rank; |
|
1484
|
1995 return lssolve (b, info, rank); |
|
458
|
1996 } |
|
|
1997 |
|
|
1998 ColumnVector |
|
5275
|
1999 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
|
458
|
2000 { |
|
5275
|
2001 octave_idx_type rank; |
|
458
|
2002 return lssolve (b, info, rank); |
|
|
2003 } |
|
|
2004 |
|
|
2005 ColumnVector |
|
5275
|
2006 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2007 { |
|
1948
|
2008 ColumnVector retval; |
|
|
2009 |
|
5275
|
2010 octave_idx_type nrhs = 1; |
|
|
2011 |
|
|
2012 octave_idx_type m = rows (); |
|
|
2013 octave_idx_type n = cols (); |
|
458
|
2014 |
|
|
2015 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
2016 (*current_liboctave_error_handler) |
|
|
2017 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
2018 else |
|
458
|
2019 { |
|
1948
|
2020 Matrix atmp = *this; |
|
|
2021 double *tmp_data = atmp.fortran_vec (); |
|
|
2022 |
|
5275
|
2023 octave_idx_type nrr = m > n ? m : n; |
|
1948
|
2024 ColumnVector result (nrr); |
|
|
2025 |
|
5275
|
2026 for (octave_idx_type i = 0; i < m; i++) |
|
1948
|
2027 result.elem (i) = b.elem (i); |
|
|
2028 |
|
|
2029 double *presult = result.fortran_vec (); |
|
|
2030 |
|
5275
|
2031 octave_idx_type len_s = m < n ? m : n; |
|
1948
|
2032 Array<double> s (len_s); |
|
|
2033 double *ps = s.fortran_vec (); |
|
|
2034 |
|
|
2035 double rcond = -1.0; |
|
|
2036 |
|
3752
|
2037 // Ask DGELSS what the dimension of WORK should be. |
|
|
2038 |
|
5275
|
2039 octave_idx_type lwork = -1; |
|
3752
|
2040 |
|
|
2041 Array<double> work (1); |
|
|
2042 |
|
|
2043 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
2044 rcond, rank, work.fortran_vec (), |
|
|
2045 lwork, info)); |
|
1948
|
2046 |
|
|
2047 if (f77_exception_encountered) |
|
|
2048 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
2049 else |
|
|
2050 { |
|
5275
|
2051 lwork = static_cast<octave_idx_type> (work(0)); |
|
3752
|
2052 work.resize (lwork); |
|
|
2053 |
|
|
2054 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
2055 nrr, ps, rcond, rank, |
|
|
2056 work.fortran_vec (), lwork, info)); |
|
|
2057 |
|
|
2058 if (f77_exception_encountered) |
|
|
2059 (*current_liboctave_error_handler) |
|
|
2060 ("unrecoverable error in dgelss"); |
|
|
2061 else |
|
|
2062 { |
|
|
2063 retval.resize (n); |
|
5275
|
2064 for (octave_idx_type i = 0; i < n; i++) |
|
3752
|
2065 retval.elem (i) = result.elem (i); |
|
|
2066 } |
|
1948
|
2067 } |
|
458
|
2068 } |
|
|
2069 |
|
|
2070 return retval; |
|
|
2071 } |
|
|
2072 |
|
|
2073 ComplexColumnVector |
|
|
2074 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
2075 { |
|
|
2076 ComplexMatrix tmp (*this); |
|
|
2077 return tmp.lssolve (b); |
|
|
2078 } |
|
|
2079 |
|
|
2080 ComplexColumnVector |
|
5275
|
2081 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
|
458
|
2082 { |
|
|
2083 ComplexMatrix tmp (*this); |
|
|
2084 return tmp.lssolve (b, info); |
|
|
2085 } |
|
|
2086 |
|
|
2087 ComplexColumnVector |
|
5275
|
2088 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const |
|
458
|
2089 { |
|
|
2090 ComplexMatrix tmp (*this); |
|
|
2091 return tmp.lssolve (b, info, rank); |
|
|
2092 } |
|
|
2093 |
|
1819
|
2094 // Constants for matrix exponential calculation. |
|
|
2095 |
|
|
2096 static double padec [] = |
|
|
2097 { |
|
|
2098 5.0000000000000000e-1, |
|
|
2099 1.1666666666666667e-1, |
|
|
2100 1.6666666666666667e-2, |
|
|
2101 1.6025641025641026e-3, |
|
|
2102 1.0683760683760684e-4, |
|
|
2103 4.8562548562548563e-6, |
|
|
2104 1.3875013875013875e-7, |
|
|
2105 1.9270852604185938e-9, |
|
|
2106 }; |
|
|
2107 |
|
|
2108 Matrix |
|
|
2109 Matrix::expm (void) const |
|
|
2110 { |
|
|
2111 Matrix retval; |
|
|
2112 |
|
|
2113 Matrix m = *this; |
|
|
2114 |
|
5275
|
2115 octave_idx_type nc = columns (); |
|
1819
|
2116 |
|
3130
|
2117 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
2118 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
2119 |
|
1819
|
2120 // trace shift value |
|
3331
|
2121 volatile double trshift = 0.0; |
|
1819
|
2122 |
|
5275
|
2123 for (octave_idx_type i = 0; i < nc; i++) |
|
1819
|
2124 trshift += m.elem (i, i); |
|
|
2125 |
|
|
2126 trshift /= nc; |
|
|
2127 |
|
3130
|
2128 if (trshift > 0.0) |
|
|
2129 { |
|
5275
|
2130 for (octave_idx_type i = 0; i < nc; i++) |
|
3130
|
2131 m.elem (i, i) -= trshift; |
|
|
2132 } |
|
1819
|
2133 |
|
3331
|
2134 // Preconditioning step 2: balancing; code follows development |
|
|
2135 // in AEPBAL |
|
|
2136 |
|
|
2137 double *p_m = m.fortran_vec (); |
|
|
2138 |
|
5275
|
2139 octave_idx_type info, ilo, ihi, ilos, ihis; |
|
3468
|
2140 Array<double> dpermute (nc); |
|
|
2141 Array<double> dscale (nc); |
|
3466
|
2142 |
|
3468
|
2143 // permutation first |
|
|
2144 char job = 'P'; |
|
4552
|
2145 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2146 nc, p_m, nc, ilo, ihi, |
|
|
2147 dpermute.fortran_vec (), info |
|
|
2148 F77_CHAR_ARG_LEN (1))); |
|
3466
|
2149 |
|
3468
|
2150 // then scaling |
|
|
2151 job = 'S'; |
|
4552
|
2152 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
|
2153 nc, p_m, nc, ilos, ihis, |
|
|
2154 dscale.fortran_vec (), info |
|
|
2155 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2156 |
|
|
2157 if (f77_exception_encountered) |
|
|
2158 { |
|
|
2159 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
2160 return retval; |
|
|
2161 } |
|
|
2162 |
|
1819
|
2163 // Preconditioning step 3: scaling. |
|
3331
|
2164 |
|
1819
|
2165 ColumnVector work(nc); |
|
3130
|
2166 double inf_norm; |
|
3331
|
2167 |
|
4552
|
2168 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
|
|
2169 nc, nc, m.fortran_vec (), nc, |
|
|
2170 work.fortran_vec (), inf_norm |
|
|
2171 F77_CHAR_ARG_LEN (1))); |
|
3331
|
2172 |
|
|
2173 if (f77_exception_encountered) |
|
|
2174 { |
|
|
2175 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
2176 return retval; |
|
|
2177 } |
|
1819
|
2178 |
|
5275
|
2179 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
|
1819
|
2180 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
2181 : 0.0); |
|
3331
|
2182 |
|
1819
|
2183 // Check whether we need to square at all. |
|
3331
|
2184 |
|
1819
|
2185 if (sqpow < 0) |
|
|
2186 sqpow = 0; |
|
3331
|
2187 |
|
1819
|
2188 if (sqpow > 0) |
|
|
2189 { |
|
|
2190 double scale_factor = 1.0; |
|
5275
|
2191 for (octave_idx_type i = 0; i < sqpow; i++) |
|
1819
|
2192 scale_factor *= 2.0; |
|
3331
|
2193 |
|
1819
|
2194 m = m / scale_factor; |
|
|
2195 } |
|
3331
|
2196 |
|
1819
|
2197 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
2198 |
|
1819
|
2199 Matrix npp (nc, nc, 0.0); |
|
|
2200 Matrix dpp = npp; |
|
3331
|
2201 |
|
1819
|
2202 // Now powers a^8 ... a^1. |
|
3331
|
2203 |
|
5275
|
2204 octave_idx_type minus_one_j = -1; |
|
|
2205 for (octave_idx_type j = 7; j >= 0; j--) |
|
1819
|
2206 { |
|
3573
|
2207 npp = m * npp + padec[j] * m; |
|
|
2208 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
2209 minus_one_j *= -1; |
|
|
2210 } |
|
3331
|
2211 |
|
1819
|
2212 // Zero power. |
|
3331
|
2213 |
|
1819
|
2214 dpp = -dpp; |
|
5275
|
2215 for (octave_idx_type j = 0; j < nc; j++) |
|
1819
|
2216 { |
|
|
2217 npp.elem (j, j) += 1.0; |
|
|
2218 dpp.elem (j, j) += 1.0; |
|
|
2219 } |
|
3331
|
2220 |
|
1819
|
2221 // Compute pade approximation = inverse (dpp) * npp. |
|
|
2222 |
|
3331
|
2223 retval = dpp.solve (npp, info); |
|
|
2224 |
|
1819
|
2225 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
2226 |
|
1819
|
2227 while (sqpow) |
|
|
2228 { |
|
|
2229 retval = retval * retval; |
|
|
2230 sqpow--; |
|
|
2231 } |
|
3331
|
2232 |
|
1819
|
2233 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
2234 // apply inverse scaling to computed exponential |
|
5275
|
2235 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2236 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2237 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
2238 |
|
4153
|
2239 OCTAVE_QUIT; |
|
|
2240 |
|
3466
|
2241 // construct balancing permutation vector |
|
5275
|
2242 Array<octave_idx_type> iperm (nc); |
|
|
2243 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2244 iperm(i) = i; // identity permutation |
|
3466
|
2245 |
|
|
2246 // leading permutations in forward order |
|
5275
|
2247 for (octave_idx_type i = 0; i < (ilo-1); i++) |
|
3468
|
2248 { |
|
5275
|
2249 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2250 octave_idx_type tmp = iperm(i); |
|
4593
|
2251 iperm(i) = iperm (swapidx); |
|
|
2252 iperm(swapidx) = tmp; |
|
3468
|
2253 } |
|
3466
|
2254 |
|
|
2255 // trailing permutations must be done in reverse order |
|
5275
|
2256 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
3468
|
2257 { |
|
5275
|
2258 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
|
2259 octave_idx_type tmp = iperm(i); |
|
4593
|
2260 iperm(i) = iperm(swapidx); |
|
|
2261 iperm(swapidx) = tmp; |
|
3468
|
2262 } |
|
3466
|
2263 |
|
|
2264 // construct inverse balancing permutation vector |
|
5275
|
2265 Array<octave_idx_type> invpvec (nc); |
|
|
2266 for (octave_idx_type i = 0; i < nc; i++) |
|
4593
|
2267 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
|
4153
|
2268 |
|
|
2269 OCTAVE_QUIT; |
|
3466
|
2270 |
|
|
2271 Matrix tmpMat = retval; |
|
5275
|
2272 for (octave_idx_type i = 0; i < nc; i++) |
|
|
2273 for (octave_idx_type j = 0; j < nc; j++) |
|
3468
|
2274 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
2275 |
|
1819
|
2276 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
2277 |
|
3130
|
2278 if (trshift > 0.0) |
|
|
2279 retval = exp (trshift) * retval; |
|
|
2280 |
|
|
2281 return retval; |
|
1819
|
2282 } |
|
|
2283 |
|
458
|
2284 Matrix& |
|
|
2285 Matrix::operator += (const DiagMatrix& a) |
|
|
2286 { |
|
5275
|
2287 octave_idx_type nr = rows (); |
|
|
2288 octave_idx_type nc = cols (); |
|
|
2289 |
|
|
2290 octave_idx_type a_nr = a.rows (); |
|
|
2291 octave_idx_type a_nc = a.cols (); |
|
2385
|
2292 |
|
|
2293 if (nr != a_nr || nc != a_nc) |
|
458
|
2294 { |
|
2385
|
2295 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
2296 return *this; |
|
|
2297 } |
|
|
2298 |
|
5275
|
2299 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2300 elem (i, i) += a.elem (i, i); |
|
|
2301 |
|
|
2302 return *this; |
|
|
2303 } |
|
|
2304 |
|
|
2305 Matrix& |
|
|
2306 Matrix::operator -= (const DiagMatrix& a) |
|
|
2307 { |
|
5275
|
2308 octave_idx_type nr = rows (); |
|
|
2309 octave_idx_type nc = cols (); |
|
|
2310 |
|
|
2311 octave_idx_type a_nr = a.rows (); |
|
|
2312 octave_idx_type a_nc = a.cols (); |
|
2385
|
2313 |
|
|
2314 if (nr != a_nr || nc != a_nc) |
|
458
|
2315 { |
|
2385
|
2316 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
2317 return *this; |
|
|
2318 } |
|
|
2319 |
|
5275
|
2320 for (octave_idx_type i = 0; i < a.length (); i++) |
|
458
|
2321 elem (i, i) -= a.elem (i, i); |
|
|
2322 |
|
|
2323 return *this; |
|
|
2324 } |
|
|
2325 |
|
|
2326 // unary operations |
|
|
2327 |
|
2964
|
2328 boolMatrix |
|
458
|
2329 Matrix::operator ! (void) const |
|
|
2330 { |
|
5275
|
2331 octave_idx_type nr = rows (); |
|
|
2332 octave_idx_type nc = cols (); |
|
458
|
2333 |
|
2964
|
2334 boolMatrix b (nr, nc); |
|
458
|
2335 |
|
5275
|
2336 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2337 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2338 b.elem (i, j) = ! elem (i, j); |
|
|
2339 |
|
|
2340 return b; |
|
|
2341 } |
|
|
2342 |
|
1205
|
2343 // column vector by row vector -> matrix operations |
|
458
|
2344 |
|
1205
|
2345 Matrix |
|
|
2346 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
2347 { |
|
1948
|
2348 Matrix retval; |
|
|
2349 |
|
5275
|
2350 octave_idx_type len = v.length (); |
|
3233
|
2351 |
|
|
2352 if (len != 0) |
|
1205
|
2353 { |
|
5275
|
2354 octave_idx_type a_len = a.length (); |
|
3233
|
2355 |
|
|
2356 retval.resize (len, a_len); |
|
|
2357 double *c = retval.fortran_vec (); |
|
|
2358 |
|
4552
|
2359 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2360 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2361 len, a_len, 1, 1.0, v.data (), len, |
|
|
2362 a.data (), 1, 0.0, c, len |
|
|
2363 F77_CHAR_ARG_LEN (1) |
|
|
2364 F77_CHAR_ARG_LEN (1))); |
|
3233
|
2365 |
|
|
2366 if (f77_exception_encountered) |
|
|
2367 (*current_liboctave_error_handler) |
|
|
2368 ("unrecoverable error in dgemm"); |
|
1205
|
2369 } |
|
458
|
2370 |
|
1948
|
2371 return retval; |
|
458
|
2372 } |
|
|
2373 |
|
|
2374 // other operations. |
|
|
2375 |
|
|
2376 Matrix |
|
2676
|
2377 Matrix::map (d_d_Mapper f) const |
|
1205
|
2378 { |
|
2676
|
2379 Matrix b (*this); |
|
|
2380 return b.apply (f); |
|
1205
|
2381 } |
|
|
2382 |
|
3248
|
2383 boolMatrix |
|
|
2384 Matrix::map (b_d_Mapper f) const |
|
|
2385 { |
|
5275
|
2386 octave_idx_type nr = rows (); |
|
|
2387 octave_idx_type nc = cols (); |
|
3248
|
2388 |
|
|
2389 boolMatrix retval (nr, nc); |
|
|
2390 |
|
5275
|
2391 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2392 for (octave_idx_type i = 0; i < nr; i++) |
|
3248
|
2393 retval(i,j) = f (elem(i,j)); |
|
|
2394 |
|
|
2395 return retval; |
|
|
2396 } |
|
|
2397 |
|
2676
|
2398 Matrix& |
|
|
2399 Matrix::apply (d_d_Mapper f) |
|
458
|
2400 { |
|
|
2401 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
2402 |
|
5275
|
2403 for (octave_idx_type i = 0; i < length (); i++) |
|
458
|
2404 d[i] = f (d[i]); |
|
2676
|
2405 |
|
|
2406 return *this; |
|
458
|
2407 } |
|
|
2408 |
|
2385
|
2409 bool |
|
4431
|
2410 Matrix::any_element_is_negative (bool neg_zero) const |
|
2385
|
2411 { |
|
5275
|
2412 octave_idx_type nel = nelem (); |
|
2385
|
2413 |
|
4431
|
2414 if (neg_zero) |
|
|
2415 { |
|
5275
|
2416 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2417 if (lo_ieee_signbit (elem (i))) |
|
|
2418 return true; |
|
4431
|
2419 } |
|
|
2420 else |
|
|
2421 { |
|
5275
|
2422 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2423 if (elem (i) < 0) |
|
|
2424 return true; |
|
4431
|
2425 } |
|
2385
|
2426 |
|
|
2427 return false; |
|
|
2428 } |
|
|
2429 |
|
|
2430 |
|
|
2431 bool |
|
|
2432 Matrix::any_element_is_inf_or_nan (void) const |
|
|
2433 { |
|
5275
|
2434 octave_idx_type nel = nelem (); |
|
|
2435 |
|
|
2436 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2437 { |
|
|
2438 double val = elem (i); |
|
|
2439 if (xisinf (val) || xisnan (val)) |
|
|
2440 return true; |
|
|
2441 } |
|
|
2442 |
|
|
2443 return false; |
|
2385
|
2444 } |
|
|
2445 |
|
|
2446 bool |
|
5943
|
2447 Matrix::any_element_not_one_or_zero (void) const |
|
|
2448 { |
|
|
2449 octave_idx_type nel = nelem (); |
|
|
2450 |
|
|
2451 for (octave_idx_type i = 0; i < nel; i++) |
|
|
2452 { |
|
|
2453 double val = elem (i); |
|
|
2454 if (val != 0 && val != 1) |
|
|
2455 return true; |
|
|
2456 } |
|
|
2457 |
|
|
2458 return false; |
|
|
2459 } |
|
|
2460 |
|
|
2461 bool |
|
2385
|
2462 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
2463 { |
|
5275
|
2464 octave_idx_type nel = nelem (); |
|
|
2465 |
|
|
2466 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2467 { |
|
|
2468 double val = elem (i); |
|
|
2469 if (xisnan (val) || D_NINT (val) == val) |
|
|
2470 continue; |
|
|
2471 else |
|
|
2472 return false; |
|
|
2473 } |
|
2385
|
2474 |
|
|
2475 return true; |
|
|
2476 } |
|
|
2477 |
|
1968
|
2478 // Return nonzero if any element of M is not an integer. Also extract |
|
|
2479 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
2480 |
|
2385
|
2481 bool |
|
1968
|
2482 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
2483 { |
|
5275
|
2484 octave_idx_type nel = nelem (); |
|
4634
|
2485 |
|
|
2486 if (nel > 0) |
|
1968
|
2487 { |
|
4634
|
2488 max_val = elem (0); |
|
|
2489 min_val = elem (0); |
|
1968
|
2490 } |
|
|
2491 else |
|
2385
|
2492 return false; |
|
1968
|
2493 |
|
5275
|
2494 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2495 { |
|
|
2496 double val = elem (i); |
|
|
2497 |
|
|
2498 if (val > max_val) |
|
|
2499 max_val = val; |
|
|
2500 |
|
|
2501 if (val < min_val) |
|
|
2502 min_val = val; |
|
|
2503 |
|
|
2504 if (D_NINT (val) != val) |
|
|
2505 return false; |
|
|
2506 } |
|
2385
|
2507 |
|
|
2508 return true; |
|
1968
|
2509 } |
|
|
2510 |
|
2385
|
2511 bool |
|
1968
|
2512 Matrix::too_large_for_float (void) const |
|
|
2513 { |
|
5275
|
2514 octave_idx_type nel = nelem (); |
|
|
2515 |
|
|
2516 for (octave_idx_type i = 0; i < nel; i++) |
|
4634
|
2517 { |
|
|
2518 double val = elem (i); |
|
|
2519 |
|
5389
|
2520 if (! (xisnan (val) || xisinf (val)) |
|
5387
|
2521 && fabs (val) > FLT_MAX) |
|
4634
|
2522 return true; |
|
|
2523 } |
|
1968
|
2524 |
|
2385
|
2525 return false; |
|
1968
|
2526 } |
|
|
2527 |
|
5775
|
2528 // FIXME Do these really belong here? Maybe they should be |
|
4015
|
2529 // in a base class? |
|
458
|
2530 |
|
2832
|
2531 boolMatrix |
|
4015
|
2532 Matrix::all (int dim) const |
|
458
|
2533 { |
|
4015
|
2534 MX_ALL_OP (dim); |
|
458
|
2535 } |
|
|
2536 |
|
2832
|
2537 boolMatrix |
|
4015
|
2538 Matrix::any (int dim) const |
|
458
|
2539 { |
|
4015
|
2540 MX_ANY_OP (dim); |
|
458
|
2541 } |
|
|
2542 |
|
|
2543 Matrix |
|
3723
|
2544 Matrix::cumprod (int dim) const |
|
458
|
2545 { |
|
4015
|
2546 MX_CUMULATIVE_OP (Matrix, double, *=); |
|
458
|
2547 } |
|
|
2548 |
|
|
2549 Matrix |
|
3723
|
2550 Matrix::cumsum (int dim) const |
|
458
|
2551 { |
|
4015
|
2552 MX_CUMULATIVE_OP (Matrix, double, +=); |
|
458
|
2553 } |
|
|
2554 |
|
|
2555 Matrix |
|
3723
|
2556 Matrix::prod (int dim) const |
|
458
|
2557 { |
|
3864
|
2558 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2559 } |
|
|
2560 |
|
|
2561 Matrix |
|
3723
|
2562 Matrix::sum (int dim) const |
|
458
|
2563 { |
|
3864
|
2564 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2565 } |
|
|
2566 |
|
|
2567 Matrix |
|
3723
|
2568 Matrix::sumsq (int dim) const |
|
458
|
2569 { |
|
3864
|
2570 #define ROW_EXPR \ |
|
|
2571 double d = elem (i, j); \ |
|
|
2572 retval.elem (i, 0) += d * d |
|
|
2573 |
|
|
2574 #define COL_EXPR \ |
|
|
2575 double d = elem (i, j); \ |
|
|
2576 retval.elem (0, j) += d * d |
|
|
2577 |
|
|
2578 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2579 |
|
|
2580 #undef ROW_EXPR |
|
|
2581 #undef COL_EXPR |
|
458
|
2582 } |
|
|
2583 |
|
2385
|
2584 Matrix |
|
|
2585 Matrix::abs (void) const |
|
|
2586 { |
|
5275
|
2587 octave_idx_type nr = rows (); |
|
|
2588 octave_idx_type nc = cols (); |
|
2385
|
2589 |
|
|
2590 Matrix retval (nr, nc); |
|
|
2591 |
|
5275
|
2592 for (octave_idx_type j = 0; j < nc; j++) |
|
|
2593 for (octave_idx_type i = 0; i < nr; i++) |
|
2385
|
2594 retval (i, j) = fabs (elem (i, j)); |
|
|
2595 |
|
|
2596 return retval; |
|
|
2597 } |
|
|
2598 |
|
458
|
2599 ColumnVector |
|
|
2600 Matrix::diag (void) const |
|
|
2601 { |
|
|
2602 return diag (0); |
|
|
2603 } |
|
|
2604 |
|
|
2605 ColumnVector |
|
5275
|
2606 Matrix::diag (octave_idx_type k) const |
|
458
|
2607 { |
|
5275
|
2608 octave_idx_type nnr = rows (); |
|
|
2609 octave_idx_type nnc = cols (); |
|
458
|
2610 if (k > 0) |
|
|
2611 nnc -= k; |
|
|
2612 else if (k < 0) |
|
|
2613 nnr += k; |
|
|
2614 |
|
|
2615 ColumnVector d; |
|
|
2616 |
|
|
2617 if (nnr > 0 && nnc > 0) |
|
|
2618 { |
|
5275
|
2619 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
|
458
|
2620 |
|
|
2621 d.resize (ndiag); |
|
|
2622 |
|
|
2623 if (k > 0) |
|
|
2624 { |
|
5275
|
2625 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2626 d.elem (i) = elem (i, i+k); |
|
|
2627 } |
|
4509
|
2628 else if (k < 0) |
|
458
|
2629 { |
|
5275
|
2630 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2631 d.elem (i) = elem (i-k, i); |
|
|
2632 } |
|
|
2633 else |
|
|
2634 { |
|
5275
|
2635 for (octave_idx_type i = 0; i < ndiag; i++) |
|
458
|
2636 d.elem (i) = elem (i, i); |
|
|
2637 } |
|
|
2638 } |
|
|
2639 else |
|
4513
|
2640 (*current_liboctave_error_handler) |
|
|
2641 ("diag: requested diagonal out of range"); |
|
458
|
2642 |
|
|
2643 return d; |
|
|
2644 } |
|
|
2645 |
|
|
2646 ColumnVector |
|
|
2647 Matrix::row_min (void) const |
|
|
2648 { |
|
5275
|
2649 Array<octave_idx_type> dummy_idx; |
|
4587
|
2650 return row_min (dummy_idx); |
|
458
|
2651 } |
|
|
2652 |
|
|
2653 ColumnVector |
|
5275
|
2654 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2655 { |
|
|
2656 ColumnVector result; |
|
|
2657 |
|
5275
|
2658 octave_idx_type nr = rows (); |
|
|
2659 octave_idx_type nc = cols (); |
|
458
|
2660 |
|
|
2661 if (nr > 0 && nc > 0) |
|
|
2662 { |
|
|
2663 result.resize (nr); |
|
4587
|
2664 idx_arg.resize (nr); |
|
458
|
2665 |
|
5275
|
2666 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2667 { |
|
5275
|
2668 octave_idx_type idx_j; |
|
4469
|
2669 |
|
|
2670 double tmp_min = octave_NaN; |
|
|
2671 |
|
|
2672 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2673 { |
|
4469
|
2674 tmp_min = elem (i, idx_j); |
|
|
2675 |
|
5389
|
2676 if (! xisnan (tmp_min)) |
|
4469
|
2677 break; |
|
|
2678 } |
|
|
2679 |
|
5275
|
2680 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2681 { |
|
|
2682 double tmp = elem (i, j); |
|
|
2683 |
|
5389
|
2684 if (xisnan (tmp)) |
|
4469
|
2685 continue; |
|
|
2686 else if (tmp < tmp_min) |
|
2354
|
2687 { |
|
4469
|
2688 idx_j = j; |
|
|
2689 tmp_min = tmp; |
|
2354
|
2690 } |
|
|
2691 } |
|
|
2692 |
|
4469
|
2693 result.elem (i) = tmp_min; |
|
5389
|
2694 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
|
458
|
2695 } |
|
|
2696 } |
|
|
2697 |
|
|
2698 return result; |
|
|
2699 } |
|
|
2700 |
|
|
2701 ColumnVector |
|
|
2702 Matrix::row_max (void) const |
|
|
2703 { |
|
5275
|
2704 Array<octave_idx_type> dummy_idx; |
|
4587
|
2705 return row_max (dummy_idx); |
|
458
|
2706 } |
|
|
2707 |
|
|
2708 ColumnVector |
|
5275
|
2709 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2710 { |
|
|
2711 ColumnVector result; |
|
|
2712 |
|
5275
|
2713 octave_idx_type nr = rows (); |
|
|
2714 octave_idx_type nc = cols (); |
|
458
|
2715 |
|
|
2716 if (nr > 0 && nc > 0) |
|
|
2717 { |
|
|
2718 result.resize (nr); |
|
4587
|
2719 idx_arg.resize (nr); |
|
458
|
2720 |
|
5275
|
2721 for (octave_idx_type i = 0; i < nr; i++) |
|
458
|
2722 { |
|
5275
|
2723 octave_idx_type idx_j; |
|
4469
|
2724 |
|
|
2725 double tmp_max = octave_NaN; |
|
|
2726 |
|
|
2727 for (idx_j = 0; idx_j < nc; idx_j++) |
|
2354
|
2728 { |
|
4469
|
2729 tmp_max = elem (i, idx_j); |
|
|
2730 |
|
5389
|
2731 if (! xisnan (tmp_max)) |
|
4469
|
2732 break; |
|
|
2733 } |
|
|
2734 |
|
5275
|
2735 for (octave_idx_type j = idx_j+1; j < nc; j++) |
|
4469
|
2736 { |
|
|
2737 double tmp = elem (i, j); |
|
|
2738 |
|
5389
|
2739 if (xisnan (tmp)) |
|
4469
|
2740 continue; |
|
|
2741 else if (tmp > tmp_max) |
|
2354
|
2742 { |
|
4469
|
2743 idx_j = j; |
|
|
2744 tmp_max = tmp; |
|
2354
|
2745 } |
|
|
2746 } |
|
|
2747 |
|
4469
|
2748 result.elem (i) = tmp_max; |
|
5389
|
2749 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
|
458
|
2750 } |
|
|
2751 } |
|
|
2752 |
|
|
2753 return result; |
|
|
2754 } |
|
|
2755 |
|
|
2756 RowVector |
|
|
2757 Matrix::column_min (void) const |
|
|
2758 { |
|
5275
|
2759 Array<octave_idx_type> dummy_idx; |
|
4587
|
2760 return column_min (dummy_idx); |
|
458
|
2761 } |
|
2354
|
2762 |
|
458
|
2763 RowVector |
|
5275
|
2764 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
|
458
|
2765 { |
|
|
2766 RowVector result; |
|
|
2767 |
|
5275
|
2768 octave_idx_type nr = rows (); |
|
|
2769 octave_idx_type nc = cols (); |
|
458
|
2770 |
|
|
2771 if (nr > 0 && nc > 0) |
|
|
2772 { |
|
|
2773 result.resize (nc); |
|
4587
|
2774 idx_arg.resize (nc); |
|
458
|
2775 |
|
5275
|
2776 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2777 { |
|
5275
|
2778 octave_idx_type idx_i; |
|
4469
|
2779 |
|
|
2780 double tmp_min = octave_NaN; |
|
|
2781 |
|
|
2782 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2783 { |
|
4469
|
2784 tmp_min = elem (idx_i, j); |
|
|
2785 |
|
5389
|
2786 if (! xisnan (tmp_min)) |
|
4469
|
2787 break; |
|
|
2788 } |
|
|
2789 |
|
5275
|
2790 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2791 { |
|
|
2792 double tmp = elem (i, j); |
|
|
2793 |
|
5389
|
2794 if (xisnan (tmp)) |
|
4469
|
2795 continue; |
|
|
2796 else if (tmp < tmp_min) |
|
2354
|
2797 { |
|
4469
|
2798 idx_i = i; |
|
|
2799 tmp_min = tmp; |
|
2354
|
2800 } |
|
|
2801 } |
|
|
2802 |
|
4469
|
2803 result.elem (j) = tmp_min; |
|
5389
|
2804 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
|
458
|
2805 } |
|
|
2806 } |
|
|
2807 |
|
|
2808 return result; |
|
|
2809 } |
|
|
2810 |
|
2354
|
2811 RowVector |
|
|
2812 Matrix::column_max (void) const |
|
|
2813 { |
|
5275
|
2814 Array<octave_idx_type> dummy_idx; |
|
4587
|
2815 return column_max (dummy_idx); |
|
2354
|
2816 } |
|
458
|
2817 |
|
|
2818 RowVector |
|
5275
|
2819 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
|
458
|
2820 { |
|
|
2821 RowVector result; |
|
|
2822 |
|
5275
|
2823 octave_idx_type nr = rows (); |
|
|
2824 octave_idx_type nc = cols (); |
|
458
|
2825 |
|
|
2826 if (nr > 0 && nc > 0) |
|
|
2827 { |
|
|
2828 result.resize (nc); |
|
4587
|
2829 idx_arg.resize (nc); |
|
458
|
2830 |
|
5275
|
2831 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2832 { |
|
5275
|
2833 octave_idx_type idx_i; |
|
4469
|
2834 |
|
|
2835 double tmp_max = octave_NaN; |
|
|
2836 |
|
|
2837 for (idx_i = 0; idx_i < nr; idx_i++) |
|
2354
|
2838 { |
|
4469
|
2839 tmp_max = elem (idx_i, j); |
|
|
2840 |
|
5389
|
2841 if (! xisnan (tmp_max)) |
|
4469
|
2842 break; |
|
|
2843 } |
|
|
2844 |
|
5275
|
2845 for (octave_idx_type i = idx_i+1; i < nr; i++) |
|
4469
|
2846 { |
|
|
2847 double tmp = elem (i, j); |
|
|
2848 |
|
5389
|
2849 if (xisnan (tmp)) |
|
4469
|
2850 continue; |
|
|
2851 else if (tmp > tmp_max) |
|
2354
|
2852 { |
|
4469
|
2853 idx_i = i; |
|
|
2854 tmp_max = tmp; |
|
2354
|
2855 } |
|
|
2856 } |
|
|
2857 |
|
4469
|
2858 result.elem (j) = tmp_max; |
|
5389
|
2859 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
|
458
|
2860 } |
|
|
2861 } |
|
|
2862 |
|
|
2863 return result; |
|
|
2864 } |
|
|
2865 |
|
3504
|
2866 std::ostream& |
|
|
2867 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2868 { |
|
5275
|
2869 for (octave_idx_type i = 0; i < a.rows (); i++) |
|
458
|
2870 { |
|
5275
|
2871 for (octave_idx_type j = 0; j < a.cols (); j++) |
|
4130
|
2872 { |
|
|
2873 os << " "; |
|
|
2874 octave_write_double (os, a.elem (i, j)); |
|
|
2875 } |
|
458
|
2876 os << "\n"; |
|
|
2877 } |
|
|
2878 return os; |
|
|
2879 } |
|
|
2880 |
|
3504
|
2881 std::istream& |
|
|
2882 operator >> (std::istream& is, Matrix& a) |
|
458
|
2883 { |
|
5275
|
2884 octave_idx_type nr = a.rows (); |
|
|
2885 octave_idx_type nc = a.cols (); |
|
458
|
2886 |
|
|
2887 if (nr < 1 || nc < 1) |
|
3504
|
2888 is.clear (std::ios::badbit); |
|
458
|
2889 else |
|
|
2890 { |
|
|
2891 double tmp; |
|
5275
|
2892 for (octave_idx_type i = 0; i < nr; i++) |
|
|
2893 for (octave_idx_type j = 0; j < nc; j++) |
|
458
|
2894 { |
|
4130
|
2895 tmp = octave_read_double (is); |
|
458
|
2896 if (is) |
|
|
2897 a.elem (i, j) = tmp; |
|
|
2898 else |
|
2795
|
2899 goto done; |
|
458
|
2900 } |
|
|
2901 } |
|
|
2902 |
|
2795
|
2903 done: |
|
|
2904 |
|
458
|
2905 return is; |
|
|
2906 } |
|
|
2907 |
|
1819
|
2908 Matrix |
|
|
2909 Givens (double x, double y) |
|
|
2910 { |
|
|
2911 double cc, s, temp_r; |
|
|
2912 |
|
3887
|
2913 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
1819
|
2914 |
|
|
2915 Matrix g (2, 2); |
|
|
2916 |
|
|
2917 g.elem (0, 0) = cc; |
|
|
2918 g.elem (1, 1) = cc; |
|
|
2919 g.elem (0, 1) = s; |
|
|
2920 g.elem (1, 0) = -s; |
|
|
2921 |
|
|
2922 return g; |
|
|
2923 } |
|
|
2924 |
|
|
2925 Matrix |
|
|
2926 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2927 { |
|
|
2928 Matrix retval; |
|
|
2929 |
|
5775
|
2930 // FIXME -- need to check that a, b, and c are all the same |
|
1819
|
2931 // size. |
|
|
2932 |
|
|
2933 // Compute Schur decompositions. |
|
|
2934 |
|
|
2935 SCHUR as (a, "U"); |
|
|
2936 SCHUR bs (b, "U"); |
|
|
2937 |
|
|
2938 // Transform c to new coordinates. |
|
|
2939 |
|
|
2940 Matrix ua = as.unitary_matrix (); |
|
|
2941 Matrix sch_a = as.schur_matrix (); |
|
|
2942 |
|
|
2943 Matrix ub = bs.unitary_matrix (); |
|
|
2944 Matrix sch_b = bs.schur_matrix (); |
|
|
2945 |
|
|
2946 Matrix cx = ua.transpose () * c * ub; |
|
|
2947 |
|
|
2948 // Solve the sylvester equation, back-transform, and return the |
|
|
2949 // solution. |
|
|
2950 |
|
5275
|
2951 octave_idx_type a_nr = a.rows (); |
|
|
2952 octave_idx_type b_nr = b.rows (); |
|
1819
|
2953 |
|
|
2954 double scale; |
|
5275
|
2955 octave_idx_type info; |
|
1819
|
2956 |
|
1950
|
2957 double *pa = sch_a.fortran_vec (); |
|
|
2958 double *pb = sch_b.fortran_vec (); |
|
|
2959 double *px = cx.fortran_vec (); |
|
|
2960 |
|
4552
|
2961 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2962 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
2963 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2964 b_nr, px, a_nr, scale, info |
|
|
2965 F77_CHAR_ARG_LEN (1) |
|
|
2966 F77_CHAR_ARG_LEN (1))); |
|
1950
|
2967 |
|
|
2968 |
|
|
2969 if (f77_exception_encountered) |
|
|
2970 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
2971 else |
|
|
2972 { |
|
5775
|
2973 // FIXME -- check info? |
|
1819
|
2974 |
|
1950
|
2975 retval = -ua*cx*ub.transpose (); |
|
|
2976 } |
|
1819
|
2977 |
|
|
2978 return retval; |
|
|
2979 } |
|
|
2980 |
|
2828
|
2981 // matrix by matrix -> matrix operations |
|
|
2982 |
|
6162
|
2983 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
|
|
2984 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) |
|
|
2985 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) |
|
|
2986 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) |
|
|
2987 */ |
|
|
2988 |
|
|
2989 /* Test some simple identities |
|
|
2990 %!shared M, cv, rv |
|
|
2991 %! M = randn(10,10); |
|
|
2992 %! cv = randn(10,1); |
|
|
2993 %! rv = randn(1,10); |
|
|
2994 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) |
|
|
2995 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) |
|
|
2996 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) |
|
|
2997 */ |
|
|
2998 |
|
|
2999 |
|
2828
|
3000 Matrix |
|
|
3001 operator * (const Matrix& m, const Matrix& a) |
|
|
3002 { |
|
|
3003 Matrix retval; |
|
|
3004 |
|
5275
|
3005 octave_idx_type nr = m.rows (); |
|
|
3006 octave_idx_type nc = m.cols (); |
|
|
3007 |
|
|
3008 octave_idx_type a_nr = a.rows (); |
|
|
3009 octave_idx_type a_nc = a.cols (); |
|
2828
|
3010 |
|
|
3011 if (nc != a_nr) |
|
|
3012 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3013 else |
|
|
3014 { |
|
|
3015 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
3016 retval.resize (nr, a_nc, 0.0); |
|
|
3017 else |
|
|
3018 { |
|
5275
|
3019 octave_idx_type ld = nr; |
|
|
3020 octave_idx_type lda = a_nr; |
|
2828
|
3021 |
|
|
3022 retval.resize (nr, a_nc); |
|
|
3023 double *c = retval.fortran_vec (); |
|
|
3024 |
|
5983
|
3025 if (a_nc == 1) |
|
|
3026 { |
|
|
3027 if (nr == 1) |
|
|
3028 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); |
|
|
3029 else |
|
|
3030 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3031 nr, nc, 1.0, m.data (), ld, |
|
|
3032 a.data (), 1, 0.0, c, 1 |
|
|
3033 F77_CHAR_ARG_LEN (1))); |
|
|
3034 } |
|
|
3035 else |
|
|
3036 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3037 F77_CONST_CHAR_ARG2 ("N", 1), |
|
|
3038 nr, a_nc, nc, 1.0, m.data (), |
|
|
3039 ld, a.data (), lda, 0.0, c, nr |
|
|
3040 F77_CHAR_ARG_LEN (1) |
|
|
3041 F77_CHAR_ARG_LEN (1))); |
|
2828
|
3042 |
|
|
3043 if (f77_exception_encountered) |
|
|
3044 (*current_liboctave_error_handler) |
|
|
3045 ("unrecoverable error in dgemm"); |
|
|
3046 } |
|
|
3047 } |
|
|
3048 |
|
|
3049 return retval; |
|
|
3050 } |
|
|
3051 |
|
5775
|
3052 // FIXME -- it would be nice to share code among the min/max |
|
4309
|
3053 // functions below. |
|
|
3054 |
|
|
3055 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3056 if (nr == 0 || nc == 0) \ |
|
|
3057 return T (nr, nc); |
|
|
3058 |
|
|
3059 Matrix |
|
|
3060 min (double d, const Matrix& m) |
|
|
3061 { |
|
5275
|
3062 octave_idx_type nr = m.rows (); |
|
|
3063 octave_idx_type nc = m.columns (); |
|
4309
|
3064 |
|
|
3065 EMPTY_RETURN_CHECK (Matrix); |
|
|
3066 |
|
|
3067 Matrix result (nr, nc); |
|
|
3068 |
|
5275
|
3069 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3070 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3071 { |
|
|
3072 OCTAVE_QUIT; |
|
|
3073 result (i, j) = xmin (d, m (i, j)); |
|
|
3074 } |
|
|
3075 |
|
|
3076 return result; |
|
|
3077 } |
|
|
3078 |
|
|
3079 Matrix |
|
|
3080 min (const Matrix& m, double d) |
|
|
3081 { |
|
5275
|
3082 octave_idx_type nr = m.rows (); |
|
|
3083 octave_idx_type nc = m.columns (); |
|
4309
|
3084 |
|
|
3085 EMPTY_RETURN_CHECK (Matrix); |
|
|
3086 |
|
|
3087 Matrix result (nr, nc); |
|
|
3088 |
|
5275
|
3089 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3090 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3091 { |
|
|
3092 OCTAVE_QUIT; |
|
|
3093 result (i, j) = xmin (m (i, j), d); |
|
|
3094 } |
|
|
3095 |
|
|
3096 return result; |
|
|
3097 } |
|
|
3098 |
|
|
3099 Matrix |
|
|
3100 min (const Matrix& a, const Matrix& b) |
|
|
3101 { |
|
5275
|
3102 octave_idx_type nr = a.rows (); |
|
|
3103 octave_idx_type nc = a.columns (); |
|
4309
|
3104 |
|
|
3105 if (nr != b.rows () || nc != b.columns ()) |
|
|
3106 { |
|
|
3107 (*current_liboctave_error_handler) |
|
|
3108 ("two-arg min expecting args of same size"); |
|
|
3109 return Matrix (); |
|
|
3110 } |
|
|
3111 |
|
|
3112 EMPTY_RETURN_CHECK (Matrix); |
|
|
3113 |
|
|
3114 Matrix result (nr, nc); |
|
|
3115 |
|
5275
|
3116 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3117 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3118 { |
|
|
3119 OCTAVE_QUIT; |
|
|
3120 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3121 } |
|
|
3122 |
|
|
3123 return result; |
|
|
3124 } |
|
|
3125 |
|
|
3126 Matrix |
|
|
3127 max (double d, const Matrix& m) |
|
|
3128 { |
|
5275
|
3129 octave_idx_type nr = m.rows (); |
|
|
3130 octave_idx_type nc = m.columns (); |
|
4309
|
3131 |
|
|
3132 EMPTY_RETURN_CHECK (Matrix); |
|
|
3133 |
|
|
3134 Matrix result (nr, nc); |
|
|
3135 |
|
5275
|
3136 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3137 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3138 { |
|
|
3139 OCTAVE_QUIT; |
|
|
3140 result (i, j) = xmax (d, m (i, j)); |
|
|
3141 } |
|
|
3142 |
|
|
3143 return result; |
|
|
3144 } |
|
|
3145 |
|
|
3146 Matrix |
|
|
3147 max (const Matrix& m, double d) |
|
|
3148 { |
|
5275
|
3149 octave_idx_type nr = m.rows (); |
|
|
3150 octave_idx_type nc = m.columns (); |
|
4309
|
3151 |
|
|
3152 EMPTY_RETURN_CHECK (Matrix); |
|
|
3153 |
|
|
3154 Matrix result (nr, nc); |
|
|
3155 |
|
5275
|
3156 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3157 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3158 { |
|
|
3159 OCTAVE_QUIT; |
|
|
3160 result (i, j) = xmax (m (i, j), d); |
|
|
3161 } |
|
|
3162 |
|
|
3163 return result; |
|
|
3164 } |
|
|
3165 |
|
|
3166 Matrix |
|
|
3167 max (const Matrix& a, const Matrix& b) |
|
|
3168 { |
|
5275
|
3169 octave_idx_type nr = a.rows (); |
|
|
3170 octave_idx_type nc = a.columns (); |
|
4309
|
3171 |
|
|
3172 if (nr != b.rows () || nc != b.columns ()) |
|
|
3173 { |
|
|
3174 (*current_liboctave_error_handler) |
|
|
3175 ("two-arg max expecting args of same size"); |
|
|
3176 return Matrix (); |
|
|
3177 } |
|
|
3178 |
|
|
3179 EMPTY_RETURN_CHECK (Matrix); |
|
|
3180 |
|
|
3181 Matrix result (nr, nc); |
|
|
3182 |
|
5275
|
3183 for (octave_idx_type j = 0; j < nc; j++) |
|
|
3184 for (octave_idx_type i = 0; i < nr; i++) |
|
4309
|
3185 { |
|
|
3186 OCTAVE_QUIT; |
|
|
3187 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3188 } |
|
|
3189 |
|
|
3190 return result; |
|
|
3191 } |
|
|
3192 |
|
2870
|
3193 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
3194 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
3195 |
|
|
3196 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
3197 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
3198 |
|
|
3199 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
3200 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
3201 |
|
458
|
3202 /* |
|
|
3203 ;;; Local Variables: *** |
|
|
3204 ;;; mode: C++ *** |
|
|
3205 ;;; End: *** |
|
|
3206 */ |
