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1993
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1 // Matrix manipulations. |
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458
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2 /* |
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3 |
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2847
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4 Copyright (C) 1996, 1997 John W. Eaton |
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458
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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21 |
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22 */ |
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23 |
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1296
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24 #if defined (__GNUG__) |
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25 #pragma implementation |
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26 #endif |
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27 |
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458
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28 #ifdef HAVE_CONFIG_H |
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1192
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29 #include <config.h> |
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458
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30 #endif |
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31 |
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1367
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32 #include <cfloat> |
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33 |
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458
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34 #include <iostream.h> |
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35 |
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2317
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36 #include "byte-swap.h" |
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2828
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37 #include "dMatrix.h" |
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1819
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38 #include "dbleAEPBAL.h" |
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458
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39 #include "dbleDET.h" |
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1819
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40 #include "dbleSCHUR.h" |
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740
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41 #include "dbleSVD.h" |
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1847
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42 #include "f77-fcn.h" |
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458
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43 #include "lo-error.h" |
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2354
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44 #include "lo-ieee.h" |
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45 #include "lo-mappers.h" |
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1968
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46 #include "lo-utils.h" |
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1367
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47 #include "mx-base.h" |
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2828
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48 #include "mx-m-dm.h" |
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3176
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49 #include "mx-dm-m.h" |
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1367
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50 #include "mx-inlines.cc" |
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1650
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51 #include "oct-cmplx.h" |
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52 |
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53 // Fortran functions we call. |
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54 |
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55 extern "C" |
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56 { |
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1253
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57 int F77_FCN (dgemm, DGEMM) (const char*, const char*, const int&, |
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58 const int&, const int&, const double&, |
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59 const double*, const int&, |
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60 const double*, const int&, |
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61 const double&, double*, const int&, |
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62 long, long); |
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63 |
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64 int F77_FCN (dgeco, DGECO) (double*, const int&, const int&, int*, |
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65 double&, double*); |
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66 |
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67 int F77_FCN (dgesl, DGESL) (const double*, const int&, const int&, |
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68 const int*, double*, const int&); |
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69 |
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70 int F77_FCN (dgedi, DGEDI) (double*, const int&, const int&, |
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71 const int*, double*, double*, |
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72 const int&); |
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73 |
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74 int F77_FCN (dgelss, DGELSS) (const int&, const int&, const int&, |
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75 double*, const int&, double*, |
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76 const int&, double*, double&, int&, |
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77 double*, const int&, int&); |
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78 |
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1360
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79 // Note that the original complex fft routines were not written for |
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80 // double complex arguments. They have been modified by adding an |
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81 // implicit double precision (a-h,o-z) statement at the beginning of |
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82 // each subroutine. |
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83 |
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84 int F77_FCN (cffti, CFFTI) (const int&, Complex*); |
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85 |
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86 int F77_FCN (cfftf, CFFTF) (const int&, Complex*, Complex*); |
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87 |
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88 int F77_FCN (cfftb, CFFTB) (const int&, Complex*, Complex*); |
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89 |
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90 int F77_FCN (dlartg, DLARTG) (const double&, const double&, double&, |
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91 double&, double&); |
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92 |
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93 int F77_FCN (dtrsyl, DTRSYL) (const char*, const char*, const int&, |
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94 const int&, const int&, const double*, |
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95 const int&, const double*, const int&, |
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96 const double*, const int&, double&, |
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97 int&, long, long); |
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98 |
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3130
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99 int F77_FCN (xdlange, XDLANGE) (const char*, const int&, |
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100 const int&, const double*, |
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101 const int&, double*, double&); |
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458
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102 } |
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103 |
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104 // Matrix class. |
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105 |
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2349
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106 Matrix::Matrix (const RowVector& rv) |
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107 : MArray2<double> (1, rv.length (), 0.0) |
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108 { |
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109 for (int i = 0; i < rv.length (); i++) |
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110 elem (0, i) = rv.elem (i); |
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111 } |
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112 |
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113 Matrix::Matrix (const ColumnVector& cv) |
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114 : MArray2<double> (cv.length (), 1, 0.0) |
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115 { |
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116 for (int i = 0; i < cv.length (); i++) |
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117 elem (i, 0) = cv.elem (i); |
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118 } |
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119 |
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120 Matrix::Matrix (const DiagMatrix& a) |
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121 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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122 { |
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123 for (int i = 0; i < a.length (); i++) |
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124 elem (i, i) = a.elem (i, i); |
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125 } |
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126 |
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1574
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127 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
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128 // here? |
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129 |
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2828
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130 Matrix::Matrix (const boolMatrix& a) |
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131 : MArray2<double> (a.rows (), a.cols ()) |
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132 { |
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133 for (int i = 0; i < a.rows (); i++) |
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134 for (int j = 0; j < a.cols (); j++) |
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135 elem (i, j) = a.elem (i, j); |
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136 } |
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137 |
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138 Matrix::Matrix (const charMatrix& a) |
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139 : MArray2<double> (a.rows (), a.cols ()) |
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140 { |
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141 for (int i = 0; i < a.rows (); i++) |
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142 for (int j = 0; j < a.cols (); j++) |
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143 elem (i, j) = a.elem (i, j); |
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144 } |
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145 |
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2385
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146 bool |
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147 Matrix::operator == (const Matrix& a) const |
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148 { |
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149 if (rows () != a.rows () || cols () != a.cols ()) |
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2385
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150 return false; |
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151 |
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152 return equal (data (), a.data (), length ()); |
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153 } |
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154 |
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2385
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155 bool |
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458
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156 Matrix::operator != (const Matrix& a) const |
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157 { |
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158 return !(*this == a); |
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159 } |
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160 |
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161 Matrix& |
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162 Matrix::insert (const Matrix& a, int r, int c) |
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163 { |
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1561
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164 Array2<double>::insert (a, r, c); |
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165 return *this; |
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166 } |
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167 |
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168 Matrix& |
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169 Matrix::insert (const RowVector& a, int r, int c) |
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170 { |
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171 int a_len = a.length (); |
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1698
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172 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
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173 { |
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174 (*current_liboctave_error_handler) ("range error for insert"); |
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175 return *this; |
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176 } |
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177 |
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178 for (int i = 0; i < a_len; i++) |
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179 elem (r, c+i) = a.elem (i); |
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180 |
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181 return *this; |
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182 } |
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183 |
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184 Matrix& |
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185 Matrix::insert (const ColumnVector& a, int r, int c) |
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186 { |
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187 int a_len = a.length (); |
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188 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
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189 { |
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190 (*current_liboctave_error_handler) ("range error for insert"); |
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191 return *this; |
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192 } |
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193 |
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194 for (int i = 0; i < a_len; i++) |
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195 elem (r+i, c) = a.elem (i); |
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196 |
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197 return *this; |
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198 } |
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199 |
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200 Matrix& |
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201 Matrix::insert (const DiagMatrix& a, int r, int c) |
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202 { |
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1697
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203 int a_nr = a.rows (); |
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204 int a_nc = a.cols (); |
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205 |
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206 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
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207 { |
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208 (*current_liboctave_error_handler) ("range error for insert"); |
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209 return *this; |
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210 } |
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211 |
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212 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
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213 |
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214 for (int i = 0; i < a.length (); i++) |
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215 elem (r+i, c+i) = a.elem (i, i); |
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216 |
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217 return *this; |
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218 } |
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219 |
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220 Matrix& |
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221 Matrix::fill (double val) |
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222 { |
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223 int nr = rows (); |
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224 int nc = cols (); |
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225 if (nr > 0 && nc > 0) |
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226 for (int j = 0; j < nc; j++) |
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227 for (int i = 0; i < nr; i++) |
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228 elem (i, j) = val; |
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229 |
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230 return *this; |
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231 } |
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232 |
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233 Matrix& |
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234 Matrix::fill (double val, int r1, int c1, int r2, int c2) |
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235 { |
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236 int nr = rows (); |
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237 int nc = cols (); |
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238 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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239 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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240 { |
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241 (*current_liboctave_error_handler) ("range error for fill"); |
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242 return *this; |
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243 } |
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244 |
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245 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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246 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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247 |
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248 for (int j = c1; j <= c2; j++) |
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249 for (int i = r1; i <= r2; i++) |
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250 elem (i, j) = val; |
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251 |
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252 return *this; |
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253 } |
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254 |
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255 Matrix |
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256 Matrix::append (const Matrix& a) const |
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257 { |
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258 int nr = rows (); |
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259 int nc = cols (); |
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260 if (nr != a.rows ()) |
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261 { |
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262 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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263 return Matrix (); |
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264 } |
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265 |
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266 int nc_insert = nc; |
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267 Matrix retval (nr, nc + a.cols ()); |
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268 retval.insert (*this, 0, 0); |
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269 retval.insert (a, 0, nc_insert); |
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270 return retval; |
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271 } |
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272 |
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273 Matrix |
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274 Matrix::append (const RowVector& a) const |
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275 { |
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276 int nr = rows (); |
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277 int nc = cols (); |
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278 if (nr != 1) |
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279 { |
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280 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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281 return Matrix (); |
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282 } |
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283 |
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284 int nc_insert = nc; |
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285 Matrix retval (nr, nc + a.length ()); |
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286 retval.insert (*this, 0, 0); |
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287 retval.insert (a, 0, nc_insert); |
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288 return retval; |
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289 } |
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290 |
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291 Matrix |
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292 Matrix::append (const ColumnVector& a) const |
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293 { |
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294 int nr = rows (); |
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295 int nc = cols (); |
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296 if (nr != a.length ()) |
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297 { |
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298 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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299 return Matrix (); |
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300 } |
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301 |
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302 int nc_insert = nc; |
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303 Matrix retval (nr, nc + 1); |
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304 retval.insert (*this, 0, 0); |
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305 retval.insert (a, 0, nc_insert); |
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306 return retval; |
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307 } |
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308 |
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309 Matrix |
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310 Matrix::append (const DiagMatrix& a) const |
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311 { |
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312 int nr = rows (); |
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313 int nc = cols (); |
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314 if (nr != a.rows ()) |
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315 { |
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316 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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317 return *this; |
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318 } |
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319 |
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320 int nc_insert = nc; |
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321 Matrix retval (nr, nc + a.cols ()); |
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322 retval.insert (*this, 0, 0); |
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323 retval.insert (a, 0, nc_insert); |
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324 return retval; |
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325 } |
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326 |
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327 Matrix |
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328 Matrix::stack (const Matrix& a) const |
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329 { |
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330 int nr = rows (); |
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331 int nc = cols (); |
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332 if (nc != a.cols ()) |
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333 { |
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334 (*current_liboctave_error_handler) |
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335 ("column dimension mismatch for stack"); |
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336 return Matrix (); |
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337 } |
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338 |
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339 int nr_insert = nr; |
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340 Matrix retval (nr + a.rows (), nc); |
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341 retval.insert (*this, 0, 0); |
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342 retval.insert (a, nr_insert, 0); |
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343 return retval; |
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344 } |
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345 |
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346 Matrix |
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347 Matrix::stack (const RowVector& a) const |
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348 { |
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349 int nr = rows (); |
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350 int nc = cols (); |
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351 if (nc != a.length ()) |
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352 { |
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353 (*current_liboctave_error_handler) |
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354 ("column dimension mismatch for stack"); |
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355 return Matrix (); |
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356 } |
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357 |
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358 int nr_insert = nr; |
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359 Matrix retval (nr + 1, nc); |
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360 retval.insert (*this, 0, 0); |
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361 retval.insert (a, nr_insert, 0); |
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362 return retval; |
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363 } |
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364 |
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365 Matrix |
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366 Matrix::stack (const ColumnVector& a) const |
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367 { |
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368 int nr = rows (); |
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369 int nc = cols (); |
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370 if (nc != 1) |
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371 { |
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372 (*current_liboctave_error_handler) |
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373 ("column dimension mismatch for stack"); |
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374 return Matrix (); |
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375 } |
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376 |
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377 int nr_insert = nr; |
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378 Matrix retval (nr + a.length (), nc); |
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379 retval.insert (*this, 0, 0); |
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380 retval.insert (a, nr_insert, 0); |
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381 return retval; |
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382 } |
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383 |
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384 Matrix |
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385 Matrix::stack (const DiagMatrix& a) const |
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386 { |
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387 int nr = rows (); |
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388 int nc = cols (); |
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389 if (nc != a.cols ()) |
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390 { |
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391 (*current_liboctave_error_handler) |
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392 ("column dimension mismatch for stack"); |
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393 return Matrix (); |
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394 } |
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395 |
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396 int nr_insert = nr; |
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397 Matrix retval (nr + a.rows (), nc); |
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398 retval.insert (*this, 0, 0); |
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399 retval.insert (a, nr_insert, 0); |
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400 return retval; |
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401 } |
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402 |
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403 Matrix |
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1205
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404 real (const ComplexMatrix& a) |
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405 { |
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406 int a_len = a.length (); |
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407 Matrix retval; |
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408 if (a_len > 0) |
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409 retval = Matrix (real_dup (a.data (), a_len), a.rows (), a.cols ()); |
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410 return retval; |
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411 } |
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412 |
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413 Matrix |
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414 imag (const ComplexMatrix& a) |
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415 { |
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416 int a_len = a.length (); |
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417 Matrix retval; |
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418 if (a_len > 0) |
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419 retval = Matrix (imag_dup (a.data (), a_len), a.rows (), a.cols ()); |
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420 return retval; |
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421 } |
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422 |
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423 Matrix |
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458
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424 Matrix::extract (int r1, int c1, int r2, int c2) const |
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425 { |
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426 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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427 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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428 |
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429 int new_r = r2 - r1 + 1; |
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430 int new_c = c2 - c1 + 1; |
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431 |
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432 Matrix result (new_r, new_c); |
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433 |
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434 for (int j = 0; j < new_c; j++) |
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435 for (int i = 0; i < new_r; i++) |
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436 result.elem (i, j) = elem (r1+i, c1+j); |
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437 |
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438 return result; |
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439 } |
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440 |
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441 // extract row or column i. |
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442 |
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443 RowVector |
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444 Matrix::row (int i) const |
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445 { |
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446 int nc = cols (); |
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447 if (i < 0 || i >= rows ()) |
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448 { |
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449 (*current_liboctave_error_handler) ("invalid row selection"); |
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450 return RowVector (); |
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451 } |
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452 |
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453 RowVector retval (nc); |
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454 for (int j = 0; j < nc; j++) |
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455 retval.elem (j) = elem (i, j); |
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456 |
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457 return retval; |
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458 } |
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459 |
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460 RowVector |
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461 Matrix::row (char *s) const |
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462 { |
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533
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463 if (! s) |
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458
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464 { |
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|
465 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
466 return RowVector (); |
|
|
467 } |
|
|
468 |
|
|
469 char c = *s; |
|
|
470 if (c == 'f' || c == 'F') |
|
|
471 return row (0); |
|
|
472 else if (c == 'l' || c == 'L') |
|
|
473 return row (rows () - 1); |
|
|
474 else |
|
|
475 { |
|
|
476 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
477 return RowVector (); |
|
|
478 } |
|
|
479 } |
|
|
480 |
|
|
481 ColumnVector |
|
|
482 Matrix::column (int i) const |
|
|
483 { |
|
|
484 int nr = rows (); |
|
|
485 if (i < 0 || i >= cols ()) |
|
|
486 { |
|
|
487 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
488 return ColumnVector (); |
|
|
489 } |
|
|
490 |
|
|
491 ColumnVector retval (nr); |
|
|
492 for (int j = 0; j < nr; j++) |
|
|
493 retval.elem (j) = elem (j, i); |
|
|
494 |
|
|
495 return retval; |
|
|
496 } |
|
|
497 |
|
|
498 ColumnVector |
|
|
499 Matrix::column (char *s) const |
|
|
500 { |
|
533
|
501 if (! s) |
|
458
|
502 { |
|
|
503 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
504 return ColumnVector (); |
|
|
505 } |
|
|
506 |
|
|
507 char c = *s; |
|
|
508 if (c == 'f' || c == 'F') |
|
|
509 return column (0); |
|
|
510 else if (c == 'l' || c == 'L') |
|
|
511 return column (cols () - 1); |
|
|
512 else |
|
|
513 { |
|
|
514 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
515 return ColumnVector (); |
|
|
516 } |
|
|
517 } |
|
|
518 |
|
|
519 Matrix |
|
|
520 Matrix::inverse (void) const |
|
|
521 { |
|
|
522 int info; |
|
|
523 double rcond; |
|
|
524 return inverse (info, rcond); |
|
|
525 } |
|
|
526 |
|
|
527 Matrix |
|
|
528 Matrix::inverse (int& info) const |
|
|
529 { |
|
|
530 double rcond; |
|
|
531 return inverse (info, rcond); |
|
|
532 } |
|
|
533 |
|
|
534 Matrix |
|
1656
|
535 Matrix::inverse (int& info, double& rcond, int force) const |
|
458
|
536 { |
|
1948
|
537 Matrix retval; |
|
|
538 |
|
458
|
539 int nr = rows (); |
|
|
540 int nc = cols (); |
|
1948
|
541 |
|
458
|
542 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
543 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
544 else |
|
|
545 { |
|
1948
|
546 info = 0; |
|
|
547 |
|
|
548 Array<int> ipvt (nr); |
|
|
549 int *pipvt = ipvt.fortran_vec (); |
|
|
550 |
|
|
551 Array<double> z (nr); |
|
|
552 double *pz = z.fortran_vec (); |
|
|
553 |
|
|
554 retval = *this; |
|
|
555 double *tmp_data = retval.fortran_vec (); |
|
|
556 |
|
|
557 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nc, pipvt, rcond, pz)); |
|
|
558 |
|
|
559 if (f77_exception_encountered) |
|
|
560 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
|
561 else |
|
|
562 { |
|
|
563 volatile double rcond_plus_one = rcond + 1.0; |
|
|
564 |
|
|
565 if (rcond_plus_one == 1.0) |
|
|
566 info = -1; |
|
|
567 |
|
|
568 if (info == -1 && ! force) |
|
|
569 retval = *this; // Restore matrix contents. |
|
|
570 else |
|
|
571 { |
|
|
572 double *dummy = 0; |
|
|
573 |
|
|
574 F77_XFCN (dgedi, DGEDI, (tmp_data, nr, nc, pipvt, dummy, |
|
|
575 pz, 1)); |
|
|
576 |
|
|
577 if (f77_exception_encountered) |
|
|
578 (*current_liboctave_error_handler) |
|
|
579 ("unrecoverable error in dgedi"); |
|
|
580 } |
|
|
581 } |
|
458
|
582 } |
|
|
583 |
|
1948
|
584 return retval; |
|
458
|
585 } |
|
|
586 |
|
740
|
587 Matrix |
|
|
588 Matrix::pseudo_inverse (double tol) |
|
|
589 { |
|
|
590 SVD result (*this); |
|
|
591 |
|
|
592 DiagMatrix S = result.singular_values (); |
|
|
593 Matrix U = result.left_singular_matrix (); |
|
|
594 Matrix V = result.right_singular_matrix (); |
|
|
595 |
|
|
596 ColumnVector sigma = S.diag (); |
|
|
597 |
|
|
598 int r = sigma.length () - 1; |
|
|
599 int nr = rows (); |
|
|
600 int nc = cols (); |
|
|
601 |
|
|
602 if (tol <= 0.0) |
|
|
603 { |
|
|
604 if (nr > nc) |
|
|
605 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
606 else |
|
|
607 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
608 } |
|
|
609 |
|
|
610 while (r >= 0 && sigma.elem (r) < tol) |
|
|
611 r--; |
|
|
612 |
|
|
613 if (r < 0) |
|
|
614 return Matrix (nc, nr, 0.0); |
|
|
615 else |
|
|
616 { |
|
|
617 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
618 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
619 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
620 return Vr * D * Ur.transpose (); |
|
|
621 } |
|
|
622 } |
|
|
623 |
|
458
|
624 ComplexMatrix |
|
|
625 Matrix::fourier (void) const |
|
|
626 { |
|
1948
|
627 ComplexMatrix retval; |
|
|
628 |
|
458
|
629 int nr = rows (); |
|
|
630 int nc = cols (); |
|
1948
|
631 |
|
458
|
632 int npts, nsamples; |
|
1948
|
633 |
|
458
|
634 if (nr == 1 || nc == 1) |
|
|
635 { |
|
|
636 npts = nr > nc ? nr : nc; |
|
|
637 nsamples = 1; |
|
|
638 } |
|
|
639 else |
|
|
640 { |
|
|
641 npts = nr; |
|
|
642 nsamples = nc; |
|
|
643 } |
|
|
644 |
|
|
645 int nn = 4*npts+15; |
|
1948
|
646 |
|
|
647 Array<Complex> wsave (nn); |
|
|
648 Complex *pwsave = wsave.fortran_vec (); |
|
|
649 |
|
|
650 retval = *this; |
|
|
651 Complex *tmp_data = retval.fortran_vec (); |
|
|
652 |
|
|
653 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
654 |
|
|
655 for (int j = 0; j < nsamples; j++) |
|
1948
|
656 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
657 |
|
|
658 return retval; |
|
458
|
659 } |
|
|
660 |
|
|
661 ComplexMatrix |
|
|
662 Matrix::ifourier (void) const |
|
|
663 { |
|
1948
|
664 ComplexMatrix retval; |
|
|
665 |
|
458
|
666 int nr = rows (); |
|
|
667 int nc = cols (); |
|
1948
|
668 |
|
458
|
669 int npts, nsamples; |
|
1948
|
670 |
|
458
|
671 if (nr == 1 || nc == 1) |
|
|
672 { |
|
|
673 npts = nr > nc ? nr : nc; |
|
|
674 nsamples = 1; |
|
|
675 } |
|
|
676 else |
|
|
677 { |
|
|
678 npts = nr; |
|
|
679 nsamples = nc; |
|
|
680 } |
|
|
681 |
|
|
682 int nn = 4*npts+15; |
|
1948
|
683 |
|
|
684 Array<Complex> wsave (nn); |
|
|
685 Complex *pwsave = wsave.fortran_vec (); |
|
|
686 |
|
|
687 retval = *this; |
|
|
688 Complex *tmp_data = retval.fortran_vec (); |
|
|
689 |
|
|
690 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
458
|
691 |
|
|
692 for (int j = 0; j < nsamples; j++) |
|
1948
|
693 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
458
|
694 |
|
1321
|
695 for (int j = 0; j < npts*nsamples; j++) |
|
2800
|
696 tmp_data[j] = tmp_data[j] / npts; |
|
458
|
697 |
|
1948
|
698 return retval; |
|
458
|
699 } |
|
|
700 |
|
677
|
701 ComplexMatrix |
|
|
702 Matrix::fourier2d (void) const |
|
|
703 { |
|
1948
|
704 ComplexMatrix retval; |
|
|
705 |
|
677
|
706 int nr = rows (); |
|
|
707 int nc = cols (); |
|
1948
|
708 |
|
677
|
709 int npts, nsamples; |
|
1948
|
710 |
|
677
|
711 if (nr == 1 || nc == 1) |
|
|
712 { |
|
|
713 npts = nr > nc ? nr : nc; |
|
|
714 nsamples = 1; |
|
|
715 } |
|
|
716 else |
|
|
717 { |
|
|
718 npts = nr; |
|
|
719 nsamples = nc; |
|
|
720 } |
|
|
721 |
|
|
722 int nn = 4*npts+15; |
|
1948
|
723 |
|
|
724 Array<Complex> wsave (nn); |
|
|
725 Complex *pwsave = wsave.fortran_vec (); |
|
|
726 |
|
|
727 retval = *this; |
|
|
728 Complex *tmp_data = retval.fortran_vec (); |
|
|
729 |
|
|
730 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
731 |
|
|
732 for (int j = 0; j < nsamples; j++) |
|
1948
|
733 F77_FCN (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
734 |
|
|
735 npts = nc; |
|
|
736 nsamples = nr; |
|
|
737 nn = 4*npts+15; |
|
1948
|
738 |
|
|
739 wsave.resize (nn); |
|
|
740 pwsave = wsave.fortran_vec (); |
|
|
741 |
|
|
742 Array<Complex> row (npts); |
|
|
743 Complex *prow = row.fortran_vec (); |
|
|
744 |
|
|
745 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
746 |
|
1321
|
747 for (int j = 0; j < nsamples; j++) |
|
677
|
748 { |
|
|
749 for (int i = 0; i < npts; i++) |
|
1948
|
750 prow[i] = tmp_data[i*nr + j]; |
|
|
751 |
|
|
752 F77_FCN (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
753 |
|
1321
|
754 for (int i = 0; i < npts; i++) |
|
1948
|
755 tmp_data[i*nr + j] = prow[i]; |
|
677
|
756 } |
|
|
757 |
|
1948
|
758 return retval; |
|
677
|
759 } |
|
|
760 |
|
|
761 ComplexMatrix |
|
|
762 Matrix::ifourier2d (void) const |
|
|
763 { |
|
1948
|
764 ComplexMatrix retval; |
|
|
765 |
|
677
|
766 int nr = rows (); |
|
|
767 int nc = cols (); |
|
1948
|
768 |
|
677
|
769 int npts, nsamples; |
|
1948
|
770 |
|
677
|
771 if (nr == 1 || nc == 1) |
|
|
772 { |
|
|
773 npts = nr > nc ? nr : nc; |
|
|
774 nsamples = 1; |
|
|
775 } |
|
|
776 else |
|
|
777 { |
|
|
778 npts = nr; |
|
|
779 nsamples = nc; |
|
|
780 } |
|
|
781 |
|
|
782 int nn = 4*npts+15; |
|
1948
|
783 |
|
|
784 Array<Complex> wsave (nn); |
|
|
785 Complex *pwsave = wsave.fortran_vec (); |
|
|
786 |
|
|
787 retval = *this; |
|
|
788 Complex *tmp_data = retval.fortran_vec (); |
|
|
789 |
|
|
790 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
791 |
|
|
792 for (int j = 0; j < nsamples; j++) |
|
1948
|
793 F77_FCN (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
677
|
794 |
|
1321
|
795 for (int j = 0; j < npts*nsamples; j++) |
|
2800
|
796 tmp_data[j] = tmp_data[j] / npts; |
|
677
|
797 |
|
|
798 npts = nc; |
|
|
799 nsamples = nr; |
|
|
800 nn = 4*npts+15; |
|
1948
|
801 |
|
|
802 wsave.resize (nn); |
|
|
803 pwsave = wsave.fortran_vec (); |
|
|
804 |
|
|
805 Array<Complex> row (npts); |
|
|
806 Complex *prow = row.fortran_vec (); |
|
|
807 |
|
|
808 F77_FCN (cffti, CFFTI) (npts, pwsave); |
|
677
|
809 |
|
1321
|
810 for (int j = 0; j < nsamples; j++) |
|
677
|
811 { |
|
|
812 for (int i = 0; i < npts; i++) |
|
1948
|
813 prow[i] = tmp_data[i*nr + j]; |
|
|
814 |
|
|
815 F77_FCN (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
816 |
|
1321
|
817 for (int i = 0; i < npts; i++) |
|
2800
|
818 tmp_data[i*nr + j] = prow[i] / npts; |
|
677
|
819 } |
|
|
820 |
|
1948
|
821 return retval; |
|
677
|
822 } |
|
|
823 |
|
458
|
824 DET |
|
|
825 Matrix::determinant (void) const |
|
|
826 { |
|
|
827 int info; |
|
|
828 double rcond; |
|
|
829 return determinant (info, rcond); |
|
|
830 } |
|
|
831 |
|
|
832 DET |
|
|
833 Matrix::determinant (int& info) const |
|
|
834 { |
|
|
835 double rcond; |
|
|
836 return determinant (info, rcond); |
|
|
837 } |
|
|
838 |
|
|
839 DET |
|
532
|
840 Matrix::determinant (int& info, double& rcond) const |
|
458
|
841 { |
|
|
842 DET retval; |
|
|
843 |
|
|
844 int nr = rows (); |
|
|
845 int nc = cols (); |
|
|
846 |
|
|
847 if (nr == 0 || nc == 0) |
|
|
848 { |
|
|
849 double d[2]; |
|
|
850 d[0] = 1.0; |
|
|
851 d[1] = 0.0; |
|
|
852 retval = DET (d); |
|
|
853 } |
|
|
854 else |
|
|
855 { |
|
|
856 info = 0; |
|
1948
|
857 |
|
|
858 Array<int> ipvt (nr); |
|
|
859 int *pipvt = ipvt.fortran_vec (); |
|
|
860 |
|
|
861 Array<double> z (nr); |
|
|
862 double *pz = z.fortran_vec (); |
|
|
863 |
|
|
864 Matrix atmp = *this; |
|
|
865 double *tmp_data = atmp.fortran_vec (); |
|
|
866 |
|
|
867 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
868 |
|
|
869 if (f77_exception_encountered) |
|
|
870 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
458
|
871 else |
|
|
872 { |
|
1948
|
873 volatile double rcond_plus_one = rcond + 1.0; |
|
|
874 |
|
|
875 if (rcond_plus_one == 1.0) |
|
|
876 { |
|
|
877 info = -1; |
|
|
878 retval = DET (); |
|
|
879 } |
|
|
880 else |
|
|
881 { |
|
|
882 double d[2]; |
|
|
883 |
|
|
884 F77_XFCN (dgedi, DGEDI, (tmp_data, nr, nr, pipvt, d, pz, 10)); |
|
|
885 |
|
|
886 if (f77_exception_encountered) |
|
|
887 (*current_liboctave_error_handler) |
|
|
888 ("unrecoverable error in dgedi"); |
|
|
889 else |
|
|
890 retval = DET (d); |
|
|
891 } |
|
458
|
892 } |
|
|
893 } |
|
|
894 |
|
|
895 return retval; |
|
|
896 } |
|
|
897 |
|
|
898 Matrix |
|
|
899 Matrix::solve (const Matrix& b) const |
|
|
900 { |
|
|
901 int info; |
|
|
902 double rcond; |
|
|
903 return solve (b, info, rcond); |
|
|
904 } |
|
|
905 |
|
|
906 Matrix |
|
|
907 Matrix::solve (const Matrix& b, int& info) const |
|
|
908 { |
|
|
909 double rcond; |
|
|
910 return solve (b, info, rcond); |
|
|
911 } |
|
|
912 |
|
|
913 Matrix |
|
532
|
914 Matrix::solve (const Matrix& b, int& info, double& rcond) const |
|
458
|
915 { |
|
|
916 Matrix retval; |
|
|
917 |
|
|
918 int nr = rows (); |
|
|
919 int nc = cols (); |
|
1948
|
920 |
|
458
|
921 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
1948
|
922 (*current_liboctave_error_handler) |
|
|
923 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
924 else |
|
|
925 { |
|
1948
|
926 info = 0; |
|
|
927 |
|
|
928 Array<int> ipvt (nr); |
|
|
929 int *pipvt = ipvt.fortran_vec (); |
|
|
930 |
|
|
931 Array<double> z (nr); |
|
|
932 double *pz = z.fortran_vec (); |
|
|
933 |
|
|
934 Matrix atmp = *this; |
|
|
935 double *tmp_data = atmp.fortran_vec (); |
|
|
936 |
|
|
937 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
938 |
|
|
939 if (f77_exception_encountered) |
|
|
940 (*current_liboctave_error_handler) ("unrecoverable error in dgeco"); |
|
|
941 else |
|
|
942 { |
|
|
943 volatile double rcond_plus_one = rcond + 1.0; |
|
|
944 |
|
|
945 if (rcond_plus_one == 1.0) |
|
|
946 { |
|
|
947 info = -2; |
|
|
948 } |
|
|
949 else |
|
|
950 { |
|
|
951 retval = b; |
|
|
952 double *result = retval.fortran_vec (); |
|
|
953 |
|
|
954 int b_nc = b.cols (); |
|
|
955 |
|
|
956 for (volatile int j = 0; j < b_nc; j++) |
|
|
957 { |
|
|
958 F77_XFCN (dgesl, DGESL, (tmp_data, nr, nr, pipvt, |
|
|
959 &result[nr*j], 0)); |
|
|
960 |
|
|
961 if (f77_exception_encountered) |
|
|
962 { |
|
|
963 (*current_liboctave_error_handler) |
|
|
964 ("unrecoverable error in dgesl"); |
|
|
965 |
|
|
966 break; |
|
|
967 } |
|
|
968 } |
|
|
969 } |
|
|
970 } |
|
458
|
971 } |
|
|
972 |
|
|
973 return retval; |
|
|
974 } |
|
|
975 |
|
|
976 ComplexMatrix |
|
|
977 Matrix::solve (const ComplexMatrix& b) const |
|
|
978 { |
|
|
979 ComplexMatrix tmp (*this); |
|
|
980 return tmp.solve (b); |
|
|
981 } |
|
|
982 |
|
|
983 ComplexMatrix |
|
|
984 Matrix::solve (const ComplexMatrix& b, int& info) const |
|
|
985 { |
|
|
986 ComplexMatrix tmp (*this); |
|
|
987 return tmp.solve (b, info); |
|
|
988 } |
|
|
989 |
|
|
990 ComplexMatrix |
|
|
991 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
|
992 { |
|
|
993 ComplexMatrix tmp (*this); |
|
|
994 return tmp.solve (b, info, rcond); |
|
|
995 } |
|
|
996 |
|
|
997 ColumnVector |
|
|
998 Matrix::solve (const ColumnVector& b) const |
|
|
999 { |
|
|
1000 int info; double rcond; |
|
|
1001 return solve (b, info, rcond); |
|
|
1002 } |
|
|
1003 |
|
|
1004 ColumnVector |
|
|
1005 Matrix::solve (const ColumnVector& b, int& info) const |
|
|
1006 { |
|
|
1007 double rcond; |
|
|
1008 return solve (b, info, rcond); |
|
|
1009 } |
|
|
1010 |
|
|
1011 ColumnVector |
|
532
|
1012 Matrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
458
|
1013 { |
|
|
1014 ColumnVector retval; |
|
|
1015 |
|
|
1016 int nr = rows (); |
|
|
1017 int nc = cols (); |
|
1948
|
1018 |
|
458
|
1019 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
1948
|
1020 (*current_liboctave_error_handler) |
|
|
1021 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1022 else |
|
|
1023 { |
|
1948
|
1024 info = 0; |
|
|
1025 |
|
|
1026 Array<int> ipvt (nr); |
|
|
1027 int *pipvt = ipvt.fortran_vec (); |
|
|
1028 |
|
|
1029 Array<double> z (nr); |
|
|
1030 double *pz = z.fortran_vec (); |
|
|
1031 |
|
|
1032 Matrix atmp = *this; |
|
|
1033 double *tmp_data = atmp.fortran_vec (); |
|
|
1034 |
|
|
1035 F77_XFCN (dgeco, DGECO, (tmp_data, nr, nr, pipvt, rcond, pz)); |
|
|
1036 |
|
|
1037 if (f77_exception_encountered) |
|
|
1038 (*current_liboctave_error_handler) |
|
|
1039 ("unrecoverable error in dgeco"); |
|
|
1040 else |
|
|
1041 { |
|
|
1042 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1043 |
|
|
1044 if (rcond_plus_one == 1.0) |
|
|
1045 { |
|
|
1046 info = -2; |
|
|
1047 } |
|
|
1048 else |
|
|
1049 { |
|
|
1050 retval = b; |
|
|
1051 double *result = retval.fortran_vec (); |
|
|
1052 |
|
|
1053 F77_XFCN (dgesl, DGESL, (tmp_data, nr, nr, pipvt, result, 0)); |
|
|
1054 |
|
|
1055 if (f77_exception_encountered) |
|
|
1056 (*current_liboctave_error_handler) |
|
|
1057 ("unrecoverable error in dgesl"); |
|
|
1058 } |
|
|
1059 } |
|
458
|
1060 } |
|
|
1061 |
|
|
1062 return retval; |
|
|
1063 } |
|
|
1064 |
|
|
1065 ComplexColumnVector |
|
|
1066 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1067 { |
|
|
1068 ComplexMatrix tmp (*this); |
|
|
1069 return tmp.solve (b); |
|
|
1070 } |
|
|
1071 |
|
|
1072 ComplexColumnVector |
|
|
1073 Matrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1074 { |
|
|
1075 ComplexMatrix tmp (*this); |
|
|
1076 return tmp.solve (b, info); |
|
|
1077 } |
|
|
1078 |
|
|
1079 ComplexColumnVector |
|
|
1080 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const |
|
|
1081 { |
|
|
1082 ComplexMatrix tmp (*this); |
|
|
1083 return tmp.solve (b, info, rcond); |
|
|
1084 } |
|
|
1085 |
|
|
1086 Matrix |
|
|
1087 Matrix::lssolve (const Matrix& b) const |
|
|
1088 { |
|
|
1089 int info; |
|
|
1090 int rank; |
|
|
1091 return lssolve (b, info, rank); |
|
|
1092 } |
|
|
1093 |
|
|
1094 Matrix |
|
|
1095 Matrix::lssolve (const Matrix& b, int& info) const |
|
|
1096 { |
|
|
1097 int rank; |
|
|
1098 return lssolve (b, info, rank); |
|
|
1099 } |
|
|
1100 |
|
|
1101 Matrix |
|
|
1102 Matrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1103 { |
|
1948
|
1104 Matrix retval; |
|
|
1105 |
|
458
|
1106 int nrhs = b.cols (); |
|
|
1107 |
|
|
1108 int m = rows (); |
|
|
1109 int n = cols (); |
|
|
1110 |
|
|
1111 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1112 (*current_liboctave_error_handler) |
|
|
1113 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1114 else |
|
458
|
1115 { |
|
1948
|
1116 Matrix atmp = *this; |
|
|
1117 double *tmp_data = atmp.fortran_vec (); |
|
|
1118 |
|
|
1119 int nrr = m > n ? m : n; |
|
|
1120 Matrix result (nrr, nrhs); |
|
|
1121 |
|
|
1122 for (int j = 0; j < nrhs; j++) |
|
|
1123 for (int i = 0; i < m; i++) |
|
|
1124 result.elem (i, j) = b.elem (i, j); |
|
|
1125 |
|
|
1126 double *presult = result.fortran_vec (); |
|
|
1127 |
|
|
1128 int len_s = m < n ? m : n; |
|
|
1129 Array<double> s (len_s); |
|
|
1130 double *ps = s.fortran_vec (); |
|
|
1131 |
|
|
1132 double rcond = -1.0; |
|
|
1133 |
|
|
1134 int lwork; |
|
|
1135 if (m < n) |
|
|
1136 lwork = 3*m + (2*m > nrhs |
|
|
1137 ? (2*m > n ? 2*m : n) |
|
|
1138 : (nrhs > n ? nrhs : n)); |
|
|
1139 else |
|
|
1140 lwork = 3*n + (2*n > nrhs |
|
|
1141 ? (2*n > m ? 2*n : m) |
|
|
1142 : (nrhs > m ? nrhs : m)); |
|
|
1143 |
|
3075
|
1144 lwork *= 16; |
|
|
1145 |
|
1948
|
1146 Array<double> work (lwork); |
|
|
1147 double *pwork = work.fortran_vec (); |
|
|
1148 |
|
|
1149 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
1150 rcond, rank, pwork, lwork, info)); |
|
|
1151 |
|
|
1152 if (f77_exception_encountered) |
|
|
1153 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1154 else |
|
|
1155 { |
|
|
1156 retval.resize (n, nrhs); |
|
|
1157 for (int j = 0; j < nrhs; j++) |
|
|
1158 for (int i = 0; i < n; i++) |
|
|
1159 retval.elem (i, j) = result.elem (i, j); |
|
|
1160 } |
|
458
|
1161 } |
|
|
1162 |
|
|
1163 return retval; |
|
|
1164 } |
|
|
1165 |
|
|
1166 ComplexMatrix |
|
|
1167 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1168 { |
|
|
1169 ComplexMatrix tmp (*this); |
|
1484
|
1170 int info; |
|
|
1171 int rank; |
|
|
1172 return tmp.lssolve (b, info, rank); |
|
458
|
1173 } |
|
|
1174 |
|
|
1175 ComplexMatrix |
|
|
1176 Matrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1177 { |
|
|
1178 ComplexMatrix tmp (*this); |
|
1484
|
1179 int rank; |
|
|
1180 return tmp.lssolve (b, info, rank); |
|
458
|
1181 } |
|
|
1182 |
|
|
1183 ComplexMatrix |
|
|
1184 Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1185 { |
|
|
1186 ComplexMatrix tmp (*this); |
|
1484
|
1187 return tmp.lssolve (b, info, rank); |
|
458
|
1188 } |
|
|
1189 |
|
|
1190 ColumnVector |
|
|
1191 Matrix::lssolve (const ColumnVector& b) const |
|
|
1192 { |
|
|
1193 int info; |
|
1484
|
1194 int rank; |
|
|
1195 return lssolve (b, info, rank); |
|
458
|
1196 } |
|
|
1197 |
|
|
1198 ColumnVector |
|
|
1199 Matrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1200 { |
|
|
1201 int rank; |
|
|
1202 return lssolve (b, info, rank); |
|
|
1203 } |
|
|
1204 |
|
|
1205 ColumnVector |
|
|
1206 Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1207 { |
|
1948
|
1208 ColumnVector retval; |
|
|
1209 |
|
458
|
1210 int nrhs = 1; |
|
|
1211 |
|
|
1212 int m = rows (); |
|
|
1213 int n = cols (); |
|
|
1214 |
|
|
1215 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1216 (*current_liboctave_error_handler) |
|
|
1217 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1218 else |
|
458
|
1219 { |
|
1948
|
1220 Matrix atmp = *this; |
|
|
1221 double *tmp_data = atmp.fortran_vec (); |
|
|
1222 |
|
|
1223 int nrr = m > n ? m : n; |
|
|
1224 ColumnVector result (nrr); |
|
|
1225 |
|
|
1226 for (int i = 0; i < m; i++) |
|
|
1227 result.elem (i) = b.elem (i); |
|
|
1228 |
|
|
1229 double *presult = result.fortran_vec (); |
|
|
1230 |
|
|
1231 int len_s = m < n ? m : n; |
|
|
1232 Array<double> s (len_s); |
|
|
1233 double *ps = s.fortran_vec (); |
|
|
1234 |
|
|
1235 double rcond = -1.0; |
|
|
1236 |
|
|
1237 int lwork; |
|
|
1238 if (m < n) |
|
|
1239 lwork = 3*m + (2*m > nrhs |
|
|
1240 ? (2*m > n ? 2*m : n) |
|
|
1241 : (nrhs > n ? nrhs : n)); |
|
|
1242 else |
|
|
1243 lwork = 3*n + (2*n > nrhs |
|
|
1244 ? (2*n > m ? 2*n : m) |
|
|
1245 : (nrhs > m ? nrhs : m)); |
|
|
1246 |
|
3075
|
1247 lwork *= 16; |
|
|
1248 |
|
1948
|
1249 Array<double> work (lwork); |
|
|
1250 double *pwork = work.fortran_vec (); |
|
|
1251 |
|
|
1252 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, |
|
|
1253 ps, rcond, rank, pwork, lwork, info)); |
|
|
1254 |
|
|
1255 if (f77_exception_encountered) |
|
|
1256 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1257 else |
|
|
1258 { |
|
|
1259 retval.resize (n); |
|
|
1260 for (int i = 0; i < n; i++) |
|
|
1261 retval.elem (i) = result.elem (i); |
|
|
1262 } |
|
458
|
1263 } |
|
|
1264 |
|
|
1265 return retval; |
|
|
1266 } |
|
|
1267 |
|
|
1268 ComplexColumnVector |
|
|
1269 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
1270 { |
|
|
1271 ComplexMatrix tmp (*this); |
|
|
1272 return tmp.lssolve (b); |
|
|
1273 } |
|
|
1274 |
|
|
1275 ComplexColumnVector |
|
|
1276 Matrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1277 { |
|
|
1278 ComplexMatrix tmp (*this); |
|
|
1279 return tmp.lssolve (b, info); |
|
|
1280 } |
|
|
1281 |
|
|
1282 ComplexColumnVector |
|
|
1283 Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const |
|
|
1284 { |
|
|
1285 ComplexMatrix tmp (*this); |
|
|
1286 return tmp.lssolve (b, info, rank); |
|
|
1287 } |
|
|
1288 |
|
1819
|
1289 // Constants for matrix exponential calculation. |
|
|
1290 |
|
|
1291 static double padec [] = |
|
|
1292 { |
|
|
1293 5.0000000000000000e-1, |
|
|
1294 1.1666666666666667e-1, |
|
|
1295 1.6666666666666667e-2, |
|
|
1296 1.6025641025641026e-3, |
|
|
1297 1.0683760683760684e-4, |
|
|
1298 4.8562548562548563e-6, |
|
|
1299 1.3875013875013875e-7, |
|
|
1300 1.9270852604185938e-9, |
|
|
1301 }; |
|
|
1302 |
|
|
1303 Matrix |
|
|
1304 Matrix::expm (void) const |
|
|
1305 { |
|
|
1306 Matrix retval; |
|
|
1307 |
|
|
1308 Matrix m = *this; |
|
|
1309 |
|
|
1310 int nc = columns (); |
|
|
1311 |
|
3130
|
1312 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1313 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1314 |
|
1819
|
1315 // trace shift value |
|
3130
|
1316 double trshift = 0.0; |
|
1819
|
1317 |
|
|
1318 for (int i = 0; i < nc; i++) |
|
|
1319 trshift += m.elem (i, i); |
|
|
1320 |
|
|
1321 trshift /= nc; |
|
|
1322 |
|
3130
|
1323 if (trshift > 0.0) |
|
|
1324 { |
|
|
1325 for (int i = 0; i < nc; i++) |
|
|
1326 m.elem (i, i) -= trshift; |
|
|
1327 } |
|
1819
|
1328 |
|
|
1329 // Preconditioning step 2: balancing. |
|
|
1330 |
|
|
1331 AEPBALANCE mbal (m, "B"); |
|
|
1332 m = mbal.balanced_matrix (); |
|
|
1333 Matrix d = mbal.balancing_matrix (); |
|
|
1334 |
|
|
1335 // Preconditioning step 3: scaling. |
|
|
1336 |
|
|
1337 ColumnVector work(nc); |
|
3130
|
1338 double inf_norm; |
|
|
1339 |
|
|
1340 F77_FCN (xdlange, XDLANGE) ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1341 work.fortran_vec (), inf_norm); |
|
1819
|
1342 |
|
|
1343 int sqpow = (int) (inf_norm > 0.0 |
|
|
1344 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
1345 : 0.0); |
|
|
1346 |
|
|
1347 // Check whether we need to square at all. |
|
|
1348 |
|
|
1349 if (sqpow < 0) |
|
|
1350 sqpow = 0; |
|
|
1351 |
|
|
1352 if (sqpow > 0) |
|
|
1353 { |
|
|
1354 double scale_factor = 1.0; |
|
|
1355 for (int i = 0; i < sqpow; i++) |
|
|
1356 scale_factor *= 2.0; |
|
|
1357 |
|
|
1358 m = m / scale_factor; |
|
|
1359 } |
|
|
1360 |
|
|
1361 // npp, dpp: pade' approx polynomial matrices. |
|
|
1362 |
|
|
1363 Matrix npp (nc, nc, 0.0); |
|
|
1364 Matrix dpp = npp; |
|
|
1365 |
|
|
1366 // Now powers a^8 ... a^1. |
|
|
1367 |
|
|
1368 int minus_one_j = -1; |
|
|
1369 for (int j = 7; j >= 0; j--) |
|
|
1370 { |
|
|
1371 npp = m * npp + m * padec[j]; |
|
|
1372 dpp = m * dpp + m * (minus_one_j * padec[j]); |
|
|
1373 minus_one_j *= -1; |
|
|
1374 } |
|
|
1375 |
|
|
1376 // Zero power. |
|
|
1377 |
|
|
1378 dpp = -dpp; |
|
3130
|
1379 for (int j = 0; j < nc; j++) |
|
1819
|
1380 { |
|
|
1381 npp.elem (j, j) += 1.0; |
|
|
1382 dpp.elem (j, j) += 1.0; |
|
|
1383 } |
|
|
1384 |
|
|
1385 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1386 |
|
|
1387 retval = dpp.solve (npp); |
|
|
1388 |
|
|
1389 // Reverse preconditioning step 3: repeated squaring. |
|
|
1390 |
|
|
1391 while (sqpow) |
|
|
1392 { |
|
|
1393 retval = retval * retval; |
|
|
1394 sqpow--; |
|
|
1395 } |
|
|
1396 |
|
|
1397 // Reverse preconditioning step 2: inverse balancing. |
|
|
1398 |
|
|
1399 retval = retval.transpose(); |
|
|
1400 d = d.transpose (); |
|
|
1401 retval = retval * d; |
|
|
1402 retval = d.solve (retval); |
|
|
1403 retval = retval.transpose (); |
|
|
1404 |
|
|
1405 // Reverse preconditioning step 1: fix trace normalization. |
|
|
1406 |
|
3130
|
1407 if (trshift > 0.0) |
|
|
1408 retval = exp (trshift) * retval; |
|
|
1409 |
|
|
1410 return retval; |
|
1819
|
1411 } |
|
|
1412 |
|
458
|
1413 Matrix& |
|
|
1414 Matrix::operator += (const Matrix& a) |
|
|
1415 { |
|
|
1416 int nr = rows (); |
|
|
1417 int nc = cols (); |
|
2385
|
1418 |
|
|
1419 int a_nr = a.rows (); |
|
|
1420 int a_nc = a.cols (); |
|
|
1421 |
|
|
1422 if (nr != a_nr || nc != a_nc) |
|
458
|
1423 { |
|
2385
|
1424 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1425 return *this; |
|
|
1426 } |
|
|
1427 |
|
|
1428 if (nr == 0 || nc == 0) |
|
|
1429 return *this; |
|
|
1430 |
|
|
1431 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1432 |
|
|
1433 add2 (d, a.data (), length ()); |
|
|
1434 |
|
|
1435 return *this; |
|
|
1436 } |
|
|
1437 |
|
|
1438 Matrix& |
|
|
1439 Matrix::operator -= (const Matrix& a) |
|
|
1440 { |
|
|
1441 int nr = rows (); |
|
|
1442 int nc = cols (); |
|
2385
|
1443 |
|
|
1444 int a_nr = a.rows (); |
|
|
1445 int a_nc = a.cols (); |
|
|
1446 |
|
|
1447 if (nr != a_nr || nc != a_nc) |
|
458
|
1448 { |
|
2385
|
1449 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1450 return *this; |
|
|
1451 } |
|
|
1452 |
|
|
1453 if (nr == 0 || nc == 0) |
|
|
1454 return *this; |
|
|
1455 |
|
|
1456 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1457 |
|
|
1458 subtract2 (d, a.data (), length ()); |
|
|
1459 |
|
|
1460 return *this; |
|
|
1461 } |
|
|
1462 |
|
|
1463 Matrix& |
|
|
1464 Matrix::operator += (const DiagMatrix& a) |
|
|
1465 { |
|
2385
|
1466 int nr = rows (); |
|
|
1467 int nc = cols (); |
|
|
1468 |
|
|
1469 int a_nr = a.rows (); |
|
|
1470 int a_nc = a.cols (); |
|
|
1471 |
|
|
1472 if (nr != a_nr || nc != a_nc) |
|
458
|
1473 { |
|
2385
|
1474 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1475 return *this; |
|
|
1476 } |
|
|
1477 |
|
|
1478 for (int i = 0; i < a.length (); i++) |
|
|
1479 elem (i, i) += a.elem (i, i); |
|
|
1480 |
|
|
1481 return *this; |
|
|
1482 } |
|
|
1483 |
|
|
1484 Matrix& |
|
|
1485 Matrix::operator -= (const DiagMatrix& a) |
|
|
1486 { |
|
2385
|
1487 int nr = rows (); |
|
|
1488 int nc = cols (); |
|
|
1489 |
|
|
1490 int a_nr = a.rows (); |
|
|
1491 int a_nc = a.cols (); |
|
|
1492 |
|
|
1493 if (nr != a_nr || nc != a_nc) |
|
458
|
1494 { |
|
2385
|
1495 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1496 return *this; |
|
|
1497 } |
|
|
1498 |
|
|
1499 for (int i = 0; i < a.length (); i++) |
|
|
1500 elem (i, i) -= a.elem (i, i); |
|
|
1501 |
|
|
1502 return *this; |
|
|
1503 } |
|
|
1504 |
|
|
1505 // unary operations |
|
|
1506 |
|
2964
|
1507 boolMatrix |
|
458
|
1508 Matrix::operator ! (void) const |
|
|
1509 { |
|
|
1510 int nr = rows (); |
|
|
1511 int nc = cols (); |
|
|
1512 |
|
2964
|
1513 boolMatrix b (nr, nc); |
|
458
|
1514 |
|
|
1515 for (int j = 0; j < nc; j++) |
|
|
1516 for (int i = 0; i < nr; i++) |
|
|
1517 b.elem (i, j) = ! elem (i, j); |
|
|
1518 |
|
|
1519 return b; |
|
|
1520 } |
|
|
1521 |
|
1205
|
1522 // column vector by row vector -> matrix operations |
|
458
|
1523 |
|
1205
|
1524 Matrix |
|
|
1525 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
1526 { |
|
1948
|
1527 Matrix retval; |
|
|
1528 |
|
1205
|
1529 int len = v.length (); |
|
3233
|
1530 |
|
|
1531 if (len != 0) |
|
1205
|
1532 { |
|
3233
|
1533 int a_len = a.length (); |
|
|
1534 |
|
|
1535 retval.resize (len, a_len); |
|
|
1536 double *c = retval.fortran_vec (); |
|
|
1537 |
|
|
1538 F77_XFCN (dgemm, DGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
1539 v.data (), len, a.data (), 1, 0.0, |
|
|
1540 c, len, 1L, 1L)); |
|
|
1541 |
|
|
1542 if (f77_exception_encountered) |
|
|
1543 (*current_liboctave_error_handler) |
|
|
1544 ("unrecoverable error in dgemm"); |
|
1205
|
1545 } |
|
458
|
1546 |
|
1948
|
1547 return retval; |
|
458
|
1548 } |
|
|
1549 |
|
|
1550 // other operations. |
|
|
1551 |
|
|
1552 Matrix |
|
2676
|
1553 Matrix::map (d_d_Mapper f) const |
|
1205
|
1554 { |
|
2676
|
1555 Matrix b (*this); |
|
|
1556 return b.apply (f); |
|
1205
|
1557 } |
|
|
1558 |
|
3248
|
1559 boolMatrix |
|
|
1560 Matrix::map (b_d_Mapper f) const |
|
|
1561 { |
|
|
1562 int nr = rows (); |
|
|
1563 int nc = cols (); |
|
|
1564 |
|
|
1565 boolMatrix retval (nr, nc); |
|
|
1566 |
|
|
1567 for (int j = 0; j < nc; j++) |
|
|
1568 for (int i = 0; i < nr; i++) |
|
|
1569 retval(i,j) = f (elem(i,j)); |
|
|
1570 |
|
|
1571 return retval; |
|
|
1572 } |
|
|
1573 |
|
2676
|
1574 Matrix& |
|
|
1575 Matrix::apply (d_d_Mapper f) |
|
458
|
1576 { |
|
|
1577 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1578 |
|
|
1579 for (int i = 0; i < length (); i++) |
|
|
1580 d[i] = f (d[i]); |
|
2676
|
1581 |
|
|
1582 return *this; |
|
458
|
1583 } |
|
|
1584 |
|
2385
|
1585 bool |
|
|
1586 Matrix::any_element_is_negative (void) const |
|
|
1587 { |
|
|
1588 int nr = rows (); |
|
|
1589 int nc = cols (); |
|
|
1590 |
|
|
1591 for (int j = 0; j < nc; j++) |
|
|
1592 for (int i = 0; i < nr; i++) |
|
|
1593 if (elem (i, j) < 0.0) |
|
|
1594 return true; |
|
|
1595 |
|
|
1596 return false; |
|
|
1597 } |
|
|
1598 |
|
|
1599 |
|
|
1600 bool |
|
|
1601 Matrix::any_element_is_inf_or_nan (void) const |
|
|
1602 { |
|
|
1603 int nr = rows (); |
|
|
1604 int nc = cols (); |
|
|
1605 |
|
|
1606 for (int j = 0; j < nc; j++) |
|
|
1607 for (int i = 0; i < nr; i++) |
|
|
1608 { |
|
|
1609 double val = elem (i, j); |
|
|
1610 if (xisinf (val) || xisnan (val)) |
|
|
1611 return 1; |
|
|
1612 } |
|
|
1613 return 0; |
|
|
1614 } |
|
|
1615 |
|
|
1616 bool |
|
|
1617 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
1618 { |
|
|
1619 int nr = rows (); |
|
|
1620 int nc = cols (); |
|
|
1621 |
|
|
1622 for (int j = 0; j < nc; j++) |
|
|
1623 for (int i = 0; i < nr; i++) |
|
|
1624 { |
|
|
1625 double val = elem (i, j); |
|
|
1626 if (xisnan (val) || D_NINT (val) == val) |
|
|
1627 continue; |
|
|
1628 else |
|
|
1629 return false; |
|
|
1630 } |
|
|
1631 |
|
|
1632 return true; |
|
|
1633 } |
|
|
1634 |
|
1968
|
1635 // Return nonzero if any element of M is not an integer. Also extract |
|
|
1636 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
1637 |
|
2385
|
1638 bool |
|
1968
|
1639 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
1640 { |
|
|
1641 int nr = rows (); |
|
|
1642 int nc = cols (); |
|
|
1643 |
|
|
1644 if (nr > 0 && nc > 0) |
|
|
1645 { |
|
|
1646 max_val = elem (0, 0); |
|
|
1647 min_val = elem (0, 0); |
|
|
1648 } |
|
|
1649 else |
|
2385
|
1650 return false; |
|
1968
|
1651 |
|
|
1652 for (int j = 0; j < nc; j++) |
|
|
1653 for (int i = 0; i < nr; i++) |
|
|
1654 { |
|
|
1655 double val = elem (i, j); |
|
|
1656 |
|
|
1657 if (val > max_val) |
|
|
1658 max_val = val; |
|
|
1659 |
|
|
1660 if (val < min_val) |
|
|
1661 min_val = val; |
|
|
1662 |
|
|
1663 if (D_NINT (val) != val) |
|
2385
|
1664 return false; |
|
1968
|
1665 } |
|
2385
|
1666 |
|
|
1667 return true; |
|
1968
|
1668 } |
|
|
1669 |
|
2385
|
1670 bool |
|
1968
|
1671 Matrix::too_large_for_float (void) const |
|
|
1672 { |
|
|
1673 int nr = rows (); |
|
2385
|
1674 int nc = cols (); |
|
1968
|
1675 |
|
|
1676 for (int j = 0; j < nc; j++) |
|
|
1677 for (int i = 0; i < nr; i++) |
|
|
1678 { |
|
|
1679 double val = elem (i, j); |
|
|
1680 |
|
|
1681 if (val > FLT_MAX || val < FLT_MIN) |
|
2385
|
1682 return true; |
|
1968
|
1683 } |
|
|
1684 |
|
2385
|
1685 return false; |
|
1968
|
1686 } |
|
|
1687 |
|
458
|
1688 // XXX FIXME XXX Do these really belong here? They should maybe be |
|
|
1689 // cleaned up a bit, no? What about corresponding functions for the |
|
|
1690 // Vectors? |
|
|
1691 |
|
2832
|
1692 boolMatrix |
|
458
|
1693 Matrix::all (void) const |
|
|
1694 { |
|
|
1695 int nr = rows (); |
|
|
1696 int nc = cols (); |
|
2832
|
1697 boolMatrix retval; |
|
458
|
1698 if (nr > 0 && nc > 0) |
|
|
1699 { |
|
|
1700 if (nr == 1) |
|
|
1701 { |
|
|
1702 retval.resize (1, 1); |
|
2832
|
1703 retval.elem (0, 0) = true; |
|
458
|
1704 for (int j = 0; j < nc; j++) |
|
|
1705 { |
|
|
1706 if (elem (0, j) == 0.0) |
|
|
1707 { |
|
2832
|
1708 retval.elem (0, 0) = false; |
|
458
|
1709 break; |
|
|
1710 } |
|
|
1711 } |
|
|
1712 } |
|
|
1713 else if (nc == 1) |
|
|
1714 { |
|
|
1715 retval.resize (1, 1); |
|
2832
|
1716 retval.elem (0, 0) = true; |
|
458
|
1717 for (int i = 0; i < nr; i++) |
|
|
1718 { |
|
|
1719 if (elem (i, 0) == 0.0) |
|
|
1720 { |
|
2832
|
1721 retval.elem (0, 0) = false; |
|
458
|
1722 break; |
|
|
1723 } |
|
|
1724 } |
|
|
1725 } |
|
|
1726 else |
|
|
1727 { |
|
|
1728 retval.resize (1, nc); |
|
|
1729 for (int j = 0; j < nc; j++) |
|
|
1730 { |
|
2832
|
1731 retval.elem (0, j) = true; |
|
458
|
1732 for (int i = 0; i < nr; i++) |
|
|
1733 { |
|
|
1734 if (elem (i, j) == 0.0) |
|
|
1735 { |
|
2832
|
1736 retval.elem (0, j) = false; |
|
458
|
1737 break; |
|
|
1738 } |
|
|
1739 } |
|
|
1740 } |
|
|
1741 } |
|
|
1742 } |
|
|
1743 return retval; |
|
|
1744 } |
|
|
1745 |
|
2832
|
1746 boolMatrix |
|
458
|
1747 Matrix::any (void) const |
|
|
1748 { |
|
|
1749 int nr = rows (); |
|
|
1750 int nc = cols (); |
|
2832
|
1751 boolMatrix retval; |
|
458
|
1752 if (nr > 0 && nc > 0) |
|
|
1753 { |
|
|
1754 if (nr == 1) |
|
|
1755 { |
|
|
1756 retval.resize (1, 1); |
|
2832
|
1757 retval.elem (0, 0) = false; |
|
458
|
1758 for (int j = 0; j < nc; j++) |
|
|
1759 { |
|
|
1760 if (elem (0, j) != 0.0) |
|
|
1761 { |
|
2832
|
1762 retval.elem (0, 0) = true; |
|
458
|
1763 break; |
|
|
1764 } |
|
|
1765 } |
|
|
1766 } |
|
|
1767 else if (nc == 1) |
|
|
1768 { |
|
|
1769 retval.resize (1, 1); |
|
2832
|
1770 retval.elem (0, 0) = false; |
|
458
|
1771 for (int i = 0; i < nr; i++) |
|
|
1772 { |
|
|
1773 if (elem (i, 0) != 0.0) |
|
|
1774 { |
|
2832
|
1775 retval.elem (0, 0) = true; |
|
458
|
1776 break; |
|
|
1777 } |
|
|
1778 } |
|
|
1779 } |
|
|
1780 else |
|
|
1781 { |
|
|
1782 retval.resize (1, nc); |
|
|
1783 for (int j = 0; j < nc; j++) |
|
|
1784 { |
|
2832
|
1785 retval.elem (0, j) = false; |
|
458
|
1786 for (int i = 0; i < nr; i++) |
|
|
1787 { |
|
|
1788 if (elem (i, j) != 0.0) |
|
|
1789 { |
|
2832
|
1790 retval.elem (0, j) = true; |
|
458
|
1791 break; |
|
|
1792 } |
|
|
1793 } |
|
|
1794 } |
|
|
1795 } |
|
|
1796 } |
|
|
1797 return retval; |
|
|
1798 } |
|
|
1799 |
|
|
1800 Matrix |
|
|
1801 Matrix::cumprod (void) const |
|
|
1802 { |
|
|
1803 Matrix retval; |
|
|
1804 |
|
|
1805 int nr = rows (); |
|
|
1806 int nc = cols (); |
|
|
1807 |
|
|
1808 if (nr == 1) |
|
|
1809 { |
|
|
1810 retval.resize (1, nc); |
|
|
1811 if (nc > 0) |
|
|
1812 { |
|
|
1813 double prod = elem (0, 0); |
|
|
1814 for (int j = 0; j < nc; j++) |
|
|
1815 { |
|
|
1816 retval.elem (0, j) = prod; |
|
|
1817 if (j < nc - 1) |
|
|
1818 prod *= elem (0, j+1); |
|
|
1819 } |
|
|
1820 } |
|
|
1821 } |
|
|
1822 else if (nc == 1) |
|
|
1823 { |
|
|
1824 retval.resize (nr, 1); |
|
|
1825 if (nr > 0) |
|
|
1826 { |
|
|
1827 double prod = elem (0, 0); |
|
|
1828 for (int i = 0; i < nr; i++) |
|
|
1829 { |
|
|
1830 retval.elem (i, 0) = prod; |
|
|
1831 if (i < nr - 1) |
|
|
1832 prod *= elem (i+1, 0); |
|
|
1833 } |
|
|
1834 } |
|
|
1835 } |
|
|
1836 else |
|
|
1837 { |
|
|
1838 retval.resize (nr, nc); |
|
|
1839 if (nr > 0 && nc > 0) |
|
|
1840 { |
|
|
1841 for (int j = 0; j < nc; j++) |
|
|
1842 { |
|
|
1843 double prod = elem (0, j); |
|
|
1844 for (int i = 0; i < nr; i++) |
|
|
1845 { |
|
|
1846 retval.elem (i, j) = prod; |
|
|
1847 if (i < nr - 1) |
|
|
1848 prod *= elem (i+1, j); |
|
|
1849 } |
|
|
1850 } |
|
|
1851 } |
|
|
1852 } |
|
|
1853 return retval; |
|
|
1854 } |
|
|
1855 |
|
|
1856 Matrix |
|
|
1857 Matrix::cumsum (void) const |
|
|
1858 { |
|
|
1859 Matrix retval; |
|
|
1860 |
|
|
1861 int nr = rows (); |
|
|
1862 int nc = cols (); |
|
|
1863 |
|
|
1864 if (nr == 1) |
|
|
1865 { |
|
|
1866 retval.resize (1, nc); |
|
|
1867 if (nc > 0) |
|
|
1868 { |
|
|
1869 double sum = elem (0, 0); |
|
|
1870 for (int j = 0; j < nc; j++) |
|
|
1871 { |
|
|
1872 retval.elem (0, j) = sum; |
|
|
1873 if (j < nc - 1) |
|
|
1874 sum += elem (0, j+1); |
|
|
1875 } |
|
|
1876 } |
|
|
1877 } |
|
|
1878 else if (nc == 1) |
|
|
1879 { |
|
|
1880 retval.resize (nr, 1); |
|
|
1881 if (nr > 0) |
|
|
1882 { |
|
|
1883 double sum = elem (0, 0); |
|
|
1884 for (int i = 0; i < nr; i++) |
|
|
1885 { |
|
|
1886 retval.elem (i, 0) = sum; |
|
|
1887 if (i < nr - 1) |
|
|
1888 sum += elem (i+1, 0); |
|
|
1889 } |
|
|
1890 } |
|
|
1891 } |
|
|
1892 else |
|
|
1893 { |
|
|
1894 retval.resize (nr, nc); |
|
|
1895 if (nr > 0 && nc > 0) |
|
|
1896 { |
|
|
1897 for (int j = 0; j < nc; j++) |
|
|
1898 { |
|
|
1899 double sum = elem (0, j); |
|
|
1900 for (int i = 0; i < nr; i++) |
|
|
1901 { |
|
|
1902 retval.elem (i, j) = sum; |
|
|
1903 if (i < nr - 1) |
|
|
1904 sum += elem (i+1, j); |
|
|
1905 } |
|
|
1906 } |
|
|
1907 } |
|
|
1908 } |
|
|
1909 return retval; |
|
|
1910 } |
|
|
1911 |
|
|
1912 Matrix |
|
|
1913 Matrix::prod (void) const |
|
|
1914 { |
|
|
1915 Matrix retval; |
|
|
1916 |
|
|
1917 int nr = rows (); |
|
|
1918 int nc = cols (); |
|
|
1919 |
|
|
1920 if (nr == 1) |
|
|
1921 { |
|
|
1922 retval.resize (1, 1); |
|
|
1923 retval.elem (0, 0) = 1.0; |
|
|
1924 for (int j = 0; j < nc; j++) |
|
|
1925 retval.elem (0, 0) *= elem (0, j); |
|
|
1926 } |
|
|
1927 else if (nc == 1) |
|
|
1928 { |
|
|
1929 retval.resize (1, 1); |
|
|
1930 retval.elem (0, 0) = 1.0; |
|
|
1931 for (int i = 0; i < nr; i++) |
|
|
1932 retval.elem (0, 0) *= elem (i, 0); |
|
|
1933 } |
|
|
1934 else |
|
|
1935 { |
|
|
1936 if (nc == 0) |
|
|
1937 { |
|
|
1938 retval.resize (1, 1); |
|
|
1939 retval.elem (0, 0) = 1.0; |
|
|
1940 } |
|
|
1941 else |
|
|
1942 retval.resize (1, nc); |
|
|
1943 |
|
|
1944 for (int j = 0; j < nc; j++) |
|
|
1945 { |
|
|
1946 retval.elem (0, j) = 1.0; |
|
|
1947 for (int i = 0; i < nr; i++) |
|
|
1948 retval.elem (0, j) *= elem (i, j); |
|
|
1949 } |
|
|
1950 } |
|
|
1951 return retval; |
|
|
1952 } |
|
|
1953 |
|
|
1954 Matrix |
|
|
1955 Matrix::sum (void) const |
|
|
1956 { |
|
|
1957 Matrix retval; |
|
|
1958 |
|
|
1959 int nr = rows (); |
|
|
1960 int nc = cols (); |
|
|
1961 |
|
|
1962 if (nr == 1) |
|
|
1963 { |
|
|
1964 retval.resize (1, 1); |
|
|
1965 retval.elem (0, 0) = 0.0; |
|
|
1966 for (int j = 0; j < nc; j++) |
|
|
1967 retval.elem (0, 0) += elem (0, j); |
|
|
1968 } |
|
|
1969 else if (nc == 1) |
|
|
1970 { |
|
|
1971 retval.resize (1, 1); |
|
|
1972 retval.elem (0, 0) = 0.0; |
|
|
1973 for (int i = 0; i < nr; i++) |
|
|
1974 retval.elem (0, 0) += elem (i, 0); |
|
|
1975 } |
|
|
1976 else |
|
|
1977 { |
|
|
1978 if (nc == 0) |
|
|
1979 { |
|
|
1980 retval.resize (1, 1); |
|
|
1981 retval.elem (0, 0) = 0.0; |
|
|
1982 } |
|
|
1983 else |
|
|
1984 retval.resize (1, nc); |
|
|
1985 |
|
|
1986 for (int j = 0; j < nc; j++) |
|
|
1987 { |
|
|
1988 retval.elem (0, j) = 0.0; |
|
|
1989 for (int i = 0; i < nr; i++) |
|
|
1990 retval.elem (0, j) += elem (i, j); |
|
|
1991 } |
|
|
1992 } |
|
|
1993 return retval; |
|
|
1994 } |
|
|
1995 |
|
|
1996 Matrix |
|
|
1997 Matrix::sumsq (void) const |
|
|
1998 { |
|
|
1999 Matrix retval; |
|
|
2000 |
|
|
2001 int nr = rows (); |
|
|
2002 int nc = cols (); |
|
|
2003 |
|
|
2004 if (nr == 1) |
|
|
2005 { |
|
|
2006 retval.resize (1, 1); |
|
|
2007 retval.elem (0, 0) = 0.0; |
|
|
2008 for (int j = 0; j < nc; j++) |
|
|
2009 { |
|
|
2010 double d = elem (0, j); |
|
|
2011 retval.elem (0, 0) += d * d; |
|
|
2012 } |
|
|
2013 } |
|
|
2014 else if (nc == 1) |
|
|
2015 { |
|
|
2016 retval.resize (1, 1); |
|
|
2017 retval.elem (0, 0) = 0.0; |
|
|
2018 for (int i = 0; i < nr; i++) |
|
|
2019 { |
|
|
2020 double d = elem (i, 0); |
|
|
2021 retval.elem (0, 0) += d * d; |
|
|
2022 } |
|
|
2023 } |
|
|
2024 else |
|
|
2025 { |
|
|
2026 retval.resize (1, nc); |
|
|
2027 for (int j = 0; j < nc; j++) |
|
|
2028 { |
|
|
2029 retval.elem (0, j) = 0.0; |
|
|
2030 for (int i = 0; i < nr; i++) |
|
|
2031 { |
|
|
2032 double d = elem (i, j); |
|
|
2033 retval.elem (0, j) += d * d; |
|
|
2034 } |
|
|
2035 } |
|
|
2036 } |
|
|
2037 return retval; |
|
|
2038 } |
|
|
2039 |
|
2385
|
2040 Matrix |
|
|
2041 Matrix::abs (void) const |
|
|
2042 { |
|
|
2043 int nr = rows (); |
|
|
2044 int nc = cols (); |
|
|
2045 |
|
|
2046 Matrix retval (nr, nc); |
|
|
2047 |
|
|
2048 for (int j = 0; j < nc; j++) |
|
|
2049 for (int i = 0; i < nr; i++) |
|
|
2050 retval (i, j) = fabs (elem (i, j)); |
|
|
2051 |
|
|
2052 return retval; |
|
|
2053 } |
|
|
2054 |
|
458
|
2055 ColumnVector |
|
|
2056 Matrix::diag (void) const |
|
|
2057 { |
|
|
2058 return diag (0); |
|
|
2059 } |
|
|
2060 |
|
|
2061 ColumnVector |
|
|
2062 Matrix::diag (int k) const |
|
|
2063 { |
|
|
2064 int nnr = rows (); |
|
|
2065 int nnc = cols (); |
|
|
2066 if (k > 0) |
|
|
2067 nnc -= k; |
|
|
2068 else if (k < 0) |
|
|
2069 nnr += k; |
|
|
2070 |
|
|
2071 ColumnVector d; |
|
|
2072 |
|
|
2073 if (nnr > 0 && nnc > 0) |
|
|
2074 { |
|
|
2075 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2076 |
|
|
2077 d.resize (ndiag); |
|
|
2078 |
|
|
2079 if (k > 0) |
|
|
2080 { |
|
|
2081 for (int i = 0; i < ndiag; i++) |
|
|
2082 d.elem (i) = elem (i, i+k); |
|
|
2083 } |
|
|
2084 else if ( k < 0) |
|
|
2085 { |
|
|
2086 for (int i = 0; i < ndiag; i++) |
|
|
2087 d.elem (i) = elem (i-k, i); |
|
|
2088 } |
|
|
2089 else |
|
|
2090 { |
|
|
2091 for (int i = 0; i < ndiag; i++) |
|
|
2092 d.elem (i) = elem (i, i); |
|
|
2093 } |
|
|
2094 } |
|
|
2095 else |
|
|
2096 cerr << "diag: requested diagonal out of range\n"; |
|
|
2097 |
|
|
2098 return d; |
|
|
2099 } |
|
|
2100 |
|
|
2101 ColumnVector |
|
|
2102 Matrix::row_min (void) const |
|
|
2103 { |
|
2354
|
2104 Array<int> index; |
|
|
2105 return row_min (index); |
|
458
|
2106 } |
|
|
2107 |
|
|
2108 ColumnVector |
|
2354
|
2109 Matrix::row_min (Array<int>& index) const |
|
458
|
2110 { |
|
|
2111 ColumnVector result; |
|
|
2112 |
|
|
2113 int nr = rows (); |
|
|
2114 int nc = cols (); |
|
|
2115 |
|
|
2116 if (nr > 0 && nc > 0) |
|
|
2117 { |
|
|
2118 result.resize (nr); |
|
2354
|
2119 index.resize (nr); |
|
458
|
2120 |
|
|
2121 for (int i = 0; i < nr; i++) |
|
|
2122 { |
|
2354
|
2123 int idx = 0; |
|
|
2124 |
|
|
2125 double tmp_min = elem (i, idx); |
|
|
2126 |
|
|
2127 if (xisnan (tmp_min)) |
|
|
2128 idx = -1; |
|
|
2129 else |
|
|
2130 { |
|
|
2131 for (int j = 1; j < nc; j++) |
|
|
2132 { |
|
|
2133 double tmp = elem (i, j); |
|
|
2134 |
|
|
2135 if (xisnan (tmp)) |
|
|
2136 { |
|
|
2137 idx = -1; |
|
|
2138 break; |
|
|
2139 } |
|
|
2140 else if (tmp < tmp_min) |
|
|
2141 { |
|
|
2142 idx = j; |
|
|
2143 tmp_min = tmp; |
|
|
2144 } |
|
|
2145 } |
|
|
2146 } |
|
|
2147 |
|
|
2148 result.elem (i) = (idx < 0) ? octave_NaN : tmp_min; |
|
|
2149 index.elem (i) = idx; |
|
458
|
2150 } |
|
|
2151 } |
|
|
2152 |
|
|
2153 return result; |
|
|
2154 } |
|
|
2155 |
|
|
2156 ColumnVector |
|
|
2157 Matrix::row_max (void) const |
|
|
2158 { |
|
2354
|
2159 Array<int> index; |
|
|
2160 return row_max (index); |
|
458
|
2161 } |
|
|
2162 |
|
|
2163 ColumnVector |
|
2354
|
2164 Matrix::row_max (Array<int>& index) const |
|
458
|
2165 { |
|
|
2166 ColumnVector result; |
|
|
2167 |
|
|
2168 int nr = rows (); |
|
|
2169 int nc = cols (); |
|
|
2170 |
|
|
2171 if (nr > 0 && nc > 0) |
|
|
2172 { |
|
|
2173 result.resize (nr); |
|
2354
|
2174 index.resize (nr); |
|
458
|
2175 |
|
|
2176 for (int i = 0; i < nr; i++) |
|
|
2177 { |
|
2354
|
2178 int idx = 0; |
|
|
2179 |
|
|
2180 double tmp_max = elem (i, idx); |
|
|
2181 |
|
|
2182 if (xisnan (tmp_max)) |
|
|
2183 idx = -1; |
|
|
2184 else |
|
|
2185 { |
|
|
2186 for (int j = 1; j < nc; j++) |
|
|
2187 { |
|
|
2188 double tmp = elem (i, j); |
|
|
2189 |
|
|
2190 if (xisnan (tmp)) |
|
|
2191 { |
|
|
2192 idx = -1; |
|
|
2193 break; |
|
|
2194 } |
|
|
2195 else if (tmp > tmp_max) |
|
|
2196 { |
|
|
2197 idx = j; |
|
|
2198 tmp_max = tmp; |
|
|
2199 } |
|
|
2200 } |
|
|
2201 } |
|
|
2202 |
|
|
2203 result.elem (i) = (idx < 0) ? octave_NaN : tmp_max; |
|
|
2204 index.elem (i) = idx; |
|
458
|
2205 } |
|
|
2206 } |
|
|
2207 |
|
|
2208 return result; |
|
|
2209 } |
|
|
2210 |
|
|
2211 RowVector |
|
|
2212 Matrix::column_min (void) const |
|
|
2213 { |
|
2354
|
2214 Array<int> index; |
|
|
2215 return column_min (index); |
|
458
|
2216 } |
|
2354
|
2217 |
|
458
|
2218 RowVector |
|
2354
|
2219 Matrix::column_min (Array<int>& index) const |
|
458
|
2220 { |
|
|
2221 RowVector result; |
|
|
2222 |
|
|
2223 int nr = rows (); |
|
|
2224 int nc = cols (); |
|
|
2225 |
|
|
2226 if (nr > 0 && nc > 0) |
|
|
2227 { |
|
|
2228 result.resize (nc); |
|
2354
|
2229 index.resize (nc); |
|
458
|
2230 |
|
|
2231 for (int j = 0; j < nc; j++) |
|
|
2232 { |
|
2354
|
2233 int idx = 0; |
|
|
2234 |
|
|
2235 double tmp_min = elem (idx, j); |
|
|
2236 |
|
|
2237 if (xisnan (tmp_min)) |
|
|
2238 idx = -1; |
|
|
2239 else |
|
|
2240 { |
|
|
2241 for (int i = 1; i < nr; i++) |
|
|
2242 { |
|
|
2243 double tmp = elem (i, j); |
|
|
2244 |
|
|
2245 if (xisnan (tmp)) |
|
|
2246 { |
|
|
2247 idx = -1; |
|
|
2248 break; |
|
|
2249 } |
|
|
2250 else if (tmp < tmp_min) |
|
|
2251 { |
|
|
2252 idx = i; |
|
|
2253 tmp_min = tmp; |
|
|
2254 } |
|
|
2255 } |
|
|
2256 } |
|
|
2257 |
|
|
2258 result.elem (j) = (idx < 0) ? octave_NaN : tmp_min; |
|
|
2259 index.elem (j) = idx; |
|
458
|
2260 } |
|
|
2261 } |
|
|
2262 |
|
|
2263 return result; |
|
|
2264 } |
|
|
2265 |
|
2354
|
2266 RowVector |
|
|
2267 Matrix::column_max (void) const |
|
|
2268 { |
|
|
2269 Array<int> index; |
|
|
2270 return column_max (index); |
|
|
2271 } |
|
458
|
2272 |
|
|
2273 RowVector |
|
2354
|
2274 Matrix::column_max (Array<int>& index) const |
|
458
|
2275 { |
|
|
2276 RowVector result; |
|
|
2277 |
|
|
2278 int nr = rows (); |
|
|
2279 int nc = cols (); |
|
|
2280 |
|
|
2281 if (nr > 0 && nc > 0) |
|
|
2282 { |
|
|
2283 result.resize (nc); |
|
2354
|
2284 index.resize (nc); |
|
458
|
2285 |
|
|
2286 for (int j = 0; j < nc; j++) |
|
|
2287 { |
|
2354
|
2288 int idx = 0; |
|
|
2289 |
|
|
2290 double tmp_max = elem (idx, j); |
|
|
2291 |
|
|
2292 if (xisnan (tmp_max)) |
|
|
2293 idx = -1; |
|
|
2294 else |
|
|
2295 { |
|
|
2296 for (int i = 1; i < nr; i++) |
|
|
2297 { |
|
|
2298 double tmp = elem (i, j); |
|
|
2299 |
|
|
2300 if (xisnan (tmp)) |
|
|
2301 { |
|
|
2302 idx = -1; |
|
|
2303 break; |
|
|
2304 } |
|
|
2305 else if (tmp > tmp_max) |
|
|
2306 { |
|
|
2307 idx = i; |
|
|
2308 tmp_max = tmp; |
|
|
2309 } |
|
|
2310 } |
|
|
2311 } |
|
|
2312 |
|
|
2313 result.elem (j) = (idx < 0) ? octave_NaN : tmp_max; |
|
|
2314 index.elem (j) = idx; |
|
458
|
2315 } |
|
|
2316 } |
|
|
2317 |
|
|
2318 return result; |
|
|
2319 } |
|
|
2320 |
|
|
2321 ostream& |
|
|
2322 operator << (ostream& os, const Matrix& a) |
|
|
2323 { |
|
|
2324 // int field_width = os.precision () + 7; |
|
1360
|
2325 |
|
458
|
2326 for (int i = 0; i < a.rows (); i++) |
|
|
2327 { |
|
|
2328 for (int j = 0; j < a.cols (); j++) |
|
|
2329 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2330 os << "\n"; |
|
|
2331 } |
|
|
2332 return os; |
|
|
2333 } |
|
|
2334 |
|
|
2335 istream& |
|
|
2336 operator >> (istream& is, Matrix& a) |
|
|
2337 { |
|
|
2338 int nr = a.rows (); |
|
|
2339 int nc = a.cols (); |
|
|
2340 |
|
|
2341 if (nr < 1 || nc < 1) |
|
|
2342 is.clear (ios::badbit); |
|
|
2343 else |
|
|
2344 { |
|
|
2345 double tmp; |
|
|
2346 for (int i = 0; i < nr; i++) |
|
|
2347 for (int j = 0; j < nc; j++) |
|
|
2348 { |
|
|
2349 is >> tmp; |
|
|
2350 if (is) |
|
|
2351 a.elem (i, j) = tmp; |
|
|
2352 else |
|
2795
|
2353 goto done; |
|
458
|
2354 } |
|
|
2355 } |
|
|
2356 |
|
2795
|
2357 done: |
|
|
2358 |
|
458
|
2359 return is; |
|
|
2360 } |
|
|
2361 |
|
2317
|
2362 template <class T> |
|
|
2363 static void |
|
|
2364 read_int (istream& is, bool swap_bytes, T& val) |
|
|
2365 { |
|
3145
|
2366 is.read (X_CAST (char *, &val), sizeof (T)); |
|
2317
|
2367 |
|
|
2368 if (swap_bytes) |
|
|
2369 { |
|
|
2370 switch (sizeof (T)) |
|
|
2371 { |
|
|
2372 case 1: |
|
|
2373 break; |
|
|
2374 |
|
|
2375 case 2: |
|
3145
|
2376 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2377 break; |
|
|
2378 |
|
|
2379 case 4: |
|
3145
|
2380 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2381 break; |
|
|
2382 |
|
|
2383 case 8: |
|
3145
|
2384 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2385 break; |
|
|
2386 |
|
|
2387 default: |
|
|
2388 (*current_liboctave_error_handler) |
|
|
2389 ("read_int: unrecognized data format!"); |
|
|
2390 } |
|
|
2391 } |
|
|
2392 } |
|
|
2393 |
|
|
2394 template void read_int (istream&, bool, char&); |
|
|
2395 template void read_int (istream&, bool, signed char&); |
|
|
2396 template void read_int (istream&, bool, unsigned char&); |
|
|
2397 template void read_int (istream&, bool, short&); |
|
|
2398 template void read_int (istream&, bool, unsigned short&); |
|
|
2399 template void read_int (istream&, bool, int&); |
|
|
2400 template void read_int (istream&, bool, unsigned int&); |
|
|
2401 template void read_int (istream&, bool, long&); |
|
|
2402 template void read_int (istream&, bool, unsigned long&); |
|
|
2403 |
|
|
2404 static inline bool |
|
|
2405 do_read (istream& is, oct_data_conv::data_type dt, |
|
|
2406 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2407 bool do_float_conversion, double& val) |
|
|
2408 { |
|
|
2409 bool retval = true; |
|
|
2410 |
|
|
2411 switch (dt) |
|
|
2412 { |
|
|
2413 case oct_data_conv::dt_char: |
|
|
2414 { |
|
|
2415 char tmp; |
|
|
2416 read_int (is, swap_bytes, tmp); |
|
|
2417 val = tmp; |
|
|
2418 } |
|
|
2419 break; |
|
|
2420 |
|
|
2421 case oct_data_conv::dt_schar: |
|
|
2422 { |
|
|
2423 signed char tmp; |
|
|
2424 read_int (is, swap_bytes, tmp); |
|
|
2425 val = tmp; |
|
|
2426 } |
|
|
2427 break; |
|
|
2428 |
|
|
2429 case oct_data_conv::dt_uchar: |
|
|
2430 { |
|
|
2431 unsigned char tmp; |
|
|
2432 read_int (is, swap_bytes, tmp); |
|
|
2433 val = tmp; |
|
|
2434 } |
|
|
2435 break; |
|
|
2436 |
|
|
2437 case oct_data_conv::dt_short: |
|
|
2438 { |
|
|
2439 short tmp; |
|
|
2440 read_int (is, swap_bytes, tmp); |
|
|
2441 val = tmp; |
|
|
2442 } |
|
|
2443 break; |
|
|
2444 |
|
|
2445 case oct_data_conv::dt_ushort: |
|
|
2446 { |
|
|
2447 unsigned short tmp; |
|
|
2448 read_int (is, swap_bytes, tmp); |
|
|
2449 val = tmp; |
|
|
2450 } |
|
|
2451 break; |
|
|
2452 |
|
|
2453 case oct_data_conv::dt_int: |
|
|
2454 { |
|
|
2455 int tmp; |
|
|
2456 read_int (is, swap_bytes, tmp); |
|
|
2457 val = tmp; |
|
|
2458 } |
|
|
2459 break; |
|
|
2460 |
|
|
2461 case oct_data_conv::dt_uint: |
|
|
2462 { |
|
|
2463 unsigned int tmp; |
|
|
2464 read_int (is, swap_bytes, tmp); |
|
|
2465 val = tmp; |
|
|
2466 } |
|
|
2467 break; |
|
|
2468 |
|
|
2469 case oct_data_conv::dt_long: |
|
|
2470 { |
|
|
2471 long tmp; |
|
|
2472 read_int (is, swap_bytes, tmp); |
|
|
2473 val = tmp; |
|
|
2474 } |
|
|
2475 break; |
|
|
2476 |
|
|
2477 case oct_data_conv::dt_ulong: |
|
|
2478 { |
|
|
2479 unsigned long tmp; |
|
|
2480 read_int (is, swap_bytes, tmp); |
|
|
2481 val = tmp; |
|
|
2482 } |
|
|
2483 break; |
|
|
2484 |
|
|
2485 case oct_data_conv::dt_float: |
|
|
2486 { |
|
|
2487 float f; |
|
|
2488 |
|
3145
|
2489 is.read (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2490 |
|
|
2491 if (do_float_conversion) |
|
|
2492 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2493 |
|
|
2494 val = f; |
|
|
2495 } |
|
|
2496 break; |
|
|
2497 |
|
|
2498 case oct_data_conv::dt_double: |
|
|
2499 { |
|
3145
|
2500 is.read (X_CAST (char *, &val), sizeof (double)); |
|
2317
|
2501 |
|
|
2502 if (do_float_conversion) |
|
|
2503 do_double_format_conversion (&val, 1, flt_fmt); |
|
|
2504 } |
|
|
2505 break; |
|
|
2506 |
|
|
2507 default: |
|
|
2508 retval = false; |
|
|
2509 (*current_liboctave_error_handler) |
|
|
2510 ("read: invalid type specification"); |
|
|
2511 break; |
|
|
2512 } |
|
|
2513 |
|
|
2514 return retval; |
|
|
2515 } |
|
1360
|
2516 |
|
458
|
2517 int |
|
2317
|
2518 Matrix::read (istream& is, int nr, int nc, |
|
|
2519 oct_data_conv::data_type dt, int skip, |
|
|
2520 oct_mach_info::float_format flt_fmt) |
|
458
|
2521 { |
|
2317
|
2522 int retval = -1; |
|
|
2523 |
|
|
2524 bool ok = true; |
|
|
2525 |
|
|
2526 int count = 0; |
|
|
2527 |
|
|
2528 double *data = 0; |
|
|
2529 int max_size = 0; |
|
|
2530 |
|
|
2531 int final_nr = 0; |
|
|
2532 int final_nc = 0; |
|
|
2533 |
|
|
2534 if (nr > 0) |
|
458
|
2535 { |
|
2317
|
2536 if (nc > 0) |
|
|
2537 { |
|
|
2538 resize (nr, nc, 0.0); |
|
|
2539 data = fortran_vec (); |
|
|
2540 max_size = nr * nc; |
|
|
2541 } |
|
|
2542 else |
|
|
2543 { |
|
|
2544 resize (nr, 32, 0.0); |
|
|
2545 data = fortran_vec (); |
|
|
2546 max_size = nr * 32; |
|
|
2547 } |
|
|
2548 } |
|
471
|
2549 else |
|
|
2550 { |
|
2317
|
2551 resize (32, 1, 0.0); |
|
|
2552 data = fortran_vec (); |
|
|
2553 max_size = 32; |
|
|
2554 } |
|
|
2555 |
|
|
2556 oct_mach_info::float_format native_flt_fmt |
|
|
2557 = oct_mach_info::float_format (); |
|
|
2558 |
|
|
2559 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2560 |
|
|
2561 // XXX FIXME XXX -- byte order for Cray? |
|
|
2562 |
|
|
2563 bool swap_bytes = false; |
|
|
2564 |
|
|
2565 if (oct_mach_info::words_big_endian ()) |
|
|
2566 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2567 || flt_fmt == oct_mach_info::vax_g |
|
|
2568 || flt_fmt == oct_mach_info::vax_g); |
|
|
2569 else |
|
|
2570 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2571 |
|
|
2572 for (;;) |
|
|
2573 { |
|
|
2574 // XXX FIXME XXX -- maybe there should be a special case for |
|
|
2575 // skip == 0. |
|
|
2576 |
|
|
2577 if (is) |
|
|
2578 { |
|
|
2579 if (nr > 0 && nc > 0 && count == max_size) |
|
|
2580 { |
|
|
2581 final_nr = nr; |
|
|
2582 final_nc = nc; |
|
|
2583 |
|
|
2584 break; |
|
|
2585 } |
|
|
2586 |
|
|
2587 if (is) |
|
|
2588 { |
|
|
2589 double tmp = 0.0; |
|
|
2590 |
|
|
2591 ok = do_read (is, dt, flt_fmt, swap_bytes, |
|
|
2592 do_float_conversion, tmp); |
|
|
2593 |
|
|
2594 if (ok) |
|
|
2595 { |
|
|
2596 if (is) |
|
|
2597 { |
|
|
2598 if (count == max_size) |
|
|
2599 { |
|
|
2600 max_size *= 2; |
|
|
2601 |
|
|
2602 if (nr > 0) |
|
2601
|
2603 resize (nr, max_size / nr, 0.0); |
|
2317
|
2604 else |
|
|
2605 resize (max_size, 1, 0.0); |
|
|
2606 |
|
|
2607 data = fortran_vec (); |
|
|
2608 } |
|
|
2609 |
|
|
2610 data[count++] = tmp; |
|
|
2611 } |
|
3180
|
2612 |
|
|
2613 if (ok && skip != 0) |
|
|
2614 is.seekg (skip, ios::cur); |
|
|
2615 |
|
3219
|
2616 if (! ok || is.eof ()) |
|
2317
|
2617 { |
|
|
2618 if (is.eof ()) |
|
|
2619 { |
|
|
2620 if (nr > 0) |
|
|
2621 { |
|
|
2622 if (count > nr) |
|
|
2623 { |
|
|
2624 final_nr = nr; |
|
|
2625 final_nc = (count - 1) / nr + 1; |
|
|
2626 } |
|
|
2627 else |
|
|
2628 { |
|
|
2629 final_nr = count; |
|
|
2630 final_nc = 1; |
|
|
2631 } |
|
|
2632 } |
|
|
2633 else |
|
|
2634 { |
|
|
2635 final_nr = count; |
|
|
2636 final_nc = 1; |
|
|
2637 } |
|
|
2638 } |
|
|
2639 |
|
|
2640 break; |
|
|
2641 } |
|
|
2642 } |
|
|
2643 else |
|
|
2644 break; |
|
|
2645 } |
|
|
2646 else |
|
|
2647 { |
|
|
2648 ok = false; |
|
|
2649 break; |
|
|
2650 } |
|
|
2651 } |
|
|
2652 else |
|
|
2653 { |
|
|
2654 ok = false; |
|
|
2655 break; |
|
|
2656 } |
|
|
2657 } |
|
|
2658 |
|
|
2659 if (ok) |
|
|
2660 { |
|
|
2661 resize (final_nr, final_nc, 0.0); |
|
|
2662 |
|
|
2663 retval = count; |
|
458
|
2664 } |
|
|
2665 |
|
2317
|
2666 return retval; |
|
|
2667 } |
|
|
2668 |
|
|
2669 template <class T> |
|
|
2670 static void |
|
|
2671 write_int (ostream& os, bool swap_bytes, T val) |
|
|
2672 { |
|
|
2673 if (swap_bytes) |
|
|
2674 { |
|
|
2675 switch (sizeof (T)) |
|
|
2676 { |
|
|
2677 case 1: |
|
|
2678 break; |
|
|
2679 |
|
|
2680 case 2: |
|
3145
|
2681 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2682 break; |
|
|
2683 |
|
|
2684 case 4: |
|
3145
|
2685 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2686 break; |
|
|
2687 |
|
|
2688 case 8: |
|
3145
|
2689 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2690 break; |
|
|
2691 |
|
|
2692 default: |
|
|
2693 (*current_liboctave_error_handler) |
|
|
2694 ("write_int: unrecognized data format!"); |
|
|
2695 } |
|
|
2696 } |
|
|
2697 |
|
3145
|
2698 os.write (X_CAST (char *, &val), sizeof (T)); |
|
458
|
2699 } |
|
|
2700 |
|
2317
|
2701 template void write_int (ostream&, bool, char); |
|
|
2702 template void write_int (ostream&, bool, signed char); |
|
|
2703 template void write_int (ostream&, bool, unsigned char); |
|
|
2704 template void write_int (ostream&, bool, short); |
|
|
2705 template void write_int (ostream&, bool, unsigned short); |
|
|
2706 template void write_int (ostream&, bool, int); |
|
|
2707 template void write_int (ostream&, bool, unsigned int); |
|
|
2708 template void write_int (ostream&, bool, long); |
|
|
2709 template void write_int (ostream&, bool, unsigned long); |
|
|
2710 |
|
|
2711 static inline bool |
|
|
2712 do_write (ostream& os, double d, oct_data_conv::data_type dt, |
|
|
2713 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2714 bool do_float_conversion) |
|
|
2715 { |
|
|
2716 bool retval = true; |
|
|
2717 |
|
|
2718 switch (dt) |
|
|
2719 { |
|
|
2720 case oct_data_conv::dt_char: |
|
3145
|
2721 write_int (os, swap_bytes, X_CAST (char, d)); |
|
2317
|
2722 break; |
|
|
2723 |
|
|
2724 case oct_data_conv::dt_schar: |
|
3145
|
2725 write_int (os, swap_bytes, X_CAST (signed char, d)); |
|
2317
|
2726 break; |
|
|
2727 |
|
|
2728 case oct_data_conv::dt_uchar: |
|
3145
|
2729 write_int (os, swap_bytes, X_CAST (unsigned char, d)); |
|
2317
|
2730 break; |
|
|
2731 |
|
|
2732 case oct_data_conv::dt_short: |
|
3145
|
2733 write_int (os, swap_bytes, X_CAST (short, d)); |
|
2317
|
2734 break; |
|
|
2735 |
|
|
2736 case oct_data_conv::dt_ushort: |
|
3145
|
2737 write_int (os, swap_bytes, X_CAST (unsigned short, d)); |
|
2317
|
2738 break; |
|
|
2739 |
|
|
2740 case oct_data_conv::dt_int: |
|
3145
|
2741 write_int (os, swap_bytes, X_CAST (int, d)); |
|
2317
|
2742 break; |
|
|
2743 |
|
|
2744 case oct_data_conv::dt_uint: |
|
3145
|
2745 write_int (os, swap_bytes, X_CAST (unsigned int, d)); |
|
2317
|
2746 break; |
|
|
2747 |
|
|
2748 case oct_data_conv::dt_long: |
|
3145
|
2749 write_int (os, swap_bytes, X_CAST (long, d)); |
|
2317
|
2750 break; |
|
|
2751 |
|
|
2752 case oct_data_conv::dt_ulong: |
|
3145
|
2753 write_int (os, swap_bytes, X_CAST (unsigned long, d)); |
|
2317
|
2754 break; |
|
|
2755 |
|
|
2756 case oct_data_conv::dt_float: |
|
|
2757 { |
|
2800
|
2758 float f = d; |
|
2317
|
2759 |
|
|
2760 if (do_float_conversion) |
|
|
2761 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2762 |
|
3145
|
2763 os.write (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2764 } |
|
|
2765 break; |
|
|
2766 |
|
|
2767 case oct_data_conv::dt_double: |
|
|
2768 { |
|
|
2769 if (do_float_conversion) |
|
|
2770 do_double_format_conversion (&d, 1, flt_fmt); |
|
|
2771 |
|
3145
|
2772 os.write (X_CAST (char *, &d), sizeof (double)); |
|
2317
|
2773 } |
|
|
2774 break; |
|
|
2775 |
|
|
2776 default: |
|
|
2777 retval = false; |
|
|
2778 (*current_liboctave_error_handler) |
|
|
2779 ("write: invalid type specification"); |
|
|
2780 break; |
|
|
2781 } |
|
|
2782 |
|
|
2783 return retval; |
|
|
2784 } |
|
1360
|
2785 |
|
458
|
2786 int |
|
2317
|
2787 Matrix::write (ostream& os, oct_data_conv::data_type dt, int skip, |
|
|
2788 oct_mach_info::float_format flt_fmt) |
|
458
|
2789 { |
|
2317
|
2790 int retval = -1; |
|
|
2791 |
|
|
2792 bool ok = true; |
|
|
2793 |
|
|
2794 int count = 0; |
|
|
2795 |
|
|
2796 const double *d = data (); |
|
|
2797 |
|
|
2798 int n = length (); |
|
|
2799 |
|
|
2800 oct_mach_info::float_format native_flt_fmt |
|
|
2801 = oct_mach_info::float_format (); |
|
|
2802 |
|
|
2803 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2804 |
|
|
2805 // XXX FIXME XXX -- byte order for Cray? |
|
|
2806 |
|
|
2807 bool swap_bytes = false; |
|
|
2808 |
|
|
2809 if (oct_mach_info::words_big_endian ()) |
|
|
2810 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2811 || flt_fmt == oct_mach_info::vax_g |
|
|
2812 || flt_fmt == oct_mach_info::vax_g); |
|
|
2813 else |
|
|
2814 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2815 |
|
|
2816 for (int i = 0; i < n; i++) |
|
458
|
2817 { |
|
2317
|
2818 if (os) |
|
|
2819 { |
|
|
2820 if (skip != 0) |
|
|
2821 os.seekp (skip, ios::cur); |
|
|
2822 |
|
|
2823 if (os) |
|
|
2824 { |
|
|
2825 ok = do_write (os, d[i], dt, flt_fmt, swap_bytes, |
|
|
2826 do_float_conversion); |
|
|
2827 |
|
|
2828 if (os && ok) |
|
|
2829 count++; |
|
|
2830 else |
|
|
2831 break; |
|
|
2832 } |
|
|
2833 else |
|
|
2834 { |
|
|
2835 ok = false; |
|
|
2836 break; |
|
|
2837 } |
|
|
2838 } |
|
|
2839 else |
|
|
2840 { |
|
|
2841 ok = false; |
|
|
2842 break; |
|
|
2843 } |
|
471
|
2844 } |
|
458
|
2845 |
|
2317
|
2846 if (ok) |
|
|
2847 retval = count; |
|
|
2848 |
|
|
2849 return retval; |
|
458
|
2850 } |
|
|
2851 |
|
2317
|
2852 |
|
|
2853 |
|
1819
|
2854 Matrix |
|
|
2855 Givens (double x, double y) |
|
|
2856 { |
|
|
2857 double cc, s, temp_r; |
|
|
2858 |
|
|
2859 F77_FCN (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
|
2860 |
|
|
2861 Matrix g (2, 2); |
|
|
2862 |
|
|
2863 g.elem (0, 0) = cc; |
|
|
2864 g.elem (1, 1) = cc; |
|
|
2865 g.elem (0, 1) = s; |
|
|
2866 g.elem (1, 0) = -s; |
|
|
2867 |
|
|
2868 return g; |
|
|
2869 } |
|
|
2870 |
|
|
2871 Matrix |
|
|
2872 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2873 { |
|
|
2874 Matrix retval; |
|
|
2875 |
|
|
2876 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2877 // size. |
|
|
2878 |
|
|
2879 // Compute Schur decompositions. |
|
|
2880 |
|
|
2881 SCHUR as (a, "U"); |
|
|
2882 SCHUR bs (b, "U"); |
|
|
2883 |
|
|
2884 // Transform c to new coordinates. |
|
|
2885 |
|
|
2886 Matrix ua = as.unitary_matrix (); |
|
|
2887 Matrix sch_a = as.schur_matrix (); |
|
|
2888 |
|
|
2889 Matrix ub = bs.unitary_matrix (); |
|
|
2890 Matrix sch_b = bs.schur_matrix (); |
|
|
2891 |
|
|
2892 Matrix cx = ua.transpose () * c * ub; |
|
|
2893 |
|
|
2894 // Solve the sylvester equation, back-transform, and return the |
|
|
2895 // solution. |
|
|
2896 |
|
|
2897 int a_nr = a.rows (); |
|
|
2898 int b_nr = b.rows (); |
|
|
2899 |
|
|
2900 double scale; |
|
|
2901 int info; |
|
|
2902 |
|
1950
|
2903 double *pa = sch_a.fortran_vec (); |
|
|
2904 double *pb = sch_b.fortran_vec (); |
|
|
2905 double *px = cx.fortran_vec (); |
|
|
2906 |
|
|
2907 F77_XFCN (dtrsyl, DTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
2908 b_nr, px, a_nr, scale, info, 1L, 1L)); |
|
|
2909 |
|
|
2910 |
|
|
2911 if (f77_exception_encountered) |
|
|
2912 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
2913 else |
|
|
2914 { |
|
|
2915 // XXX FIXME XXX -- check info? |
|
1819
|
2916 |
|
1950
|
2917 retval = -ua*cx*ub.transpose (); |
|
|
2918 } |
|
1819
|
2919 |
|
|
2920 return retval; |
|
|
2921 } |
|
|
2922 |
|
2828
|
2923 // matrix by matrix -> matrix operations |
|
|
2924 |
|
|
2925 Matrix |
|
|
2926 operator * (const Matrix& m, const Matrix& a) |
|
|
2927 { |
|
|
2928 Matrix retval; |
|
|
2929 |
|
|
2930 int nr = m.rows (); |
|
|
2931 int nc = m.cols (); |
|
|
2932 |
|
|
2933 int a_nr = a.rows (); |
|
|
2934 int a_nc = a.cols (); |
|
|
2935 |
|
|
2936 if (nc != a_nr) |
|
|
2937 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
2938 else |
|
|
2939 { |
|
|
2940 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
2941 retval.resize (nr, a_nc, 0.0); |
|
|
2942 else |
|
|
2943 { |
|
|
2944 int ld = nr; |
|
|
2945 int lda = a_nr; |
|
|
2946 |
|
|
2947 retval.resize (nr, a_nc); |
|
|
2948 double *c = retval.fortran_vec (); |
|
|
2949 |
|
|
2950 F77_XFCN (dgemm, DGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
2951 m.data (), ld, a.data (), lda, 0.0, |
|
|
2952 c, nr, 1L, 1L)); |
|
|
2953 |
|
|
2954 if (f77_exception_encountered) |
|
|
2955 (*current_liboctave_error_handler) |
|
|
2956 ("unrecoverable error in dgemm"); |
|
|
2957 } |
|
|
2958 } |
|
|
2959 |
|
|
2960 return retval; |
|
|
2961 } |
|
|
2962 |
|
2870
|
2963 MS_CMP_OPS(Matrix, , double, ) |
|
|
2964 MS_BOOL_OPS(Matrix, double) |
|
|
2965 |
|
|
2966 SM_CMP_OPS(double, , Matrix, ) |
|
|
2967 SM_BOOL_OPS(double, Matrix) |
|
|
2968 |
|
|
2969 MM_CMP_OPS(Matrix, , Matrix, ) |
|
|
2970 MM_BOOL_OPS(Matrix, Matrix) |
|
|
2971 |
|
458
|
2972 /* |
|
|
2973 ;;; Local Variables: *** |
|
|
2974 ;;; mode: C++ *** |
|
|
2975 ;;; End: *** |
|
|
2976 */ |
