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1 // Matrix manipulations. -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include "config.h" |
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26 #endif |
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27 |
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28 #include <sys/types.h> |
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29 #include <iostream.h> |
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30 #include <stdio.h> |
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31 #include <float.h> |
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32 |
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33 #include <Complex.h> |
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34 |
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35 #include "mx-base.h" |
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36 #include "dbleDET.h" |
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37 #include "dbleSVD.h" |
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38 #include "mx-inlines.cc" |
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39 #include "lo-error.h" |
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40 #include "f77-uscore.h" |
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41 |
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42 // Fortran functions we call. |
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43 |
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44 extern "C" |
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45 { |
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46 int F77_FCN (dgemm) (const char*, const char*, const int*, |
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47 const int*, const int*, const double*, |
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48 const double*, const int*, const double*, |
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49 const int*, const double*, double*, const int*, |
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50 long, long); |
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51 |
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52 int F77_FCN (dgemv) (const char*, const int*, const int*, |
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53 const double*, const double*, const int*, |
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54 const double*, const int*, const double*, |
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55 double*, const int*, long); |
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56 |
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57 int F77_FCN (dgeco) (double*, const int*, const int*, int*, double*, |
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58 double*); |
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59 |
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60 int F77_FCN (dgesl) (const double*, const int*, const int*, |
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61 const int*, double*, const int*); |
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62 |
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63 int F77_FCN (dgedi) (double*, const int*, const int*, const int*, |
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64 double*, double*, const int*); |
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65 |
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66 int F77_FCN (dgelss) (const int*, const int*, const int*, double*, |
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67 const int*, double*, const int*, double*, |
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68 const double*, int*, double*, const int*, |
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69 int*); |
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70 |
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71 // Note that the original complex fft routines were not written for |
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72 // double complex arguments. They have been modified by adding an |
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73 // implicit double precision (a-h,o-z) statement at the beginning of |
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74 // each subroutine. |
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75 |
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76 int F77_FCN (cffti) (const int*, Complex*); |
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77 |
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78 int F77_FCN (cfftf) (const int*, Complex*, Complex*); |
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79 |
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80 int F77_FCN (cfftb) (const int*, Complex*, Complex*); |
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81 } |
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82 |
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83 #define KLUDGE_MATRICES |
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84 #define TYPE double |
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85 #define KL_MAT_TYPE Matrix |
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86 #include "mx-kludge.cc" |
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87 #undef KLUDGE_MATRICES |
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88 #undef TYPE |
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89 #undef KL_MAT_TYPE |
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90 |
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91 /* |
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92 * Matrix class. |
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93 */ |
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94 |
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95 Matrix::Matrix (const DiagMatrix& a) |
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96 : Array2<double> (a.rows (), a.cols (), 0.0) |
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97 { |
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98 for (int i = 0; i < a.length (); i++) |
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99 elem (i, i) = a.elem (i, i); |
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100 } |
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101 |
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102 #if 0 |
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103 Matrix& |
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104 Matrix::resize (int r, int c) |
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105 { |
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106 if (r < 0 || c < 0) |
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107 { |
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108 (*current_liboctave_error_handler) |
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109 ("can't resize to negative dimensions"); |
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110 return *this; |
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111 } |
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112 |
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113 int new_len = r * c; |
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114 double* new_data = 0; |
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115 if (new_len > 0) |
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116 { |
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117 new_data = new double [new_len]; |
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118 |
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119 int min_r = nr < r ? nr : r; |
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120 int min_c = nc < c ? nc : c; |
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121 |
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122 for (int j = 0; j < min_c; j++) |
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123 for (int i = 0; i < min_r; i++) |
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124 new_data[r*j+i] = elem (i, j); |
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125 } |
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126 |
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127 delete [] data; |
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128 nr = r; |
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129 nc = c; |
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130 len = new_len; |
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131 data = new_data; |
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132 |
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133 return *this; |
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134 } |
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135 |
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136 Matrix& |
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137 Matrix::resize (int r, int c, double val) |
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138 { |
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139 if (r < 0 || c < 0) |
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140 { |
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141 (*current_liboctave_error_handler) |
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142 ("can't resize to negative dimensions"); |
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143 return *this; |
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144 } |
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145 |
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146 int new_len = r * c; |
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147 double *new_data = 0; |
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148 if (new_len > 0) |
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149 { |
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150 new_data = new double [new_len]; |
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151 |
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152 // There may be faster or cleaner ways to do this. |
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153 |
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154 if (r > nr || c > nc) |
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155 copy (new_data, new_len, val); |
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156 |
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157 int min_r = nr < r ? nr : r; |
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158 int min_c = nc < c ? nc : c; |
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159 |
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160 for (int j = 0; j < min_c; j++) |
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161 for (int i = 0; i < min_r; i++) |
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162 new_data[r*j+i] = elem (i, j); |
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163 } |
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164 |
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165 delete [] data; |
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166 nr = r; |
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167 nc = c; |
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168 len = new_len; |
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169 data = new_data; |
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170 |
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171 return *this; |
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172 } |
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173 #endif |
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174 |
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175 int |
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176 Matrix::operator == (const Matrix& a) const |
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177 { |
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178 if (rows () != a.rows () || cols () != a.cols ()) |
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179 return 0; |
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180 |
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181 return equal (data (), a.data (), length ()); |
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182 } |
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183 |
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184 int |
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185 Matrix::operator != (const Matrix& a) const |
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186 { |
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187 return !(*this == a); |
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188 } |
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189 |
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190 Matrix& |
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191 Matrix::insert (const Matrix& a, int r, int c) |
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192 { |
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193 int a_rows = a.rows (); |
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194 int a_cols = a.cols (); |
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195 if (r < 0 || r + a_rows - 1 > rows () |
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196 || c < 0 || c + a_cols - 1 > cols ()) |
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197 { |
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198 (*current_liboctave_error_handler) ("range error for insert"); |
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199 return *this; |
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200 } |
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201 |
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202 for (int j = 0; j < a_cols; j++) |
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203 for (int i = 0; i < a_rows; i++) |
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204 elem (r+i, c+j) = a.elem (i, j); |
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205 |
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206 return *this; |
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207 } |
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208 |
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209 Matrix& |
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210 Matrix::insert (const RowVector& a, int r, int c) |
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211 { |
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212 int a_len = a.length (); |
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213 if (r < 0 || r >= rows () || c < 0 || c + a_len - 1 > cols ()) |
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214 { |
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215 (*current_liboctave_error_handler) ("range error for insert"); |
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216 return *this; |
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217 } |
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218 |
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219 for (int i = 0; i < a_len; i++) |
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220 elem (r, c+i) = a.elem (i); |
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221 |
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222 return *this; |
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223 } |
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224 |
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225 Matrix& |
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226 Matrix::insert (const ColumnVector& a, int r, int c) |
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227 { |
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228 int a_len = a.length (); |
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229 if (r < 0 || r + a_len - 1 > rows () || c < 0 || c >= cols ()) |
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230 { |
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231 (*current_liboctave_error_handler) ("range error for insert"); |
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232 return *this; |
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233 } |
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234 |
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235 for (int i = 0; i < a_len; i++) |
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236 elem (r+i, c) = a.elem (i); |
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237 |
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238 return *this; |
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239 } |
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240 |
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241 Matrix& |
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242 Matrix::insert (const DiagMatrix& a, int r, int c) |
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243 { |
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244 if (r < 0 || r + a.rows () - 1 > rows () |
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245 || c < 0 || c + a.cols () - 1 > cols ()) |
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246 { |
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247 (*current_liboctave_error_handler) ("range error for insert"); |
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248 return *this; |
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249 } |
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250 |
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251 for (int i = 0; i < a.length (); i++) |
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252 elem (r+i, c+i) = a.elem (i, i); |
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253 |
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254 return *this; |
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255 } |
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256 |
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257 Matrix& |
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258 Matrix::fill (double val) |
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259 { |
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260 int nr = rows (); |
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261 int nc = cols (); |
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262 if (nr > 0 && nc > 0) |
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263 for (int j = 0; j < nc; j++) |
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264 for (int i = 0; i < nr; i++) |
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265 elem (i, j) = val; |
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266 |
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267 return *this; |
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268 } |
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269 |
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270 Matrix& |
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271 Matrix::fill (double val, int r1, int c1, int r2, int c2) |
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272 { |
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273 int nr = rows (); |
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274 int nc = cols (); |
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275 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
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276 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
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277 { |
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278 (*current_liboctave_error_handler) ("range error for fill"); |
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279 return *this; |
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280 } |
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281 |
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282 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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283 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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284 |
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285 for (int j = c1; j <= c2; j++) |
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286 for (int i = r1; i <= r2; i++) |
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287 elem (i, j) = val; |
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288 |
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289 return *this; |
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290 } |
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291 |
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292 Matrix |
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293 Matrix::append (const Matrix& a) const |
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294 { |
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295 int nr = rows (); |
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296 int nc = cols (); |
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297 if (nr != a.rows ()) |
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298 { |
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299 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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300 return Matrix (); |
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301 } |
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302 |
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303 int nc_insert = nc; |
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304 Matrix retval (nr, nc + a.cols ()); |
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305 retval.insert (*this, 0, 0); |
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306 retval.insert (a, 0, nc_insert); |
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307 return retval; |
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308 } |
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309 |
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310 Matrix |
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311 Matrix::append (const RowVector& a) const |
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312 { |
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313 int nr = rows (); |
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314 int nc = cols (); |
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315 if (nr != 1) |
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316 { |
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317 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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318 return Matrix (); |
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319 } |
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320 |
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321 int nc_insert = nc; |
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322 Matrix retval (nr, nc + a.length ()); |
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323 retval.insert (*this, 0, 0); |
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324 retval.insert (a, 0, nc_insert); |
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325 return retval; |
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326 } |
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327 |
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328 Matrix |
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329 Matrix::append (const ColumnVector& a) const |
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330 { |
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331 int nr = rows (); |
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332 int nc = cols (); |
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333 if (nr != a.length ()) |
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334 { |
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335 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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336 return Matrix (); |
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337 } |
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338 |
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339 int nc_insert = nc; |
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340 Matrix retval (nr, nc + 1); |
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341 retval.insert (*this, 0, 0); |
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342 retval.insert (a, 0, nc_insert); |
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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::append (const DiagMatrix& 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 (nr != a.rows ()) |
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352 { |
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353 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
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354 return *this; |
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355 } |
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356 |
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357 int nc_insert = nc; |
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358 Matrix retval (nr, nc + a.cols ()); |
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359 retval.insert (*this, 0, 0); |
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360 retval.insert (a, 0, nc_insert); |
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361 return retval; |
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362 } |
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363 |
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364 Matrix |
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365 Matrix::stack (const Matrix& a) const |
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366 { |
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367 int nr = rows (); |
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368 int nc = cols (); |
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369 if (nc != a.cols ()) |
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370 { |
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371 (*current_liboctave_error_handler) |
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372 ("column dimension mismatch for stack"); |
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373 return Matrix (); |
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374 } |
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375 |
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376 int nr_insert = nr; |
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377 Matrix retval (nr + a.rows (), nc); |
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378 retval.insert (*this, 0, 0); |
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379 retval.insert (a, nr_insert, 0); |
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380 return retval; |
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381 } |
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382 |
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383 Matrix |
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384 Matrix::stack (const RowVector& a) const |
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385 { |
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386 int nr = rows (); |
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387 int nc = cols (); |
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388 if (nc != a.length ()) |
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389 { |
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390 (*current_liboctave_error_handler) |
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391 ("column dimension mismatch for stack"); |
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392 return Matrix (); |
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393 } |
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394 |
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395 int nr_insert = nr; |
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396 Matrix retval (nr + 1, nc); |
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397 retval.insert (*this, 0, 0); |
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398 retval.insert (a, nr_insert, 0); |
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399 return retval; |
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400 } |
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401 |
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402 Matrix |
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403 Matrix::stack (const ColumnVector& a) const |
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404 { |
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405 int nr = rows (); |
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406 int nc = cols (); |
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407 if (nc != 1) |
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408 { |
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409 (*current_liboctave_error_handler) |
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410 ("column dimension mismatch for stack"); |
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411 return Matrix (); |
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412 } |
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413 |
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414 int nr_insert = nr; |
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415 Matrix retval (nr + a.length (), nc); |
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416 retval.insert (*this, 0, 0); |
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417 retval.insert (a, nr_insert, 0); |
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418 return retval; |
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419 } |
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420 |
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421 Matrix |
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422 Matrix::stack (const DiagMatrix& a) const |
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423 { |
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424 int nr = rows (); |
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425 int nc = cols (); |
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426 if (nc != a.cols ()) |
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427 { |
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428 (*current_liboctave_error_handler) |
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429 ("column dimension mismatch for stack"); |
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430 return Matrix (); |
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431 } |
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432 |
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433 int nr_insert = nr; |
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434 Matrix retval (nr + a.rows (), nc); |
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435 retval.insert (*this, 0, 0); |
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436 retval.insert (a, nr_insert, 0); |
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437 return retval; |
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438 } |
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439 |
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440 Matrix |
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441 Matrix::transpose (void) const |
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442 { |
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443 int nr = rows (); |
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444 int nc = cols (); |
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445 Matrix result (nc, nr); |
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446 if (length () > 0) |
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447 { |
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448 for (int j = 0; j < nc; j++) |
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449 for (int i = 0; i < nr; i++) |
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450 result.elem (j, i) = elem (i, j); |
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451 } |
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452 return result; |
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453 } |
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454 |
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455 Matrix |
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456 Matrix::extract (int r1, int c1, int r2, int c2) const |
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457 { |
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458 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
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459 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
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460 |
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461 int new_r = r2 - r1 + 1; |
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462 int new_c = c2 - c1 + 1; |
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463 |
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464 Matrix result (new_r, new_c); |
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465 |
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466 for (int j = 0; j < new_c; j++) |
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467 for (int i = 0; i < new_r; i++) |
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468 result.elem (i, j) = elem (r1+i, c1+j); |
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469 |
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470 return result; |
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471 } |
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472 |
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473 // extract row or column i. |
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474 |
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475 RowVector |
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476 Matrix::row (int i) const |
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477 { |
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478 int nc = cols (); |
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479 if (i < 0 || i >= rows ()) |
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480 { |
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481 (*current_liboctave_error_handler) ("invalid row selection"); |
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482 return RowVector (); |
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483 } |
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484 |
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485 RowVector retval (nc); |
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486 for (int j = 0; j < nc; j++) |
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487 retval.elem (j) = elem (i, j); |
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488 |
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489 return retval; |
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490 } |
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491 |
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492 RowVector |
|
|
493 Matrix::row (char *s) const |
|
|
494 { |
|
533
|
495 if (! s) |
|
458
|
496 { |
|
|
497 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
498 return RowVector (); |
|
|
499 } |
|
|
500 |
|
|
501 char c = *s; |
|
|
502 if (c == 'f' || c == 'F') |
|
|
503 return row (0); |
|
|
504 else if (c == 'l' || c == 'L') |
|
|
505 return row (rows () - 1); |
|
|
506 else |
|
|
507 { |
|
|
508 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
509 return RowVector (); |
|
|
510 } |
|
|
511 } |
|
|
512 |
|
|
513 ColumnVector |
|
|
514 Matrix::column (int i) const |
|
|
515 { |
|
|
516 int nr = rows (); |
|
|
517 if (i < 0 || i >= cols ()) |
|
|
518 { |
|
|
519 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
520 return ColumnVector (); |
|
|
521 } |
|
|
522 |
|
|
523 ColumnVector retval (nr); |
|
|
524 for (int j = 0; j < nr; j++) |
|
|
525 retval.elem (j) = elem (j, i); |
|
|
526 |
|
|
527 return retval; |
|
|
528 } |
|
|
529 |
|
|
530 ColumnVector |
|
|
531 Matrix::column (char *s) const |
|
|
532 { |
|
533
|
533 if (! s) |
|
458
|
534 { |
|
|
535 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
536 return ColumnVector (); |
|
|
537 } |
|
|
538 |
|
|
539 char c = *s; |
|
|
540 if (c == 'f' || c == 'F') |
|
|
541 return column (0); |
|
|
542 else if (c == 'l' || c == 'L') |
|
|
543 return column (cols () - 1); |
|
|
544 else |
|
|
545 { |
|
|
546 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
547 return ColumnVector (); |
|
|
548 } |
|
|
549 } |
|
|
550 |
|
|
551 Matrix |
|
|
552 Matrix::inverse (void) const |
|
|
553 { |
|
|
554 int info; |
|
|
555 double rcond; |
|
|
556 return inverse (info, rcond); |
|
|
557 } |
|
|
558 |
|
|
559 Matrix |
|
|
560 Matrix::inverse (int& info) const |
|
|
561 { |
|
|
562 double rcond; |
|
|
563 return inverse (info, rcond); |
|
|
564 } |
|
|
565 |
|
|
566 Matrix |
|
532
|
567 Matrix::inverse (int& info, double& rcond) const |
|
458
|
568 { |
|
|
569 int nr = rows (); |
|
|
570 int nc = cols (); |
|
|
571 int len = length (); |
|
|
572 if (nr != nc || nr == 0 || nc == 0) |
|
|
573 { |
|
|
574 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
|
575 return Matrix (); |
|
|
576 } |
|
|
577 |
|
|
578 info = 0; |
|
|
579 |
|
|
580 int *ipvt = new int [nr]; |
|
|
581 double *z = new double [nr]; |
|
|
582 double *tmp_data = dup (data (), len); |
|
|
583 |
|
|
584 F77_FCN (dgeco) (tmp_data, &nr, &nc, ipvt, &rcond, z); |
|
|
585 |
|
532
|
586 volatile double tmp_rcond = rcond; |
|
|
587 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
588 { |
|
|
589 info = -1; |
|
|
590 copy (tmp_data, data (), len); // Restore matrix contents. |
|
|
591 } |
|
|
592 else |
|
|
593 { |
|
|
594 int job = 1; |
|
|
595 double dummy; |
|
|
596 |
|
|
597 F77_FCN (dgedi) (tmp_data, &nr, &nc, ipvt, &dummy, z, &job); |
|
|
598 } |
|
|
599 |
|
|
600 delete [] ipvt; |
|
|
601 delete [] z; |
|
|
602 |
|
|
603 return Matrix (tmp_data, nr, nc); |
|
|
604 } |
|
|
605 |
|
740
|
606 Matrix |
|
|
607 Matrix::pseudo_inverse (double tol) |
|
|
608 { |
|
|
609 SVD result (*this); |
|
|
610 |
|
|
611 DiagMatrix S = result.singular_values (); |
|
|
612 Matrix U = result.left_singular_matrix (); |
|
|
613 Matrix V = result.right_singular_matrix (); |
|
|
614 |
|
|
615 ColumnVector sigma = S.diag (); |
|
|
616 |
|
|
617 int r = sigma.length () - 1; |
|
|
618 int nr = rows (); |
|
|
619 int nc = cols (); |
|
|
620 |
|
|
621 if (tol <= 0.0) |
|
|
622 { |
|
|
623 if (nr > nc) |
|
|
624 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
625 else |
|
|
626 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
627 } |
|
|
628 |
|
|
629 while (r >= 0 && sigma.elem (r) < tol) |
|
|
630 r--; |
|
|
631 |
|
|
632 if (r < 0) |
|
|
633 return Matrix (nc, nr, 0.0); |
|
|
634 else |
|
|
635 { |
|
|
636 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
637 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
638 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
639 return Vr * D * Ur.transpose (); |
|
|
640 } |
|
|
641 } |
|
|
642 |
|
458
|
643 ComplexMatrix |
|
|
644 Matrix::fourier (void) const |
|
|
645 { |
|
|
646 int nr = rows (); |
|
|
647 int nc = cols (); |
|
|
648 int npts, nsamples; |
|
|
649 if (nr == 1 || nc == 1) |
|
|
650 { |
|
|
651 npts = nr > nc ? nr : nc; |
|
|
652 nsamples = 1; |
|
|
653 } |
|
|
654 else |
|
|
655 { |
|
|
656 npts = nr; |
|
|
657 nsamples = nc; |
|
|
658 } |
|
|
659 |
|
|
660 int nn = 4*npts+15; |
|
|
661 Complex *wsave = new Complex [nn]; |
|
|
662 Complex *tmp_data = make_complex (data (), length ()); |
|
|
663 |
|
|
664 F77_FCN (cffti) (&npts, wsave); |
|
|
665 |
|
|
666 for (int j = 0; j < nsamples; j++) |
|
|
667 F77_FCN (cfftf) (&npts, &tmp_data[npts*j], wsave); |
|
|
668 |
|
|
669 delete [] wsave; |
|
|
670 |
|
|
671 return ComplexMatrix (tmp_data, nr, nc); |
|
|
672 } |
|
|
673 |
|
|
674 ComplexMatrix |
|
|
675 Matrix::ifourier (void) const |
|
|
676 { |
|
|
677 int nr = rows (); |
|
|
678 int nc = cols (); |
|
|
679 int npts, nsamples; |
|
|
680 if (nr == 1 || nc == 1) |
|
|
681 { |
|
|
682 npts = nr > nc ? nr : nc; |
|
|
683 nsamples = 1; |
|
|
684 } |
|
|
685 else |
|
|
686 { |
|
|
687 npts = nr; |
|
|
688 nsamples = nc; |
|
|
689 } |
|
|
690 |
|
|
691 int nn = 4*npts+15; |
|
|
692 Complex *wsave = new Complex [nn]; |
|
|
693 Complex *tmp_data = make_complex (data (), length ()); |
|
|
694 |
|
|
695 F77_FCN (cffti) (&npts, wsave); |
|
|
696 |
|
|
697 for (int j = 0; j < nsamples; j++) |
|
|
698 F77_FCN (cfftb) (&npts, &tmp_data[npts*j], wsave); |
|
|
699 |
|
|
700 for (j = 0; j < npts*nsamples; j++) |
|
|
701 tmp_data[j] = tmp_data[j] / (double) npts; |
|
|
702 |
|
|
703 delete [] wsave; |
|
|
704 |
|
|
705 return ComplexMatrix (tmp_data, nr, nc); |
|
|
706 } |
|
|
707 |
|
677
|
708 ComplexMatrix |
|
|
709 Matrix::fourier2d (void) const |
|
|
710 { |
|
|
711 int nr = rows (); |
|
|
712 int nc = cols (); |
|
|
713 int npts, nsamples; |
|
|
714 if (nr == 1 || nc == 1) |
|
|
715 { |
|
|
716 npts = nr > nc ? nr : nc; |
|
|
717 nsamples = 1; |
|
|
718 } |
|
|
719 else |
|
|
720 { |
|
|
721 npts = nr; |
|
|
722 nsamples = nc; |
|
|
723 } |
|
|
724 |
|
|
725 int nn = 4*npts+15; |
|
|
726 Complex *wsave = new Complex [nn]; |
|
|
727 Complex *tmp_data = make_complex (data (), length ()); |
|
|
728 |
|
|
729 F77_FCN (cffti) (&npts, wsave); |
|
|
730 |
|
|
731 for (int j = 0; j < nsamples; j++) |
|
|
732 F77_FCN (cfftf) (&npts, &tmp_data[npts*j], wsave); |
|
|
733 |
|
|
734 delete [] wsave; |
|
|
735 |
|
|
736 npts = nc; |
|
|
737 nsamples = nr; |
|
|
738 nn = 4*npts+15; |
|
|
739 wsave = new Complex [nn]; |
|
|
740 Complex *row = new Complex[npts]; |
|
|
741 |
|
|
742 F77_FCN (cffti) (&npts, wsave); |
|
|
743 |
|
|
744 for (j = 0; j < nsamples; j++) |
|
|
745 { |
|
|
746 for (int i = 0; i < npts; i++) |
|
|
747 row[i] = tmp_data[i*nr + j]; |
|
|
748 |
|
|
749 F77_FCN (cfftf) (&npts, row, wsave); |
|
|
750 |
|
|
751 for (i = 0; i < npts; i++) |
|
|
752 tmp_data[i*nr + j] = row[i]; |
|
|
753 } |
|
|
754 |
|
|
755 delete [] wsave; |
|
|
756 delete [] row; |
|
|
757 |
|
|
758 return ComplexMatrix (tmp_data, nr, nc); |
|
|
759 } |
|
|
760 |
|
|
761 ComplexMatrix |
|
|
762 Matrix::ifourier2d (void) const |
|
|
763 { |
|
|
764 int nr = rows (); |
|
|
765 int nc = cols (); |
|
|
766 int npts, nsamples; |
|
|
767 if (nr == 1 || nc == 1) |
|
|
768 { |
|
|
769 npts = nr > nc ? nr : nc; |
|
|
770 nsamples = 1; |
|
|
771 } |
|
|
772 else |
|
|
773 { |
|
|
774 npts = nr; |
|
|
775 nsamples = nc; |
|
|
776 } |
|
|
777 |
|
|
778 int nn = 4*npts+15; |
|
|
779 Complex *wsave = new Complex [nn]; |
|
|
780 Complex *tmp_data = make_complex (data (), length ()); |
|
|
781 |
|
|
782 F77_FCN (cffti) (&npts, wsave); |
|
|
783 |
|
|
784 for (int j = 0; j < nsamples; j++) |
|
|
785 F77_FCN (cfftb) (&npts, &tmp_data[npts*j], wsave); |
|
|
786 |
|
|
787 delete [] wsave; |
|
|
788 |
|
|
789 for (j = 0; j < npts*nsamples; j++) |
|
|
790 tmp_data[j] = tmp_data[j] / (double) npts; |
|
|
791 |
|
|
792 npts = nc; |
|
|
793 nsamples = nr; |
|
|
794 nn = 4*npts+15; |
|
|
795 wsave = new Complex [nn]; |
|
|
796 Complex *row = new Complex[npts]; |
|
|
797 |
|
|
798 F77_FCN (cffti) (&npts, wsave); |
|
|
799 |
|
|
800 for (j = 0; j < nsamples; j++) |
|
|
801 { |
|
|
802 for (int i = 0; i < npts; i++) |
|
|
803 row[i] = tmp_data[i*nr + j]; |
|
|
804 |
|
|
805 F77_FCN (cfftb) (&npts, row, wsave); |
|
|
806 |
|
|
807 for (i = 0; i < npts; i++) |
|
|
808 tmp_data[i*nr + j] = row[i] / (double) npts; |
|
|
809 } |
|
|
810 |
|
|
811 delete [] wsave; |
|
|
812 delete [] row; |
|
|
813 |
|
|
814 return ComplexMatrix (tmp_data, nr, nc); |
|
|
815 } |
|
|
816 |
|
458
|
817 DET |
|
|
818 Matrix::determinant (void) const |
|
|
819 { |
|
|
820 int info; |
|
|
821 double rcond; |
|
|
822 return determinant (info, rcond); |
|
|
823 } |
|
|
824 |
|
|
825 DET |
|
|
826 Matrix::determinant (int& info) const |
|
|
827 { |
|
|
828 double rcond; |
|
|
829 return determinant (info, rcond); |
|
|
830 } |
|
|
831 |
|
|
832 DET |
|
532
|
833 Matrix::determinant (int& info, double& rcond) const |
|
458
|
834 { |
|
|
835 DET retval; |
|
|
836 |
|
|
837 int nr = rows (); |
|
|
838 int nc = cols (); |
|
|
839 |
|
|
840 if (nr == 0 || nc == 0) |
|
|
841 { |
|
|
842 double d[2]; |
|
|
843 d[0] = 1.0; |
|
|
844 d[1] = 0.0; |
|
|
845 retval = DET (d); |
|
|
846 } |
|
|
847 else |
|
|
848 { |
|
|
849 info = 0; |
|
|
850 int *ipvt = new int [nr]; |
|
|
851 |
|
|
852 double *z = new double [nr]; |
|
|
853 double *tmp_data = dup (data (), length ()); |
|
|
854 |
|
|
855 F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
856 |
|
532
|
857 volatile double tmp_rcond = rcond; |
|
|
858 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
859 { |
|
|
860 info = -1; |
|
|
861 retval = DET (); |
|
|
862 } |
|
|
863 else |
|
|
864 { |
|
|
865 int job = 10; |
|
|
866 double d[2]; |
|
|
867 F77_FCN (dgedi) (tmp_data, &nr, &nr, ipvt, d, z, &job); |
|
|
868 retval = DET (d); |
|
|
869 } |
|
|
870 |
|
|
871 delete [] tmp_data; |
|
|
872 delete [] ipvt; |
|
|
873 delete [] z; |
|
|
874 } |
|
|
875 |
|
|
876 return retval; |
|
|
877 } |
|
|
878 |
|
|
879 Matrix |
|
|
880 Matrix::solve (const Matrix& b) const |
|
|
881 { |
|
|
882 int info; |
|
|
883 double rcond; |
|
|
884 return solve (b, info, rcond); |
|
|
885 } |
|
|
886 |
|
|
887 Matrix |
|
|
888 Matrix::solve (const Matrix& b, int& info) const |
|
|
889 { |
|
|
890 double rcond; |
|
|
891 return solve (b, info, rcond); |
|
|
892 } |
|
|
893 |
|
|
894 Matrix |
|
532
|
895 Matrix::solve (const Matrix& b, int& info, double& rcond) const |
|
458
|
896 { |
|
|
897 Matrix retval; |
|
|
898 |
|
|
899 int nr = rows (); |
|
|
900 int nc = cols (); |
|
|
901 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
|
902 { |
|
|
903 (*current_liboctave_error_handler) |
|
|
904 ("matrix dimension mismatch solution of linear equations"); |
|
|
905 return Matrix (); |
|
|
906 } |
|
|
907 |
|
|
908 info = 0; |
|
|
909 int *ipvt = new int [nr]; |
|
|
910 |
|
|
911 double *z = new double [nr]; |
|
|
912 double *tmp_data = dup (data (), length ()); |
|
|
913 |
|
|
914 F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
915 |
|
532
|
916 volatile double tmp_rcond = rcond; |
|
|
917 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
918 { |
|
|
919 info = -2; |
|
|
920 } |
|
|
921 else |
|
|
922 { |
|
|
923 int job = 0; |
|
|
924 |
|
|
925 double *result = dup (b.data (), b.length ()); |
|
|
926 |
|
|
927 int b_nc = b.cols (); |
|
|
928 for (int j = 0; j < b_nc; j++) |
|
|
929 F77_FCN (dgesl) (tmp_data, &nr, &nr, ipvt, &result[nr*j], &job); |
|
|
930 |
|
|
931 retval = Matrix (result, b.rows (), b_nc); |
|
|
932 } |
|
|
933 |
|
|
934 delete [] tmp_data; |
|
|
935 delete [] ipvt; |
|
|
936 delete [] z; |
|
|
937 |
|
|
938 return retval; |
|
|
939 } |
|
|
940 |
|
|
941 ComplexMatrix |
|
|
942 Matrix::solve (const ComplexMatrix& b) const |
|
|
943 { |
|
|
944 ComplexMatrix tmp (*this); |
|
|
945 return tmp.solve (b); |
|
|
946 } |
|
|
947 |
|
|
948 ComplexMatrix |
|
|
949 Matrix::solve (const ComplexMatrix& b, int& info) const |
|
|
950 { |
|
|
951 ComplexMatrix tmp (*this); |
|
|
952 return tmp.solve (b, info); |
|
|
953 } |
|
|
954 |
|
|
955 ComplexMatrix |
|
|
956 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
|
957 { |
|
|
958 ComplexMatrix tmp (*this); |
|
|
959 return tmp.solve (b, info, rcond); |
|
|
960 } |
|
|
961 |
|
|
962 ColumnVector |
|
|
963 Matrix::solve (const ColumnVector& b) const |
|
|
964 { |
|
|
965 int info; double rcond; |
|
|
966 return solve (b, info, rcond); |
|
|
967 } |
|
|
968 |
|
|
969 ColumnVector |
|
|
970 Matrix::solve (const ColumnVector& b, int& info) const |
|
|
971 { |
|
|
972 double rcond; |
|
|
973 return solve (b, info, rcond); |
|
|
974 } |
|
|
975 |
|
|
976 ColumnVector |
|
532
|
977 Matrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
458
|
978 { |
|
|
979 ColumnVector retval; |
|
|
980 |
|
|
981 int nr = rows (); |
|
|
982 int nc = cols (); |
|
|
983 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
|
984 { |
|
|
985 (*current_liboctave_error_handler) |
|
|
986 ("matrix dimension mismatch solution of linear equations"); |
|
|
987 return ColumnVector (); |
|
|
988 } |
|
|
989 |
|
|
990 info = 0; |
|
|
991 int *ipvt = new int [nr]; |
|
|
992 |
|
|
993 double *z = new double [nr]; |
|
|
994 double *tmp_data = dup (data (), length ()); |
|
|
995 |
|
|
996 F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z); |
|
|
997 |
|
532
|
998 volatile double tmp_rcond = rcond; |
|
|
999 if (tmp_rcond + 1.0 == 1.0) |
|
458
|
1000 { |
|
|
1001 info = -2; |
|
|
1002 } |
|
|
1003 else |
|
|
1004 { |
|
|
1005 int job = 0; |
|
|
1006 |
|
|
1007 int b_len = b.length (); |
|
|
1008 |
|
|
1009 double *result = dup (b.data (), b_len); |
|
|
1010 |
|
|
1011 F77_FCN (dgesl) (tmp_data, &nr, &nr, ipvt, result, &job); |
|
|
1012 |
|
|
1013 retval = ColumnVector (result, b_len); |
|
|
1014 } |
|
|
1015 |
|
|
1016 delete [] tmp_data; |
|
|
1017 delete [] ipvt; |
|
|
1018 delete [] z; |
|
|
1019 |
|
|
1020 return retval; |
|
|
1021 } |
|
|
1022 |
|
|
1023 ComplexColumnVector |
|
|
1024 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1025 { |
|
|
1026 ComplexMatrix tmp (*this); |
|
|
1027 return tmp.solve (b); |
|
|
1028 } |
|
|
1029 |
|
|
1030 ComplexColumnVector |
|
|
1031 Matrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1032 { |
|
|
1033 ComplexMatrix tmp (*this); |
|
|
1034 return tmp.solve (b, info); |
|
|
1035 } |
|
|
1036 |
|
|
1037 ComplexColumnVector |
|
|
1038 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const |
|
|
1039 { |
|
|
1040 ComplexMatrix tmp (*this); |
|
|
1041 return tmp.solve (b, info, rcond); |
|
|
1042 } |
|
|
1043 |
|
|
1044 Matrix |
|
|
1045 Matrix::lssolve (const Matrix& b) const |
|
|
1046 { |
|
|
1047 int info; |
|
|
1048 int rank; |
|
|
1049 return lssolve (b, info, rank); |
|
|
1050 } |
|
|
1051 |
|
|
1052 Matrix |
|
|
1053 Matrix::lssolve (const Matrix& b, int& info) const |
|
|
1054 { |
|
|
1055 int rank; |
|
|
1056 return lssolve (b, info, rank); |
|
|
1057 } |
|
|
1058 |
|
|
1059 Matrix |
|
|
1060 Matrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1061 { |
|
|
1062 int nrhs = b.cols (); |
|
|
1063 |
|
|
1064 int m = rows (); |
|
|
1065 int n = cols (); |
|
|
1066 |
|
|
1067 if (m == 0 || n == 0 || m != b.rows ()) |
|
|
1068 { |
|
|
1069 (*current_liboctave_error_handler) |
|
|
1070 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1071 return Matrix (); |
|
|
1072 } |
|
|
1073 |
|
|
1074 double *tmp_data = dup (data (), length ()); |
|
|
1075 |
|
|
1076 int nrr = m > n ? m : n; |
|
|
1077 Matrix result (nrr, nrhs); |
|
|
1078 |
|
|
1079 int i, j; |
|
|
1080 for (j = 0; j < nrhs; j++) |
|
|
1081 for (i = 0; i < m; i++) |
|
|
1082 result.elem (i, j) = b.elem (i, j); |
|
|
1083 |
|
|
1084 double *presult = result.fortran_vec (); |
|
|
1085 |
|
|
1086 int len_s = m < n ? m : n; |
|
|
1087 double *s = new double [len_s]; |
|
|
1088 double rcond = -1.0; |
|
|
1089 int lwork; |
|
|
1090 if (m < n) |
|
|
1091 lwork = 3*m + (2*m > nrhs ? (2*m > n ? 2*m : n) : (nrhs > n ? nrhs : n)); |
|
|
1092 else |
|
|
1093 lwork = 3*n + (2*n > nrhs ? (2*n > m ? 2*n : m) : (nrhs > m ? nrhs : m)); |
|
|
1094 |
|
|
1095 double *work = new double [lwork]; |
|
|
1096 |
|
|
1097 F77_FCN (dgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s, |
|
|
1098 &rcond, &rank, work, &lwork, &info); |
|
|
1099 |
|
|
1100 Matrix retval (n, nrhs); |
|
|
1101 for (j = 0; j < nrhs; j++) |
|
|
1102 for (i = 0; i < n; i++) |
|
|
1103 retval.elem (i, j) = result.elem (i, j); |
|
|
1104 |
|
|
1105 delete [] tmp_data; |
|
|
1106 delete [] s; |
|
|
1107 delete [] work; |
|
|
1108 |
|
|
1109 return retval; |
|
|
1110 } |
|
|
1111 |
|
|
1112 ComplexMatrix |
|
|
1113 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1114 { |
|
|
1115 ComplexMatrix tmp (*this); |
|
|
1116 return tmp.lssolve (b); |
|
|
1117 } |
|
|
1118 |
|
|
1119 ComplexMatrix |
|
|
1120 Matrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1121 { |
|
|
1122 ComplexMatrix tmp (*this); |
|
|
1123 return tmp.lssolve (b); |
|
|
1124 } |
|
|
1125 |
|
|
1126 ComplexMatrix |
|
|
1127 Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1128 { |
|
|
1129 ComplexMatrix tmp (*this); |
|
|
1130 return tmp.lssolve (b); |
|
|
1131 } |
|
|
1132 |
|
|
1133 ColumnVector |
|
|
1134 Matrix::lssolve (const ColumnVector& b) const |
|
|
1135 { |
|
|
1136 int info; |
|
|
1137 int rank; return lssolve (b, info, rank); |
|
|
1138 } |
|
|
1139 |
|
|
1140 ColumnVector |
|
|
1141 Matrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1142 { |
|
|
1143 int rank; |
|
|
1144 return lssolve (b, info, rank); |
|
|
1145 } |
|
|
1146 |
|
|
1147 ColumnVector |
|
|
1148 Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1149 { |
|
|
1150 int nrhs = 1; |
|
|
1151 |
|
|
1152 int m = rows (); |
|
|
1153 int n = cols (); |
|
|
1154 |
|
|
1155 if (m == 0 || n == 0 || m != b.length ()) |
|
|
1156 { |
|
|
1157 (*current_liboctave_error_handler) |
|
|
1158 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1159 return ColumnVector (); |
|
|
1160 } |
|
|
1161 |
|
|
1162 double *tmp_data = dup (data (), length ()); |
|
|
1163 |
|
|
1164 int nrr = m > n ? m : n; |
|
|
1165 ColumnVector result (nrr); |
|
|
1166 |
|
|
1167 int i; |
|
|
1168 for (i = 0; i < m; i++) |
|
|
1169 result.elem (i) = b.elem (i); |
|
|
1170 |
|
|
1171 double *presult = result.fortran_vec (); |
|
|
1172 |
|
|
1173 int len_s = m < n ? m : n; |
|
|
1174 double *s = new double [len_s]; |
|
|
1175 double rcond = -1.0; |
|
|
1176 int lwork; |
|
|
1177 if (m < n) |
|
|
1178 lwork = 3*m + (2*m > nrhs ? (2*m > n ? 2*m : n) : (nrhs > n ? nrhs : n)); |
|
|
1179 else |
|
|
1180 lwork = 3*n + (2*n > nrhs ? (2*n > m ? 2*n : m) : (nrhs > m ? nrhs : m)); |
|
|
1181 |
|
|
1182 double *work = new double [lwork]; |
|
|
1183 |
|
|
1184 F77_FCN (dgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s, |
|
|
1185 &rcond, &rank, work, &lwork, &info); |
|
|
1186 |
|
|
1187 ColumnVector retval (n); |
|
|
1188 for (i = 0; i < n; i++) |
|
|
1189 retval.elem (i) = result.elem (i); |
|
|
1190 |
|
|
1191 delete [] tmp_data; |
|
|
1192 delete [] s; |
|
|
1193 delete [] work; |
|
|
1194 |
|
|
1195 return retval; |
|
|
1196 } |
|
|
1197 |
|
|
1198 ComplexColumnVector |
|
|
1199 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
1200 { |
|
|
1201 ComplexMatrix tmp (*this); |
|
|
1202 return tmp.lssolve (b); |
|
|
1203 } |
|
|
1204 |
|
|
1205 ComplexColumnVector |
|
|
1206 Matrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1207 { |
|
|
1208 ComplexMatrix tmp (*this); |
|
|
1209 return tmp.lssolve (b, info); |
|
|
1210 } |
|
|
1211 |
|
|
1212 ComplexColumnVector |
|
|
1213 Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const |
|
|
1214 { |
|
|
1215 ComplexMatrix tmp (*this); |
|
|
1216 return tmp.lssolve (b, info, rank); |
|
|
1217 } |
|
|
1218 |
|
|
1219 Matrix& |
|
|
1220 Matrix::operator += (const Matrix& a) |
|
|
1221 { |
|
|
1222 int nr = rows (); |
|
|
1223 int nc = cols (); |
|
|
1224 if (nr != a.rows () || nc != a.cols ()) |
|
|
1225 { |
|
|
1226 (*current_liboctave_error_handler) |
|
|
1227 ("nonconformant matrix += operation attempted"); |
|
|
1228 return *this; |
|
|
1229 } |
|
|
1230 |
|
|
1231 if (nr == 0 || nc == 0) |
|
|
1232 return *this; |
|
|
1233 |
|
|
1234 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1235 |
|
|
1236 add2 (d, a.data (), length ()); |
|
|
1237 |
|
|
1238 return *this; |
|
|
1239 } |
|
|
1240 |
|
|
1241 Matrix& |
|
|
1242 Matrix::operator -= (const Matrix& a) |
|
|
1243 { |
|
|
1244 int nr = rows (); |
|
|
1245 int nc = cols (); |
|
|
1246 if (nr != a.rows () || nc != a.cols ()) |
|
|
1247 { |
|
|
1248 (*current_liboctave_error_handler) |
|
|
1249 ("nonconformant matrix -= operation attempted"); |
|
|
1250 return *this; |
|
|
1251 } |
|
|
1252 |
|
|
1253 if (nr == 0 || nc == 0) |
|
|
1254 return *this; |
|
|
1255 |
|
|
1256 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1257 |
|
|
1258 subtract2 (d, a.data (), length ()); |
|
|
1259 |
|
|
1260 return *this; |
|
|
1261 } |
|
|
1262 |
|
|
1263 Matrix& |
|
|
1264 Matrix::operator += (const DiagMatrix& a) |
|
|
1265 { |
|
|
1266 if (rows () != a.rows () || cols () != a.cols ()) |
|
|
1267 { |
|
|
1268 (*current_liboctave_error_handler) |
|
|
1269 ("nonconformant matrix += operation attempted"); |
|
|
1270 return *this; |
|
|
1271 } |
|
|
1272 |
|
|
1273 for (int i = 0; i < a.length (); i++) |
|
|
1274 elem (i, i) += a.elem (i, i); |
|
|
1275 |
|
|
1276 return *this; |
|
|
1277 } |
|
|
1278 |
|
|
1279 Matrix& |
|
|
1280 Matrix::operator -= (const DiagMatrix& a) |
|
|
1281 { |
|
|
1282 if (rows () != a.rows () || cols () != a.cols ()) |
|
|
1283 { |
|
|
1284 (*current_liboctave_error_handler) |
|
|
1285 ("nonconformant matrix += operation attempted"); |
|
|
1286 return *this; |
|
|
1287 } |
|
|
1288 |
|
|
1289 for (int i = 0; i < a.length (); i++) |
|
|
1290 elem (i, i) -= a.elem (i, i); |
|
|
1291 |
|
|
1292 return *this; |
|
|
1293 } |
|
|
1294 |
|
|
1295 // unary operations |
|
|
1296 |
|
|
1297 Matrix |
|
|
1298 Matrix::operator ! (void) const |
|
|
1299 { |
|
|
1300 int nr = rows (); |
|
|
1301 int nc = cols (); |
|
|
1302 |
|
|
1303 Matrix b (nr, nc); |
|
|
1304 |
|
|
1305 for (int j = 0; j < nc; j++) |
|
|
1306 for (int i = 0; i < nr; i++) |
|
|
1307 b.elem (i, j) = ! elem (i, j); |
|
|
1308 |
|
|
1309 return b; |
|
|
1310 } |
|
|
1311 |
|
|
1312 // matrix by scalar -> matrix operations. |
|
|
1313 |
|
|
1314 ComplexMatrix |
|
|
1315 operator + (const Matrix& a, const Complex& s) |
|
|
1316 { |
|
|
1317 return ComplexMatrix (add (a.data (), a.length (), s), |
|
|
1318 a.rows (), a.cols ()); |
|
|
1319 } |
|
|
1320 |
|
|
1321 ComplexMatrix |
|
|
1322 operator - (const Matrix& a, const Complex& s) |
|
|
1323 { |
|
|
1324 return ComplexMatrix (subtract (a.data (), a.length (), s), |
|
|
1325 a.rows (), a.cols ()); |
|
|
1326 } |
|
|
1327 |
|
|
1328 ComplexMatrix |
|
|
1329 operator * (const Matrix& a, const Complex& s) |
|
|
1330 { |
|
|
1331 return ComplexMatrix (multiply (a.data (), a.length (), s), |
|
|
1332 a.rows (), a.cols ()); |
|
|
1333 } |
|
|
1334 |
|
|
1335 ComplexMatrix |
|
|
1336 operator / (const Matrix& a, const Complex& s) |
|
|
1337 { |
|
|
1338 return ComplexMatrix (divide (a.data (), a.length (), s), |
|
|
1339 a.rows (), a.cols ()); |
|
|
1340 } |
|
|
1341 |
|
|
1342 // scalar by matrix -> matrix operations. |
|
|
1343 |
|
|
1344 ComplexMatrix |
|
|
1345 operator + (const Complex& s, const Matrix& a) |
|
|
1346 { |
|
|
1347 return ComplexMatrix (add (s, a.data (), a.length ()), |
|
|
1348 a.rows (), a.cols ()); |
|
|
1349 } |
|
|
1350 |
|
|
1351 ComplexMatrix |
|
|
1352 operator - (const Complex& s, const Matrix& a) |
|
|
1353 { |
|
|
1354 return ComplexMatrix (subtract (s, a.data (), a.length ()), |
|
|
1355 a.rows (), a.cols ()); |
|
|
1356 } |
|
|
1357 |
|
|
1358 ComplexMatrix |
|
|
1359 operator * (const Complex& s, const Matrix& a) |
|
|
1360 { |
|
|
1361 return ComplexMatrix (multiply (a.data (), a.length (), s), |
|
|
1362 a.rows (), a.cols ()); |
|
|
1363 } |
|
|
1364 |
|
|
1365 ComplexMatrix |
|
|
1366 operator / (const Complex& s, const Matrix& a) |
|
|
1367 { |
|
|
1368 return ComplexMatrix (divide (s, a.data (), a.length ()), |
|
|
1369 a.rows (), a.cols ()); |
|
|
1370 } |
|
|
1371 |
|
|
1372 // matrix by column vector -> column vector operations |
|
|
1373 |
|
|
1374 ColumnVector |
|
|
1375 operator * (const Matrix& m, const ColumnVector& a) |
|
|
1376 { |
|
|
1377 int nr = m.rows (); |
|
|
1378 int nc = m.cols (); |
|
|
1379 if (nc != a.length ()) |
|
|
1380 { |
|
|
1381 (*current_liboctave_error_handler) |
|
|
1382 ("nonconformant matrix multiplication attempted"); |
|
|
1383 return ColumnVector (); |
|
|
1384 } |
|
|
1385 |
|
|
1386 if (nr == 0 || nc == 0) |
|
|
1387 return ColumnVector (0); |
|
|
1388 |
|
|
1389 char trans = 'N'; |
|
|
1390 int ld = nr; |
|
|
1391 double alpha = 1.0; |
|
|
1392 double beta = 0.0; |
|
|
1393 int i_one = 1; |
|
|
1394 |
|
|
1395 double *y = new double [nr]; |
|
|
1396 |
|
|
1397 F77_FCN (dgemv) (&trans, &nr, &nc, &alpha, m.data (), &ld, a.data (), |
|
|
1398 &i_one, &beta, y, &i_one, 1L); |
|
|
1399 |
|
|
1400 return ColumnVector (y, nr); |
|
|
1401 } |
|
|
1402 |
|
|
1403 ComplexColumnVector |
|
|
1404 operator * (const Matrix& m, const ComplexColumnVector& a) |
|
|
1405 { |
|
|
1406 ComplexMatrix tmp (m); |
|
|
1407 return tmp * a; |
|
|
1408 } |
|
|
1409 |
|
|
1410 // matrix by diagonal matrix -> matrix operations |
|
|
1411 |
|
|
1412 Matrix |
|
|
1413 operator + (const Matrix& m, const DiagMatrix& a) |
|
|
1414 { |
|
|
1415 int nr = m.rows (); |
|
|
1416 int nc = m.cols (); |
|
|
1417 if (nr != a.rows () || nc != a.cols ()) |
|
|
1418 { |
|
|
1419 (*current_liboctave_error_handler) |
|
|
1420 ("nonconformant matrix addition attempted"); |
|
|
1421 return Matrix (); |
|
|
1422 } |
|
|
1423 |
|
|
1424 if (nr == 0 || nc == 0) |
|
|
1425 return Matrix (nr, nc); |
|
|
1426 |
|
|
1427 Matrix result (m); |
|
|
1428 int a_len = a.length (); |
|
|
1429 for (int i = 0; i < a_len; i++) |
|
|
1430 result.elem (i, i) += a.elem (i, i); |
|
|
1431 |
|
|
1432 return result; |
|
|
1433 } |
|
|
1434 |
|
|
1435 Matrix |
|
|
1436 operator - (const Matrix& m, const DiagMatrix& a) |
|
|
1437 { |
|
|
1438 int nr = m.rows (); |
|
|
1439 int nc = m.cols (); |
|
|
1440 if (nr != a.rows () || nc != a.cols ()) |
|
|
1441 { |
|
|
1442 (*current_liboctave_error_handler) |
|
|
1443 ("nonconformant matrix subtraction attempted"); |
|
|
1444 return Matrix (); |
|
|
1445 } |
|
|
1446 |
|
|
1447 if (nr == 0 || nc == 0) |
|
|
1448 return Matrix (nr, nc); |
|
|
1449 |
|
|
1450 Matrix result (m); |
|
|
1451 int a_len = a.length (); |
|
|
1452 for (int i = 0; i < a_len; i++) |
|
|
1453 result.elem (i, i) -= a.elem (i, i); |
|
|
1454 |
|
|
1455 return result; |
|
|
1456 } |
|
|
1457 |
|
|
1458 Matrix |
|
|
1459 operator * (const Matrix& m, const DiagMatrix& a) |
|
|
1460 { |
|
|
1461 int nr = m.rows (); |
|
|
1462 int nc = m.cols (); |
|
|
1463 int a_nr = a.rows (); |
|
|
1464 int a_nc = a.cols (); |
|
|
1465 if (nc != a_nr) |
|
|
1466 { |
|
|
1467 (*current_liboctave_error_handler) |
|
|
1468 ("nonconformant matrix multiplication attempted"); |
|
|
1469 return Matrix (); |
|
|
1470 } |
|
|
1471 |
|
|
1472 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
1473 return Matrix (nr, a_nc, 0.0); |
|
|
1474 |
|
|
1475 double *c = new double [nr*a_nc]; |
|
533
|
1476 double *ctmp = 0; |
|
458
|
1477 |
|
|
1478 int a_len = a.length (); |
|
|
1479 for (int j = 0; j < a_len; j++) |
|
|
1480 { |
|
|
1481 int idx = j * nr; |
|
|
1482 ctmp = c + idx; |
|
|
1483 if (a.elem (j, j) == 1.0) |
|
|
1484 { |
|
|
1485 for (int i = 0; i < nr; i++) |
|
|
1486 ctmp[i] = m.elem (i, j); |
|
|
1487 } |
|
|
1488 else if (a.elem (j, j) == 0.0) |
|
|
1489 { |
|
|
1490 for (int i = 0; i < nr; i++) |
|
|
1491 ctmp[i] = 0.0; |
|
|
1492 } |
|
|
1493 else |
|
|
1494 { |
|
|
1495 for (int i = 0; i < nr; i++) |
|
|
1496 ctmp[i] = a.elem (j, j) * m.elem (i, j); |
|
|
1497 } |
|
|
1498 } |
|
|
1499 |
|
|
1500 if (a_nr < a_nc) |
|
|
1501 { |
|
|
1502 for (int i = nr * nc; i < nr * a_nc; i++) |
|
|
1503 ctmp[i] = 0.0; |
|
|
1504 } |
|
|
1505 |
|
|
1506 return Matrix (c, nr, a_nc); |
|
|
1507 } |
|
|
1508 |
|
|
1509 ComplexMatrix |
|
|
1510 operator + (const Matrix& m, const ComplexDiagMatrix& a) |
|
|
1511 { |
|
|
1512 int nr = m.rows (); |
|
|
1513 int nc = m.cols (); |
|
|
1514 if (nr != a.rows () || nc != a.cols ()) |
|
|
1515 { |
|
|
1516 (*current_liboctave_error_handler) |
|
|
1517 ("nonconformant matrix addition attempted"); |
|
|
1518 return ComplexMatrix (); |
|
|
1519 } |
|
|
1520 |
|
|
1521 if (nr == 0 || nc == 0) |
|
|
1522 return ComplexMatrix (nr, nc); |
|
|
1523 |
|
|
1524 ComplexMatrix result (m); |
|
|
1525 for (int i = 0; i < a.length (); i++) |
|
|
1526 result.elem (i, i) += a.elem (i, i); |
|
|
1527 |
|
|
1528 return result; |
|
|
1529 } |
|
|
1530 |
|
|
1531 ComplexMatrix |
|
|
1532 operator - (const Matrix& m, const ComplexDiagMatrix& a) |
|
|
1533 { |
|
|
1534 int nr = m.rows (); |
|
|
1535 int nc = m.cols (); |
|
|
1536 if (nr != a.rows () || nc != a.cols ()) |
|
|
1537 { |
|
|
1538 (*current_liboctave_error_handler) |
|
|
1539 ("nonconformant matrix subtraction attempted"); |
|
|
1540 return ComplexMatrix (); |
|
|
1541 } |
|
|
1542 |
|
|
1543 if (nr == 0 || nc == 0) |
|
|
1544 return ComplexMatrix (nr, nc); |
|
|
1545 |
|
|
1546 ComplexMatrix result (m); |
|
|
1547 for (int i = 0; i < a.length (); i++) |
|
|
1548 result.elem (i, i) -= a.elem (i, i); |
|
|
1549 |
|
|
1550 return result; |
|
|
1551 } |
|
|
1552 |
|
|
1553 ComplexMatrix |
|
|
1554 operator * (const Matrix& m, const ComplexDiagMatrix& a) |
|
|
1555 { |
|
|
1556 int nr = m.rows (); |
|
|
1557 int nc = m.cols (); |
|
|
1558 int a_nr = a.rows (); |
|
|
1559 int a_nc = a.cols (); |
|
|
1560 if (nc != a_nr) |
|
|
1561 { |
|
|
1562 (*current_liboctave_error_handler) |
|
|
1563 ("nonconformant matrix multiplication attempted"); |
|
|
1564 return ComplexMatrix (); |
|
|
1565 } |
|
|
1566 |
|
|
1567 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
1568 return ComplexMatrix (nr, a_nc, 0.0); |
|
|
1569 |
|
|
1570 Complex *c = new Complex [nr*a_nc]; |
|
533
|
1571 Complex *ctmp = 0; |
|
458
|
1572 |
|
|
1573 for (int j = 0; j < a.length (); j++) |
|
|
1574 { |
|
|
1575 int idx = j * nr; |
|
|
1576 ctmp = c + idx; |
|
|
1577 if (a.elem (j, j) == 1.0) |
|
|
1578 { |
|
|
1579 for (int i = 0; i < nr; i++) |
|
|
1580 ctmp[i] = m.elem (i, j); |
|
|
1581 } |
|
|
1582 else if (a.elem (j, j) == 0.0) |
|
|
1583 { |
|
|
1584 for (int i = 0; i < nr; i++) |
|
|
1585 ctmp[i] = 0.0; |
|
|
1586 } |
|
|
1587 else |
|
|
1588 { |
|
|
1589 for (int i = 0; i < nr; i++) |
|
|
1590 ctmp[i] = a.elem (j, j) * m.elem (i, j); |
|
|
1591 } |
|
|
1592 } |
|
|
1593 |
|
|
1594 if (a_nr < a_nc) |
|
|
1595 { |
|
|
1596 for (int i = nr * nc; i < nr * a_nc; i++) |
|
|
1597 ctmp[i] = 0.0; |
|
|
1598 } |
|
|
1599 |
|
|
1600 return ComplexMatrix (c, nr, a_nc); |
|
|
1601 } |
|
|
1602 |
|
|
1603 // matrix by matrix -> matrix operations |
|
|
1604 |
|
|
1605 Matrix |
|
|
1606 operator * (const Matrix& m, const Matrix& a) |
|
|
1607 { |
|
|
1608 int nr = m.rows (); |
|
|
1609 int nc = m.cols (); |
|
|
1610 int a_nr = a.rows (); |
|
|
1611 int a_nc = a.cols (); |
|
|
1612 if (nc != a_nr) |
|
|
1613 { |
|
|
1614 (*current_liboctave_error_handler) |
|
|
1615 ("nonconformant matrix multiplication attempted"); |
|
|
1616 return Matrix (); |
|
|
1617 } |
|
|
1618 |
|
|
1619 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
1620 return Matrix (nr, a_nc, 0.0); |
|
|
1621 |
|
|
1622 char trans = 'N'; |
|
|
1623 char transa = 'N'; |
|
|
1624 |
|
|
1625 int ld = nr; |
|
|
1626 int lda = a_nr; |
|
|
1627 |
|
|
1628 double alpha = 1.0; |
|
|
1629 double beta = 0.0; |
|
|
1630 |
|
|
1631 double *c = new double [nr*a_nc]; |
|
|
1632 |
|
|
1633 F77_FCN (dgemm) (&trans, &transa, &nr, &a_nc, &nc, &alpha, m.data (), |
|
|
1634 &ld, a.data (), &lda, &beta, c, &nr, 1L, 1L); |
|
|
1635 |
|
|
1636 return Matrix (c, nr, a_nc); |
|
|
1637 } |
|
|
1638 |
|
|
1639 ComplexMatrix |
|
|
1640 operator * (const Matrix& m, const ComplexMatrix& a) |
|
|
1641 { |
|
|
1642 ComplexMatrix tmp (m); |
|
|
1643 return tmp * a; |
|
|
1644 } |
|
|
1645 |
|
|
1646 ComplexMatrix |
|
|
1647 operator + (const Matrix& m, const ComplexMatrix& a) |
|
|
1648 { |
|
|
1649 int nr = m.rows (); |
|
|
1650 int nc = m.cols (); |
|
|
1651 if (nr != a.rows () || nc != a.cols ()) |
|
|
1652 { |
|
|
1653 (*current_liboctave_error_handler) |
|
|
1654 ("nonconformant matrix addition attempted"); |
|
|
1655 return ComplexMatrix (); |
|
|
1656 } |
|
|
1657 |
|
|
1658 return ComplexMatrix (add (m.data (), a.data (), m.length ()), nr, nc); |
|
|
1659 } |
|
|
1660 |
|
|
1661 ComplexMatrix |
|
|
1662 operator - (const Matrix& m, const ComplexMatrix& a) |
|
|
1663 { |
|
|
1664 int nr = m.rows (); |
|
|
1665 int nc = m.cols (); |
|
|
1666 if (nr != a.rows () || nc != a.cols ()) |
|
|
1667 { |
|
|
1668 (*current_liboctave_error_handler) |
|
|
1669 ("nonconformant matrix subtraction attempted"); |
|
|
1670 return ComplexMatrix (); |
|
|
1671 } |
|
|
1672 |
|
|
1673 if (nr == 0 || nc == 0) |
|
|
1674 return ComplexMatrix (nr, nc); |
|
|
1675 |
|
|
1676 return ComplexMatrix (subtract (m.data (), a.data (), m.length ()), nr, nc); |
|
|
1677 } |
|
|
1678 |
|
|
1679 ComplexMatrix |
|
|
1680 product (const Matrix& m, const ComplexMatrix& a) |
|
|
1681 { |
|
|
1682 int nr = m.rows (); |
|
|
1683 int nc = m.cols (); |
|
|
1684 if (nr != a.rows () || nc != a.cols ()) |
|
|
1685 { |
|
|
1686 (*current_liboctave_error_handler) |
|
|
1687 ("nonconformant matrix product attempted"); |
|
|
1688 return ComplexMatrix (); |
|
|
1689 } |
|
|
1690 |
|
|
1691 if (nr == 0 || nc == 0) |
|
|
1692 return ComplexMatrix (nr, nc); |
|
|
1693 |
|
|
1694 return ComplexMatrix (multiply (m.data (), a.data (), m.length ()), nr, nc); |
|
|
1695 } |
|
|
1696 |
|
|
1697 ComplexMatrix |
|
|
1698 quotient (const Matrix& m, const ComplexMatrix& a) |
|
|
1699 { |
|
|
1700 int nr = m.rows (); |
|
|
1701 int nc = m.cols (); |
|
|
1702 if (nr != a.rows () || nc != a.cols ()) |
|
|
1703 { |
|
|
1704 (*current_liboctave_error_handler) |
|
|
1705 ("nonconformant matrix quotient attempted"); |
|
|
1706 return ComplexMatrix (); |
|
|
1707 } |
|
|
1708 |
|
|
1709 if (nr == 0 || nc == 0) |
|
|
1710 return ComplexMatrix (nr, nc); |
|
|
1711 |
|
|
1712 return ComplexMatrix (divide (m.data (), a.data (), m.length ()), nr, nc); |
|
|
1713 } |
|
|
1714 |
|
|
1715 // other operations. |
|
|
1716 |
|
|
1717 Matrix |
|
|
1718 map (d_d_Mapper f, const Matrix& a) |
|
|
1719 { |
|
|
1720 Matrix b (a); |
|
|
1721 b.map (f); |
|
|
1722 return b; |
|
|
1723 } |
|
|
1724 |
|
|
1725 void |
|
|
1726 Matrix::map (d_d_Mapper f) |
|
|
1727 { |
|
|
1728 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1729 |
|
|
1730 for (int i = 0; i < length (); i++) |
|
|
1731 d[i] = f (d[i]); |
|
|
1732 } |
|
|
1733 |
|
|
1734 // XXX FIXME XXX Do these really belong here? They should maybe be |
|
|
1735 // cleaned up a bit, no? What about corresponding functions for the |
|
|
1736 // Vectors? |
|
|
1737 |
|
|
1738 Matrix |
|
|
1739 Matrix::all (void) const |
|
|
1740 { |
|
|
1741 int nr = rows (); |
|
|
1742 int nc = cols (); |
|
|
1743 Matrix retval; |
|
|
1744 if (nr > 0 && nc > 0) |
|
|
1745 { |
|
|
1746 if (nr == 1) |
|
|
1747 { |
|
|
1748 retval.resize (1, 1); |
|
|
1749 retval.elem (0, 0) = 1.0; |
|
|
1750 for (int j = 0; j < nc; j++) |
|
|
1751 { |
|
|
1752 if (elem (0, j) == 0.0) |
|
|
1753 { |
|
|
1754 retval.elem (0, 0) = 0.0; |
|
|
1755 break; |
|
|
1756 } |
|
|
1757 } |
|
|
1758 } |
|
|
1759 else if (nc == 1) |
|
|
1760 { |
|
|
1761 retval.resize (1, 1); |
|
|
1762 retval.elem (0, 0) = 1.0; |
|
|
1763 for (int i = 0; i < nr; i++) |
|
|
1764 { |
|
|
1765 if (elem (i, 0) == 0.0) |
|
|
1766 { |
|
|
1767 retval.elem (0, 0) = 0.0; |
|
|
1768 break; |
|
|
1769 } |
|
|
1770 } |
|
|
1771 } |
|
|
1772 else |
|
|
1773 { |
|
|
1774 retval.resize (1, nc); |
|
|
1775 for (int j = 0; j < nc; j++) |
|
|
1776 { |
|
|
1777 retval.elem (0, j) = 1.0; |
|
|
1778 for (int i = 0; i < nr; i++) |
|
|
1779 { |
|
|
1780 if (elem (i, j) == 0.0) |
|
|
1781 { |
|
|
1782 retval.elem (0, j) = 0.0; |
|
|
1783 break; |
|
|
1784 } |
|
|
1785 } |
|
|
1786 } |
|
|
1787 } |
|
|
1788 } |
|
|
1789 return retval; |
|
|
1790 } |
|
|
1791 |
|
|
1792 Matrix |
|
|
1793 Matrix::any (void) const |
|
|
1794 { |
|
|
1795 int nr = rows (); |
|
|
1796 int nc = cols (); |
|
|
1797 Matrix retval; |
|
|
1798 if (nr > 0 && nc > 0) |
|
|
1799 { |
|
|
1800 if (nr == 1) |
|
|
1801 { |
|
|
1802 retval.resize (1, 1); |
|
|
1803 retval.elem (0, 0) = 0.0; |
|
|
1804 for (int j = 0; j < nc; j++) |
|
|
1805 { |
|
|
1806 if (elem (0, j) != 0.0) |
|
|
1807 { |
|
|
1808 retval.elem (0, 0) = 1.0; |
|
|
1809 break; |
|
|
1810 } |
|
|
1811 } |
|
|
1812 } |
|
|
1813 else if (nc == 1) |
|
|
1814 { |
|
|
1815 retval.resize (1, 1); |
|
|
1816 retval.elem (0, 0) = 0.0; |
|
|
1817 for (int i = 0; i < nr; i++) |
|
|
1818 { |
|
|
1819 if (elem (i, 0) != 0.0) |
|
|
1820 { |
|
|
1821 retval.elem (0, 0) = 1.0; |
|
|
1822 break; |
|
|
1823 } |
|
|
1824 } |
|
|
1825 } |
|
|
1826 else |
|
|
1827 { |
|
|
1828 retval.resize (1, nc); |
|
|
1829 for (int j = 0; j < nc; j++) |
|
|
1830 { |
|
|
1831 retval.elem (0, j) = 0.0; |
|
|
1832 for (int i = 0; i < nr; i++) |
|
|
1833 { |
|
|
1834 if (elem (i, j) != 0.0) |
|
|
1835 { |
|
|
1836 retval.elem (0, j) = 1.0; |
|
|
1837 break; |
|
|
1838 } |
|
|
1839 } |
|
|
1840 } |
|
|
1841 } |
|
|
1842 } |
|
|
1843 return retval; |
|
|
1844 } |
|
|
1845 |
|
|
1846 Matrix |
|
|
1847 Matrix::cumprod (void) const |
|
|
1848 { |
|
|
1849 Matrix retval; |
|
|
1850 |
|
|
1851 int nr = rows (); |
|
|
1852 int nc = cols (); |
|
|
1853 |
|
|
1854 if (nr == 1) |
|
|
1855 { |
|
|
1856 retval.resize (1, nc); |
|
|
1857 if (nc > 0) |
|
|
1858 { |
|
|
1859 double prod = elem (0, 0); |
|
|
1860 for (int j = 0; j < nc; j++) |
|
|
1861 { |
|
|
1862 retval.elem (0, j) = prod; |
|
|
1863 if (j < nc - 1) |
|
|
1864 prod *= elem (0, j+1); |
|
|
1865 } |
|
|
1866 } |
|
|
1867 } |
|
|
1868 else if (nc == 1) |
|
|
1869 { |
|
|
1870 retval.resize (nr, 1); |
|
|
1871 if (nr > 0) |
|
|
1872 { |
|
|
1873 double prod = elem (0, 0); |
|
|
1874 for (int i = 0; i < nr; i++) |
|
|
1875 { |
|
|
1876 retval.elem (i, 0) = prod; |
|
|
1877 if (i < nr - 1) |
|
|
1878 prod *= elem (i+1, 0); |
|
|
1879 } |
|
|
1880 } |
|
|
1881 } |
|
|
1882 else |
|
|
1883 { |
|
|
1884 retval.resize (nr, nc); |
|
|
1885 if (nr > 0 && nc > 0) |
|
|
1886 { |
|
|
1887 for (int j = 0; j < nc; j++) |
|
|
1888 { |
|
|
1889 double prod = elem (0, j); |
|
|
1890 for (int i = 0; i < nr; i++) |
|
|
1891 { |
|
|
1892 retval.elem (i, j) = prod; |
|
|
1893 if (i < nr - 1) |
|
|
1894 prod *= elem (i+1, j); |
|
|
1895 } |
|
|
1896 } |
|
|
1897 } |
|
|
1898 } |
|
|
1899 return retval; |
|
|
1900 } |
|
|
1901 |
|
|
1902 Matrix |
|
|
1903 Matrix::cumsum (void) const |
|
|
1904 { |
|
|
1905 Matrix retval; |
|
|
1906 |
|
|
1907 int nr = rows (); |
|
|
1908 int nc = cols (); |
|
|
1909 |
|
|
1910 if (nr == 1) |
|
|
1911 { |
|
|
1912 retval.resize (1, nc); |
|
|
1913 if (nc > 0) |
|
|
1914 { |
|
|
1915 double sum = elem (0, 0); |
|
|
1916 for (int j = 0; j < nc; j++) |
|
|
1917 { |
|
|
1918 retval.elem (0, j) = sum; |
|
|
1919 if (j < nc - 1) |
|
|
1920 sum += elem (0, j+1); |
|
|
1921 } |
|
|
1922 } |
|
|
1923 } |
|
|
1924 else if (nc == 1) |
|
|
1925 { |
|
|
1926 retval.resize (nr, 1); |
|
|
1927 if (nr > 0) |
|
|
1928 { |
|
|
1929 double sum = elem (0, 0); |
|
|
1930 for (int i = 0; i < nr; i++) |
|
|
1931 { |
|
|
1932 retval.elem (i, 0) = sum; |
|
|
1933 if (i < nr - 1) |
|
|
1934 sum += elem (i+1, 0); |
|
|
1935 } |
|
|
1936 } |
|
|
1937 } |
|
|
1938 else |
|
|
1939 { |
|
|
1940 retval.resize (nr, nc); |
|
|
1941 if (nr > 0 && nc > 0) |
|
|
1942 { |
|
|
1943 for (int j = 0; j < nc; j++) |
|
|
1944 { |
|
|
1945 double sum = elem (0, j); |
|
|
1946 for (int i = 0; i < nr; i++) |
|
|
1947 { |
|
|
1948 retval.elem (i, j) = sum; |
|
|
1949 if (i < nr - 1) |
|
|
1950 sum += elem (i+1, j); |
|
|
1951 } |
|
|
1952 } |
|
|
1953 } |
|
|
1954 } |
|
|
1955 return retval; |
|
|
1956 } |
|
|
1957 |
|
|
1958 Matrix |
|
|
1959 Matrix::prod (void) const |
|
|
1960 { |
|
|
1961 Matrix retval; |
|
|
1962 |
|
|
1963 int nr = rows (); |
|
|
1964 int nc = cols (); |
|
|
1965 |
|
|
1966 if (nr == 1) |
|
|
1967 { |
|
|
1968 retval.resize (1, 1); |
|
|
1969 retval.elem (0, 0) = 1.0; |
|
|
1970 for (int j = 0; j < nc; j++) |
|
|
1971 retval.elem (0, 0) *= elem (0, j); |
|
|
1972 } |
|
|
1973 else if (nc == 1) |
|
|
1974 { |
|
|
1975 retval.resize (1, 1); |
|
|
1976 retval.elem (0, 0) = 1.0; |
|
|
1977 for (int i = 0; i < nr; i++) |
|
|
1978 retval.elem (0, 0) *= elem (i, 0); |
|
|
1979 } |
|
|
1980 else |
|
|
1981 { |
|
|
1982 if (nc == 0) |
|
|
1983 { |
|
|
1984 retval.resize (1, 1); |
|
|
1985 retval.elem (0, 0) = 1.0; |
|
|
1986 } |
|
|
1987 else |
|
|
1988 retval.resize (1, nc); |
|
|
1989 |
|
|
1990 for (int j = 0; j < nc; j++) |
|
|
1991 { |
|
|
1992 retval.elem (0, j) = 1.0; |
|
|
1993 for (int i = 0; i < nr; i++) |
|
|
1994 retval.elem (0, j) *= elem (i, j); |
|
|
1995 } |
|
|
1996 } |
|
|
1997 return retval; |
|
|
1998 } |
|
|
1999 |
|
|
2000 Matrix |
|
|
2001 Matrix::sum (void) const |
|
|
2002 { |
|
|
2003 Matrix retval; |
|
|
2004 |
|
|
2005 int nr = rows (); |
|
|
2006 int nc = cols (); |
|
|
2007 |
|
|
2008 if (nr == 1) |
|
|
2009 { |
|
|
2010 retval.resize (1, 1); |
|
|
2011 retval.elem (0, 0) = 0.0; |
|
|
2012 for (int j = 0; j < nc; j++) |
|
|
2013 retval.elem (0, 0) += elem (0, j); |
|
|
2014 } |
|
|
2015 else if (nc == 1) |
|
|
2016 { |
|
|
2017 retval.resize (1, 1); |
|
|
2018 retval.elem (0, 0) = 0.0; |
|
|
2019 for (int i = 0; i < nr; i++) |
|
|
2020 retval.elem (0, 0) += elem (i, 0); |
|
|
2021 } |
|
|
2022 else |
|
|
2023 { |
|
|
2024 if (nc == 0) |
|
|
2025 { |
|
|
2026 retval.resize (1, 1); |
|
|
2027 retval.elem (0, 0) = 0.0; |
|
|
2028 } |
|
|
2029 else |
|
|
2030 retval.resize (1, nc); |
|
|
2031 |
|
|
2032 for (int j = 0; j < nc; j++) |
|
|
2033 { |
|
|
2034 retval.elem (0, j) = 0.0; |
|
|
2035 for (int i = 0; i < nr; i++) |
|
|
2036 retval.elem (0, j) += elem (i, j); |
|
|
2037 } |
|
|
2038 } |
|
|
2039 return retval; |
|
|
2040 } |
|
|
2041 |
|
|
2042 Matrix |
|
|
2043 Matrix::sumsq (void) const |
|
|
2044 { |
|
|
2045 Matrix retval; |
|
|
2046 |
|
|
2047 int nr = rows (); |
|
|
2048 int nc = cols (); |
|
|
2049 |
|
|
2050 if (nr == 1) |
|
|
2051 { |
|
|
2052 retval.resize (1, 1); |
|
|
2053 retval.elem (0, 0) = 0.0; |
|
|
2054 for (int j = 0; j < nc; j++) |
|
|
2055 { |
|
|
2056 double d = elem (0, j); |
|
|
2057 retval.elem (0, 0) += d * d; |
|
|
2058 } |
|
|
2059 } |
|
|
2060 else if (nc == 1) |
|
|
2061 { |
|
|
2062 retval.resize (1, 1); |
|
|
2063 retval.elem (0, 0) = 0.0; |
|
|
2064 for (int i = 0; i < nr; i++) |
|
|
2065 { |
|
|
2066 double d = elem (i, 0); |
|
|
2067 retval.elem (0, 0) += d * d; |
|
|
2068 } |
|
|
2069 } |
|
|
2070 else |
|
|
2071 { |
|
|
2072 retval.resize (1, nc); |
|
|
2073 for (int j = 0; j < nc; j++) |
|
|
2074 { |
|
|
2075 retval.elem (0, j) = 0.0; |
|
|
2076 for (int i = 0; i < nr; i++) |
|
|
2077 { |
|
|
2078 double d = elem (i, j); |
|
|
2079 retval.elem (0, j) += d * d; |
|
|
2080 } |
|
|
2081 } |
|
|
2082 } |
|
|
2083 return retval; |
|
|
2084 } |
|
|
2085 |
|
|
2086 ColumnVector |
|
|
2087 Matrix::diag (void) const |
|
|
2088 { |
|
|
2089 return diag (0); |
|
|
2090 } |
|
|
2091 |
|
|
2092 ColumnVector |
|
|
2093 Matrix::diag (int k) const |
|
|
2094 { |
|
|
2095 int nnr = rows (); |
|
|
2096 int nnc = cols (); |
|
|
2097 if (k > 0) |
|
|
2098 nnc -= k; |
|
|
2099 else if (k < 0) |
|
|
2100 nnr += k; |
|
|
2101 |
|
|
2102 ColumnVector d; |
|
|
2103 |
|
|
2104 if (nnr > 0 && nnc > 0) |
|
|
2105 { |
|
|
2106 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2107 |
|
|
2108 d.resize (ndiag); |
|
|
2109 |
|
|
2110 if (k > 0) |
|
|
2111 { |
|
|
2112 for (int i = 0; i < ndiag; i++) |
|
|
2113 d.elem (i) = elem (i, i+k); |
|
|
2114 } |
|
|
2115 else if ( k < 0) |
|
|
2116 { |
|
|
2117 for (int i = 0; i < ndiag; i++) |
|
|
2118 d.elem (i) = elem (i-k, i); |
|
|
2119 } |
|
|
2120 else |
|
|
2121 { |
|
|
2122 for (int i = 0; i < ndiag; i++) |
|
|
2123 d.elem (i) = elem (i, i); |
|
|
2124 } |
|
|
2125 } |
|
|
2126 else |
|
|
2127 cerr << "diag: requested diagonal out of range\n"; |
|
|
2128 |
|
|
2129 return d; |
|
|
2130 } |
|
|
2131 |
|
|
2132 ColumnVector |
|
|
2133 Matrix::row_min (void) const |
|
|
2134 { |
|
|
2135 ColumnVector result; |
|
|
2136 |
|
|
2137 int nr = rows (); |
|
|
2138 int nc = cols (); |
|
|
2139 |
|
|
2140 if (nr > 0 && nc > 0) |
|
|
2141 { |
|
|
2142 result.resize (nr); |
|
|
2143 |
|
|
2144 for (int i = 0; i < nr; i++) |
|
|
2145 { |
|
|
2146 double res = elem (i, 0); |
|
|
2147 for (int j = 1; j < nc; j++) |
|
|
2148 if (elem (i, j) < res) |
|
|
2149 res = elem (i, j); |
|
|
2150 result.elem (i) = res; |
|
|
2151 } |
|
|
2152 } |
|
|
2153 |
|
|
2154 return result; |
|
|
2155 } |
|
|
2156 |
|
|
2157 ColumnVector |
|
|
2158 Matrix::row_min_loc (void) const |
|
|
2159 { |
|
|
2160 ColumnVector result; |
|
|
2161 |
|
|
2162 int nr = rows (); |
|
|
2163 int nc = cols (); |
|
|
2164 |
|
|
2165 if (nr > 0 && nc > 0) |
|
|
2166 { |
|
|
2167 result.resize (nr); |
|
|
2168 |
|
|
2169 for (int i = 0; i < nr; i++) |
|
|
2170 { |
|
|
2171 int res = 0; |
|
|
2172 for (int j = 0; j < nc; j++) |
|
|
2173 if (elem (i, j) < elem (i, res)) |
|
|
2174 res = j; |
|
|
2175 result.elem (i) = (double) (res + 1); |
|
|
2176 } |
|
|
2177 } |
|
|
2178 |
|
|
2179 return result; |
|
|
2180 } |
|
|
2181 |
|
|
2182 ColumnVector |
|
|
2183 Matrix::row_max (void) const |
|
|
2184 { |
|
|
2185 ColumnVector result; |
|
|
2186 |
|
|
2187 int nr = rows (); |
|
|
2188 int nc = cols (); |
|
|
2189 |
|
|
2190 if (nr > 0 && nc > 0) |
|
|
2191 { |
|
|
2192 result.resize (nr); |
|
|
2193 |
|
|
2194 for (int i = 0; i < nr; i++) |
|
|
2195 { |
|
|
2196 double res = elem (i, 0); |
|
|
2197 for (int j = 1; j < nc; j++) |
|
|
2198 if (elem (i, j) > res) |
|
|
2199 res = elem (i, j); |
|
|
2200 result.elem (i) = res; |
|
|
2201 } |
|
|
2202 } |
|
|
2203 |
|
|
2204 return result; |
|
|
2205 } |
|
|
2206 |
|
|
2207 ColumnVector |
|
|
2208 Matrix::row_max_loc (void) const |
|
|
2209 { |
|
|
2210 ColumnVector result; |
|
|
2211 |
|
|
2212 int nr = rows (); |
|
|
2213 int nc = cols (); |
|
|
2214 |
|
|
2215 if (nr > 0 && nc > 0) |
|
|
2216 { |
|
|
2217 result.resize (nr); |
|
|
2218 |
|
|
2219 for (int i = 0; i < nr; i++) |
|
|
2220 { |
|
|
2221 int res = 0; |
|
|
2222 for (int j = 0; j < nc; j++) |
|
|
2223 if (elem (i, j) > elem (i, res)) |
|
|
2224 res = j; |
|
|
2225 result.elem (i) = (double) (res + 1); |
|
|
2226 } |
|
|
2227 } |
|
|
2228 |
|
|
2229 return result; |
|
|
2230 } |
|
|
2231 |
|
|
2232 RowVector |
|
|
2233 Matrix::column_min (void) const |
|
|
2234 { |
|
|
2235 RowVector result; |
|
|
2236 |
|
|
2237 int nr = rows (); |
|
|
2238 int nc = cols (); |
|
|
2239 |
|
|
2240 if (nr > 0 && nc > 0) |
|
|
2241 { |
|
|
2242 result.resize (nc); |
|
|
2243 |
|
|
2244 for (int j = 0; j < nc; j++) |
|
|
2245 { |
|
|
2246 double res = elem (0, j); |
|
|
2247 for (int i = 1; i < nr; i++) |
|
|
2248 if (elem (i, j) < res) |
|
|
2249 res = elem (i, j); |
|
|
2250 result.elem (j) = res; |
|
|
2251 } |
|
|
2252 } |
|
|
2253 |
|
|
2254 return result; |
|
|
2255 } |
|
|
2256 RowVector |
|
|
2257 Matrix::column_min_loc (void) const |
|
|
2258 { |
|
|
2259 RowVector result; |
|
|
2260 |
|
|
2261 int nr = rows (); |
|
|
2262 int nc = cols (); |
|
|
2263 |
|
|
2264 if (nr > 0 && nc > 0) |
|
|
2265 { |
|
|
2266 result.resize (nc); |
|
|
2267 |
|
|
2268 for (int j = 0; j < nc; j++) |
|
|
2269 { |
|
|
2270 int res = 0; |
|
|
2271 for (int i = 0; i < nr; i++) |
|
|
2272 if (elem (i, j) < elem (res, j)) |
|
|
2273 res = i; |
|
|
2274 result.elem (j) = (double) (res + 1); |
|
|
2275 } |
|
|
2276 } |
|
|
2277 |
|
|
2278 return result; |
|
|
2279 } |
|
|
2280 |
|
|
2281 |
|
|
2282 RowVector |
|
|
2283 Matrix::column_max (void) const |
|
|
2284 { |
|
|
2285 RowVector result; |
|
|
2286 |
|
|
2287 int nr = rows (); |
|
|
2288 int nc = cols (); |
|
|
2289 |
|
|
2290 if (nr > 0 && nc > 0) |
|
|
2291 { |
|
|
2292 result.resize (nc); |
|
|
2293 |
|
|
2294 for (int j = 0; j < nc; j++) |
|
|
2295 { |
|
|
2296 double res = elem (0, j); |
|
|
2297 for (int i = 1; i < nr; i++) |
|
|
2298 if (elem (i, j) > res) |
|
|
2299 res = elem (i, j); |
|
|
2300 result.elem (j) = res; |
|
|
2301 } |
|
|
2302 } |
|
|
2303 |
|
|
2304 return result; |
|
|
2305 } |
|
|
2306 |
|
|
2307 RowVector |
|
|
2308 Matrix::column_max_loc (void) const |
|
|
2309 { |
|
|
2310 RowVector result; |
|
|
2311 |
|
|
2312 int nr = rows (); |
|
|
2313 int nc = cols (); |
|
|
2314 |
|
|
2315 if (nr > 0 && nc > 0) |
|
|
2316 { |
|
|
2317 result.resize (nc); |
|
|
2318 |
|
|
2319 for (int j = 0; j < nc; j++) |
|
|
2320 { |
|
|
2321 int res = 0; |
|
|
2322 for (int i = 0; i < nr; i++) |
|
|
2323 if (elem (i, j) > elem (res, j)) |
|
|
2324 res = i; |
|
|
2325 result.elem (j) = (double) (res + 1); |
|
|
2326 } |
|
|
2327 } |
|
|
2328 |
|
|
2329 return result; |
|
|
2330 } |
|
|
2331 |
|
|
2332 ostream& |
|
|
2333 operator << (ostream& os, const Matrix& a) |
|
|
2334 { |
|
|
2335 // int field_width = os.precision () + 7; |
|
|
2336 for (int i = 0; i < a.rows (); i++) |
|
|
2337 { |
|
|
2338 for (int j = 0; j < a.cols (); j++) |
|
|
2339 os << " " /* setw (field_width) */ << a.elem (i, j); |
|
|
2340 os << "\n"; |
|
|
2341 } |
|
|
2342 return os; |
|
|
2343 } |
|
|
2344 |
|
|
2345 istream& |
|
|
2346 operator >> (istream& is, Matrix& a) |
|
|
2347 { |
|
|
2348 int nr = a.rows (); |
|
|
2349 int nc = a.cols (); |
|
|
2350 |
|
|
2351 if (nr < 1 || nc < 1) |
|
|
2352 is.clear (ios::badbit); |
|
|
2353 else |
|
|
2354 { |
|
|
2355 double tmp; |
|
|
2356 for (int i = 0; i < nr; i++) |
|
|
2357 for (int j = 0; j < nc; j++) |
|
|
2358 { |
|
|
2359 is >> tmp; |
|
|
2360 if (is) |
|
|
2361 a.elem (i, j) = tmp; |
|
|
2362 else |
|
|
2363 break; |
|
|
2364 } |
|
|
2365 } |
|
|
2366 |
|
|
2367 return is; |
|
|
2368 } |
|
|
2369 |
|
|
2370 /* |
|
|
2371 * Read an array of data froma file in binary format. |
|
|
2372 */ |
|
|
2373 int |
|
471
|
2374 Matrix::read (FILE *fptr, char *type) |
|
458
|
2375 { |
|
|
2376 // Allocate buffer pointers. |
|
|
2377 |
|
|
2378 union |
|
|
2379 { |
|
|
2380 void *vd; |
|
|
2381 char *ch; |
|
|
2382 u_char *uc; |
|
|
2383 short *sh; |
|
|
2384 u_short *us; |
|
|
2385 int *in; |
|
|
2386 u_int *ui; |
|
|
2387 long *ln; |
|
|
2388 u_long *ul; |
|
|
2389 float *fl; |
|
|
2390 double *db; |
|
|
2391 } |
|
|
2392 buf; |
|
|
2393 |
|
|
2394 // Convert data to double. |
|
|
2395 |
|
471
|
2396 if (! type) |
|
458
|
2397 { |
|
471
|
2398 (*current_liboctave_error_handler) |
|
|
2399 ("fread: invalid NULL type parameter"); |
|
|
2400 return 0; |
|
|
2401 } |
|
458
|
2402 |
|
471
|
2403 int count; |
|
|
2404 int nitems = length (); |
|
458
|
2405 |
|
471
|
2406 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
458
|
2407 |
|
471
|
2408 #define DO_FREAD(TYPE,ELEM) \ |
|
|
2409 do \ |
|
|
2410 { \ |
|
|
2411 size_t size = sizeof (TYPE); \ |
|
|
2412 buf.ch = new char [size * nitems]; \ |
|
|
2413 count = fread (buf.ch, size, nitems, fptr); \ |
|
|
2414 for (int k = 0; k < count; k++) \ |
|
|
2415 d[k] = buf.ELEM[k]; \ |
|
|
2416 delete [] buf.ch; \ |
|
|
2417 } \ |
|
|
2418 while (0) |
|
458
|
2419 |
|
471
|
2420 if (strcasecmp (type, "double") == 0) |
|
|
2421 DO_FREAD (double, db); |
|
|
2422 else if (strcasecmp (type, "char") == 0) |
|
|
2423 DO_FREAD (char, ch); |
|
|
2424 else if (strcasecmp (type, "uchar") == 0) |
|
|
2425 DO_FREAD (u_char, uc); |
|
|
2426 else if (strcasecmp (type, "short") == 0) |
|
|
2427 DO_FREAD (short, sh); |
|
|
2428 else if (strcasecmp (type, "ushort") == 0) |
|
|
2429 DO_FREAD (u_short, us); |
|
|
2430 else if (strcasecmp (type, "int") == 0) |
|
|
2431 DO_FREAD (int, in); |
|
|
2432 else if (strcasecmp (type, "uint") == 0) |
|
|
2433 DO_FREAD (u_int, ui); |
|
|
2434 else if (strcasecmp (type, "long") == 0) |
|
|
2435 DO_FREAD (long, ul); |
|
|
2436 else if (strcasecmp (type, "float") == 0) |
|
|
2437 DO_FREAD (float, fl); |
|
|
2438 else |
|
|
2439 { |
|
|
2440 (*current_liboctave_error_handler) |
|
|
2441 ("fread: invalid NULL type parameter"); |
|
458
|
2442 return 0; |
|
|
2443 } |
|
|
2444 |
|
|
2445 return count; |
|
|
2446 } |
|
|
2447 |
|
|
2448 /* |
|
|
2449 * Write the data array to a file in binary format. |
|
|
2450 */ |
|
|
2451 int |
|
471
|
2452 Matrix::write (FILE *fptr, char *type) |
|
458
|
2453 { |
|
|
2454 // Allocate buffer pointers. |
|
|
2455 |
|
|
2456 union |
|
|
2457 { |
|
|
2458 void *vd; |
|
|
2459 char *ch; |
|
|
2460 u_char *uc; |
|
|
2461 short *sh; |
|
|
2462 u_short *us; |
|
|
2463 int *in; |
|
|
2464 u_int *ui; |
|
|
2465 long *ln; |
|
|
2466 u_long *ul; |
|
|
2467 float *fl; |
|
|
2468 double *db; |
|
|
2469 } |
|
|
2470 buf; |
|
|
2471 |
|
471
|
2472 int nitems = length (); |
|
458
|
2473 |
|
471
|
2474 double *d = fortran_vec (); |
|
458
|
2475 |
|
|
2476 // Convert from double to correct size. |
|
|
2477 |
|
471
|
2478 if (! type) |
|
458
|
2479 { |
|
471
|
2480 (*current_liboctave_error_handler) |
|
|
2481 ("fwrite: invalid NULL type parameter"); |
|
|
2482 return 0; |
|
|
2483 } |
|
458
|
2484 |
|
471
|
2485 size_t size; |
|
|
2486 int count; |
|
458
|
2487 |
|
471
|
2488 #define DO_FWRITE(TYPE,ELEM) \ |
|
|
2489 do \ |
|
|
2490 { \ |
|
|
2491 size = sizeof (TYPE); \ |
|
|
2492 buf.ELEM = new TYPE [nitems]; \ |
|
|
2493 for (int k = 0; k < nitems; k++) \ |
|
|
2494 buf.ELEM[k] = (TYPE) d[k]; \ |
|
|
2495 count = fwrite (buf.ELEM, size, nitems, fptr); \ |
|
|
2496 delete [] buf.ELEM; \ |
|
|
2497 } \ |
|
|
2498 while (0) |
|
458
|
2499 |
|
471
|
2500 if (strcasecmp (type, "double") == 0) |
|
|
2501 DO_FWRITE (double, db); |
|
|
2502 else if (strcasecmp (type, "char") == 0) |
|
|
2503 DO_FWRITE (char, ch); |
|
|
2504 else if (strcasecmp (type, "uchar") == 0) |
|
|
2505 DO_FWRITE (u_char, uc); |
|
|
2506 else if (strcasecmp (type, "short") == 0) |
|
|
2507 DO_FWRITE (short, sh); |
|
|
2508 else if (strcasecmp (type, "ushort") == 0) |
|
|
2509 DO_FWRITE (u_short, us); |
|
|
2510 else if (strcasecmp (type, "int") == 0) |
|
|
2511 DO_FWRITE (int, in); |
|
|
2512 else if (strcasecmp (type, "uint") == 0) |
|
|
2513 DO_FWRITE (u_int, ui); |
|
|
2514 else if (strcasecmp (type, "long") == 0) |
|
|
2515 DO_FWRITE (long, ln); |
|
|
2516 else if (strcasecmp (type, "ulong") == 0) |
|
|
2517 DO_FWRITE (u_long, ul); |
|
|
2518 else if (strcasecmp (type, "float") == 0) |
|
|
2519 DO_FWRITE (float, fl); |
|
|
2520 else |
|
|
2521 { |
|
|
2522 (*current_liboctave_error_handler) |
|
|
2523 ("fwrite: unrecognized type parameter %s", type); |
|
458
|
2524 return 0; |
|
471
|
2525 } |
|
458
|
2526 |
|
|
2527 return count; |
|
|
2528 } |
|
|
2529 |
|
|
2530 /* |
|
|
2531 ;;; Local Variables: *** |
|
|
2532 ;;; mode: C++ *** |
|
|
2533 ;;; page-delimiter: "^/\\*" *** |
|
|
2534 ;;; End: *** |
|
|
2535 */ |
